A Beauty Cold and Austere
by Mike Spivey (2017)

That survey course in conceptual mathematics seemed like a good idea at the start of the term - no graded homework, no midterm exams - just an oral final at the end. But now that final is tomorrow morning. After months of procrastination you've got one night left to learn enough to pass the course. You might even be desperate enough to try one of your roommate's sketchy memory pills.

action: %
response: "Mathematics, rightly viewed, possesses not only truth, but supreme beauty - a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show." -- Bertrand Russell

"Closing time!" The voice echoes in the space around you.

You slowly open your eyes to find your face pressed against a book. A book you've been drooling on.

One thing at a time. Let's focus on the book.
action: Examine book
response: This is your textbook for Math 058, Concepts of Mathematics. (Or is it Math 314? Or Math 272? You really ought to remember this.)  The book has some drool on it.

So it's your math book. That helps some. You might be up to a wider glance around now. Try LOOK, or just L for short.
action: Look around
response: Right. The library.

The library is a great place to study - or so you've been told. You hadn't seen the inside of it until today.

(You've also been told it's a good place to sleep. Well, you can vouch for that now.)

On the study table in front of you are your math book and an empty yogurt cup.

The librarian spots you and begins walking in your direction. Oh, no.

You might have time to look up one more topic in your math book. Newton, maybe. He'll probably show up on the final tomorrow. Or maybe Professor Glasser will expect you to wax philosophical about mathematics in general. You could LOOK UP NEWTON or LOOK UP MATH.
action: You look up the MATH
response: (in your math book)
There is considerable debate as to the exact definition of mathematics. Is it the study of numbers? Shapes? Is it discovered, or is it invented? Aristotle called mathematics "the science of quantity," but some modern areas of mathematics like topology don't really fit that definition. Bertrand Russell said that mathematics can be reduced to logic, but his own efforts in that area were punctured by Gödel's incompleteness theorems. Most modern mathematicians take a "I know it when I see it" view, when they bother to think about the definition of mathematics at all.

Regardless of its definition, since the 1600s mathematics has proven to be particularly useful to science. For example, Isaac Newton's second law of motion, F = ma, or force equals mass times
acceleration, single-handedly reduced a wide variety of problems in physics to a simple equation. Modern physics, engineering, chemistry, economics, computers, and even large parts of biology and the social sciences would not be possible without mathematics. Galileo even went so far as to claim that mathematics is the language with which God has written the universe.

Is mathematics art or science? Science owes much to mathematics, and Gauss called mathematics "the queen of the sciences." But some mathematicians sound more like artists when describing their work. Russell, in the following quote, makes that comparison explicit:

"Mathematics, rightly viewed, possesses not only truth, but supreme beauty - a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show. The true spirit of delight, the exaltation, the sense of being more than Man, which is the touchstone of the highest excellence, is to be found in mathematics as surely as poetry."

Wow. That's a lot to digest. You're never going to remember all of this for tomorrow.

The librarian is getting closer. You probably should take the initiative and GREET HER. Maybe if you're friendly she'll let you stay a little longer.
action: You greet the LIBRARIAN
response: "Hello!" you say brightly.

"Hello," the librarian responds. "I'm afraid it's time for you to leave."

It looks like you might need more than friendliness here. Let's go for pathos. Try TELL LIBRARIAN ABOUT FINAL.
action: You tell the libririan about final
response: (to the librarian)
"Um, I have my final exam in conceptual mathematics tomorrow," you say in your best respectful-of-authority voice. "I really need to do some more studying. May I please, please stay here for just a little longer?"

"No," she replies. "I'm sorry, but I have to close up the library now."

Well, that didn't work. She's probably heard it all before.

You might as well just head back to your dorm room. You'll need to pick up your things first, though. Try GET BOOK AND CUP.
action: You get the book and the cup
response: your math book: You pick up your math book.
empty yogurt cup: You pick up the yogurt cup.

(Notice that you can GET more than one object at a time.)

"I hope you're not planning to remove any library books," the librarian says. "The borrowing period for this academic year has ended."

You should check your inventory to show her. Try INVENTORY, or just I for short.
action: You check what you're carrying
response: You are carrying:
an empty yogurt cup
your math book

"Good," says the librarian. Then her eyes focus on the yogurt cup. She frowns. "I'll take that," she says.

Try GIVE CUP TO LIBRARIAN.
action: You give the cup to the LIBRARIAN
response: You give the empty yogurt cup to the librarian.

"Thank you," the librarian says. "Next time, please try to follow the rules about food in the library.

"Good luck on your final," she adds, pointedly indicating the exit to the south.

There's really nothing left to do but head back to your dorm room.
Try SOUTH, or just S.
action: You go south
response: You walk out, flashing the librarian a weak smile as you go. She closes and locks the doors behind you.

Then you trudge back to your dorm room, thinking about how you got here...
This ends the tutorial.

You've just seen several of the most useful commands in the game: EXAMINE object (or X object)
LOOK (or L)
LOOK UP topic (in your math book)
GREET character
TELL character ABOUT topic
GET an object (more than one if you want)
GIVE object TO character
INVENTORY (or I)
SOUTH (or S. The other seven compass directions - and their abbreviations - are allowed, too, plus UP and DOWN).

You can review these commands and many others by typing HELP at any time. In-game HINTS are available as well.



Professor Glasser's survey course in conceptual mathematics seemed like a good idea at the start of the term - no graded homework, no midterm exams - just an oral final at the end. As the semester progressed, cutting a few classes didn't really seem to matter. Neither did skipping a reading assignment - or a homework set - here and there. But "a few, here and there" slowly turned into "several," which turned into "most." Eventually you were too embarrassed to show up to class anymore, and for the better part of the second half of the term you did an impressive job of forgetting about the final exam.

Until this morning.

Cramming has never worked for you, but what choice did you have? You already made your choices, you suppose - repeatedly, throughout the semester.

Blaming yourself now isn't going to do any good, though. You can blame yourself all you want after tomorrow. Focus on the final.
Focus on the final.

How, though? It's late. You need more sleep. But you're not sure you remember much (anything?) from today's library cram session.

You've got to pass that final because you've got to pass the class. What will happen to your scholarship if you don't?

With these pleasant thoughts running through your head as you walk across campus, you finally return to...
Your Dorm Room
Apparently your roommate moved out today. The room looks pretty bare with only your stuff left in it...not that you had much to begin with. The only decorations that remain are a few of your posters hanging on the walls.

You hear loud noises coming from the hallway to the south. It sounds like your hallmates have begun celebrating the end of the academic year.

You can see your bed and your desk (on which are a medicine bottle and a note) here.
action: You read the note
response: It's from your roommate. "Good luck on your final! I've left you the last of my study pills. I promise you they are perfectly safe, all-natural, and organic - although they may not work exactly like you expect."
action: You examine the pills
response: Your roommate claims these pills are good for your memory, but you've always been skeptical.
action: You look at the bed
response: Your bedsheets feature characters from one of your favorite childhood shows. Particularly prominent is a purple puppet vampire, who is endearing rather than scary. You don't care that your friends occasionally make fun of you for these sheets.
action: You examine bottle
response: These study pills are ones that your roommate picked up at that sketchy health-food store downtown. Your roommate swears by them, but you've always been skeptical. The bottle is closed, and there is something written on it.
action: You read the bottle
response: On the bottle is written "Blorple Pills: Explore a nearby object's mystic energy field via the power of dreams!"

Mystic energy field? Power of dreams?! You thought these were supposed to be study pills.
action: You open the bottle
response: You push down on the bottle's cap, twist it, and pull... and the bottle opens easily. Whew! Sometimes these "childproof" medicine bottles are really hard to open. There is one pill left in the bottle.
action: You take the pill
response: A bit hesitantly, you swallow the pill. Hopefully this will help with your studying.
action: You get on the bed
response: You get onto your bed.
action: Sleep
response: You curl up with the math book. Whether by exhaustion or the effects of the pill (or both), you quickly fall asleep.

Your dreams are strange. Images from today's cramfest run through your mind in rapid succession, combining, reforming, and producing new images, each of which sinks into your unconscious. Eventually your thoughts slow down, and as they do you can feel your mind empty. Your dream coalesces into...
Point
You find yourself in a deep dark blue - almost black - expanse of space that extends as far as you can see in all three dimensions. The only thing that breaks up this space is the white disk floating in mid-air that you are standing on. While the disk doesn't appear to be supported by anything, there is a hole in the middle of it.

[Your understanding of Arithmetic has increased. You estimate
that your score on tomorrow's final has just gone up by two
points.]
action: You examine the disk
response: The disk is pure white and has a diameter of about 8 feet. There is a hole in the middle of it, large enough for you to enter.
action: You enter the disk
response: You clamber down the hole.

This is more of an abstract space than a physical place, but it gives you a sense of unity, wholeness, and beginnings. A hole leads back up. You sense another exit, too - one in a deeper, "downward" direction from this space.
action: Go down
response: You make your way down.

This space feels formless, as if it consists of as-yet unshaped matter. You can sense a way out above you.

The only solid thing you can discern here is a white wand, floating upright in the void.
action: You take the wand
response: You take the white wand from the void.
action: You look at it
response: This white wand is in the shape of a snake - a one-eyed adder, actually. The adder's eye is a dark sapphire. The wand has the word "Increment" inscribed along it.
action: Describe the surroundings
response: This space feels formless, as if it consists of as-yet unshaped matter. You can sense a way out above you.
action: Go upward
response: You make your way up through the void.

This is more of an abstract space than a physical place, but it gives you a sense of unity, wholeness, and beginnings. A hole leads back up. You sense another exit, too - one in a deeper, "downward" direction from this space.
action: Wave wand
response: You wave the wand, and the word "Increment" on it begins to glow. It glows brighter and brighter. Finally, the wand emits a dazzling flash of light - and disappears! Wandless, you feel yourself
increment.

This is more of an abstract space than a physical place, but it's marked by a feeling of duality, as if it somehow contains opposites within itself. The only exit is a hole leading up.
action: Go up
response: You make your way up.

As you climb through the hole, at first it appears you are entering a dark blue nothingness. But then you see, off to the "west," the white disk you were standing on earlier. The white wand is lying on it, pointed in your direction. As you stare at it, the wand begins to change shape! It widens and flattens until it is the width of the disk. Then the tip stretches toward you, the wand soon extending far beyond its original length. The tip picks up speed, and it passes you almost faster than you can follow. You get a last glimpse of the tip off in the distance before it is lost from sight. Looking around, you find that the wand has become a line with numbers marked on it, a line that extends as far as you can see to the "east." With some trepidation, you step onto this new line.

Positive Axis: 2
You are in a dark blue expanse of space, standing on a white line that stretches to the west and as far as you can see to the east. The number 2 is marked on the line here. There is a hole next to the 2 large enough for you to climb down into.

[Your understanding of Arithmetic has increased. You estimate
that your score on tomorrow's final has just gone up by one
point.]
action: Go downwards
response: You clamber down the hole.

This is more of an abstract space than a physical place, but it's marked by a feeling of duality, as if it somehow contains opposites within itself. The only exit is a hole leading back up to the positive axis.
action: You go up
response: You make your way up.

Positive Axis: 2
You are in a dark blue expanse of space, standing on a white line that stretches to the west and as far as you can see to the east. The number 2 is marked on the line here. There is a hole next to the 2 large enough for you to climb down into.
action: Go east
response: You walk along the positive axis for a while, tracing the passage of the tip of the white wand. You see marks for 3, 4, 5, and larger numbers. There are no holes or anything else featured on this part of the positive axis, though, and you soon decide return to the 2 mark.
action: Go west
response: Positive Axis: 1
You find yourself in a deep dark blue - almost black - expanse of space that extends as far as you can see in all three dimensions. The space is broken up by the straight, flat white line floating in mid-air that you are standing on. The line begins here and stretches out of sight to the east. The number 1 is marked on the line. While the line doesn't appear to be supported by anything, there is a hole in the middle of it here, next to the 1.

Since the disk you were standing on earlier has now become the location of 1 on the positive axis, you find yourself wondering if this is the only space that has changed.
action: Go downward
response: You clamber down the hole.

This is more of an abstract space than a physical place, but it gives you a sense of unity, wholeness, and beginnings. A hole leads back up to the positive axis. You sense another exit, too - one in a deeper, "downward" direction from this space.
action: You go down
response: You make your way down.

This space seems more formed than it did the last time you were here.

The space is now partially-formed, but it is still mostly unshaped matter. Besides the way up to the manifestation of one, you can now sense several more "paths" through the void: north, south, east, and west.
action: You go west
response: You make your way west through the void. As you do, you feel an electrical impulse course through you. You find yourself in...

You are standing in the great hall of a large, cobwebby castle. A long table stretches from one end of the hall to the other. The entryway of the castle is to the east. Exits west and south lead to other parts of the castle.

On the long table is a pile of old coins.

A large purple puppet is here, counting several coins laid out on the table. He is talking to himself. "... eight, nine, ten! Ten coins!"
action: You look at the puppet
response: The Count is not a man but a purple puppet. There is no one animating him, yet he talks and moves about. You're definitely dreaming.
action: You look at the coins
response: This is a huge pile of coins. You wonder if the Count knows exactly how many there are. He probably does.
action: You ask Count about the coins
response: It would be more polite to greet the Count first.
action: Greet count
response: The puppet looks up at your approach. "I am the Count of this castle, and I love to count! But I have a problem. Maybe you can help.

"I have ten different coins here that I have been flipping. I want to count how many ways I can flip the ten coins and have half of them come up heads and half come up tails. For example, one way is HHHHHTTTTT. Another way is HTHTHTHTHT. A third way is HTHHTTTTHH. That's three. But there are a lot more than that, and I can't seem to count them because I can't keep track of all the combinations!

"Here are some ideas. I know that if I want 0 heads, then the answer is 1: TTTTTTTTTT. I know that if I want 1 head, the answer is 10: HTTTTTTTTT, THTTTTTTTT, and so on, with one head for each of the other coins. It took me a long time to find the answer with two heads, but I'm pretty sure I got it: 45. But with three or more I can't keep track of what I've counted and what I haven't.

"If you know the answer, please tell me!

"I will be happy to let you have one of my coins if you can help me."
action: You ask Count about the big bird
response: "I haven't seen him in a while," the Count says. "I probably should go visit sometime soon."
action: 99
response: I didn't recognize that command. (There is a list of recognized commands in the HELP menus.)
action: You go east
response: As you move east, you feel an electrical impulse course through you. The space around you seems to fold in on itself.

The space is now partially-formed, but it is still mostly unshaped matter. Besides the way up to the manifestation of one, you can now sense several more "paths" through the void: north, south, east, and west to the Great Hall.
action: You go north
response: You make your way north through the void. As you do, you feel an electrical impulse course through you. You find yourself in...

You stand in the Lyceum, a collection of buildings and open spaces in ancient Athens. There is a stadium to the west, a temple lies north, and you can see a private home with an ornate doorway to the east. A road leads northeast out of Athens, and the rest of the city lies south.
action: You go to the north
response: Temple of Number, Southern End
You stand in the southern end of the Temple of Number. The temple is made of white stone and features imposing Ionic columns. There is an inscription on the wall, the rest of the temple is to the north, and the exit to the Lyceum is south.
action: You read inscription
response: "Number is the origin of all things."
action: Go north
response: Temple of Number, Northern End
You stand in the northern end of the Temple of Number. The temple is made of white stone and features imposing Ionic columns. Instead of the half-expected statue of Athena Parthenos, though, stands a large statue of Pythagoras. Behind the statue is a small passageway heading north.

An acolyte is here, silently cleaning up the area around the statue.

You can also see a trash urn and a scrap of papyrus here.

The acolyte picks up the scrap of papyrus from the floor. She reads it carefully, nods, and tosses it in the urn.
action: You look at the urn
response: This large urn is decorated with tasteful depictions of various numbers.

In the trash urn is a scrap of papyrus.

The acolyte polishes an already spotless part of the statue.
action: You take the scrap
response: Taken.

The acolyte pokes at a corner of the temple with her broom.
action: You read it
response: This appears to be a piece torn from some religious scroll.

"Number is the origin of all things.

Number has two basic forms: The odd and the even. Each thing is odd or even or is a ΛΟΓΟΣ, or ratio, made from odd and even.

1. Odd things include the statue of Him in our temple, which is one.

2. Even things include the primary sources of light in our sky - the sun and moon, which are two.

3. ΛΟΓΟΣ things include the seasons, which represent the ratio of
one
year into four parts.

Nothing which is not odd, even, or a ratio from odd and even can exist."

[If the Greek letters are not displaying correctly, you may type SYMBOLS OFF to turn off the use of Greek letters and mathematical symbols for the remainder of the game.]

The acolyte polishes an already spotless part of the statue.
action: You examine statue
response: This large statue of Pythagoras dominates the north end of the temple. A small passageway is behind the statue, leading north.

The acolyte picks up a speck of dust from the floor of the temple.
action: You greet the acolyte
response: The acolyte is focused on her cleaning, and she ignores you.

The acolyte sweeps the area in front of the statue.
action: You go north
response: The acolyte stops you. She shakes her head silently.

The acolyte polishes an already spotless part of the statue.
action: Inventory
response: You are carrying:
a scrap of papyrus
your math book

The acolyte pokes at a corner of the temple with her broom.
action: You put the scrap in the urn
response: You put the scrap of papyrus into the trash urn.

The acolyte sweeps the area in front of the statue.
action: Go north
response: The acolyte stops you. She shakes her head silently.

The acolyte gazes up at the statue with a reverent look on her face.
action: You climb the statue
response: That would be rather sacrilegious.

The acolyte polishes an already spotless part of the statue.
action: Drop book
response: Dropped.

The acolyte picks up a speck of dust from the floor of the temple.

The acolyte walks over to where you dropped the math book and looks around. Not seeing anything, she returns to her work.
action: You take the book
response: Taken.

The acolyte gazes up at the statue with a reverent look on her face.
action: You look at the statue
response: This large statue of Pythagoras dominates the north end of the temple. A small passageway is behind the statue, leading north.

The acolyte pokes at a corner of the temple with her broom.
action: You look up Pythagoras
response: (in your math book)
Pythagoras was an ancient Greek mathematician. He also founded a quasi-religious order whose key belief was that numbers (by which they meant the positive integers) are the basis of everything in the universe.

The Pythagorean Theorem says that the square of the diagonal of a right triangle is equal to the sum of the squares of the sides, or, in symbols, a² + b² = c². While this
theorem
is named for Pythagoras, there is no conclusive evidence that he actually proved the theorem. It probably led to the downfall of his religious cult, though. If you take a right triangle with sides of length 1, the Pythagorean Theorem says that the length of the diagonal must be the square root of 2. The proof that the square root of 2 is irrational - by one of the Pythagoreans - invalidated their key belief in numbers.

The acolyte picks up a speck of dust from the floor of the temple.
action: You examine the acolyte
response: The acolyte is wearing pure white robes and wields a broom. She doesn't look much like the conversational type.

The acolyte pokes at a corner of the temple with her broom.
action: You look at columns
response: These imposing columns are made of white stone and feature Ionic capitals.
action: Go south
response: You stand in the Lyceum, a collection of buildings and open spaces in ancient Athens. There is a stadium to the west, a temple lies north, and you can see a private home with an ornate doorway to the east. A road leads northeast out of Athens, and the rest of the city lies south.
action: You go to the east
response: Some force blocks you from stepping through the doorway of the home. Ignorance may be bliss, but a little knowledge would go a long way here.
action: You examine the doorway
response: There is a rather ornate doorway here - but no door. Written above the doorway is the phrase "Let no one ignorant of geometry enter."
action: Go west
response: This is a stadium in ancient Athens. The stadium itself consists of raised ground on either side of a race track about 200 meters long. The rest of the Lyceum is back east.

Achilles sits by the side of the race track with his head in his hands.
action: You greet Achilles
response: Achilles looks up. "I'm the fastest man in Greece. Then this guy Zeno challenged me to a 200-meter race with a tortoise, under two conditions: (1) I had to be willing to give the tortoise a head start of 100 meters, and (2) every time I got to where I last saw the tortoise I had to look up and mark its position. Of course I can beat a tortoise, even with that much head start, right? But no. Watch."

Achilles snaps his fingers, and from somewhere in the grass of the raised ground comes a tortoise. The tortoise ambles to the 100-meter mark, and Achilles heads to the start. They take off. When Achilles reaches the halfway mark, he looks up, and the tortoise is ahead of him. Achilles notes its position, races to that position, and looks up. The tortoise is still ahead of him. He does this again. The tortoise is still ahead. And again. The tortoise is, once more, ahead. Every time Achilles looks up he's closer to the tortoise, but he never quite catches up to it! Finally he stops running and looks over at you forlornly. The tortoise crosses the finish line, flashes a chelonian smile at Achilles, and disappears to wherever it was before.

Achilles says, "You see? I can't catch up to the tortoise if every time I run to where it was before, it's still ahead of me!"
action: You examine the track
response: The race track is made of hard-packed clay and is about 200 meters long.
action: You go south
response: As you move south, you feel an electrical impulse course through you. The space around you seems to fold in on itself.

The space is now partially-formed, but it is still mostly unshaped matter. Besides the way up to the manifestation of one, you can now sense several more "paths" through the void: north to the Lyceum, south, east, and west to the Great Hall.
action: You go north
response: You make your way north through the void. As you do, you feel an electrical impulse course through you. You find yourself in...

You stand in the Lyceum, a collection of buildings and open spaces in ancient Athens. There is a stadium to the west, a temple lies north, and you can see a private home with an ornate doorway to the east. A road leads northeast out of Athens, and the rest of the city lies south.
action: You go northeast
response: This flat, paved road runs from southwest to northeast. However, you also spot a steep path leaving the road and winding its way north up the hillside.
action: Go north
response: It's an arduous trek up the path. By the time you reach the top you are winded.

You stand on top of a small hill just north of Athens. A winding path leads south, back down to the Royal Road.

The great geometer Euclid is sitting here. He appears to be lost in thought.
action: You greet the geometer
response: "Oh! Hello. Sorry. Please accept my apologies if you've been standing there a while. Sometimes I don't notice what's going on around me when I'm doing geometry."

You give Euclid a nod, as if to say that there's no need to apologize. He interprets it as interest.

"I was just thinking about the postulates in my Elements.
These are what I call the basic truths on which I build all of my geometric arguments. I'm happy with the first four, but the fifth one is too... I don't know... wordy?

"It's basically equivalent to saying this: Given any straight line and a point not on that line, there exists exactly one other straight line that passes through the point and never intersects the first line. This is true no matter how far you extend the two lines. So there's exactly one other line that's parallel to the first line and
that goes through the point.

"I'm trying to figure out how to derive this one from the first four so that I don't have to claim it as a postulate. But I can't seem to do it.

"Is it obvious that if you start with a point and a line, there's exactly one other line that goes through the point and never touches the first line? Or is that not even true?

"If you have any ideas about how to prove this, or run across any examples where there are no lines or two or more lines through the point that don't touch the first line, please tell me about them!

"And here. This will help you remember my postulates." He hands you a scroll.
action: You read the scroll
response: "First postulate: You can draw a straight line from any point to any other point.

Second postulate: You can extend a finite straight line continuously in a straight line.

Third postulate: You can draw a circle with any center and any radius.

Fourth postulate: All right (90 degree) angles are equal to each other.

Fifth postulate (rephrased, also known as the parallel
postulate): Given a line and a point not on the line, there is
exactly one other line that goes through the point that never touches the first line."
action: You go downwards
response: You make the somewhat less arduous trek back down the path.

This flat, paved road runs from southwest to northeast. However, you also spot a steep path leaving the road and winding its way north up the hillside.
action: You go northeast
response: Apparently the royal road doesn't lead anywhere; you've come to a dead end. You may follow it back to the southwest.
action: Go west
response: You make your way west through the void. As you do, you feel an electrical impulse course through you. You find yourself in...

You are standing in the great hall of a large, cobwebby castle. A long table stretches from one end of the hall to the other. The entryway of the castle is to the east. Exits west and south lead to other parts of the castle.

On the long table is a pile of old coins.

The Count is here, sitting at the table. He mumbles something that sounds like "three."
action: Go west
response: This small chapel does not appear to be dedicated to God or gods; instead, it looks like a place for the worship of numbers. Icons are placed at regular intervals around the walls. The exit to the Great Hall is back east.
action: You look at the icons
response: Most of the icons are highly stylized representations of a single number, such as three, one, or four. One icon, though, is a little different: It consists of a number triangle.
action: You examine the triangle
response: The number triangle on the icon looks like this:

1   2   1
1   3   3   1
1   4   6   4   1
1   5  10  10   5   1
1   6  15  20  15   6   1
1   7  21  35  35  21   7   1
1   8  28  56  70  56  28   8   1

The words "Pascal's Triangle" appear underneath the numbers.
action: You look up pascal
response: (in your math book)
Blaise Pascal was a French mathematician, scientist, philosopher, and theologian. He is known for constructing one of the first mechanical calculators, for his work in projective geometry, and for his work in hydrodynamics. A unit of pressure is named after him, as is the triangle of numbers known as "Pascal's triangle."

Pascal was also one of the founders of the field of probability.
While his initial work in probability was to solve gambling problems, he applied his insights to other areas of human knowledge as well.
For example, Pascal's wager consists of one of the first uses
of expected values. In it, Pascal argues that, in the absence of conclusive evidence as to the existence of God, the payoffs for believing in God (infinite happiness if God exists, nothing if God does not) versus not believing in God (eternal damnation if God exists, nothing if God does not) are such that it is more reasonable for humans to bet on belief in God.
action: You look up pascal's triangle
response: (in your math book)
Pascal's triangle is a triangle of numbers that have several interpretations. One meaning is that the number in the nth
row, kth column (denoted C(n,k)) is the number of
committees of size k that can be formed from n
people. An equivalent interpretation is that C(n,k) is the
number of sequences of 1's and 0's that have length n and
contain exactly k 1's.

Another, different kind of meaning of the numbers in Pascal's triangle is that they are the coefficients when expanding
(x+1)ⁿ in powers of x. For example,
(x+1)⁵ = x⁵ + 5x⁴ + 10x³ +
10x²+ 5x + 1, and the coefficients 1, 5, 10, 10, 5,
1 are the numbers in row 5 in Pascal's triangle.

Pascal's triangle can be generated very easily: The numbers in the leftmost column are all 1's, and the numbers in the right diagonal are all 1's as well. Otherwise, to get C(n,k), you add
C(n-1,k) and C(n-1,k-1). In other words, to obtain
the number you want, you add the number to its "north" and to its "northwest" in the triangle.

Pascal's triangle is indexed starting with 0 rather than 1: The initial row is row 0, not row 1, and the leftmost column is column 0, not column 1.

(Unfortunately, the page giving the first several rows of Pascal's triangle appears to be torn out of your math book. You did buy it used, after all.)
action: You go to the east
response: You are standing in the great hall of a large, cobwebby castle. A long table stretches from one end of the hall to the other. The entryway of the castle is to the east. Exits west and south lead to other parts of the castle.

On the long table is a pile of old coins.

The Count is here, sitting at the table. He mumbles something that sounds like "two."
action: You go south
response: This is a smaller, cozier room than the great hall to the north. A sumptuous tapestry hangs on one wall, and there is a side table beneath it.

A large bronze box lies on the side table.

Another large purple puppet is here, fiddling disgruntledly with the bronze box.
action: You look at the puppet
response: She looks much like the Count, except that she sports a large mop of blonde hair.
action: Greet the puppet
response: You approach the purple puppet and introduce yourself. She steps back from the bronze box and says, "Please forgive my manners! I was preoccupied with my mechanical calculator.

"I am the Countess of this castle. Like my husband, I love to count! And I love to work large multiplication problems with my mechanical calculator. Unfortunately, it seems to be broken now, and I'm not sure how to fix it.

"If you have any questions for me, please feel free to ask.
Otherwise, I'd really like to get this fixed."

She turns back to the bronze box.
action: Examine box
response: This bronze box has several knobs and small wheels on it. It appears to be a primitive mechanical calculator.
action: You ask the puppet about the box
response: "It seems to be broken. It would be nice to have it fixed!"
action: You look at the tapestry
response: This is a beautiful tapestry, consisting of several mathematical symbols woven together in an intricate pattern.
action: You examine the symbols
response: They're symbolic.
action: You go to the north
response: You are standing in the great hall of a large, cobwebby castle. A long table stretches from one end of the hall to the other. The entryway of the castle is to the east. Exits west and south lead to other parts of the castle.

On the long table is a pile of old coins.

The Count is here, sitting at the table. He mumbles something that sounds like "three."
action: Go east
response: As you move east, you feel an electrical impulse course through you. The space around you seems to fold in on itself.

The space is now partially-formed, but it is still mostly unshaped matter. Besides the way up to the manifestation of one, you can now sense several more "paths" through the void: north to the Lyceum, south, east, and west to the Great Hall.
action: You go to the south
response: You make your way south through the void. As you do, you feel an electrical impulse course through you. You find yourself in...

This appears to be the head librarian's office in the Great Library of Alexandria. Scrolls litter the floor. The main part of the library is north of you.

The numbers from 1 to 100 are carved on the wall here, in some kind of puzzle.
action: You examine the puzzle
response: On the wall are carved numbers from 1 to 100, in ten rows of ten each. It looks like you could push any of the numbers. Next to the numbers is a switch, with two settings: "Remove Number," and "Remove Larger Multiples of the Number." The switch is currently set to "Remove Number," although you could easily move it to the other setting by flipping the switch. The numbers currently look like this:

21  22  23  24  25  26  27  28  29  30
31  32  33  34  35  36  37  38  39  40
41  42  43  44  45  46  47  48  49  50
51  52  53  54  55  56  57  58  59  60
61  62  63  64  65  66  67  68  69  70
71  72  73  74  75  76  77  78  79  80
81  82  83  84  85  86  87  88  89  90
91  92  93  94  95  96  97  98  99  100

At the bottom is a challenge from the librarian: "To access the map room, leave just the primes between 1 and 100 by pushing only five numbers."
action: You look up the primes in the book
response: A positive integer is prime if it is divisible by exactly two positive integers: itself and 1. The numbers 7, 29, and 43 are all examples of primes. The number 1 is not prime because it is only divisible by one positive integer (itself), rather than two.
action: You look up the prime numbers
response: (in your math book)
A positive integer is prime if it is divisible by exactly two positive integers: itself and 1. The numbers 7, 29, and 43 are all examples of primes. The number 1 is not prime because it is only divisible by one positive integer (itself), rather than two.
action: Go south
response: This room is quite large to be a side room just off the librarian's office. The walls are covered with maps, and an exit leads back north to the librarian's office.

A huge globe sits on a pedestal in the center of the room.
action: You examine the globe
response: This appears to be the librarian's model of the earth, and it is much larger than you are. It's incomplete, as it only shows the parts of the world that were known in Alexandria at this time. However, it does have lines of latitude and meridians of longitude marked on it.

The globe doesn't fit perfectly on its pedestal, though; there is a small gap between the pedestal and the globe.
action: You look at the pedestal
response: This short pedestal supports the globe. The globe doesn't fit perfectly on the pedestal, though; there is a small gap between the pedestal and the globe.
action: You look at the maps
response: The maps are mostly of parts of the eastern Mediterranean world: Egypt, Libya, Greece, Palestine, Anatolia. None of them look particularly useful.
action: Go north
response: This appears to be the head librarian's office in the Great Library of Alexandria. Scrolls litter the floor. The main part of the library is north of you, and a side room lies to the south.

You have solved the number puzzle on the wall here.
action: You look at scrolls
response: There are many scrolls here. None of them particularly catches your eye.
action: You go north
response: As you move north, you feel an electrical impulse course through you. The space around you seems to fold in on itself.

The space is now partially-formed, but it is still mostly unshaped matter. Besides the way up to the manifestation of one, you can now sense several more "paths" through the void: north to the Lyceum, south to the Librarian's Office, east, and west to the Great Hall.
action: You greet Euclid
response: "Do you have any ideas about how to prove my parallel postulate?" Euclid asks. "Or have you found any examples with no other lines through the point that don't touch the first line? Or maybe examples with two or more lines through the point that don't touch the first line? If so, please tell me about them!"
action: You tell Euclid about the globe
response: "A spherical model of the earth, huh? Aristotle argued that the world is round, and so I'm not surprised that someone has created one of these. Anything interesting marked on it?"
action: You tell about the latitudes
response: (to Euclid)
Euclid says, "I don't think that will help me prove or disprove my parallel postulate."
action: You tell about the latitudes and the longitudes
response: (to Euclid)
You describe the meridians of longitude that you saw on the globe in the Library of Alexandria. Euclid becomes more and more agitated. As you finish, Euclid almost cuts you off in his excitement.

"That's it!" he says. "If you take a meridian of longitude and a point not on that meridian, a second - parallel - meridian that goes through the point must intersect the first meridian at both the north and south poles! So my parallel postulate is actually false: If we think of lines as meridians of longitude, then there is no other line through the point that doesn't intersect the first line!

"Wait." He stops himself and thinks carefully for several minutes. You're afraid to interrupt him. Suddenly, he starts laughing. Soon he is laughing so hard he is doubled over, holding his stomach. It takes him a few minutes to pull himself together.

"I've been asking the wrong question! The meridians of longitude don't prove my parallel postulate false; they just represent a different system of geometry! The parallel postulate as I first stated it is true on a flat plane. The meridians of longitude
help describe a 'parallel postulate' that would be true on a
sphere! You get a different system of geometry if you're on a
flat plane versus a sphere!

"The meridians of longitude were a brilliant suggestion! I can't thank you enough, but please take this as a token of my appreciation." He hands you a copy of his Elements.

"I've got to go write this down.

"Hmmm... No, on second thought I won't bother. Trying to prove my parallel postulate will give mathematicians something to do for the next two thousand years!"

Euclid walks down the winding path, laughing as he goes.

[Your understanding of Geometry has increased. You estimate
that your score on tomorrow's final has just gone up by three
points.]
action: Inventory
response: You are carrying:
Elements
a scribbled scroll
your math book
action: You examine Elements
response: This is a copy of the Elements of Euclid. It's actually
divided into thirteen books.
action: You go downwards
response: You make the somewhat less arduous trek back down the path.

This flat, paved road runs from southwest to northeast. However, you also spot a steep path leaving the road and winding its way north up the hillside.
action: Go east
response: A force pushes back on you at the doorway. You feel it testing your knowledge of geometry. It seems to relent, grudgingly, allowing you to step into the private home.

You are standing in the courtyard of a home in ancient Athens. The owner does not appear to be about. A passage leads down, and the Lyceum is to the west.

In the middle of the courtyard stands a group of six elegant pedestals.
action: You look at the pedestals
response: Five of the pedestals are arranged in a circle around the sixth. The pedestals are distinguished by their tops: The five on the outside have tops in the form of a large triangle, a medium-sized triangle, a small triangle, a square, and a pentagon. The top of the pedestal in the center is in the shape of a circle.
action: Go downwards
response: Shadows dance along the wall of this dark cave, in the dim light filtering down from the courtyard above. Pieces of broken chains lie scattered about the floor of the cave.
action: You examine the pieces
response: The chains are all in pieces. Whoever was imprisoned here must have escaped.
action: You take the pieces
response: The broken chain pieces are all worthless; they are not worth bothering with.
action: Go up
response: You are standing in the courtyard of a home in ancient Athens. The owner does not appear to be about. A passage leads down, and the Lyceum is to the west.

In the middle of the courtyard stands a group of six elegant pedestals.
action: You go south
response: As you move south, you feel an electrical impulse course through you. The space around you seems to fold in on itself.

The space is now partially-formed, but it is still mostly unshaped matter. Besides the way up to the manifestation of one, you can now sense several more "paths" through the void: north to the Lyceum, south to the Librarian's Office, east, and west to the Great Hall.
action: You go to the east
response: You make your way east through the void. As you do, you feel an electrical impulse course through you. You find yourself in...

You are in the House of Wisdom in early-medieval Baghdad, standing in what appears to be someone's private study. The walls are covered in intricate geometric designs, and a low table stands in the middle of the room. A small room lies to the south, and the rest of the House of Wisdom is to the west.

On the low table are a small coffer, a square root, and a formal note.
action: You examine the coffer
response: This coffer appears to be of Indian origin. It is currently closed.
action: You open the coffer
response: You open the small coffer, revealing a white ring.
action: You take the ring
response: Taken.
action: You look around
response: You are in the House of Wisdom in early-medieval Baghdad, standing in what appears to be someone's private study. The walls are covered in intricate geometric designs, and a low table stands in the middle of the room. A small room lies to the south, and the rest of the House of Wisdom is to the west.

On the low table are a small coffer, a square root, and a formal note.
action: You read the note
response: The note reads,

"Al-Khwarizmi,

Our most recent investigations indicate at least two types of objects of power: Those activated by more-or-less normal use, and those activated by the appropriate word of power.

This square object was recently given to the caliph. It appears to be of the latter type. Please examine it and let us know what you discover of it."

Instead of a name, the note is signed with the first few digits of π: 3.1415.

There is also a postscript: "By the way, thank you for the hint on your problem with the balances. I had not realized that the weight of an object has nothing to do with that object's color."
action: You examine the root
response: This is an unusual object. It appears to be made of some tough vegetable matter - perhaps the root of a tree. It's also in the shape of a perfect square. The word "EXTRACT" is written on it.
action: You go to the south
response: This is a small, plain room just south of the study.

The room is dominated by three large double-pan balance scales: a bronze one, a silver one, and a gold one.
action: You look at the gold
response: (the gold balance scale)
This is a double-pan balance scale made of gold. The left pan contains a yellow x block, a yellow z block, and
four sand pebbles; the right pan contains a yellow y block
and eight maize pebbles. Inscribed on the base of the gold scale is the single letter z.
action: You examine the silver
response: (the silver balance scale)
This is a double-pan balance scale made of silver. The left pan contains three gray y blocks and six ash pebbles; the right
pan contains a gray x block and ten slate pebbles. Inscribed
on the base of the silver scale is the single letter y.
action: You look at the bronze
response: (the bronze balance scale)
This is a double-pan balance scale made of bronze. The left pan contains two brown x blocks and two tan pebbles; the right
pan contains twelve sepia pebbles. Inscribed on the base of the bronze scale is the single letter x.
action: You take one X
response: (the brown x block)
As you lift one of the brown x blocks off the left bronze pan
it disappears. The left pan rises somewhat and the right pan drops somewhat.

and two tan pebbles, while the right pan contains twelve sepia pebbles.

The bronze scale is out of balance and tips over. As it rights itself, you see that all the blocks and pebbles have returned to the bronze pans just as if you had never taken any of them.
action: You take two tan and two sepia
response: two tan pebbles: After you lift the tan pebbles from the left bronze pan, they disappear. The left pan rises somewhat and the right pan drops somewhat.
two sepia pebbles: After you lift the sepia pebbles from the right bronze pan, they disappear. The right pan rises somewhat and the left pan drops somewhat.

blocks, while the right pan contains ten sepia pebbles.
action: You look at the bronze
response: (the bronze balance scale)
This is a double-pan balance scale made of bronze. The left pan contains two brown x blocks; the right pan contains ten sepia
pebbles. Inscribed on the base of the bronze scale is the single letter x.
action: You take one brown and five sepia
response: brown x block: As you lift one of the brown x blocks
off the left bronze pan it disappears. The left pan rises somewhat and the right pan drops somewhat.
five sepia pebbles: After you lift the sepia pebbles from the right bronze pan, they disappear. The right pan rises somewhat and the left pan drops somewhat.

block, while the right pan contains five sepia pebbles.

From the bronze balance scale you hear a click.
action: You examine the bronze
response: (the bronze balance scale)
This is a double-pan balance scale made of bronze. The left pan contains a brown x block; the right pan contains five sepia
pebbles. Inscribed on the base of the bronze scale is the single letter x.
action: You get one gray the x and five ash
response: gray x block: After you lift the gray x block from
the right silver pan, it disappears. The right pan rises somewhat and the left pan drops somewhat.
five ash pebbles: After you lift the ash pebbles from the left silver pan, they disappear. The left pan rises somewhat and the right pan drops somewhat.

blocks and an ash pebble, while the right pan contains ten slate pebbles.
action: You get the ash and one slate
response: ash pebble: After you lift the ash pebble from the left silver pan, it disappears. The left pan rises a little and the right pan drops a little.
slate pebble: After you lift the slate pebble from the right silver pan, it disappears. The right pan rises a little and the left pan drops a little.

blocks, while the right pan contains nine slate pebbles.
action: You get two gray y and six slate
response: two gray y blocks: As you lift two of the gray y
blocks off the left silver pan they disappear. The left pan rises somewhat and the right pan drops somewhat.
six slate pebbles: After you lift the slate pebbles from the left silver pan, they disappear. The left pan rises somewhat and the right pan drops somewhat.

Now the left pan of the silver scale contains a gray y block,
while the right pan contains three slate pebbles.

From the silver balance scale you hear a click.
action: You get the yellow x and five maize
response: yellow x block: After you lift the yellow x block
from the left gold pan, it disappears. The left pan rises somewhat and the right pan drops somewhat.
five maize pebbles: After you lift the maize pebbles from the right gold pan, they disappear. The right pan rises somewhat and the left pan drops somewhat.

and four sand pebbles, while the right pan contains a yellow
y block and three maize pebbles.
action: You get the yellow y and three sand
response: yellow y block: After you lift the yellow y block
from the right gold pan, it disappears. The right pan rises somewhat and the left pan drops somewhat.
three sand pebbles: After you lift the sand pebbles from the left gold pan, they disappear. The left pan rises somewhat and the right pan drops somewhat.

and a sand pebble, while the right pan contains three maize pebbles.
action: You get one sand and one maize
response: sand pebble: After you lift the sand pebble from the left gold pan, it disappears. The left pan rises a little and the right pan drops a little.
maize pebble: After you lift the maize pebble from the right gold pan, it disappears. The right pan rises a little and the left pan drops a little.

Now the left pan of the gold scale contains a yellow z block,
while the right pan contains two maize pebbles.

From the gold balance scale you hear a click.

As you isolate the last variable on the scales, a small compartment near the base of the gold scale opens. Out falls a blue gem. The compartment then closes, leaving no trace.

[Your understanding of Algebra has increased. You estimate that
your score on tomorrow's final has just gone up by four
points.]
action: You get the gem
response: Taken.
action: You examine it
response: This small, dark blue sapphire is quite beautiful.
action: Go north
response: You are in the House of Wisdom in early-medieval Baghdad, standing in what appears to be someone's private study. The walls are covered in intricate geometric designs, and a low table stands in the middle of the room. A small room lies to the south, and the rest of the House of Wisdom is to the west.

On the low table are a small coffer and a formal note.
action: You look at the designs
response: These designs consist of intricate combinations of squares, circles, and other geometric figures. The overall structure of the patterns is clear to you, and you can make out several buttons hidden in the designs.
action: You look at the buttons
response: There are five buttons hidden in the geometric designs: a circular button, a button in the shape of two juxtaposed parentheses, a triangular button, a square button, and a pentagonal button.
action: You go east
response: From here, south and west are the only possibilities.
action: Go west
response: As you move west, you feel an electrical impulse course through you. The space around you seems to fold in on itself.

The space here feels much more formed than before.

The space here is now mostly formed, though the floor is still hazy. You can now see an inscription on the wall. Several "paths" through the space are clear: up to the manifestation of one, north to the Lyceum, south to the Librarian's Office, east to the Scholar's Study, and west to the Great Hall.
action: You examine the inscription
response: The inscription reads,

"Euclid alone has looked on Beauty bare.
Let all who prate of Beauty hold their peace,
And lay them prone upon the earth and cease
To ponder on themselves, the while they stare
At nothing, intricately drawn nowhere
In shapes of shifting lineage; let geese
Gabble and hiss, but heroes seek release
From dusty bondage into luminous air.
O blinding hour, O holy, terrible day,
When first the shaft into his vision shone
Of light anatomized! Euclid alone
Has looked on Beauty bare. Fortunate they
Who, though once only and then but far away,
Have heard her massive sandal set on stone."
action: You check what you're carrying
response: You are carrying:
a sapphire gem
a square root
a white ring
Elements
a scribbled scroll
your math book
action: Go up
response: You make your way up.

This is more of an abstract space than a physical place, but it gives you a sense of unity, wholeness, and beginnings. A hole leads back up to the positive axis. You sense another exit, too - one in a deeper, "downward" direction from this space.
action: You go up
response: You make your way up.

Positive Axis: 1
You find yourself in a deep dark blue - almost black - expanse of space that extends as far as you can see in all three dimensions. The space is broken up by the straight, flat white line floating in mid-air that you are standing on. The line begins here and stretches out of sight to the east. The number 1 is marked on the line. While the line doesn't appear to be supported by anything, there is a hole in the middle of it here, next to the 1.
action: You go east
response: Positive Axis: 2
You are in a dark blue expanse of space, standing on a white line that stretches to the west and as far as you can see to the east. The number 2 is marked on the line here. There is a hole next to the 2 large enough for you to climb down into.
action: You enter the hole 2
response: I didn't understand that. The first word or two on their own might suffice, though; perhaps it would work to just enter the hole.
action: You enter the hole
response: You clamber down the hole.

This is more of an abstract space than a physical place, but it's marked by a feeling of duality, as if it somehow contains opposites within itself. The only exit is a hole leading back up to the positive axis.
action: You go west
response: Positive Axis: 1
You find yourself in a deep dark blue - almost black - expanse of space that extends as far as you can see in all three dimensions. The space is broken up by the straight, flat white line floating in mid-air that you are standing on. The line begins here and stretches out of sight to the east. The number 1 is marked on the line. While the line doesn't appear to be supported by anything, there is a hole in the middle of it here, next to the 1.
action: Go west
response: You can see absolutely nothing in the blue darkness off the positive axis. Stepping off it doesn't sound like a good idea. Going down is an option, though.
action: You throw the ring west
response: I didn't understand that. The first word or two on their own might suffice, though; perhaps it would work to just throw the white ring.
action: You examine the ring
response: This ring is white and is in the shape of a one-eyed adder biting its tail. The adder's eye is a dark sapphire. The ring has the word "Identity" inscribed along the outside.
action: You wear the ring
response: You put on the ring. The word "Identity" on it glows briefly before fading. The ring enlarges slightly - just enough to slip off your finger. Then the ring shrinks back to its original size.
action: Go down
response: You make your way down.

The space here is now mostly formed, though the floor is still hazy. You can now see an inscription on the wall. Several "paths" through the space are clear: up to the manifestation of one, north to the Lyceum, south to the Librarian's Office, east to the Scholar's Study, and west to the Great Hall.
action: You go north
response: You make your way north. As you do, you feel an electrical impulse course through you. You find yourself in...

You stand in the Lyceum, a collection of buildings and open spaces in ancient Athens. There is a stadium to the west, a temple lies north, and you can see a private home with an ornate doorway to the east. A road leads northeast out of Athens, and the rest of the city lies south.
action: You go to the north
response: Temple of Number, Southern End
You stand in the southern end of the Temple of Number. The temple is made of white stone and features imposing Ionic columns. There is an inscription on the wall, the rest of the temple is to the north, and the exit to the Lyceum is south.
action: Go north
response: Temple of Number, Northern End
You stand in the northern end of the Temple of Number. The temple is made of white stone and features imposing Ionic columns. Instead of the half-expected statue of Athena Parthenos, though, stands a large statue of Pythagoras. Behind the statue is a small passageway heading north.

An acolyte is here, silently cleaning up the area around the statue.

You can also see a trash urn (in which is a scrap of papyrus) here.

The acolyte gazes up at the statue with a reverent look on her face.
action: Go north
response: The acolyte stops you. She shakes her head silently.

The acolyte sweeps the area in front of the statue.
action: Go south
response: As you move south, you feel an electrical impulse course through you. The space around you seems to fold in on itself.

The space here is now mostly formed, though the floor is still hazy. You can now see an inscription on the wall. Several "paths" through the space are clear: up to the manifestation of one, north to the Lyceum, south to the Librarian's Office, east to the Scholar's Study, and west to the Great Hall.
action: You go east
response: You make your way east. As you do, you feel an electrical impulse course through you. You find yourself in...

You are in the House of Wisdom in early-medieval Baghdad, standing in what appears to be someone's private study. The walls are covered in intricate geometric designs, and a low table stands in the middle of the room. A small room lies to the south, and the rest of the House of Wisdom is to the west.

With your increased knowledge of geometry, the designs on the walls make more sense to you now.

On the low table are a small coffer and a formal note.
action: You examine the designs
response: These designs consist of intricate combinations of squares, circles, and other geometric figures. The overall structure of the patterns is now clear to you, and you can make out several buttons hidden in the designs.
action: You go to the south
response: This is a small, plain room just south of the study.

The room is dominated by three large double-pan balance scales: a bronze one, a silver one, and a gold one.
action: You put the root on the square
response: (the square root)
I'm not sure even a master topologist could pull that off.
action: You examine the root
response: This is an unusual object. It appears to be made of some tough vegetable matter - perhaps the root of a tree. It's also in the shape of a perfect square. The word "EXTRACT" is written on it.
action: Go west
response: As you move west, you feel an electrical impulse course through you. The space around you seems to fold in on itself.

The space here is now mostly formed, though the floor is still hazy. You can now see an inscription on the wall. Several "paths" through the space are clear: up to the manifestation of one, north to the Lyceum, south to the Librarian's Office, east to the Scholar's Study, and west to the Great Hall.
action: You go to the north
response: Temple of Number, Northern End
You stand in the northern end of the Temple of Number. The temple is made of white stone and features imposing Ionic columns. Instead of the half-expected statue of Athena Parthenos, though, stands a large statue of Pythagoras. Behind the statue is a small passageway heading north.

An acolyte is here, silently cleaning up the area around the statue.

You can also see a trash urn (in which is a scrap of papyrus) here.

The acolyte pokes at a corner of the temple with her broom.
action: You give the root to the woman
response: The acolyte is focused on her cleaning, and she ignores you.

The acolyte gazes up at the statue with a reverent look on her face.
action: You examine statue
response: This large statue of Pythagoras dominates the north end of the temple. A small passageway is behind the statue, leading north.

The acolyte picks up a speck of dust from the floor of the temple.
action: You put the root on the statue
response: Putting things on the statue of Pythagoras would achieve nothing.

The acolyte polishes an already spotless part of the statue.
action: You put the root on the gem
response: Putting things on the sapphire gem would achieve nothing.

The acolyte picks up a speck of dust from the floor of the temple.
action: You look through the gem
response: You find nothing of interest.

The acolyte gazes up at the statue with a reverent look on her face.
action: You drop the gem
response: Dropped.
action: You examine the line
response: This flat white line begins here and runs as far as you can see to the east.
action: Wait
response: Time passes.
action: Exits
response: I didn't recognize that command. (There is a list of recognized commands in the HELP menus.)
action: You turn ring
response: Nothing obvious happens.
action: You check what you're carrying
response: You are carrying:
a sapphire gem
a square root
a white ring
Elements
a scribbled scroll
your math book
action: You look at it
response: It's just a pair of curly braces. You could probably put things into it.
action: You look at your surroundings
response: This is more of an abstract space than a physical place. Besides the hole leading up, you sense nothing here.
action: Go upward
response: You make your way up.

Climbing through the hole, you enter what seems to be a mostly empty, dark blue expanse of nothingness. The only thing you can see is the end of the positive axis off to the "east." The enlarged white ring is resting on the axis. Then the ring begins to roll toward you. As it does, the ring widens and flattens until it is the width of the positive axis. The ring rolls past the end of the axis, still heading toward you, but it is now unrolling as it goes, effectively
extending the positive axis in your direction. The end of the ring soon reaches you, at which point it ceases unrolling. No traces that this new line segment was ever a ring remain. With only a bit of hesitation, you step onto the new line.

Beginning of Positive Axis: 0
You are in a dark blue expanse of space, standing on a straight, flat white line that stretches as far as you can see to the east. The number 0 is marked at the very beginning of the line here. There is a hole next to the 0 large enough for you to climb down into.

[Your understanding of Arithmetic has increased. You estimate
that your score on tomorrow's final has just gone up by one
point.]
action: You go down
response: You clamber down the hole.

This is more of an abstract space than a physical place. Besides the hole leading back up to the positive axis, you sense nothing here.
action: Go upwards
response: You make your way up.

Beginning of Positive Axis: 0
You are in a dark blue expanse of space, standing on a straight, flat white line that stretches as far as you can see to the east. The number 0 is marked at the very beginning of the line here. There is a hole next to the 0 large enough for you to climb down into.
action: Go east
response: Positive Axis: 1
You find yourself in a deep dark blue - almost black - expanse of space that extends as far as you can see in all three dimensions. The space is broken up by the straight, flat white line floating in mid-air that you are standing on. The line stretches to the west and out of sight to the east. The number 1 is marked on the line. While the line doesn't appear to be supported by anything, there is a hole in the middle of it here, next to the 1.
action: R.
response: %% Enter a save filename to read:
action: You look around
response: This is more of an abstract space than a physical place, but it gives you a sense of unity, wholeness, and beginnings. A hole leads back up to the positive axis. You sense another exit, too - one in a deeper, "downward" direction from this space.
action: Inventory
response: You are carrying:
a set (no longer empty)
a square root
a sapphire gem
Elements
a scribbled scroll
your math book
action: You examine the scroll
response: This scroll is made from papyrus. Euclid has scribbled his five geometric postulates on it.
action: You read it
response: "First postulate: You can draw a straight line from any point to any other point.

Second postulate: You can extend a finite straight line continuously in a straight line.

Third postulate: You can draw a circle with any center and any radius.

Fourth postulate: All right (90 degree) angles are equal to each other.

Fifth postulate (rephrased, also known as the parallel
postulate): Given a line and a point not on the line, there is
exactly one other line that goes through the point that never touches the first line."
action: You read Elements
response: This is a copy of the Elements of Euclid. It's actually
divided into thirteen books.

Elements contains far too much material to read through.
action: You go upwards
response: You make your way up.

Positive Axis: 1
You find yourself in a deep dark blue - almost black - expanse of space that extends as far as you can see in all three dimensions. The space is broken up by the straight, flat white line floating in mid-air that you are standing on. The line stretches to the west and out of sight to the east. The number 1 is marked on the line. While the line doesn't appear to be supported by anything, there is a hole in the middle of it here, next to the 1.
action: You go east
response: Positive Axis: 2
You are in a dark blue expanse of space, standing on a white line that stretches to the west and as far as you can see to the east. The number 2 is marked on the line here. There is a hole next to the 2 large enough for you to climb down into.
action: Extract root
response: The root vibrates quietly, as it extracts the square root of the essence of the space around it. You feel yourself shift.

Irrational: Between 1 and 2
This is more of an abstract space than a physical place, but it feels large beyond your understanding, as if it encompasses infinitely more space than the single-number locations beneath the positive axis. A hole leads up to the positive axis.

A proof is lying here.

[Your understanding of Number Theory has increased. You
estimate that your score on tomorrow's final has just gone up by two points.]
action: You examine the proof
response: This is a mathematical proof that the square root of 2 is irrational.
action: You get the proof
response: (putting your math book into the empty set to make room)
Taken.
action: You go upward
response: You make your way up.

As you step onto the positive axis, the hole behind you closes.
Rather than standing at an unmarked spot between 1 and 2, you head back to 1.

Positive Axis: 1
You find yourself in a deep dark blue - almost black - expanse of space that extends as far as you can see in all three dimensions. The space is broken up by the straight, flat white line floating in mid-air that you are standing on. The line stretches to the west and out of sight to the east. The number 1 is marked on the line. While the line doesn't appear to be supported by anything, there is a hole in the middle of it here, next to the 1.
action: Go west
response: You make your way west. As you do, you feel an electrical impulse course through you. You find yourself in...

You are standing in the great hall of a large, cobwebby castle. A long table stretches from one end of the hall to the other. The entryway of the castle is to the east. Exits west and south lead to other parts of the castle.

On the long table is a pile of old coins.

The Count is here, sitting at the table. He mumbles something that sounds like "six."
action: Inventory
response: You are carrying:
a proof
a square root
a set (no longer empty)
your math book
a sapphire gem
Elements
a scribbled scroll
action: You put the coins into the set
response: (first taking the pile of old coins)
Those belong to the Count. I wouldn't just take one without his permission.
action: Greet count
response: "If you know, please tell me how many ways you can flip ten coins and have them come out half heads and half tails!" the Count says.
action: Show set to count
response: The Count is unimpressed.
action: You ask count for the coins
response: (the Count first taking the pile of old coins)
The Count ignores your request.
action: You say 42
response: (to the Count)
The Count arches his eyebrow. "That's not the right answer."
action: You say 252
response: (to the Count)
"That's it! That's it! I know that's it! Thank you, thank you, thank you!" The Count hands you one of the coins from his pile. "If you lose this one, feel free to come back and take another. I have plenty!"

(You put the scribbled scroll into the set to make room.)

[Your understanding of Combinatorics has increased. You
estimate that your score on tomorrow's final has just gone up by three points.]
action: You look at the coin
response: This old coin is of eastern European origin. It is probably quite valuable.
action: You go to the east
response: On the long table is a pile of old coins.

The Count is here, looking rather bored.
action: You go east
response: The Count calls after you, "If you find something else for me to count I would be grateful!"

As you move east, you feel an electrical impulse course through you. The space around you seems to fold in on itself.
action: You go north
response: You make your way north. As you do, you feel an electrical impulse course through you. You find yourself in...
action: You go north
response: Temple of Number, Southern End
action: You go north
response: Temple of Number, Northern End
An acolyte is here, silently cleaning up the area around the statue.

You can also see a trash urn (in which is a scrap of papyrus) here.

The acolyte polishes an already spotless part of the statue.
action: You show the proof to the acolyte
response: The acolyte is focused on her cleaning, and she ignores you. There must be some way to make her notice the proof.

The acolyte picks up a speck of dust from the floor of the temple.
action: Go north
response: The acolyte stops you. She shakes her head silently.

The acolyte gazes up at the statue with a reverent look on her face.
action: You read the proof
response: Suppose the square root of 2 is rational. Then it can be expressed as a fraction x/y in lowest terms, so that x
and y are integers with no common factors. Since
x/y is the square root of 2, squaring
x/y must yield 2, and so we get 2 = x² /
y². This means that 2y² = x².

Since y is an integer, so is y². Since x²
is 2 times an integer, x² must be an even number. The only
way that the square of a number can be even, though, is for the number itself to be even. Thus x is even. So x =
2z, where z is some other integer.

Substituting 2z for x, our equation now looks like
2y² = (2z)² = 4z². Divide both sides by
2
to get y² = 2z². By the same logic as before, this
means y is even. So x and y are both even.

common factors. We now have a logical contradiction. Since our supposition that the square root of 2 is rational leads to a logical contradiction, the only possibility left is that the square root of 2 is, in fact, irrational.

The acolyte picks up a speck of dust from the floor of the temple.
action: Drop proof
response: Dropped.

The acolyte sweeps the area in front of the statue.

Then the acolyte picks up the proof. On her way to the trash urn, she glances at it. Then she stops and reads through it carefully. Her face tightens. She shakes the proof at you, spluttering. "This... this is blasphemy! All things must be odd or even or a ratio! You are in error! I will show it to you!"

She reads over the proof again. "The error is here, in the second line. No... the mistake is in the assumption that... In this place, you can't claim that this follows from... Aarrrgghh! This proof is wrong! I know it is!"

She reads the proof a third time. And then a fourth time. The anger slowly fades from her face. "How did you come by such sacred knowledge, and why, why did you share it with me?" Tears drop onto her cheeks. Giving you a last mournful glance, she runs sobbing out of the temple.
action: Describe the surroundings
response: Temple of Number, Northern End
You stand in the northern end of the Temple of Number. The temple is made of white stone and features imposing Ionic columns. Instead of the half-expected statue of Athena Parthenos, though, stands a large statue of Pythagoras. Behind the statue is a small passageway heading north.

You can see a trash urn (in which is a scrap of papyrus) here.
action: Go north
response: With the acolyte gone, no one prevents you from entering the passageway behind the statue.

This small room tucked away behind the statue of Pythagoras is made from the same pure white stone as the more public parts of the temple. It feels like a holy space.

You can see an octahedron, Archimedes's staff, and some exhaustion sandals here.
action: You look at the octahedron
response: The octahedron has eight sides, each of which is in the shape of an equilateral triangle. It looks kind of like someone took two pyramids and glued their bases together. This octahedron is about one cubic foot in volume.
action: You get it
response: You take the octahedron. Looking curiously at it, you note that it has eight sides, each of which is in the shape of an equilateral triangle. You feel you understand three-dimensional solid geometry a little better.

[Your understanding of Geometry has increased. You estimate
that your score on tomorrow's final has just gone up by one
point.]
action: You examine the staff
response: This thin staff is surprisingly strong. It is longer than you are tall.
action: You get it
response: (putting Elements into the set to make room)
Taken.
action: You look at the sandals
response: This pair of exhaustion sandals is the embodiment of Eudoxus's principle of exhaustion.
action: You get the sandals
response: (putting the sapphire gem into the set to make room)
Taken.
action: You look up the eudoxus in the math book
response: Eudoxus was an ancient Greek mathematician. He is most well-known for his method of exhaustion.
action: You look up the exhaustion
response: (in your math book)
The method of exhaustion was a technique used by various ancient Greek mathematicians to find areas and volumes of geometric objects like circles, spheres, cones, and cylinders. It can be thought of as a precursor to more modern techniques that use limits.
action: Inventory
response: You are carrying:
a proof
a square root
a set (no longer empty)
your math book
a sapphire gem
Elements
a scribbled scroll
action: You say 252
response: (to the Count)
"That's it! That's it! I know that's it! Thank you, thank you, thank you!" The Count hands you one of the coins from his pile. "If you lose this one, feel free to come back and take another. I have plenty!"

(You put the scribbled scroll into the set to make room.)

[Your understanding of Combinatorics has increased. You
estimate that your score on tomorrow's final has just gone up by three points.]
action: You go east
response: As you move east, you feel an electrical impulse course through you. The space around you seems to fold in on itself.

The space here is now mostly formed, though the floor is still hazy. You can now see an inscription on the wall. Several "paths" through the space are clear: up to the manifestation of one, north to the Lyceum, south to the Librarian's Office, east to the Scholar's Study, and west to the Great Hall.
action: You get all
response: octahedron: You take the octahedron. Looking curiously at it, you note that it has eight sides, each of which is in the shape of an equilateral triangle. You feel you understand three-dimensional solid geometry a little better.
Archimedes's staff: (putting Elements into the set to make
room)
Taken.
exhaustion sandals: (putting the sapphire gem into the set to make room)
Taken.

[Your understanding of Geometry has increased. You estimate
that your score on tomorrow's final has just gone up by one
point.]
action: Go south
response: Temple of Number, Northern End
You can see a trash urn (in which is a scrap of papyrus) here.
action: Go east
response: You step through the doorway of the private home, confident in your knowledge of geometry.

In the middle of the courtyard stands a group of six elegant pedestals.
action: You put the octahedron on the large triangle
response: You put the octahedron on the large triangular top pedestal.
action: Go south
response: As you move south, you feel an electrical impulse course through you. The space around you seems to fold in on itself.

You enter a now fully-formed space.
action: You look at your surroundings
response: This space is made of some spongy gray matter. You can see an inscription here, and you can go north to the Lyceum, south to the Librarian's Office, east to the Scholar's Study, and west to the Great Hall, or up to the manifestation of one from this space. Now that the space has taken on a complete shape, you can also see a passage leading down.
action: Go south
response: You make your way south. As you do, you feel an electrical impulse course through you. You find yourself in...

You have solved the number puzzle on the wall here.
action: Describe the surroundings
response: This appears to be the head librarian's office in the Great Library of Alexandria. Scrolls litter the floor. The main part of the library is north of you, and a side room lies to the south.

You have solved the number puzzle on the wall here.
action: You go to the south
response: A huge globe sits on a pedestal in the center of the room.
action: Lever globe with staff
response: You slide the staff into the gap between the pedestal and the globe.

You push down on the staff. The globe starts to shift. You push harder. With this additional leverage, the globe pops off the pedestal! It rolls a few feet and comes to rest against the wall. It looks like there was something underneath the globe.

[Your understanding of Physics has increased. You estimate that
your score on tomorrow's final has just gone up by two points.]
action: INVENTORY
response: You are carrying:
an octahedron
some exhaustion sandals
an old coin
a square root
a set (no longer empty)
a sapphire gem
Elements
a scribbled scroll
your math book
action: You look at your surroundings
response: This room is quite large to be a side room just off the librarian's office. The walls are covered with maps, and an exit leads back north to the librarian's office. A short pedestal stands in the center of the room.

The huge globe lies on the floor.

On the short pedestal is a tetrahedron.

You can also see Archimedes's staff here.
action: You examine the tetrahedron
response: The tetrahedron, more commonly known as a pyramid, has four sides. Each side is in the shape of an equilateral triangle. This tetrahedron is about one cubic foot in volume.
action: You get it
response: You take the tetrahedron. Looking curiously at it, you note that it has four sides, each of which is in the shape of an equilateral triangle. You feel you understand three-dimensional solid geometry a little better.

[Your understanding of Geometry has increased. You estimate
that your score on tomorrow's final has just gone up by one
point.]
action: Go north
response: You have solved the number puzzle on the wall here.
action: Go north
response: As you move north, you feel an electrical impulse course through you. The space around you seems to fold in on itself.
action: You go north
response: You make your way north. As you do, you feel an electrical impulse course through you. You find yourself in...
action: You put the tetrahedron on the large triangle
response: You put the tetrahedron on the large triangular top pedestal.
action: You go south
response: As you move south, you feel an electrical impulse course through you. The space around you seems to fold in on itself.
action: Go west
response: Achilles sits by the side of the race track with his head in his hands.
action: You give the sandals to Achilles
response: Achilles looks at the exhaustion sandals rather skeptically ("I always run barefoot," he says), but he agrees to try them. After lacing them up, he snaps his fingers, and the tortoise appears. They find their places as before, and take off. Achilles runs to the halfway mark, looks up, and sees the tortoise ahead of him. He notes the tortoise's new position, races to it, and sees the tortoise still ahead.
Achilles doesn't give up, though, and every time he looks up he finds himself closer to the tortoise. As they approach the finish, Achilles is so close to the tortoise you can't see much distance between them. However, the tortoise crosses the finish line just barely ahead of Achilles.

The tortoise disappears again, and Achilles jogs back to you. He returns the exhaustion sandals. "Thanks for letting me try the sandals. I felt myself almost overtaking the tortoise, but the sandals weren't quite enough."
action: Go downwards
response: You make your way down.

The darkness in this space feels different than simply the absence of light - both weaker and stronger, somehow. You can still perceive yourself and what you're carrying, but a foot or so away from you the darkness seems palpable, almost alive. You do sense an exit above you, though.

You can just perceive a white mirror floating here in the darkness.
action: You examine the mirror
response: You would probably get a better look at the mirror if you were holding it.
action: You get it
response: (putting the square root into the set to make room)
You take the white-framed mirror from the darkness.
action: You look at it
response: This mirror is not made of glass but rather of some tougher material. Encircling the mirror and forming its frame is a one-eyed white adder, although there is a small hole where the eye should be. The word "Inverse" is inscribed on the bottom of the frame.
action: You put gem in the mirror
response: You push the sapphire gem into the eye hole of the adder on the white-framed mirror. The sapphire glows briefly as it slides into place.
action: Go upward
response: You make your way up through the darkness.
action: Go upward
response: You make your way up.
action: Inverse mirror
response: Nothing happens. Perhaps the mirror is activated some other way.
action: You look in the mirror
response: You look in the mirror and see an inverted image of yourself reflected back at you. As you gaze at your image, the word "Inverse" on the mirror's frame begins to glow. In response, your image in the mirror grows larger. Soon your face fills the entire mirror. You lean in closer, and your nose brushes the mirror's surface. The mirror emits a dazzling flash of light, and you feel yourself invert as
you are pulled through the mirror.

This is more of an abstract space than a physical place. You get a general feeling of opposition here. The only exit is a hole leading up.

You can see a phase inverter here.
action: You look at the inverter
response: This complicated mechanism appears to have a place to insert objects.
action: You check what you're carrying
response: You are carrying:
some exhaustion sandals
a tetrahedron
an octahedron
an old coin
a set (no longer empty)
a square root
Elements
a scribbled scroll
your math book
action: You put the sandals in the inverter
response: You briefly insert the exhaustion sandals into the phase inverter.
The inverter hums as it adds π units to the essence of the exhaustion sandals. If something has changed about the exhaustion sandals, it's difficult to see what.
action: You put the coin in the inverter
response: You briefly insert the old coin into the phase inverter. The inverter hums as it adds π units to the essence of the old coin. If something has changed about the old coin, it's difficult to see what.
action: You ascend
response: You make your way up.

As you climb through the hole, you enter the dark blue expanse of space surrounding the positive axis. Off to the "east" you can see the back of the now-enlarged white-framed mirror, supported by nothing but standing upright just on the edge of the positive axis. The top of the mirror begins to pivot towards you, while the bottom of the mirror remains where it is. As the mirror continues to rotate, you see that it is reflecting a second copy of the positive axis. This copy is rotating with the mirror, as if it is a ray of light bouncing off the mirror. At the instant the mirror passes through the plane of the positive axis, the mirror disappears! The reflected copy of the positive axis remains, though, passing right by you and running as far as you can see to the "west." You feel fairly comfortable stepping on the now fully-formed number line.

Number Line: -1
You are in a dark blue expanse of space, standing on a white line that stretches as far as you can see from west to east. The number -1 is marked on the line here. There is a hole next to the -1 large enough for you to climb down into.

[Your understanding of Arithmetic has increased. You estimate
that your score on tomorrow's final has just gone up by one
point.]
action: Go west
response: You walk along the number line for a while, noting marks for -2, -3, -4, and the other negative integers. There are no holes or anything else featured on the this part of the number line, though, and you soon decide return to the -1 mark.
action: Go east
response: Number Line: 0
action: Go east
response: Number Line: 1
action: You go downwards
response: You clamber down the hole.
action: Go downwards
response: You make your way down.
action: Look around
response: The darkness in this space feels different than simply the absence of light - both weaker and stronger, somehow. You can still perceive yourself and what you're carrying, but a foot or so away from you the darkness seems palpable, almost alive. You do sense an exit above you, though.
action: You examine the darkness
response: The darkness surrounding you feels like more than just the absence of light.
action: You touch it
response: You've got to be kidding.
action: You go to the south
response: As you move south, you feel an electrical impulse course through you. The space around you seems to fold in on itself.

This space is made of some spongy gray matter. You can see an inscription here, and you can go north to the Lyceum, south to the Librarian's Office, east to the Scholar's Study, and west to the Great Hall, or up to the manifestation of one from this space. Now that the space has taken on a complete shape, you can also see a passage leading down to Darkness.
action: South
response: You make your way south. As you do, you feel an electrical impulse course through you. You find yourself in...

This appears to be the head librarian's office in the Great Library of Alexandria. Scrolls litter the floor. The main part of the library is north of you, and a side room lies to the south.

You have solved the number puzzle on the wall here.
action: Go north
response: As you move north, you feel an electrical impulse course through you. The space around you seems to fold in on itself.
action: Go east
response: You make your way east. As you do, you feel an electrical impulse course through you. You find yourself in...

On the low table are a small coffer and a formal note.
action: You look at the buttons
response: There are five buttons hidden in the geometric designs: a circular button, a button in the shape of two juxtaposed parentheses, a triangular button, a square button, and a pentagonal button.
action: You go east
response: This is a small, nondescript room to the east of the study. Its walls are plain and unadorned.

In the center of the room is a large wooden chest.

You can also see a cube here.
action: You look at the cube
response: This featureless cube has six sides, each of which is in the shape of a square. The cube is about one cubic foot in volume.
action: You get it
response: You take the cube. It is just a cube, but there's something about it that holds your attention. You feel you understand three-dimensional solid geometry a little better.

[Your understanding of Geometry has increased. You estimate
that your score on tomorrow's final has just gone up by one
point.]
action: You examine the chest
response: (x+1)⁴. It also has a set of five dials embedded in its
lid.
It appears each dial can be set to an integer between 0 and 9.

The first dial has x⁴ marked below it. The first dial is
set
to 0.

The second dial has x³ marked below it. The second dial is
set to 0.

The third dial has x² marked below it. The third dial is set
to 0.

The fourth dial has x¹ marked below it. The fourth dial is
set to 0.

The fifth dial has x⁰ marked below it. The fifth dial is
set
to 0.

The chest is currently closed.
action: You set the first dial to 1
response: You set the first dial to 1.
action: You set second to 1
response: You set the second dial to 1.
action: You set the third to 1
response: You set the third dial to 1.
action: You set the fourth to 1
response: You set the fourth dial to 1.
action: Set fifth to 1
response: You set the fifth dial to 1.
action: Open chest
response: You can't get the chest open. It appears to be locked.
action: You look at the chest
response: (x+1)^4. It also has a set of five dials embedded in its
lid. It appears each dial can be set to an integer between 0 and 9.

The first dial has x^4 marked below it. The first dial is
set to 1.

The second dial has x^3 marked below it. The second dial is
set to 1.

The third dial has x^2 marked below it. The third dial is
set to 1.

The fourth dial has x^2 marked below it. The fourth dial is
set to 1.

The fifth dial has x^0 marked below it. The fifth dial is
set to 1.

The chest is currently closed.
action: You set second to 4
response: You set the second dial to 4.
action: You set the third to 6
response: You set the third dial to 6.
action: You set fourth to 4
response: You set the fourth dial to 4. The lid of the chest gives a
click.

[Your understanding of Algebra has increased. You estimate that
your score on tomorrow's final has just gone up by four
points.]
action: Open chest
response: You open the large wooden chest, revealing The Compendious Book on Calculation by Completion and Balancing.
action: You look at Book
response: Which do you mean, The Compendious Book on Calculation by
Completion and Balancing, Elements, or your math book?
action: You examine compendious
response: This is a copy of al-Khwarizmi's Compendious Book on Calculation
by Completion and Balancing, or, more simply, Algebra.
action: You read the Algebra
response: This is a copy of al-Khwarizmi's Compendious Book on Calculation

Balancing contains far too much material to read through.
action: You get it
response: (putting the old coin into the set to make room)
Taken.
action: You go to the west
response: On the low table are a small coffer and a formal note.
action: Go west
response: As you move west, you feel an electrical impulse course through you. The space around you seems to fold in on itself.
action: Go west
response: You make your way west. As you do, you feel an electrical impulse course through you. You find yourself in...

On the long table is a pile of old coins.

The Count is here, looking rather bored.
action: Go west
response: The Count calls after you, "If you find something else for me to count I would be grateful!"
action: Go south
response: The Count calls after you, "If you find something else for me to count I would be grateful!"

A large bronze box lies on the side table.

The Countess is here, fiddling disgruntledly with the bronze box.
action: Examine box
response: This bronze box has several knobs and small wheels on it. It appears to be a primitive mechanical calculator.
action: You look up the calculator
response: (in your math book)
That topic is not listed in the index.
action: You check your inventory
response: You are carrying:
The Compendious Book on Calculation by Completion and
Balancing
a cube
some exhaustion sandals
a tetrahedron
an octahedron
a set (no longer empty)
an old coin
a square root
Elements
a scribbled scroll
your math book
action: Go downward
response: You make your way down.

This space feels a little less dark than the last time you were here.
action: You look around
response: This space now exhibits a kind of semidarkness. You can't see anything clearly in the space itself, but you do perceive exits north, south, east, and west, as well as one above you to Gray Matter.
action: You go to the north
response: You make your way north through the darkness. As you do, you feel an electrical impulse course through you. You find yourself in...

This is a grassy area between buildings at some university. Dusk is falling, and no one else is around. There is a log table at the edge of the grassy area. It looks like there is a small laundry facility in the building to east, and a gate lies south of you.

Someone has left their trigonometry homework on the log table. A slide rule is lying next to the trig homework.

On the grass lies a funny-looking soccer ball.
action: You look at the table
response: This wooden table was constructed from several large logs.

On the log table are the trig homework and a slide rule.
action: You examine the homework
response: The homework is covered with equations involving sines, cosines, and tangents. There are also a couple of graphs drawn on the homework, labeled "sin x" and "cos x." Each graph consists of
a wavy line that switches from positive to negative every Pi units. Circled at the top of the homework is the phrase "Review Logarithms!!!"
action: You examine the slide
response: The slide rule consists of three pieces of wood: the two on the outside are attached to each other, while the third - in the middle - can slide between the other two. Numbers are marked on all three pieces of wood. You have no idea how to use a slide rule.
action: You get ball
response: You reach for the soccer ball, but it rolls away as your hand gets near.
action: You get the rule
response: (putting the octahedron into the set to make room)
Taken.
action: Go east
response: This small laundry room, presumably for student use, contains a single washing machine and a single dryer. A sign hangs nearby. The exit is west.
action: You look at the sign
response: The sign is handwritten in black ink. It reads, "The dryer won't tumble, and the washing machine is completely broken. Won't anyone fix anything around here?!"
action: You examine the washing
response: This washing machine does not look like it has been treated well. The washing machine is currently open and off.
action: You look at the dryer
response: This dryer does not look as if it has been treated well. The dryer is currently open and off.
action: Go west
response: Someone has left their trigonometry homework on the log table.

On the grass lies a funny-looking soccer ball.
action: You go south
response: As you move south, you feel an electrical impulse course through you. The space around you seems to fold in on itself.
action: You go to the east
response: You make your way east through the darkness. As you do, you feel an electrical impulse course through you. You find yourself in...

You are standing in an open field west of a white house, with a boarded front door. A path leads west into the forest.

There is a small mailbox here.
action: You look at the mailbox
response: The mailbox is closed. It has a small hole in it.
action: You open it
response: The mailbox is closed tight. You can't see how to get it open.
action: You examine the hole
response: The small hole contains screw threads that are oriented counterclockwise.
action: You look at the door
response: There are boards over the front door, but the boards look somewhat rotten. There is also an inscription on the door.
action: You examine the inscription
response: The inscription reads,

"You have to spend some energy and effort to see the beauty of math." - Maryam Mirzakhani.
action: Exits
response: I didn't recognize that command. (There is a list of recognized commands in the HELP menus.)
action: You remove the boards
response: The rotting boards fall apart in your hands as you remove them from the front door.
action: Go inside
response: (first opening the front door)

This is the living room of the white house, and it looks to be the only room still intact. A sofa sits against one wall, and a bookcase stands against another. The sole unblocked exit is through the front door to the west.
action: You look at the sofa
response: The sofa features a faded floral-print pattern.
action: You examine the bookcase
response: The bookcase looks like it has space for twelve books. It is currently empty.
action: You check your inventory
response: You are carrying:
a slide rule
The Compendious Book on Calculation by Completion and
Balancing
a cube
some exhaustion sandals
a tetrahedron
a set (no longer empty)
an octahedron
an old coin
a square root
Elements
a scribbled scroll
your math book
action: You put Elements in the bookcase
response: (first taking Elements)
(putting the tetrahedron into the set to make room)
You put Elements on the bookcase. As it slides into place
you hear a faint click. Then you hear a voice. You're not
sure where it's coming from, but it sounds like Professor Glasser.

The voice says, "Euclid's Elements is the most influential
mathematics book of all time. Containing numerous results on geometry and number theory, and used as a textbook for over 2000 years, its logical, deductive approach has also served as a model for how pure mathematics should be done."

[Your understanding of Mathematics Texts has increased. You
estimate that your score on tomorrow's final has just gone up by one point.]
action: You put the Algebra in the bookcase
response: You put The Compendious Book on Calculation by Completion and Balancing on the bookcase. As it slides into place you hear a
faint click. Then you hear the same voice as before - the
one that sounds like Professor Glasser.

The voice says, "While systematic methods for solving equations had been used before, the branch of mathematics known as algebra is often dated to this work by Al-Khwarizmi. In fact, the Arabic word
al-jabr, translated here as 'Completion,' is the origin of
our word 'algebra.' Among the book's other contributions is a classification of quadratic equations and a discussion of their solutions."

[Your understanding of Mathematics Texts has increased. You
estimate that your score on tomorrow's final has just gone up by one point.]
action: Go west
response: There is a small mailbox here.
action: Go west
response: As you move west, you feel an electrical impulse course through you. The space around you seems to fold in on itself.
action: You go to the west
response: You make your way west through the darkness. As you do, you feel an electrical impulse course through you. You find yourself in...

Your senses are assaulted by the gleaming lights and jangly sounds of this casino. An interesting poker game is going on to the north of you, while the casino's exit appears to lie to the east.

A gaming machine near you catches your eye.
action: You examine the machine
response: This gaming machine has the words "TOP TWO GAME" written across its side. There are several buttons on the machine, each with a different label.

White: "Instructions."
Black: "Start New Game."
Green: "Accept Current Number."
Orange: "Reject Current Number."
Red: "Reject Next 10 Numbers."
Blue: The label for the blue button has been torn off.

The screen currently reads, "Press white button for instructions, or press black button to start a new game."
action: You press the white
response: You push the white button. The screen clears, and the following text appears.

"In this game you will be presented with 100 numbers, one at a time. For each number you are presented, you must decide whether to accept it or reject it. Once you reject a number it is gone and you cannot go back and select it. Once you accept a number the game ends.

You win the game by having the number you selected be one of the two largest numbers out of the 100 total numbers.

Hint: The best strategy for this game gives you a greater than 50% chance of winning."

The instructions disappear from the screen, and it once again reads, "Press white button for instructions, or press black button to start a new game."
action: Go north
response: You stand next to a poker table in the casino. The lights and noise here are just as overwhelming as in the rest of the casino. The gaming machine is to the south.

Pascal, Bayes, Kolmogorov, and Diaconis are here, playing an intense game of poker.
action: You look at the poker
response: Which do you mean, the poker game, the poker cards, or the poker table?
action: Game
response: You watch the poker game for a while. Pascal is making huge wagers and winning big. Bayes is trying to use prior knowledge of previous hands to plan his strategy, but that doesn't seem to be working out too well for him. Kolmogorov appears to be more interested in constructing some elaborate theory of poker than winning; not surprisingly, he is losing as well. Diaconis is dealing, and he is winning more than losing. Cards fly out of his hands as if by magic.
action: You look at the cards
response: They look like a standard set of poker cards.
action: You look at the table
response: This is a standard casino poker table. The only thing somewhat unusual about it is that its top is five-sided. Pascal, Bayes, Kolmogorov, and Diaconis are playing an animated game of poker at the table.
action: You go south
response: A gaming machine near you catches your eye.
action: Go east
response: As you move east, you feel an electrical impulse course through you. The space around you seems to fold in on itself.
action: You go to the south
response: You make your way south through the darkness. As you do, you feel an electrical impulse course through you. You find yourself in...

Judging from the odd assortment of medical instruments scattered around this room, you are in the office of some Renaissance-era physician. You can leave the office to the north.

There is a strange mechanism in the center of the office.

You can also see a parchment and a square piece of metal here.
action: You examine the parchment
response: This is a small, square piece of parchment. Written on the parchment are a couple of equations:

2A + X = 5Y + 8Z,

3B - Z = 7C + 4Y.
action: You look at the metal
response: (the square piece of metal)
This small, square, flat piece of metal has five rectangular holes cut into it.
action: You examine the mechanism
response: This mechanical device contains, among other things, a turnable crank, three interlocking gears, a metal bar attached to one of the smaller gears, and an access panel.
action: You look at the crank
response: It's fairly large. It looks like you could probably turn it.
action: You examine the gears
response: The two smaller gears have about half the radius of the large gear.
action: Examine bar
response: This bar is attached to one of the smaller gears.
action: You look at the panel
response: The access panel is closed.
action: You open it
response: You open the access panel.

Inside is some complicated machinery. A sine wave is intertwined with the machinery.
action: Examine wave
response: The sine wave goes up and down and up and down and up and down...
action: You turn the crank
response: You turn the crank, which causes the two small gears to rotate around the large gear. As the small gears rotate, they move the metal bar back and forth in a straight line.

Then the strange mechanism emits an aura of positive power that fills the room. You briefly feel happier, as well as more optimistic about your chances on tomorrow's exam.
action: You get wave
response: You carefully take the sine wave from the strange mechanism.
action: You turn crank
response: You turn the crank, which causes the two small gears to rotate around the large gear. As the small gears rotate, they move the metal bar back and forth in a straight line.

Nothing else happens (although converting rotational motion to linear motion is pretty cool in and of itself).
action: You examine instruments
response: You search through the medical instruments, but they all look more painful than useful. One does say, "Property of G. Cardano" on it, though.
action: You look up Cardano
response: (in your math book)
Girolamo Cardano was a practicing physician, mathematician, and inventor: a true Renaissance man. His inventions include the Cardan gear, used to convert rotational motion to linear motion, and the Cardan grille, an early cryptographic technique in which secret messages are revealed by placing a thin sheet with holes cut out of it over a paper containing an ordinary-looking message. Cardano also contributed to the development of (and sometimes is credited with the invention of) the combination lock.

Mathematically, he was the first person to make systematic use of negative numbers. His work features the first use of complex numbers, too, as well as the first published solutions to the general cubic and quartic equations.
action: You check your inventory
response: You are carrying:
a sine wave
a square piece of metal
a slide rule
a cube
some exhaustion sandals
a set (no longer empty)
a tetrahedron
an octahedron
an old coin
a square root
a scribbled scroll
your math book
action: You put the metal on the scroll
response: (the square piece of metal on the scribbled scroll)
You place the piece of metal on the scribbled scroll, but you can't seem to align it in such a way that letters clearly show through the holes.
action: Go north
response: As you move north, you feel an electrical impulse course through you. The space around you seems to fold in on itself.
action: Go south
response: You make your way south through the darkness. As you do, you feel an electrical impulse course through you. You find yourself in...

There is a strange mechanism in the center of the office.

You can also see a parchment here.
action: You put the metal on the parchment
response: (the square piece of metal on the parchment)
You place the piece of metal on the parchment, aligning it so that it covers the parchment completely. Through the holes you can see five letters: "XYZZY."

[Your understanding of Cryptography has increased. You estimate
that your score on tomorrow's final has just gone up by two
points.]
action: Xyzzy
response: You speak the word of power confidently. A part of the wall slides open, revealing a niche. Inside the niche is Ars Magna.
action: You read it
response: This is a copy of Ars Magna, by Girolamo Cardano.

Ars Magna contains far too much material to read through.
action: You get it
response: (putting the exhaustion sandals into the set to make room)
Taken.
action: You go to the north
response: As you move north, you feel an electrical impulse course through you. The space around you seems to fold in on itself.

The darkness has mostly lifted.

Off to the side sits a gray storage bin.

A gray, translucent ghost flits around the storage bin.
action: You examine bin
response: It's just a storage bin that happens to be gray.
action: You examine the ghost
response: She looks a lot like the college librarian - except older, more translucent, and, well, grayer.
action: You greet the ghost
response: "Hello?" you say tentatively, unsure of the proper greeting for a ghost.

"Hello!" she replies. She looks at you carefully. "You know, you've got enough running around in your head right now." As an aside she adds, "I suppose that includes me."

Shimmering slightly, she continues. "Anyway, I'm here to help you organize your thoughts. Show me any possession of yours, and I'll tell you whether I think it will still be useful for you. Go on. Try me!"
action: Inventory
response: You are carrying:
Ars Magna
a sine wave
a square piece of metal
a slide rule
a cube
a set (no longer empty)
some exhaustion sandals
a tetrahedron
an octahedron
an old coin
a square root
a scribbled scroll
your math book
action: You show the root to the ghost
response: (first taking the square root)
(putting the cube into the set to make room)
The gray lady looks carefully at the square root. "I would definitely hold on to that," she says. "You're not likely to find much that is more useful."
action: You show the scroll to the ghost
response: (first taking the scribbled scroll)
(putting the slide rule into the set to make room)
The gray lady looks carefully at the scribbled scroll. Then she says, "I'm not sure you'll have any more use for that." She takes the scribbled scroll from you and places it in the gray storage bin. "If you ever want it back, though, feel free to just take it," she adds. "I might be wrong."
action: You show metal to the ghost
response: The gray lady looks carefully at the square piece of metal. Then she says, "I'm not sure you'll have any more use for that." She takes the square piece of metal from you and places it in the gray storage bin. "If you ever want it back, though, feel free to just take it," she adds. "I might be wrong."
action: You go east
response: You make your way east. As you do, you feel an electrical impulse course through you. You find yourself in...

There is a small mailbox here.
action: You go east
response: There are currently two books on the bookcase:
The Compendious Book on Calculation by Completion and
Balancing
Elements
action: You put the Ars in the bookcase
response: You put Ars Magna on the bookcase. As it slides into place
you hear a faint click. Then you hear the same voice as
before - the one that sounds like Professor Glasser.

The voice says, "Cardano's great work on algebra contains the first published solutions to the general cubic and quartic equations. It includes the use of negative numbers, which were not widely accepted in Europe at the time, and it also features the first use of complex numbers (in the context of solving a quadratic equation)."

[Your understanding of Mathematics Texts has increased. You
estimate that your score on tomorrow's final has just gone up by one point.]
action: You go west
response: As you move west, you feel an electrical impulse course through you. The space around you seems to fold in on itself.

Off to the side sits a gray storage bin. In the storage bin you see a square piece of metal and a scribbled scroll.

A gray, translucent ghost flits around the storage bin.
action: You look around
response: The darkness has mostly lifted, but now everything in this space looks gray. The darkness does continue to pool around your feet, though. There is an inscription on the wall, and there are exits up to Gray Matter, as well as north to the Grassy Area, south to the Physician's Office, east to the white house, and west to the Casino.

Off to the side sits a gray storage bin. In the storage bin you see a square piece of metal and a scribbled scroll.

A gray, translucent ghost flits around the storage bin.
action: Go upwards
response: You make your way up.

Number Line: 1
action: You go west
response: Number Line: -1
action: You go downwards
response: You clamber down the hole.

You can see a phase inverter here.
action: You put the sine in the inverter
response: You briefly insert the sine wave into the phase inverter. The inverter hums as it adds Pi units to the essence of the sine wave.
The sine wave shifts phase, becoming a negative sine wave.

[Your understanding of Trigonometry has increased. You estimate
that your score on tomorrow's final has just gone up by two
points.]
action: Go upwards
response: You make your way up.

Number Line: -1
action: Go down
response: You make your way down.

Off to the side sits a gray storage bin. In the storage bin you see a square piece of metal and a scribbled scroll.

A gray, translucent ghost flits around the storage bin.
action: Inventory
response: You are carrying:
a square root
a negative sine wave
a set (no longer empty)
a slide rule
a cube
some exhaustion sandals
a tetrahedron
an octahedron
an old coin
your math book
action: Go south
response: You make your way south. As you do, you feel an electrical impulse course through you. You find yourself in...

A part of the wall has slid open, revealing a niche.

There is a strange mechanism in the center of the office.

You can also see a parchment here.
action: You put the wave in the panel
response: You carefully insert the negative sine wave back into the strange mechanism.
action: You turn the crank
response: You turn the crank, which causes the two small gears to rotate around the large gear. As the small gears rotate, they move the metal bar back and forth in a straight line.

Then the strange mechanism emits an aura of negative power that fills the room. You briefly feel more depressed, as well as more pessimistic about your chances on tomorrow's exam.

For just a moment, the square root glows, as it absorbs the negative power emitted by the mechanism.
action: You look at the root
response: This is an unusual object. It appears to be made of some tough vegetable matter - perhaps the root of a tree. It's also in the shape of a perfect square. The word "EXTRACT" is written on it.

The square root has also absorbed negative power from the machine in the physician's office.
action: Go north
response: As you move north, you feel an electrical impulse course through you. The space around you seems to fold in on itself.

Off to the side sits a gray storage bin. In the storage bin you see a square piece of metal and a scribbled scroll.

A gray, translucent ghost flits around the storage bin.
action: Go upwards
response: You can see absolutely nothing in the blue darkness off the number line. Stepping off it doesn't sound like a good idea.
action: Go east
response: Number Line: 2
action: Extract root
response: The root vibrates quietly, as it extracts the square root of the essence of the space around it. You feel yourself shift.

Irrational: Between 1 and 2
This is more of an abstract space than a physical place, but it feels large beyond your understanding, as if it encompasses infinitely more space than the single-number locations beneath the number line. A hole leads up to the number line.
action: Go up
response: You make your way up.

As you step onto the number line, the hole behind you closes. Rather than standing at an unmarked spot between 1 and 2, you head back to 1.

Number Line: 1
action: You go west
response: Number Line: 0
action: You go west
response: Number Line: -1
action: Extract root
response: The root vibrates quietly, as it extracts the square root of the essence of the space around it. You feel yourself rotate
clockwise, swinging in an arc that takes you halfway back to the positive part of the number line.

This is more of an abstract space than a physical place. It feels different than the spaces just below the number line - not less real, but more as if this space exists in a different dimension. A hole leads up, maybe to the number line?
action: Go upwards
response: You make your way up.

As you climb through the hole, at first it appears as if you are climbing into a dark blue nothingness. But then a thin, infinitely long vertical line appears out of that nothingness, widens, and rotates 90 degrees to run north-to-south. You confidently step onto the new line.

Imaginary Axis: i
You are in a dark blue expanse of space, standing on a white line that stretches as far as you can see to the north. To the south you can perceive where the imaginary axis crosses the number line. The number i is marked on the line here. There is a hole next to the
i that you might be able to climb down into.

[Your understanding of Complex Numbers has increased. You
estimate that your score on tomorrow's final has just gone up by two points.]
action: You go east
response: Real Axis: 1
action: You go to the north
response: You make your way north. As you do, you feel an electrical impulse course through you. You find yourself in...

Someone has left their trigonometry homework on the log table.

On the grass lies a funny-looking soccer ball.
action: You examine the homework
response: The homework is covered with equations involving sines, cosines, and tangents. There are also a couple of graphs drawn on the homework, labeled "sin x" and "cos x." Each graph consists of
a wavy line that switches from positive to negative every Pi units. Circled at the top of the homework is the phrase "Review Logarithms!!!"
action: You kick it
response: The soccer ball remains still, and your foot connects with a solid "thud." As the ball flies through the air it begins to transform, becoming less round and more pointed. It bounces off one of the buildings and rolls across the grass, coming to a stop near you. You look down to see an object that is no longer quite a soccer ball.
action: You look at it
response: The icosahedron has twenty sides, each of which is in the shape of an equilateral triangle. It kind of looks like a more pointy version of a soccer ball. In fact, you realize that if you cut its vertices off in the right way and inflated it to make it more round you would have a soccer ball. This icosahedron is about one cubic foot in volume.
action: You get it
response: You take the icosahedron. Looking curiously at it, you note that it has twenty sides, each of which is in the shape of an equilateral triangle. You feel you understand three-dimensional solid geometry a little better.

[Your understanding of Geometry has increased. You estimate
that your score on tomorrow's final has just gone up by one
point.]
action: You look in the dryer
response: The dryer is empty.
action: You look in the washer
response: The washing machine is empty.
action: You look at your surroundings
response: This is a grassy area between buildings at some university. Dusk is falling, and no one else is around. There is a log table at the edge of the grassy area. It looks like there is a small laundry facility in the building to east, and a gate lies south of you.

Someone has left their trigonometry homework on the log table.
action: You check what you're carrying
response: You are carrying:
an icosahedron
a square root
a set (no longer empty)
a slide rule
a cube
some exhaustion sandals
a tetrahedron
an octahedron
an old coin
your math book
action: You examine the slide
response: The slide rule consists of three pieces of wood: the two on the outside are attached to each other, while the third - in the middle - can slide between the other two. Numbers are marked on all three pieces of wood. You have no idea how to use a slide rule.
action: Go south
response: As you move south, you feel an electrical impulse course through you. The space around you seems to fold in on itself.

Off to the side sits a gray storage bin. In the storage bin you see a square piece of metal and a scribbled scroll.

A gray, translucent ghost flits around the storage bin.
action: You show the homework to the ghost
response: The gray lady looks carefully at the trig homework. Then she says, "I think you may still find some use for that. You never know, though," she adds. "I might be wrong."
action: You check your inventory
response: You are carrying:
the trig homework
an icosahedron
a square root
a set (no longer empty)
a slide rule
a cube
some exhaustion sandals
a tetrahedron
an octahedron
an old coin
your math book
action: You look up Plato
response: (in your math book)
Plato held that mathematical reasoning serves as a model for how to think philosophically. There is a legend that the phrase "Let no one ignorant of geometry enter" was written over the door to his Academy. The five Platonic solids - the tetrahedron, the cube, the octahedron, the dodecahedron, and the icosahedron - are named for him.
action: Slide rule
response: What do you want to slide the slide rule under?
action: You go up
response: You must name something more substantial.
action: You show the rule to Achilles
response: (first taking the slide rule)
Achilles frowns. "I don't see how that will help me beat the tortoise."
action: You look up Achilles in the MATH
response: The story of Achilles and the tortoise is a paradox related to the nature of infinity. It was devised by Zeno of Elea.

In the paradox, Achilles is racing a tortoise who is given a head start. Zeno claims that Achilles can never catch up to the tortoise because "In a race, the quickest runner can never overtake the slowest, since the pursuer must first reach the point whence the pursued started, so that the slower must always hold a lead."

The paradox of Achilles and the tortoise, as well as Zeno's paradoxes in general, are important in mathematics because they helped force mathematicians to consider carefully what they mean by continuous quantities that are infinitely divisible, as well as infinity itself.

Some mathematicians believe that the limit concept, which not only provides a rigorous method for handling infinite quantities but also put calculus on a firm theoretical foundation, resolves the paradox of Achilles and the tortoise. However, limits were not developed until over 2000 years after the death of Zeno.
action: Go west
response: From here, the only exit is east.
action: You show rule to Countess
response: You show the slide rule to the Countess. "This is an interesting device," she says. "Do you know how to work it?" You shake your head, and she returns the slide rule to you.
action: You look up the slide rule
response: (in your math book)
The only mention of slide rules in the index refers to a unit on logarithms, so you turn to that section.

A logarithm is a function whose output is an exponent or power. For example, the base 10 logarithm of 1000 is 3, since 10^3 is 1000.

The earliest practical use of logarithms was to convert a multiplication calculation to an addition calculation via the logarithm property log(xy) = log x + log y.
The slide rule operates on this and other properties of logarithms.

(There follows a detailed description of how to work a slide rule to do multiplication using logarithms.)

Using the example, you practice with the slide rule until you understand how to use it to do multiplication.

[Your understanding of Logarithms has increased. You estimate
that your score on tomorrow's final has just gone up by two
points.]
action: You show the rule to Countess
response: You show the slide rule to the Countess, and you carefully explain to her how to use it to do multiplication. She immediately grasps the concept. "With this, I don't need to fix my mechanical calculator!
Do you mind if I have it?" You give your assent, and the Countess smiles widely.

"If this does multiplication, it could also do division." She begins playing with the slide rule. "And it should be able to calculate powers of a number." She performs a few more calculations on the slide rule. "Yes!" she says. "Here, let me show you what I've done."

As the Countess explains how to use the slide rule to do division and exponentiation, you realize that she is essentially showing you two more logarithm properties: log(x/y) = log x - log
y, converting division to subtraction, and log x^n =
n log x, converting exponentiation to
multiplication.

"Thank you so much for the slide rule. What an ingenious device and valuable gift!" she says. "I must reciprocate!" She produces a small bell from somewhere and rings it. A servant rushes in, and the Countess whispers something to him. The servant disappears, but he soon returns, hands a book to the Countess, and disappears once more.

The Countess gives the book to you. "This is a wide-margin copy of Diophantus's Arithmetica. We used to have a copy with narrow
margins, too, but we gave that one to Fermat."

[Your understanding of Logarithms has increased. You estimate
that your score on tomorrow's final has just gone up by two
points.]
action: You look at the arithmetica
response: This is a copy of Diophantus's Arithmetica. As the Countess indicated, it does have wide margins.
action: You look up Fermat
response: (in your math book)
Pierre de Fermat was a contemporary and sometime rival of Descartes. He was the greatest number theorist of his era, invented analytic geometry about the same time as Descartes (but did not publish his results), and his method of tangents was a forerunner to the derivative concept used in calculus. Fermat was actually a lawyer and did mathematics for fun in his spare time.

Fermat is most well-known for his conjecture that become known as "Fermat's Last Theorem": There do not exist solutions in nonzero integers a, b, c, and n > 2, such
that a^n  + b^n = c^n. In his copy of
Diophantus's Arithmetica Fermat claimed to have found a
"truly remarkable proof of this theorem which this margin is too narrow to contain." No one has ever found Fermat's proof, and, despite an enormous amount of effort, nobody succeeded in proving it themselves until 1995, more than 350 years later.
action: Count count
response: You get exactly the number you expected.
action: You go east
response: The Count calls after you, "If you find something else for me to count I would be grateful!"

As you move east, you feel an electrical impulse course through you. The space around you seems to fold in on itself.
action: Go downward
response: You make your way down.

The darkness is completely gone now, revealing a passage down.

Gray Matter, Level Two
Off to the side sits a gray storage bin. In the storage bin you see a square piece of metal and a scribbled scroll.

A gray, translucent ghost flits around the storage bin.
action: Go downwards
response: You make your way down.

This space is filled with some kind of swirling, ethereal fog that plays tricks with your mind. You can't make much sense of the space or anything in it. However, you do sense an exit above you.
action: You examine the fog
response: This gray fog is confusing your mind. It's hard to focus on it.
action: Go upwards
response: You make your way up through the fog.

Gray Matter, Level Two
Off to the side sits a gray storage bin. In the storage bin you see a square piece of metal and a scribbled scroll.

A gray, translucent ghost flits around the storage bin.
action: You look around
response: Gray Matter, Level Two
This space is made of the same gray matter as the one above you.
There is an inscription on the wall, as well as exits up to Gray Matter, Level One, north to the Grassy Area, south to the Physician's Office, east to the white house, and west to the Casino. Now that the darkness is gone, you can also see a passage leading down to Confusion.

Off to the side sits a gray storage bin. In the storage bin you see a square piece of metal and a scribbled scroll.

A gray, translucent ghost flits around the storage bin.
action: You go east
response: You make your way east. As you do, you feel an electrical impulse course through you. You find yourself in...

There is a small mailbox here.
action: You go east
response: There are currently three books on the bookcase:
Ars Magna
The Compendious Book on Calculation by Completion and
Balancing
Elements
action: Put the Arithmetica in the shelf
response: You put Diophantus's Arithmetica on the bookcase. As it
slides into place you hear a faint click. Then you hear the
same voice as before - the one that sounds like Professor Glasser.

The voice says, "Diophantus's Arithmetica introduced symbols
to the study of the solutions of equations, in contrast to the prior method of writing everything out in words. The book itself discusses a variety of techniques for solving what we would now call algebraic equations.

Arithmetica is also famous (or perhaps infamous) for a note
Fermat once wrote on his copy of the book. The note conjectures that there do not exist solutions in nonzero integers a,
b, c, and n > 2, such that a^n  +
b^n = c^n. Then Fermat writes, 'I have discovered a
truly remarkable proof of this theorem which this margin is too narrow to contain.' No one has ever found Fermat's proof. This conjecture, which became known as "Fermat's Last Theorem," was not actually proved until 1995, more than 350 years later, using mathematical techniques far more sophisticated than the ones available to Fermat in the mid-1600s."

[Your understanding of Mathematics Texts has increased. You
estimate that your score on tomorrow's final has just gone up by one point.]
action: Go west
response: As you move west, you feel an electrical impulse course through you. The space around you seems to fold in on itself.

Gray Matter, Level Two
Off to the side sits a gray storage bin. In the storage bin you see a square piece of metal and a scribbled scroll.

A gray, translucent ghost flits around the storage bin.
action: Look around
response: This space is filled with some kind of swirling, ethereal fog that plays tricks with your mind. You can't make much sense of the space or anything in it. However, you do sense an exit above you.
action: Inventory
response: You are carrying:
the trig homework
an icosahedron
a square root
a set (no longer empty)
a cube
some exhaustion sandals
a tetrahedron
an octahedron
an old coin
your math book
action: Go upwards
response: You make your way up through the fog.

Gray Matter, Level Two
Off to the side sits a gray storage bin. In the storage bin you see a square piece of metal and a scribbled scroll.

A gray, translucent ghost flits around the storage bin.
action: Go west
response: You make your way west. As you do, you feel an electrical impulse course through you. You find yourself in...

A gaming machine near you catches your eye.
action: You look up the optimal stopping
response: (in your math book)
An optimal stopping problem is one in which you are faced with the problem of when to take a particular action in order to maximize a reward or minimize a cost.

problem: You want to hire a secretary. You have n
candidates, and you interview them one-by-one. After each interview, you must decide whether to hire or reject the person you just interviewed. You cannot go back and hire a candidate you have already rejected. If you want to maximize your chances of hiring the best person for the job the optimal strategy turns out to be to automatically reject the first X candidates and then hire the
next candidate after that who is better than all of the candidates you have seen thus far. Surprisingly, if X corresponds to the
first n/e (in other words, the first 37% of)
candidates, then the probability of selecting the single best candidate out of the entire n candidates is about 37%.

If you want one of the two best candidates instead, then you can get above a 50% chance using a similar strategy. In fact, there's a wide range of values of X that work well in the top two case. For
example, if n is 100, then any choice of X between
22 and 39 will give you a better than 50% chance of selecting one of the two best candidates.
action: You go to the east
response: As you move east, you feel an electrical impulse course through you. The space around you seems to fold in on itself.

Gray Matter, Level Two
Off to the side sits a gray storage bin. In the storage bin you see a square piece of metal and a scribbled scroll.

A gray, translucent ghost flits around the storage bin.
action: Go downward
response: You make your way down.

The fog in this space has dissipated some since the last time you were here. You can make more sense of it now.
action: You look at your surroundings
response: This space contains some kind of swirling, ethereal fog that is affecting your ability to think clearly. You can make enough sense of this space to know that there is an exit above you to Gray Matter, Level Two, as well as exits north, south, east, and west.
action: Go north
response: You make your way north through the fog. As you do, you feel an electrical impulse course through you. You find yourself in...

The pleasant smell of fresh hay mingles with the less pleasant smells of farm animals here. The barn opens outside to the south.

A farmer is here, staring thoughtfully at a pile of wood.
action: You examine wood
response: It's just a pile of wood to you, but it must mean something to the farmer.
action: You examine farmer
response: The farmer is wearing blue overalls and a wide-brimmed hat.
action: You greet the farmer
response: "Hi," you say, and the farmer turns to look at you. "Howdy," he responds. "What are you doing?" you ask.

He says, "Well, I was just thinking about the water barrel I'm going to make out of this wood. I'm trying to decide whether it should be short and fat or tall and skinny."

"Why does it matter?" you ask.

"Well, I'd like it to hold as much water as possible. Does a short, wider barrel hold more water? Or does a tall and thin one? Or would it be better to make the barrel somewhere in between? Oh, and the barrel will have a lid.

"I've got this far," he says, pulling a thin card and a pencil from an inside pocket of his overalls. He scribbles an equation on the card, puts the pencil back in his overalls, and hands the card to you. "If you take the equation on this card and plug the radius of the barrel in for x, the value of y will tell you the resulting
volume of the barrel."

You take the card. "Don't you need this?" you ask.

"No," he says. "The card was junk mail - part of a promotion for some theme park. And I've got the equation memorized, too."
action: You look at the card
response: This small, very thin card reads "Farmer's Problem: y =
50x - Pi*x^3." You remember that y
represents the volume of the barrel the farmer is trying to build, while x represents the radius.
action: You go to the south
response: Before you can leave, you hear what sounds like a cowbell ringing.
The farmer grimaces. "Bessie's probably got herself tangled in the barbed wire again," he says. "I ought to go check on her."

Just then, a dog comes running into the barn, barking excitedly.
"Yes, I heard," the farmer says to the dog. "I'm going."

He turns to you. "If you can figure out the best solution to my barrel problem, I would be much obliged. I need to go help Bessie now, but Pennings here can bring me anything with the solution on it."

The farmer strides out of the barn.
action: You look at the dog
response: Pennings is a Welsh Corgi. He wags his tail happily but expectantly when he sees you looking at him; he seems to want you to give him something.
action: Pet dog
response: Pennings licks your face happily.
action: You go west
response: You make your way west through the fog. As you do, you feel an electrical impulse course through you. You find yourself in...

With its ornate central stone fountain, this can only be the great court of Trinity College, Cambridge. From here you can visit the chapel to the north or the college hall to the west. The main gate of Trinity College lies east.
action: You examine the fountain
response: This ornate stone fountain in the center of the court is its most prominent feature. The fountain is currently dry.
action: You go north
response: You stand in the magnificent chapel of Trinity College. You make a mental note to visit this place sometime when you're truly awake. The exit is to the south.

At the west end of the chapel stands a statue of Isaac Newton.

A beam of light shines through a window and forms a circle on the floor.
action: You look at the statue
response: This statue in white marble depicts Newton holding a prism as he gazes upward.

Prelude, describing this very statue:

"The antechapel where the statue stood
Of Newton with his prism and silent face,
The marble index of a mind for ever
Voyaging through strange seas of Thought, alone."

Wait - did Newton just wink at you?
action: You examine the prism
response: The prism, like the rest of the statue, is made of marble. The ambient light in the chapel seems to play across the surface of the prism.
action: Examine beam
response: This beam of light shines through a window and forms a circle on the floor.
action: You examine the circle
response: The light in the circle seems to sparkle.
action: Go west
response: You walk into the middle of a lecture on mathematics. The atmosphere feels a bit tense.

The speaker glares briefly at you as you enter, and you - somewhat sheepishly - step back into the shadows against the wall.

The speaker continues. "And so, as I was saying, the calculus of Newton does not rest on a logical foundation! Newton claims that the fluxion of x^2 is 2x, but one cannot have the
"infinitely small quantity" he uses in the calculation equal to zero in one place and not equal to zero in another!"
You hear several "Boo" shouts from the audience. "Go back to Oxford, Berkeley!" says one mathematician. "But calculus works!" yells a physicist.
"I repeat myself," replies Berkeley. "A quantity cannot be simultaneously equal to zero and not equal to zero. As Newton himself says, 'The minutest errors are not to be neglected in mathematics!'"

You can feel the audience's anger level rising, as Berkeley quotes Newton in his attack on Newton's calculus.
Then, after a tense few moments, a man in the front row storms the podium. The shocked look on Berkeley's face is visible from your place against the wall. Berkeley slowly backs away from the podium. Emboldened, several other audience members join the first man. Berkeley turns and runs out of the room. The rest of the audience rises and chases after him.
action: Look around
response: The normally-impressive great hall, with its wood paneling and Tudor-style interior, is in a state of disarray in the wake of Berkeley's lecture. A podium stands at the front of the room. The great court lies to the east.

In his haste to flee the crowd of angry mathematicians, Berkeley has left his lecture notes on the podium.
action: You look at the notes
response: These are Berkeley's notes describing what he considers to be serious logical flaws in the theoretical foundation of calculus. The notes are rather extensive, but the details of his attack on the fluxion of x^2 catch your eye.

"Newton says that the fluxion, or derivative, of x^2 is to be calculated like so: Adding the infinitely small quantity o to
x causes x^2 to become (x+o)^2. Then
(x+o)^2 expands to x^2 + 2ox + o^2.
Subtracting x^2 from the expansion of (x+o)^2 gives
us 2ox + o^2.

"The next step in the procedure is to divide by the infinitely small quantity o, producing 2x + o. Newton says now that since o
is infinitely small we can ignore it. This means that the fluxion of x^2 is 2x.

"However, is the 'infinitely small quantity' denoted 'o' equal to zero or not? If it is zero, then we cannot divide by it, since there is no meaning to dividing by zero. If it is not zero, then we cannot ignore it in the last step, and so the fluxion of x^2 cannot be
2x.

"You cannot have it both ways: Either o is equal to zero or it is not!"
action: You look up berkeley
response: (in your math book)
Along with John Locke and David Hume, Bishop George Berkeley is considered part of the trio of great British empirical philosophers of the 17th and 18th centuries. His major contribution to mathematics was his critique of the logical foundations of calculus. This critique helped inspire mathematicians to look more closely at what they meant by the "infinitesimally small" quantities used in calculus, ultimately leading to a precise definition of the limit concept. Incidentally, the main campus of the University of California and the surrounding city are named for him.
action: You look up the limit
response: (in your math book)
The limit is one of the most important concepts in mathematics.
Limits allow us to define exactly what we mean by concepts like "arbitrarily large" and "infinitesimally small."

Limits had been used implicitly in calculus since the time of Newton and Leibniz, but it was not until over 150 years later that the definition of a limit was made precise by Weierstrass, thereby placing calculus on a more solid theoretical foundation. Limits are also used to make sense of sequences and infinite series. Some argue that limits resolve Zeno's paradoxes.
action: You examine the podium
response: This podium is made of the same wood as the paneling you see around the room.
action: You look at the paneling
response: It's quite beautiful. Nothing at your university looks looks like this room.
action: You go east
response: You make your way east through the fog. As you do, you feel an electrical impulse course through you. You find yourself in...

The floor and ceiling of this room are black, while the walls feature eerie, pulsating, dark blue neon lights. An exit leads west.

A sleek laser bike is parked in the center of the room.

Someone has left a crudely-drawn comic on the floor.
action: Examine comic
response: The comic consists simply of two pictures: A man singing Christmas carols and a man wearing an old Houston football jersey. The Yuler has a large red X next to him, while the Oiler sports a large green check mark.
action: You get it
response: (putting the square root into the set to make room)
Taken.
action: You look at the bike
response: Built for speed, this laser bike pulses with the same dark blue neon light as the rest of the room.
action: Ride bike
response: You mount the laser bike. A door slides open in the east wall, and, without warning, the laser bike shoots through it!

You briefly catch a glimpse of a grid laid out before you, with intersection points, lines connecting them, and several ramps scattered throughout the intersections. A mechanical voice intones, "Starting new game. Illuminate all grid lines. Intersections will not be illuminated. One ramp jump allowed."

Then the bike launches into space, coming down in...

Intersection (on the laser bike)
You are riding a laser bike, traveling rapidly east through an intersection. Dark blue neon walls surround the intersection, but there are grid lines that lead northeast, south, southeast, and east.
action: You go to the south
response: You give the laser bike a sharp turn south, and it speeds through the grid line to the south. The bike leaves a laser beam of light in its wake.

Intersection (on the laser bike)
You are riding a laser bike, traveling rapidly south through an intersection. Dark blue neon walls surround the intersection, but there are grid lines that lead north and east.

However, the grid line to the north is lit up by a beam of light.

There is also a ramp to the northeast.
action: You go to the east
response: You give the laser bike a sharp turn east, and it speeds through the grid line to the east. The bike leaves a laser beam of light in its wake.

Intersection (on the laser bike)
You are riding a laser bike, traveling rapidly east through an intersection. Dark blue neon walls surround the intersection, but there are grid lines that lead north, northwest, east, and west.

However, the grid line to the west is lit up by a beam of light.

There is also a ramp to the northeast.
action: You go east
response: You keep going east, and the laser bike speeds through the grid line to the east. The bike leaves a laser beam of light in its wake.

Intersection (on the laser bike)
You are riding a laser bike, traveling rapidly east through an intersection. Dark blue neon walls surround the intersection, but there are grid lines that lead north and west.

However, the grid line to the west is lit up by a beam of light.

There is also a ramp to the northwest.
action: Go north
response: You give the laser bike a sharp turn north, and it speeds through the grid line to the north. The bike leaves a laser beam of light in its wake.

Intersection (on the laser bike)
You are riding a laser bike, traveling rapidly north through an intersection. Dark blue neon walls surround the intersection, but there are grid lines that lead north, south, and west.

However, the grid line to the south is lit up by a beam of light.

There are also ramps to the northwest and southwest.
action: You go to the north
response: You keep going north, and the laser bike speeds through the grid line to the north. The bike leaves a laser beam of light in its wake.

Intersection (on the laser bike)
You are riding a laser bike, traveling rapidly north through an intersection. Dark blue neon walls surround the intersection, but there are grid lines that lead south and west.

However, the grid line to the south is lit up by a beam of light.

There is also a ramp to the southwest.
action: Go west
response: You give the laser bike a sharp turn west, and it speeds through the grid line to the west. The bike leaves a laser beam of light in its wake.

Intersection (on the laser bike)
You are riding a laser bike, traveling rapidly west through an intersection. Dark blue neon walls surround the intersection, but there are grid lines that lead south, southwest, and east.

However, the grid line to the east is lit up by a beam of light.

There is also a ramp to the southeast.
action: You go south
response: You give the laser bike a sharp turn south, and it speeds through the grid line to the south. The bike leaves a laser beam of light in its wake.

Intersection (on the laser bike)
You are riding a laser bike, traveling rapidly south through an intersection. Dark blue neon walls surround the intersection, but there are grid lines that lead north, south, east, and west.

However, the grid line to the north is lit up by a beam of light.

There are also ramps to the northeast, southeast, and southwest.
action: You go west
response: You give the laser bike a sharp turn west, and it speeds through the grid line to the west. The bike leaves a laser beam of light in its wake.

Intersection (on the laser bike)
action: Look around
response: Intersection (on the laser bike)
You are riding a laser bike, traveling rapidly west through an intersection. Dark blue neon walls surround the intersection, but there are grid lines that lead northeast, south, southeast, and east.

However, the grid lines to the south and east are lit up by beams of light.
action: Go northeast
response: You give the laser bike a sharp turn northeast, and it speeds through the grid line to the northeast. The bike leaves a laser beam of light in its wake.

Intersection (on the laser bike)
You are riding a laser bike, traveling rapidly northeast through an intersection. Dark blue neon walls surround the intersection, but there are grid lines that lead south, southwest, and east.

However, all the grid lines are lit up by beams of light.

There is also a ramp to the southeast.
action: You go to the southeast
response: You give the laser bike a sharp turn southeast, and it takes the ramp at a high speed, launching you into the air. As you look down you notice that all the ramps in the grid are lowering to the level of the intersection. The bike touches down in...

Intersection (on the laser bike)
You are riding a laser bike, traveling rapidly southeast through an intersection. Dark blue neon walls surround the intersection, but there are grid lines that lead north, south, and west.

However, the grid lines to the north and south are lit up by beams of light.
action: Go west
response: You give the laser bike a sharp turn west, and it speeds through the grid line to the west. The bike leaves a laser beam of light in its wake.

Intersection (on the laser bike)
You are riding a laser bike, traveling rapidly west through an intersection. Dark blue neon walls surround the intersection, but there are grid lines that lead north, south, east, and west.

However, the grid lines to the north, east, and west are lit up by beams of light.
action: You go south
response: You give the laser bike a sharp turn south, and it speeds through the grid line to the south. The bike leaves a laser beam of light in its wake.

Intersection (on the laser bike)
You are riding a laser bike, traveling rapidly south through an intersection. Dark blue neon walls surround the intersection, but there are grid lines that lead north, northwest, east, and west.

However, the grid lines to the north, east, and west are lit up by beams of light.
action: You go to the northwest
response: You give the laser bike a sharp turn northwest, and it speeds through the grid line to the northwest. The bike leaves a laser beam of light in its wake.

The laser bike slows down as it comes to the middle of the intersection. A long ramp drops down from the west, and the bike automatically turns toward it. As the bike ascends the ramp, a mechanical voice intones, "Congratulations. You have found an Euler circuit. Your prize awaits."

The bike re-enters the neon-lit room and comes to rest in the middle of the floor. The door to the east closes once more.

Neon-Lit Room (on the laser bike)
The floor and ceiling of this room are black, while the walls feature eerie, pulsating, dark blue neon lights. An exit leads west.

Your prize appears to be a book: Introduction to the Analysis of
the Infinite.

[Your understanding of Combinatorics has increased. You
estimate that your score on tomorrow's final has just gone up by five points.]
action: You get Book
response: (Introduction to the Analysis of the Infinite)
You can't reach Introduction to the Analysis of the Infinite
from the laser bike.
action: You stand
response: You dismount the laser bike.

The floor and ceiling of this room are black, while the walls feature eerie, pulsating, dark blue neon lights. An exit leads west.

A sleek laser bike is parked in the center of the room.

Your prize appears to be a book: Introduction to the Analysis of
the Infinite.
action: You get Book
response: (Introduction to the Analysis of the Infinite)
(putting the icosahedron into the set to make room)
Taken.
action: You examine it
response: This is a copy of Leonhard Euler's two-volume Introduction to the Analysis of the Infinite.
action: You look up the euler circuit
response: (in your math book)
An Euler circuit is a path through a graph that traverses every edge exactly once. Euler proved that the only graphs that have Euler circuits are those whose vertices all have an even number of connections. The key idea behind this is that every time you go through a vertex you must enter by one edge and leave by a different edge, thus traversing two edges. In order to have an Euler circuit, then, the total number of edges incident on each vertex must be even.
action: You go west
response: As you move west, you feel an electrical impulse course through you. The space around you seems to fold in on itself.

The confusing fog is much less now than it was at first.

Gray Matter, Level Three
Most of the fog that was filling up this space is now gone - the only bit that remains swirls about your feet. You can see now that you are in another space made of the same gray matter as the two above you. You can see an inscription on the wall, and there are exits up to Gray Matter, Level Two, north to the Barn, south, east to the Neon-Lit Room, and west to the Great Court of Trinity College.
action: You examine the inscription
response: The inscription reads,

"Even as the finite encloses an infinite series
And in the unlimited limits appear,
So the soul of immensity dwells in minutia
And in narrowest limits no limits inhere.
What joy to discern the minute in infinity!
The vast to perceive in the small, what divinity!"
action: Go south
response: You make your way south. As you do, you feel an electrical impulse course through you. You find yourself in...

You stand at the entrance to a huge roller coaster, which sprawls above and around you in every direction - even into the river below.
A notice hangs nearby. You could climb up to the boarding platform above you. The operator's office is to the east, and you can exit the roller coaster area to the north.

Someone has dropped a brochure here.
action: You examine the notice
response: The notice reads, "Has anyone seen Descartes? He seems to have disappeared!"
action: You examine the brochure
response: This brightly-colored brochure is an advertisement for the roller coaster.
action: You read it
response: "Descartes's Roller Coaster and Water Ride: Experience the thrills of cutting-edge analytic geometry!

"With our proprietary technology, we can change the shape of the track to any algebraic curve! We feature a new curve each month, so ride often!

"For special events such as birthday parties and weddings we can even accommodate curve requests! Just write the algebraic equation for the curve you want on one of our special cards and give it to the operator! (Guests are encouraged to book well in advance, as we do have an extensive waiting list.)

"There's more: Our patented "air bubble" technology prevents anything inside the car from getting wet while the car travels underwater!"

Underneath, in smaller print, are some disclaimers: "Riders should be aware that the boarding platform may be moved to different x coordinates to accommodate differently-shaped tracks. Any such coordinate changes are purely to maximize the riders' experience. In addition, in the rare case that a track is completely underwater, riders will be prevented from entering the boarding area."

Finally, very tiny print at the bottom reads "Construction by Meretzky and Co."
action: You look at the card
response: This small, very thin card reads "Farmer's Problem: y =
50x - Pi*x^3." You remember that y
represents the volume of the barrel the farmer is trying to build, while x represents the radius.
action: You get the brochure
response: (putting the trig homework into the set to make room)
Taken.
action: You examine the roller coaster
response: The roller coaster consists of a track mounted on a grid-like frame marked with coordinates. For the horizontal - or x -
coordinates, the entrance is marked at 0, and the numbers increase as you go east. For the vertical - or y - coordinates, the
water line is marked at 0, and the numbers increase as you go up.

The roller coaster track starts high, goes through a loop-the-loop, enters the water, and returns to the platform.
action: Go east
response: The roller coaster operator's office is a small, dingy affair. The only thing to commend it is that it still has a good view of the roller coaster. The exit is to the west.

A display is set into the wall, with a slot next to it.

A saying hangs loosely on the wall above the display.

You can also see some correspondence and an x-finder here.
action: You examine the display
response: The display reads "x^3 + y^3 = 3xy."
action: Examine slot
response: It looks like only a thin card of a certain size and shape will fit in it.
action: You look at saying
response: The saying reads, "Cogito Ergo Sum."
action: You look at the correspondence
response: You read through the correspondence. It's a series of letters from Fermat to Descartes. The discussions center on Fermat's method of tangents, which Descartes criticizes.

The final letter, though, is addressed to Fermat. In it, Descartes claims that his new Folium curve is so complicated that Fermat's method cannot be used to find its tangent lines.

The letter ends with Descartes asking rhetorically, "And you believe your method will still work? I think not!" The ink is blotted after the final sentence, as if the quill pen Descartes had been using was dropped abruptly.
action: You look at the finder
response: position. It was probably used for testing the roller coaster. The x-finder is covered by some kind of waterproof plastic film,
and it also includes a primitive-looking carabiner.

The x-finder currently reads... nothing. I suppose you're
not at a location that has a meaningful x-coordinate.
action: You get all
response: Descartes's saying: (putting the thin card into the set to make room) Taken.
correspondence: (putting Berkeley's lecture notes into the set to make room)
Taken.
x-finder: (putting the comic strip into the set to make room)
Taken.
action: You put the card in the slot
response: You place the card in the slot. With a screeching of metal and wood, the roller coaster track tears itself apart and reforms as the graph of the equation on the card. The roller coaster appears to be undamaged by this process.

The display now reads "y = 50x - Pi*x^3."
action: You look at the coaster
response: The roller coaster consists of a track mounted on a grid-like frame marked with coordinates. For the horizontal - or x -
coordinates, the entrance is marked at 0, and the numbers increase as you go east. For the vertical - or y - coordinates, the
water line is marked at 0, and the numbers increase as you go up.

The roller coaster track consists of a hill above the water and a valley below the water. The track climbs the single hill, descends it, enters the water, turns around, dips down into the valley, and then returns to the platform.
action: Go upwards
response: You climb up to the boarding platform. The ascent is a bit disorienting, and you're not sure exactly where you ended up relative to the roller coaster entrance.

You stand at the boarding platform to a huge roller coaster, which sprawls above and around you in every direction - even into the river far below.

A car sits at the platform, enticing you to enter.
action: You enter the car
response: You glance at the track to remind yourself what you're getting yourself into.

The roller coaster track consists of a hill above the water and a valley below the water. The track climbs the single hill, descends it, enters the water, turns around, dips down into the valley, and then returns to the platform.

You enter the car, and it pulls away from the platform. The numbers on the x-finder start to increase.

on the x-finder start to increase.The car slows down as the
track begins its climb up the single hill of this track. The numbers on the x-finder are increasing slowly now.

on the x-finder are increasing slowly now.You reach the crest
of the hill, and the car starts rapidly down the other side. The numbers on the x-finder are still increasing.

numbers on the x-finder are still increasing.Unfortunately,
the car was moving too fast for you to read the x coordinate
at the crest, but it looked like it was some number between 2 and 3.

at the crest, but it looked like it was some number between 2 and 3.Then the car hurtles down the far side of the hill, picking up speed. You splash into the river! Yet some force field seems to be keeping you and your possessions dry. The numbers on the
x-finder continue to increase rapidly.

x-finder continue to increase rapidly.The car makes a turn,
and you travel underwater for a while. You're having trouble following the numbers on the x-finder here.

following the numbers on the x-finder here.The car takes a
dip down further into the water, but soon comes up again, emerges from the river and returns to the platform. The numbers on the
x-finder stop changing. You exit the car.

You stand at the boarding platform to a huge roller coaster, which sprawls above and around you in every direction - even into the river far below.

A car sits at the platform, enticing you to enter.
action: You examine the finder
response: position. It was probably used for testing the roller coaster. The x-finder is covered by some kind of waterproof plastic film,
and it also includes a primitive-looking carabiner.

The x-finder currently reads... 0.2.
action: You examine the carabiner
response: something.
action: You check your inventory
response: You are carrying:
an x-finder
some correspondence
Descartes's saying
a brochure
Introduction to the Analysis of the Infinite
a set (no longer empty)
a comic strip
Berkeley's lecture notes
the trig homework
an icosahedron
a square root
a cube
some exhaustion sandals
a tetrahedron
an octahedron
an old coin
your math book
action: You examine the car
response: This car is primed for speed. A small metal loop is attached to the side of the car.
action: You look at the loop
response: The metal loop is attached to the side of the car.
action: You attach the finder to the loop
response: Using the carabiner, you attach the x-finder to the metal
loop on the car.
action: You enter the car
response: You glance at the track to remind yourself what you're getting yourself into.

The roller coaster track consists of a hill above the water and a valley below the water. The track climbs the single hill, descends it, enters the water, turns around, dips down into the valley, and then returns to the platform.

You enter the car, and it pulls away from the platform. The numbers on the x-finder start to increase.

on the x-finder start to increase.The car slows down as the
track begins its climb up the single hill of this track. The numbers on the x-finder are increasing slowly now.

on the x-finder are increasing slowly now.You reach the crest
of the hill, and the car starts rapidly down the other side. The numbers on the x-finder are still increasing.

numbers on the x-finder are still increasing.Unfortunately,
the car was moving too fast for you to read the x coordinate
at the crest, but it looked like it was some number between 2 and 3.

at the crest, but it looked like it was some number between 2 and 3.Then the car hurtles down the far side of the hill, picking up speed. You splash into the river! Yet some force field seems to be keeping you and your possessions dry. The numbers on the
x-finder continue to increase rapidly.

x-finder continue to increase rapidly.The car makes a turn,
and you travel underwater for a while. You're having trouble following the numbers on the x-finder here.

following the numbers on the x-finder here.The car takes a
dip down further into the water, but soon comes up again, emerges from the river and returns to the platform. The numbers on the
x-finder stop changing. You exit the car.

You stand at the boarding platform to a huge roller coaster, which sprawls above and around you in every direction - even into the river far below.

A car sits at the platform, enticing you to enter.
action: You get the finder
response: You remove the x-finder from the metal loop.
action: You examine it
response: position. It was probably used for testing the roller coaster. The x-finder is covered by some kind of waterproof plastic film,
and it also includes a primitive-looking carabiner.

The x-finder currently reads... 0.2.
action: You examine the brochure
response: This brightly-colored brochure is an advertisement for the roller coaster.
action: You read it
response: "Descartes's Roller Coaster and Water Ride: Experience the thrills of cutting-edge analytic geometry!

"With our proprietary technology, we can change the shape of the track to any algebraic curve! We feature a new curve each month, so ride often!

"For special events such as birthday parties and weddings we can even accommodate curve requests! Just write the algebraic equation for the curve you want on one of our special cards and give it to the operator! (Guests are encouraged to book well in advance, as we do have an extensive waiting list.)

"There's more: Our patented "air bubble" technology prevents anything inside the car from getting wet while the car travels underwater!"

Underneath, in smaller print, are some disclaimers: "Riders should be aware that the boarding platform may be moved to different x coordinates to accommodate differently-shaped tracks. Any such coordinate changes are purely to maximize the riders' experience. In addition, in the rare case that a track is completely underwater, riders will be prevented from entering the boarding area."

Finally, very tiny print at the bottom reads "Construction by Meretzky and Co."
action: You examine the platform
response: You stand at the boarding platform to a huge roller coaster, which sprawls above and around you in every direction - even into the river far below.

A car sits at the platform, enticing you to enter.
action: You move the platform
response: It is fixed in place.
action: Go down
response: You climb down to the roller coaster entrance. The descent is a bit disorienting, and you're not sure exactly where you ended up relative to the platform.
action: You go east
response: A display is set into the wall, with a slot next to it. There is a thin card in the slot.
action: You look at the display
response: The display reads "y = 50x - Pi*x^3."
action: You examine the film
response: This waterproof plastic film covers the x-finder. You could
probably remove it if you wanted.
action: %
response: "Mathematics, rightly viewed, possesses not only truth, but supreme beauty - a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show." -- Bertrand Russell
action: You describe your surroundings
response: The roller coaster operator's office is a small, dingy affair. The only thing to commend it is that it still has a good view of the roller coaster. The exit is to the west.

A display is set into the wall, with a slot next to it. There is a thin card in the slot.
action: You check your inventory
response: You are carrying:
an x-finder
some correspondence
Descartes's saying
a brochure
Introduction to the Analysis of the Infinite
a set (no longer empty)
a comic strip
Berkeley's lecture notes
the trig homework
an icosahedron
a square root
a cube
some exhaustion sandals
a tetrahedron
an octahedron
an old coin
your math book
action: You look up the differential calculus
response: (in your math book)
That topic is not listed in the index.
action: You look up derivative
response: (in your math book)
The derivative is one of the major concepts in calculus. Roughly speaking, it gives a precise way to determine the ratio of two quantities as they become infinitely small. Thus it can be used to measure rates of change, with applications like velocity, acceleration, and marginal cost. It can also be used to find the slope, or steepness, of the graph of a function, as this can be thought of as the ratio of the vertical change in the graph of a function to a corresponding horizontal change.

Another major application of the derivative is to find the maximum or minimum value of a function. The maximum of a function occurs when the graph of the function switches from ascending to descending.
Since the derivative is positive when the graph of a function is ascending, and the derivative is negative when the graph of a function is descending, at the maximum the derivative has a value of zero. A similar scenario holds true for the minimum of a function. In that case the graph of the function switches from descending to ascending, and so its derivative switches from negative to positive. The value of the derivative at the minimum is also zero. There are some other technicalities to consider, but this is the basic situation.
action: Derive card
response: I didn't understand that. The first word or two on their own might suffice, though; perhaps it would work to just derive.
action: Derive
response: Nothing happens. Perhaps you need to be holding an object to serve as the focus of the word of power.
action: Go north
response: As you move north, you feel an electrical impulse course through you. The space around you seems to fold in on itself.

Gray Matter, Level Three
action: Go upward
response: You make your way up.

Gray Matter, Level Two
Off to the side sits a gray storage bin. In the storage bin you see a square piece of metal and a scribbled scroll.

A gray, translucent ghost flits around the storage bin.
action: Go west
response: You make your way west. As you do, you feel an electrical impulse course through you. You find yourself in...

A gaming machine is here.
action: Go north
response: Pascal, Bayes, Kolmogorov, and Diaconis are here, playing an intense game of poker.
action: You play the poker
response: (the poker game)
You place the old coin on the poker table. Diaconis gives you a pile of money in exchange for the coin, and then he deals the cards.

You play several hands. At first you lose more than you win, but thanks to your knowledge of probability, you find that you are pretty good at calculating exactly how strong your hand is and what would be a reasonable amount to bet for each hand. As the game continues, your skill increases, and your calculations become more and more accurate. Even though you don't know what cards the other players hold, your ability to determine precisely both your hand strength and the optimal betting amount mean that, over time, you win much more than you lose. The other players start to drop out - first Kolmogorov, then Bayes, and then Diaconis.

You and Pascal continue to play, each winning several hands. Finally Pascal gets a hand he's very confident of. "All in," he says, as he pushes the rest of his money to the center of the table. Glancing at your cards, you decide to call his bet.

Pascal, grinning from ear to ear, lays down an ace-high straight. You slowly put one, then a second, a third, a fourth, and finally a fifth spade on the table. Pascal's smile slides awkwardly off his face.
You gather your winnings into a pile.

Shaking his head, Pascal congratulates you, as do Kolmogorov, Bayes, and Diaconis. The four of them get up from the table and walk off.
As they leave, you hear Pascal berating himself to Bayes over his last bet: "I should have known better. The only thing worth wagering all you have is infinite happiness."

[Your understanding of Probability has increased. You estimate
that your score on tomorrow's final has just gone up by two
points.]
action: You look at your surroundings
response: You stand next to a poker table in the casino. The lights and noise here are just as overwhelming as in the rest of the casino. The gaming machine is to the south.

A piece of paper is on the floor here. It must have fallen out of someone's pocket.

On the poker table are a pile of money and an old coin.
action: You get all
response: piece of paper: (putting Introduction to the Analysis of the
Infinite into the set to make room)
Taken.
pile of money: (putting the brochure into the set to make room)
Taken.
old coin: (putting Descartes's saying into the set to make room) Taken.
action: You look at the paper
response: On this paper several numbers have been written, in a triangular pattern:

1   2   1
1   3   3   1
1   4   6   4   1
1   5  10  10   5   1
1   6  15  20  15   6   1
1   7  21  35  35  21   7   1
1   8  28  56  70  56  28   8   1
1   9  36  84 126 126  84  36   9   1
1  10  45 120 210     210 120  45  10   1

The middle number in the last row has been smudged, and you cannot make it out. Underneath the numbers is written: "Note to self: Start counting with row 0 and column 0, not row 1 and column 1."
action: You examine the money
response: The huge pile of money represents your winnings from beating Pascal, Bayes, Kolmogorov, and Diaconis at poker. If this weren't a dream you would be rich.
action: You go to the south
response: As you start to leave, something catches your eye. You turn and see that the five-sided poker table is shaking. The poker table begins to transform, shrinking while maintaining its pentagonal top. Soon you are no longer looking at a poker table; you are looking at a dodecahedron.
action: You get dodeca
response: (putting the correspondence into the set to make room)
You take the dodecahedron. Looking curiously at it, you note that it has twelve sides, each of which is in the shape of a regular pentagon. You feel you understand three-dimensional solid geometry a little better.

[Your understanding of Geometry has increased. You estimate
that your score on tomorrow's final has just gone up by one
point.]
action: Go south
response: A gaming machine is here.
action: You go to the east
response: There are currently four books on the bookcase:
Diophantus's Arithmetica
Ars Magna
The Compendious Book on Calculation by Completion and
Balancing
Elements
action: You put infinite in the shelf
response: (first taking Introduction to the Analysis of the Infinite)
(putting the x-finder into the set to make room)
You put Introduction to the Analysis of the Infinite on the
bookcase. As it slides into place you hear a faint click.
Then you hear the same voice as before - the one that sounds like Professor Glasser.

The voice says, "Much of the modern notation and many of the concepts for handling exponential, logarithmic, and trigonometric functions ultimately derive from this comprehensive treatment of infinite series by Leonhard Euler."

[Your understanding of Mathematics Texts has increased. You
estimate that your score on tomorrow's final has just gone up by one point.]
action: Go upward
response: You make your way up.

Gray Matter, Level One
action: You check your inventory
response: You are carrying:
a dodecahedron
an old coin
a pile of money
a piece of paper
a set (no longer empty)
an x-finder
some correspondence
Descartes's saying
a brochure
a comic strip
Berkeley's lecture notes
the trig homework
an icosahedron
a square root
a cube
some exhaustion sandals
a tetrahedron
an octahedron
your math book
action: You put the cube on the square
response: (the square top pedestal)
(first taking the cube)
You put the cube on the square top pedestal.
action: You put the tetra on large
response: (first taking the tetrahedron)
You put the tetrahedron on the large triangular top pedestal.
action: You put the dodeca on the pentagon
response: You put the dodecahedron on the pentagonal top pedestal.
action: You put the octa on the medium
response: (first taking the octahedron)
You put the octahedron on the medium triangular top pedestal.
action: You put the ico on small
response: (first taking the icosahedron)
You place the icosahedron on the small triangular top pedestal and step back. As you do so, the air grows still. Then a strong wind whips through the courtyard. The five Platonic solids rise from their pedestals, rotating slowly. Then they begin spinning in the air, forming a single ring that revolves around and above the circular pedestal in the center. They spin faster and faster - until you cannot distinguish them from each other. Then, with a final loud clap and a blinding flash of light, the ring of solids collapses in on itself! After your vision clears you look back at the pedestals to see a sphere resting on the circular one in the center.

[Your understanding of Geometry has increased. You estimate
that your score on tomorrow's final has just gone up by two
points.]
action: You examine the sphere
response: This beautiful translucent sphere seems to sparkle as you gaze at it.
action: You go east
response: You wander around the home for a while, but you find nothing of interest. Eventually you return to the courtyard.
action: Go south
response: As you move south, you feel an electrical impulse course through you. The space around you seems to fold in on itself.

Gray Matter, Level One
action: Go west
response: You make your way west. As you do, you feel an electrical impulse course through you. You find yourself in...

On the long table is a pile of old coins.

The Count is here, looking rather bored.
action: You give the money to count
response: The Count eyes the money. Then he shakes his head and says, "I'm sorry, but I'm really tired of counting money." He indicates the pile of coins. "Thank you anyway. Something different would be nice."
action: You give the correspondence to Count
response: (first taking the correspondence)
The Count doesn't seem interested.
action: Go east
response: The Count calls after you, "If you find something else for me to count I would be grateful!"

As you move east, you feel an electrical impulse course through you. The space around you seems to fold in on itself.

Gray Matter, Level One
action: Go south
response: You make your way south. As you do, you feel an electrical impulse course through you. You find yourself in...

You have solved the number puzzle on the wall here.
action: You go to the south
response: The huge globe lies on the floor.

You can also see Archimedes's staff here.
action: You get the staff
response: (putting the piece of paper into the set to make room)
Taken.
action: Go north
response: You have solved the number puzzle on the wall here.
action: Go north
response: As you move north, you feel an electrical impulse course through you. The space around you seems to fold in on itself.

Gray Matter, Level One
action: Go downward
response: You make your way down.

Gray Matter, Level Two
Off to the side sits a gray storage bin. In the storage bin you see a square piece of metal and a scribbled scroll.

A gray, translucent ghost flits around the storage bin.
action: You show the staff to ghost
response: The gray lady looks carefully at Archimedes's staff. Then she says, "This would certainly be useful - and valuable - if you weren't dreaming. However, I think you've exhausted its usefulness for now." She takes the staff from you and places it in the gray storage bin.
action: Go south
response: As you move south, you feel an electrical impulse course through you. The space around you seems to fold in on itself.

Gray Matter, Level Two
Off to the side sits a gray storage bin. In the storage bin you see Archimedes's staff, a square piece of metal, and a scribbled scroll.

A gray, translucent ghost flits around the storage bin.
action: Go downwards
response: You make your way down.

Gray Matter, Level Three
action: Go west
response: You make your way west. As you do, you feel an electrical impulse course through you. You find yourself in...
action: Go north
response: At the west end of the chapel stands a statue of Isaac Newton.

A beam of light shines through a window and forms a circle on the floor.
action: You put the sphere in circle
response: You place the sphere into the circle of light. The beam of light passes through the surface of the sphere, refracting into a beautiful rainbow that shines across the statue of Newton.

To your surprise, the statue grins at you, steps down off its plinth, and takes your hand.

The chapel slowly fades from view, and you find yourself on...

You stand on the broad shoulder of a giant. From this location you have a sweeping view of the surrounding landscape - a valley below with a lake in its center, surrounded by a forest. A snow-capped mountain range is off in the distance.

Sir Isaac Newton is here, gazing out over the landscape.

[Your understanding of Physics has increased. You estimate that
your score on tomorrow's final has just gone up by two points.]
action: Greet Newton
response: Newton stares at you for a long time. "You're on an epic Quest, aren't you?" he finally says.

You nod in response.

"I'm willing to assist you," Newton replies, "but if I give you my help now then you won't understand how to use it.

"I want you to prove to me that you are worthy of my help. Answer my questions, and my help is yours.

"Two hints: (1) Each answer consists of a single word; you should ANSWER the single-word-answer. (2) If you want me to repeat a question, TALK TO me.

"Oh, and if you want to leave this place, just jump off the giant's shoulder. Trust me on that." Newton grins.

"First question: There are three major concepts in calculus. One is the limit, and a second is the integral. What's the third?"
action: You answer derivative
response: (to Isaac Newton)
"That's correct. The three major concepts in calculus are the limit, the derivative, and the integral.

"In fact, the fundamental theorem of calculus, (cough, cough) which I first proved (cough, cough), shows that the derivative and the integral are inverse operations - kind of like addition and subtraction are inverse operations, but in a more complicated way. Limits get precisely defined much later, as mathematicians try to solve the theoretical problems with calculus pointed out by people like George Berkeley."

Newton sighs. "It pains me somewhat to say that 'derivative' and 'integral' were not my terms - I preferred 'fluxion' and
'fluent.' But Leibniz won that particular battle."

"Here's the second question: What's the primary graphical interpretation of the derivative?"
action: You answer the tangent
response: (to Isaac Newton)
"No, that's not correct. I'll repeat the question: What's the primary graphical interpretation of the derivative?"
action: You answer slope
response: (to Isaac Newton)
"That's correct. The derivative measures the slope of the graph of a function - how steeply it is rising or falling.

"So if the graph of a function is rising, its derivative is positive, and if it is rising sharply, its derivative is even more positive. Similarly, if the graph of a function is decreasing, its derivative is negative.

"Next question: If a function's derivative is positive when the function is increasing, and the function's derivative is negative when the function is decreasing, what's the value of the derivative when a function is at its largest value? At that place the function is neither increasing nor decreasing."
action: You answer zero
response: (to Isaac Newton)
"That's correct. When a function crosses through its maximum, its graph switches from rising to falling. Thus its derivative switches from positive to negative. At the instant the function hits its maximum, its derivative must be zero.

"Well, there are some other technical considerations, like if the derivative doesn't exist, but we don't need to go into those.

"Last question!" Newton grins mischievously. "What have you seen in your travels - something not man-made - that has slopes?"
action: You answer sine
response: (to Isaac Newton)
"The sine wave you've seen does have slopes, but that particular one was made by Cardano. Try again," Newton replies.
action: You answer the hill
response: (to Isaac Newton)
Newton grins. "Close enough," he says.

Newton reaches out his hand toward the mountain range off in the distance and closes his eyes. You follow the line of his outstretched hand, and you see the mountains moving - moving towards you. Newton appears to be summoning them!

Not sure of what you're seeing, you blink, shake your head, and look once more. The mountain range off in the distance is gone.

Instead, Newton is holding a toy model of a mountain range in his hand. He gives it to you. "Use this well," he says. "It will transform the graph of a function into the graph of its derivative function."

"A word of caution, though: this is only powerful enough to handle curves where y is equal to some expression involving
x - in other words, where y is explicitly
some function of x. It will not handle situations in which
x and y are merely related in some equation; i.e.,
where y may be implicitly some function of
x. (You need a more powerful technique, 'implicit
differentiation,' for that.)

"Also, remember what we've discussed: The derivative measures the slope of the graph of a function. If you can find where the derivative function is 0, that should tell you where the original function hits its maximum. If you would like a reminder of this, feel free to come back and speak with me again.

"Finally, please return the mountain range when you're done with it."

[Your understanding of Calculus has increased. You estimate
that your score on tomorrow's final has just gone up by three
points.]
action: You jump off
response: You jump off the giant's shoulder and hurtle toward the ground. You hear Newton calling after you, "Don't forget to return the mountain range when you're finished with it!"

It's a long fall. You're falling, and falling, and falling...
It's a long fall. You're falling, and falling, and falling...And you hit the ground back in the chapel of Trinity College.

You stand in the magnificent chapel of Trinity College. You make a mental note to visit this place sometime when you're truly awake. The exit is to the south.

At the west end of the chapel stands a statue of Isaac Newton.

A beam of light shines through a window and forms a circle on the floor.

You can also see a sphere here.
action: You look at the range
response: This small model of a mountain range wouldn't be out of place as a backdrop to someone's train set. It features a variety of slopes: up, down, steep, gentle, flat. The word "DERIVE" is written on it.
action: You go east
response: As you move east, you feel an electrical impulse course through you. The space around you seems to fold in on itself.

The fog is completely gone now, and with it, any confusion you may have had about this space. You can now see a passage leading down.

Gray Matter, Level Three
action: You go south
response: You make your way south. As you do, you feel an electrical impulse course through you. You find yourself in...
action: Derive
response: The toy mountain range vibrates quietly. With a screeching of metal and wood, the roller coaster track tears itself apart and reforms in the shape of its derivative curve. The roller coaster appears to be undamaged by this process.
action: Go upwards
response: You climb up to the boarding platform. The ascent is a bit disorienting, and you're not sure exactly where you ended up relative to the roller coaster entrance.

A car sits at the platform, enticing you to enter.
action: You look at the finder
response: position. It was probably used for testing the roller coaster. The x-finder is covered by some kind of waterproof plastic film,
and it also includes a primitive-looking carabiner.

The x-finder currently reads... -2.
action: You get the film
response: You pull the plastic film off the x-finder, tearing it in the
process. After removing it completely, you wad it up into a ball.
action: You attach the finder to the car
response: Using the carabiner, you attach the x-finder to the metal
loop on the car.
action: You enter the car
response: You glance at the track to remind yourself what you're getting yourself into.

The roller coaster track climbs a single hill, then descends it, enters the water, turns around, and returns to the platform.

You enter the car, and it pulls away from the platform. The numbers on the x-finder are negative, and they start to increase.

on the x-finder are negative, and they start to increase.The
car slows down as the track begins its climb up the single hill of this track. The numbers on the x-finder are increasing
slowly now.

slowly now.You reach the crest of the hill, and the car starts rapidly down the other side. The numbers on the x-finder are still increasing.

increasing.Then the car hurtles down the far side of the hill, picking up speed. You splash into the river! Yet some force field seems to be keeping you and your possessions dry.

be keeping you and your possessions dry.The numbers on the
x-finder were increasing until you hit the water, but they
are no longer doing so.

are no longer doing so.The car makes a turn, and you travel underwater for a while.

for a while.Soon the car emerges from the river and returns to the platform. You exit the car.

You stand at the boarding platform to a huge roller coaster, which sprawls above and around you in every direction - even into the river far below.

A car sits at the platform, enticing you to enter.
action: You examine the finder
response: position. It was probably used for testing the roller coaster. It includes a primitive-looking carabiner. Unfortunately, the
x-finder has gotten waterlogged and so no longer works
properly.

The x-finder currently reads... 2.30329.
action: You go to the north
response: You make your way north. As you do, you feel an electrical impulse course through you. You find yourself in...

Pennings the dog is here, looking expectantly at you.
action: You go south
response: As you move south, you feel an electrical impulse course through you. The space around you seems to fold in on itself.

Gray Matter, Level Three
action: You get the finder
response: You remove the x-finder from the metal loop.

(You put the pile of money into the set to make room.)
action: You give finder to the dog
response: the barn, his tail wagging happily.

Soon he returns with the farmer, who has an interested look on his face. "I just finished freeing Bessie," the farmer says. "This looks promising!"

He does some calculations, and his look of interest turns to surprise. "With a radius of 2.30329 feet, the height turns out to be 4.60659 feet, which (other than a little rounding error) is exactly twice the radius! And it gives a volume of 76.7765 cubic feet, which is better than any other volume I've been able to find! How did you come up with this?"

You explain about the derivative of a function, how it measures how steeply the graph of the function is ascending or descending, and how ascending means a positive derivative and descending means a negative derivative. The you describe how the largest value of the barrel volume function occurs where its graph switches from ascending to descending - a location where the derivative of the function is zero.

"And so," you say, "once I hit the water on the derivative track, the x-finder got stuck at the radius that gives the largest
possible value for the volume of the barrel."

"Impressive!" says the farmer. "Most impressive."

He turns to Pennings. "Go on now," he says. "Go. There's a treat for you at the back door." Pennings gives a happy bark and runs out of the barn.

Thanking you profusely, the farmer returns the x-finder to
you and starts working on the pile of wood.

[Your understanding of Calculus has increased. You estimate
that your score on tomorrow's final has just gone up by seven
points.]
action: Go upward
response: You make your way up.

Gray Matter, Level Two
Off to the side sits a gray storage bin. In the storage bin you see Archimedes's staff, a square piece of metal, and a scribbled scroll.

A gray, translucent ghost flits around the storage bin.
action: You show the finder to ghost
response: The gray lady looks carefully at the x-finder. Then she
says, "I'm not sure you'll have any more use for that." She takes the x-finder from you and places it in the gray storage bin. "If
you ever want it back, though, feel free to just take it," she adds. "I might be wrong."
action: Go downwards
response: You make your way down.

Gray Matter, Level Three
action: Go down
response: You make your way down.

A bright, blinding - almost painful - light fills this space. You can't see anything for the light, but you do sense the exit up.
action: You look at the light
response: The light is so bright it's almost painful. It feels like you've just stepped from a dark building into the sunlight, yet your eyes don't seem to be adjusting. You can't tell where the light is coming from.
action: You check what you're carrying
response: You are carrying:
a wad of plastic
a toy mountain range
some correspondence
an old coin
a set (no longer empty)
a pile of money
a piece of paper
Descartes's saying
a brochure
a comic strip
Berkeley's lecture notes
the trig homework
a square root
some exhaustion sandals
your math book
action: You look at the wad
response: This useless wad was once the plastic film on the x-finder.
action: Go up
response: You make your way up through the bright light.

Gray Matter, Level Three
action: Go upward
response: You make your way up.

Gray Matter, Level Two
Off to the side sits a gray storage bin. In the storage bin you see an x-finder, Archimedes's staff, a square piece of metal, and
a scribbled scroll.

A gray, translucent ghost flits around the storage bin.
action: You show the wad to the ghost
response: The gray lady looks carefully at the wad of plastic. Then she says, "I'm not sure you'll have any more use for that." She takes the wad of plastic from you and places it in the gray storage bin. "If you ever want it back, though, feel free to just take it," she adds. "I might be wrong."
action: You show the piece of the paper to ghost
response: (first taking the piece of paper)
The gray lady looks carefully at the piece of paper. Then she says, "I'm not sure you'll have any more use for that." She takes the piece of paper from you and places it in the gray storage bin. "If you ever want it back, though, feel free to just take it," she adds. "I might be wrong."
action: You show the notes to the ghost
response: (first taking Berkeley's lecture notes)
The gray lady looks carefully at Berkeley's lecture notes. Then she says, "I think you may still find some use for those. You never know, though," she adds. "I might be wrong."
action: You show the brochure to the ghost
response: (first taking the brochure)
The gray lady looks carefully at the brochure. Then she says, "I'm not sure you'll have any more use for that." She takes the brochure from you and places it in the gray storage bin. "If you ever want it back, though, feel free to just take it," she adds. "I might be wrong."
action: You show the money to the ghost
response: (first taking the pile of money)
The gray lady looks carefully at the pile of money. Finally she says, "That would certainly be useful if you weren't dreaming. However, I suspect it's not that useful here." She takes the pile of money from you and places it in the gray storage bin. "I'm not certain about this, so feel free to come back and take it."
action: You show the strip to the ghost
response: (first taking the comic strip)
The gray lady looks carefully at the comic strip. Then she says, "I'm not sure you'll have any more use for that." She takes the comic strip from you and places it in the gray storage bin. "If you ever want it back, though, feel free to just take it," she adds. "I might be wrong."
action: You show the old coin to the ghost
response: The gray lady looks carefully at the old coin. Then she says, "I'm not sure you'll have any more use for that." She takes the old coin from you and places it in the gray storage bin. "If you ever want it back, though, feel free to just take it," she adds. "I might be wrong."
action: Go downwards
response: You make your way down.

Gray Matter, Level Three
action: Go downwards
response: You make your way down.

You seem to have gotten more used to the light in this space.
action: Look around
response: This space is still filled with a bright light. While the light isn't painful anymore, it is still difficult to see. You can now tell, though, that the source of the light seems to be coming from the floor. In addition, there are exits north, south, east, and west, as well as the one above you to Gray Matter, Level Three.
action: You go north
response: You make your way north through the bright light. As you do, you feel an electrical impulse course through you. You find yourself in...

The smell of tobacco hangs in the air in this small, dark pub. It is nearly deserted; even the bartender appears to have stepped out. An exit leads south.

Cauchy is sitting at the bar, sipping from a glass of wine.

Weierstrass is next to Cauchy, drowning his sorrows in a pint of beer.
action: You examine cauchy
response: Cauchy looks like he is trying to cheer up Weierstrass. He occasionally takes a sip from a glass of wine.
action: You look at Weierstrass
response: Weierstrass is deep into a pint of beer. He stares morosely into his mug from time to time.
action: You look up weierstrass
response: (in your math book)
Karl Weierstrass, one of the great mathematicians of the 19th century, never actually completed a college degree. He is particularly famous for his precise definitions of limits and continuity, which helped put calculus on a solid theoretical foundation.
action: You look up cauchy
response: (in your math book)
Frenchman Augustin-Louis Cauchy was the most prolific mathematician of the 19th century. While he made important contributions in many areas, he is particularly known for his emphasis on rigor in mathematics and his pathbreaking work in complex analysis.
action: You go west
response: You make your way west through the bright light. As you do, you feel an electrical impulse course through you. You find yourself in...

Wires and pieces of metal indicate that highly complex experiments must have once been performed in this room. Now, though, they lie scattered haphazardly here and there: Someone has cleared this place out. There are open doors to the north and south, and the exit to the lab lies east. A door to the west is closed.

Not all of the experiments are gone, though; near the west door is a platform, raised slightly off the floor. A control panel is attached to the wall near the platform.

There is also a large fan set into the east wall.

A printout has fallen to the floor.
action: You examine the platform
response: Nothing is on the platform.
action: You examine the panel
response: The control panel is labeled "Transformation Matrix Prototype." It features numbers in a 3 by 3 matrix. Each number in the top row has a slider above it that controls the setting of that number. The numbers in the second and third rows, though, seem to be fixed. A button is next to the 3 by 3 matrix.

The matrix currently looks like this:
0  -1   0
1   0   0
0   0   1
action: You examine the fan
response: This is a large, industrial-strength wall fan. You wonder what experiments it was used for.

The wall fan is currently switched off.
action: You go to the north
response: The seminar room is dominated by the large table running the length of it. A small window in the north wall looks out onto a courtyard, and a door leads south back into the lab.

On the seminar table are some presentation slides.
action: You look at slides
response: There are seven pages to these slides. If you want to look more closely at them you should read a particular page.
action: You read the page 1
response: The first page begins a discussion of three-dimensional transformation matrices. It points out that the columns in a transformation matrix consist of the "inputs," while the rows consist of the "outputs." For instance, the entry in column 1, row 2 indicates the effect of the first, or x, dimension of the original object on producing
the second, or y, dimension of the transformed object.
action: You read the page 2
response: Starting with the second page, there are some examples of three-dimensional transformation matrices. The first involves the matrix
1  0  0
0  1  0
0  0  1.
The fact that the first row of this transformation matrix consists of 1, 0, 0, means that, to produce the x coordinates of the
output object the matrix takes only the x coordinates of the
input object and multiplies each of them by 1. The 0, 1, 0 in the second row means that, to produce the y coordinates of the
output object the matrix takes only the y coordinates of the
input object and multiplies each of them by 1. The same is true for the 0, 0, 1 in the third row and the z coordinates. This transformation matrix doesn't really do anything, then; since none of the coordinates are changed, the output object is the same as the input object.
action: You read the page 3
response: 0  1  0
0  0  2
simply doubles the z coordinates. The output object would be
twice as tall as the input object.
action: You read the page 4
response: 0  0  1
0  1  0
swaps the y coordinates with the z coordinates,
while keeping the x coordinates the same. An object would be transformed via this matrix to a mirror image of itself that is also lying on its side.
action: You read the page 5
response: 0  1  0
0  0  1
keeps the y and z coordinates the same from the
original object to the transformed object. However, to create the
x coordinates of the transformed object, it adds the
x and y coordinates of the original object. A cube,
for example, would be transformed into an object that looks like a box that has been partially crushed so that its sides are at an angle. (Technically the transformed object is a parallelepiped, a three-dimensional version of a parallelogram.)  This kind of transformation is known as a shear transformation.
action: You read the page 6
response: 0  0  1
0  -1 0
keeps the x coordinates the same from the original object to
the transformed object, makes the z coordinates in the
original into y coordinates in the new object, and turns the
y coordinates in the original into negative z
coordinates in the transformed object. The effect of this is to rotate the object 90 degrees clockwise when viewed from the front.
action: You read the page 7
response: The final page mentions that combinations of these effects as well as other effects can be achieved by using different matrices. A three-dimensional object can even be turned into a two-dimensional or even a one-dimensional object by using the appropriate transformation matrix.

At the end of the final page is a brief description of one of the graduate student experiments involving transformation matrices. Thus far the student has constructed a prototype that allows one to apply a transformation matrix to a physical object. For the prototype the transformations that produce the y and z coordinates
are hard-coded; the user can only affect the transformations for the
x coordinates of the new object. In addition, only a few
choices have thus far been implemented for the top row of the matrix. Finally, the transformation effect is thus far permanent only for objects made of lead. Even for lead objects, though, the process seems to be permanent only once; subsequent transformations on a transformed lead object have so far only been temporary. The current hypothesis is that the transformation process changes something about the lead object at the atomic level.
action: Inventory
response: You are carrying:
Berkeley's lecture notes
a toy mountain range
some correspondence
a set (no longer empty)
Descartes's saying
the trig homework
a square root
some exhaustion sandals
your math book
action: You go south
response: Not all of the experiments are gone; near the west door is a platform, raised slightly off the floor. A control panel is attached to the wall near the platform.

There is also a large fan set into the east wall.

A printout has fallen to the floor.
action: You look at the printout
response: The note is a printout of an email. It reads, "To my graduate students: Greetings from Hawaii! I'm having a great time at the conference. It's too bad none of you could come.

"Unfortunately, I have some bad news. Most of my funding has run out. While I have enough to support myself, I do not have enough left to support any of you anymore. Thus, all of your current projects are hereby cancelled. If you want to finish your degrees you'll need to find another adviser."

Underneath someone has written an unprintable commentary on the contents of the email.
action: You go south
response: This office is small and cramped, although that hasn't prevented someone from squeezing several desks in here. A door leads north, back into the lab. A small window in the south wall looks out onto a dingy part of campus.
action: You examine the desks
response: The desks have all been cleaned out.
action: Search desks
response: The empty desks are a sad testament to the graduate students who used to work here. They're not worth bothering with.
action: You go south
response: The window is closed. Even if it was open, though, you're too high up. There is no way you would survive the drop to the hard ground below.
action: You go east
response: You make your way east through the bright light. As you do, you feel an electrical impulse course through you. You find yourself in...

Brass wheels, gears, knobs, and pipes emitting smoke are everywhere: This is a room out of some steampunk's dream. The south end of the room opens onto a gold-colored path. This path appears to be suspended in the air, with no apparent support, and to run for as far as you can see. You may also exit west.

The room is dominated by a large, complicated-looking machine in its center.
action: You examine the machine
response: This machine is just as steampunk as everything else here, although there are several parts to it that look at least somewhat recognizable.

For one, the machine has a switch that can be set to "Sequence" or "Series." It is currently set to "Sequence," although you could easily move it to the other setting by flipping the switch.

There is a button labeled "Alternate" that is currently pushed off.

The machine also has a dial that can be set to "Constant," "Identity," "Squared," or "Reciprocal." It is currently set to "Constant."

There is a small circular hole near the button.

Finally, there is a warning light on top of the machine. The warning light is dark.
action: You look at the hole
response: The circular hole is empty.
action: You go south
response: As you approach the golden path you take a look at it.

The path is level with the floor of the room you are currently in. It consists of golden steps that seem to run on forever. Each step has two numbers appearing on it, although from here you can only read the numbers on the six closest steps. The first numbers on the steps are all the same: 1, 1, 1, 1, 1, and 1. The second numbers are the same as the first numbers: 1, 1, 1, 1, 1, and 1.

Just before you reach the path, though, it shifts: The heights of the steps change. The first step is now up. After that, though, the path is level with the first step.

You step onto the path and follow it for a while. It seems to stretch on forever, though, and so you eventually decide to turn back. As you step off the golden path back into the room with the complicated machine the path shifts once again: It returns to being level with the floor.
action: You switch the switch
response: You flip the switch to "Series." Some of the numbers on the golden path change. The warning light is still dark.
action: You look at the light
response: The warning light is dark.
action: Go south
response: As you approach the golden path you take another look at it.

The path is level with the floor of the room you are currently in. It consists of golden steps that seem to run on forever. Each step has two numbers appearing on it, although from here you can only read the numbers on the six closest steps. The first numbers on the steps are all the same: 1, 1, 1, 1, 1, and 1. The second numbers are 1, 2, 3, 4, 5, and 6.

Just before you reach the path, though, it shifts: The heights of the steps change. The first step is now up. After that, the path rises evenly, each step just as much of an upstep as the previous one. In fact, the path looks like a set of stairs.

You step onto the path and follow it for a while. It seems to stretch on forever, though, and so you eventually decide to turn back. As you step off the golden path back into the room with the complicated machine the path shifts once again: It returns to being level with the floor.
action: Go west
response: As you move west, you feel an electrical impulse course through you. The space around you seems to fold in on itself.
action: Go south
response: You make your way south through the bright light. As you do, you feel an electrical impulse course through you. You find yourself in...

This rather plain room is dominated by a large window that fills the entire southern wall. An open doorway lies to the north.

A tray is attached to the wall next to the window.
action: You examine the window
response: This window looks onto an endless flat, gray plane. You can see a large pile of discarded objects a short distance away in the plane.

Standing near the pile, rocking back and forth and muttering to himself, is René Descartes.
action: You look at descartes
response: (René Descartes)
Descartes is holding his head and muttering to himself, "I can't think here. I can't think here."
action: You examine the pile
response: This pile consists of a large number of unusual objects that seem to fade in and out of view.

A square circle catches your eye for a moment before disappearing again.
action: You examine the pile
response: This pile consists of a large number of unusual objects that seem to fade in and out of view.

A formula for solving the general quintic equation catches your eye for a moment before disappearing again.
action: You look at the pile
response: This pile consists of a large number of unusual objects that seem to fade in and out of view.

A solution in positive integers to x^n + y^n =
z^n for n > 2 catches your eye for a moment before
disappearing again.
action: You examine the pile
response: This pile consists of a large number of unusual objects that seem to fade in and out of view.

An algorithm to solve the Halting Problem catches your eye for a moment before disappearing again.
action: You look at the pile
response: This pile consists of a large number of unusual objects that seem to fade in and out of view.

A proof of the continuum hypothesis catches your eye for a moment before disappearing again.
action: You examine the tray
response: The tray is made of metal. It looks like it could hold one thing at a time.
action: You greet descartes
response: (René Descartes)
Descartes looks up at you briefly, a request for help in his eyes. Then he grabs his head once more. "I can't think here. I can't think here," he mutters.
action: You put the saying in the tray
response: (first taking Descartes's saying)
You place Descartes's saying on the tray. The tray beeps softly, and a voice says, "Existence detected."
action: You put the saying in the tray
response: You place Descartes's saying on the tray. The tray beeps softly, and a voice says, "Existence detected."
action: You go north
response: You make your way north through the bright light. As you do, you feel an electrical impulse course through you. You find yourself in...

Cauchy is sitting at the bar, sipping from a glass of wine.

Weierstrass is next to Cauchy, drowning his sorrows in a pint of beer.
action: You greet Cauchy
response: You walk over to Cauchy. "Are you guys O.K.?" you ask.

Cauchy looks up from his wine. "Hello," he says. "Weierstrass and I were just commiserating on the state of our research programs."

Weierstrass snorts. "Cauchy is being kind. I don't have a research program! I need an important problem to solve, something to show the mathematical world I'm capable of more than teaching high school. Not that there's anything wrong with that," he quickly adds, "but it would be nice to have a university position.

"Cauchy, though, is already internationally famous. He practically invented complex analysis, for one thing!" Weierstrass falls silent, staring back into his mug.
action: You talk to Weierstrass
response: Weierstrass grunts at you in response before returning to his mug.
action: You talk to Cauchy
response: Cauchy says quietly, "I'm worried about Weierstrass. I'm sure he's capable of being one of the great mathematicians of our age, but he needs the right problem to work on in order to prove it."
action: You show the notes to Weierstrass
response: Weierstrass lifts his head from his mug long enough to glance at the proffered notes. He grunts and starts to return to his mug - but then he stops. He takes the notes from you and reads through them. "Berkeley's criticisms of the foundations of calculus... Yes..." He thinks for a while.

Then he turns to Cauchy. "The limit concept you've used in your work - I wonder if that would help here. But it needs to be more rigorous."

Cauchy and Weierstrass are soon deep in conversation, scribbling mathematical symbols and scratching them out again on a bar napkin. About all of the conversation you can follow are the words "function," "distance," "error," and "limit," each repeated several times. Finally, Weierstrass says, "And if we use delta for 'distance' and epsilon for 'error,' that should do it!" He pockets the napkin.

Weierstrass looks at you excitedly. "I think I've got some ideas that would put calculus on a sound theoretical footing! This should make my name, mathematically-speaking.

"I owe you more than I can say, but I don't know how best to reward you. Perhaps I can improve something of yours with the power of the limit concept?"
action: You show the sandals to Weierstrass
response: (first taking the exhaustion sandals)
Weierstrass takes the sandals and looks at them carefully. "These embody the principle of exhaustion, don't they?" he says. Then he closes his eyes and concentrates for a moment. The sandals begin to glow, and then they start to morph. Soon Weierstrass is holding a pair of shoes in his hands. "There," he says, opening his eyes and handing the shoes to you. "I've improved your exhaustion sandals to a pair of limit shoes.

"Thanks again," he says. He stands up, an eager look on his face. "I need to explore these concepts further. I've got an idea for a continuous function that is not differentiable anywhere..." Weierstrass downs the rest of his beer, places his mug on the bar, and walks out of the pub. The bartender appears out of nowhere and whisks the mug away before disappearing again.

Cauchy remains behind. "Weierstrass has expressed his personal gratitude," he says. "Let me offer my gratitude on behalf of mathematics as a whole. Weierstrass mentioned earlier that I know a little something about complex analysis. I can imbue an item of yours with the power of complex analysis, much as Weierstrass improved those sandals with the power of the limit."
action: You look at what you're carrying with you
response: You are carrying:
some limit shoes
Descartes's saying
a printout
a toy mountain range
some correspondence
a set (no longer empty)
the trig homework
a square root
your math book
action: Show range to Cauchy
response: Cauchy looks carefully at you for a while, as if reading your thoughts. Finally, he gives a satisfied nod.

Then Cauchy takes the toy mountain range and looks at it carefully. Then he closes his eyes and rubs his hands over it. The mountain range begins to glow. After a while Cauchy opens his eyes again, and the toy stops glowing. "There," he says, handing the it back to you. "I've improved your toy mountain range. It should be able to differentiate complex functions now. However, unless you actually find a complex function the additional power won't be of any use. I think I can reward you better than this."
action: You show the root to Cauchy
response: (first taking the square root)
(putting the correspondence into the set to make room)
Cauchy looks carefully at you for a while, as if reading your thoughts. Finally, he gives a satisfied nod.

Then Cauchy takes the square root and looks at it carefully. Then he closes his eyes and rubs his hands over it. The square root begins to glow. After a while Cauchy opens his eyes again, and the square root stops glowing. "There," he says, handing the square root back to you. "I've improved your square root. It should be able to extract complex numbers now.

"Thank you, once again, on behalf of mathematics," Cauchy says. "The discipline will be stronger if Weierstrass can put calculus on a more solid foundation." He stands up and finishes the last of his wine, placing the glass on the bar before walking out of the pub. The bartender appears out of nowhere once more and whisks the empty glass away before disappearing again.
action: You look around
response: The smell of tobacco hangs in the air in this small, dark pub. It is deserted; even the bartender appears to have stepped out. An exit leads south.
action: You go south
response: As you move south, you feel an electrical impulse course through you. The space around you seems to fold in on itself.
action: Go up
response: You make your way up through the bright light.

Gray Matter, Level Three
action: Go upwards
response: You make your way up.

Gray Matter, Level Two
Off to the side sits a gray storage bin. In the storage bin you see an old coin, a comic strip, a pile of money, a brochure, a piece of paper, a wad of plastic, an x-finder, Archimedes's staff, a
square piece of metal, and a scribbled scroll.

A gray, translucent ghost flits around the storage bin.
action: Go upward
response: You make your way up.

Gray Matter, Level One
action: You show shoes to Achilles
response: "Do you think these will work any better than those sandals I tried earlier?"
action: You say yes
response: (to Achilles)
Achilles just looks at you miserably, and then he puts his head back down.
action: You give the shoes to Achilles
response: Achilles looks at the limit shoes rather skeptically, but you assure him that these shoes are different - more powerful than the exhaustion sandals - and so he agrees to try them. After lacing them up, he snaps his fingers, and the tortoise appears. They find their places as before, and take off. Achilles runs to the halfway mark, looks up, and sees the tortoise ahead of him. He notes the tortoise's new position, races to it, and sees the tortoise still ahead. You start to think that the limit shoes aren't going to do Achilles any good. About this time, though, their inherent virtue starts to kick in.
Yes, there are infinitely many times Achilles must note the tortoise's position, leading to infinitely many distances he must run, but each successive distance is shorter than the one before. The power of the limit shoes successfully sums the lengths of these infinitely many shorter and shorter distances, and Achilles passes the tortoise for the win!

Achilles jogs back to the start, a huge grin on his face, and gives you a crushing hug. Slightly abashed, he steps back, thanks you profusely, and returns the limit shoes. He runs away to celebrate.

As you're recovering from Achilles's excitement, Zeno walks over from where he has been discreetly watching the race. He picks up the tortoise. As he gazes quizzically at it, he's joined by Aristotle. They head off, arguing over whether the limit process actually solves the paradox of Achilles and the tortoise. You notice something fall from Aristotle's robes.

[Your understanding of Infinity has increased. You estimate
that your score on tomorrow's final has just gone up by two
points.]
action: Look around
response: This is a stadium in ancient Athens. The stadium itself consists of raised ground on either side of a race track about 200 meters long. The rest of the Lyceum is back east.

Aristotle has dropped a papyrus scroll here.
action: You look at the scroll
response: This scroll contains a discussion of logical fallacies. Two prominent ones mentioned are "Affirming the Consequent" and "Denying the Antecedent."

An example of "Affirming the Consequent" is the following argument. "If one drinks hemlock then they will die. Thucydides is dead. Therefore, Thucydides must have drunk hemlock." The first two statements are true, but the third is false. The argument is invalid because there are other ways that Thucydides could have died than drinking hemlock. In other words, the truth of the consequent, "they died," does not imply the truth of the antecedent, "they drank hemlock."

An example of "Denying the Antecedent" is the following argument. "If one writes the Iliad then they will be famous. Plato didn't
write the Iliad. Therefore, Plato will not be famous." The
first two statements are true, but the third is false. The argument is invalid because there are other ways that Plato could be famous besides writing the Iliad. In other words, the falseness of
the antecedent, "one writes the Iliad," does not imply the
falseness of the consequent, "they will not be famous."
action: You get scroll
response: (putting the toy mountain range into the set to make room)
Taken.
action: Go downwards
response: You make your way down.

Gray Matter, Level Two
Off to the side sits a gray storage bin. In the storage bin you see an old coin, a comic strip, a pile of money, a brochure, a piece of paper, a wad of plastic, an x-finder, Archimedes's staff, a
square piece of metal, and a scribbled scroll.

A gray, translucent ghost flits around the storage bin.
action: You check your inventory
response: You are carrying:
a logic scroll
some limit shoes
a square root
Descartes's saying
a printout
a set (no longer empty)
a toy mountain range
some correspondence
the trig homework
your math book
action: You show the shoes to the ghost
response: The gray lady looks carefully at the limit shoes. "I would definitely hold on to those," she says. "You're not likely to find much that is more useful."
action: You show the printout to the ghost
response: The gray lady looks carefully at the printout. Then she says, "I think you may still find some use for that. You never know, though," she adds. "I might be wrong."
action: Go downwards
response: You make your way down.

Gray Matter, Level Three
action: You go downwards
response: You make your way down.

You can see most of this space now.

Gray Matter, Level Four
action: You look around
response: Gray Matter, Level Four
The light has dimmed enough (or your eyes have adjusted enough) that you can now see that this space contains the same gray, spongy matter as the spaces above you. The only part of this space that is still painful to look at is a very bright patch on the floor. There is the expected inscription on the wall, as well as the exits up to Gray Matter, Level Three, north to the Smoky Pub, south to the Window into Oblivion, east to the Machine Room, and west to the Research Lab.
action: You examine the inscription
response: The inscription reads,

"Tell all the truth but tell it slant -
Success in Circuit lies
Too bright for our infirm Delight
The Truth's superb surprise
As Lightning to the Children eased
With explanation kind
The Truth must dazzle gradually
Or every man be blind -"
action: Go upwards
response: You make your way up.

Gray Matter, Level Three
action: Go upwards
response: You make your way up.

Gray Matter, Level Two
Off to the side sits a gray storage bin. In the storage bin you see an old coin, a comic strip, a pile of money, a brochure, a piece of paper, a wad of plastic, an x-finder, Archimedes's staff, a
square piece of metal, and a scribbled scroll.

A gray, translucent ghost flits around the storage bin.
action: You go upwards
response: You make your way up.

Real Axis: 1
action: You go east
response: Real Axis: 2
action: You go west
response: Real Axis: 1
action: Go north
response: Imaginary Axis: i
action: Extract root
response: The root vibrates quietly, as it extracts the square root of the essence of the space around it. You feel yourself rotate
clockwise, swinging in an arc that takes you halfway back to the positive part of the real axis.

Complex: Modulus 1 and Acute Angle
This is more of an abstract space than a physical place. It strikes you, somehow, as a mixture of both the real and the imaginary spaces you have visited. It also feels large beyond your understanding, but not any more so than the irrational space you've already seen. A hole leads up.

Complex Variable here.
action: You get the foundations
response: (putting the printout into the set to make room)
Taken.
action: You examine it
response: This appears to be Riemann's doctoral dissertation. In German, the first word is Grundlagen.
action: You look up riemann
response: (in your math book)
In his relatively short life, Bernhard Riemann made several important contributions to mathematics. His doctoral dissertation contained groundbreaking ideas in geometry and complex analysis. He gave the first rigorous definition of the integral (one of the three major concepts in calculus). He proved the Riemann Rearrangement Theorem for infinite series, and a conjecture of his - the Riemann hypothesis - is, over 150 years later, the most important unsolved problem in mathematics.
action: You go upwards
response: You make your way up.

As soon as you climb through the hole, it closes behind you. Looking around, at first it appears you are standing unsupported in the dark blue nothingness that surrounds everything here. All you can see is the real axis to the "south" and the imaginary axis to the "west."

Then a light twinkles at your feet. You glance to the side to see another light blink briefly near you before disappearing. A third light, off in the distances, flashes once. More lights sparkle, and then more and more - until there are so many that you cannot even count them. The deep dark expanse of space is no longer empty: It now contains a plane, stretching as far as you can see and filled with twinkling lights that look like stars.

A curve appears, starting at your feet and continuing in a perfect arc of a circle until it touches the real axis. You follow the arc. As you step onto the real axis, the arc disappears.

Real Axis: 1
The dark blue expanse of space now contains a plane that stretches as far as you can see in all directions. It includes both the real axis you are standing on and the imaginary axis you can see off in the distance, and it is filled with starry, twinkling lights.

[Your understanding of Complex Numbers has increased. You
estimate that your score on tomorrow's final has just gone up by two points.]
action: Go downwards
response: You make your way down.

Gray Matter, Level One
action: Go downwards
response: You make your way down.

Gray Matter, Level Two
Off to the side sits a gray storage bin. In the storage bin you see an old coin, a comic strip, a pile of money, a brochure, a piece of paper, a wad of plastic, an x-finder, Archimedes's staff, a
square piece of metal, and a scribbled scroll.

A gray, translucent ghost flits around the storage bin.
action: Go downwards
response: You make your way down.

Gray Matter, Level Three
action: Go east
response: You make your way east. As you do, you feel an electrical impulse course through you. You find yourself in...

A sleek laser bike is parked in the center of the room.
action: Go west
response: As you move west, you feel an electrical impulse course through you. The space around you seems to fold in on itself.

Gray Matter, Level Three
action: Go downwards
response: You make your way down.

Gray Matter, Level Four
action: Go east
response: You make your way east. As you do, you feel an electrical impulse course through you. You find yourself in...

The room is dominated by a large, complicated-looking machine in its center.
action: You examine Machine
response: This machine is just as steampunk as everything else here, although there are several parts to it that look at least somewhat recognizable.

For one, the machine has a switch that can be set to "Sequence" or "Series." It is currently set to "Series," although you could easily move it to the other setting by flipping the switch.

There is a button labeled "Alternate" that is currently pushed off.

The machine also has a dial that can be set to "Constant," "Identity," "Squared," or "Reciprocal." It is currently set to "Constant."

There is a small circular hole near the button.

Finally, there is a warning light on top of the machine. The warning light is dark.
action: Inventory
response: You are carrying:
Foundations for a General Theory of Functions of a Complex
Variable
a logic scroll
some limit shoes
a square root
Descartes's saying
a set (no longer empty)
a printout
a toy mountain range
some correspondence
the trig homework
your math book
action: You wear the shoes
response: You put on the limit shoes.
action: You go south
response: As you approach the golden path you take another look at it.

The path is level with the floor of the room you are currently in. It consists of golden steps that seem to run on forever. Each step has two numbers appearing on it, although from here you can only read the numbers on the six closest steps. The first numbers on the steps are all the same: 1, 1, 1, 1, 1, and 1. The second numbers are 1, 2, 3, 4, 5, and 6.

Just before you reach the path, though, it shifts: The heights of the steps change. The first step is now up. After that, the path rises evenly, each step just as much of an upstep as the previous one. In fact, the path looks like a set of stairs.

Then you walk out onto the path. The limit shoes react to the contact with the first step: They propel you up to the next step, and to the next, and to the next - faster and faster. Soon you are moving up so fast the path is a blur, and then you can't even see it anymore.

You find yourself hurtling upwards through space, only to land in...
Infinity
This is more of an abstract space than a physical place. It feels far, far beyond your understanding, though. Even the language needed to describe it seems beyond your comprehension.

You can see a large glass booth, about the size of an old telephone box.

There is a small patch of nothingness floating in the space here.

You can also see Srinivasa Ramanujan here.

[Your understanding of Infinity has increased. You estimate
that your score on tomorrow's final has just gone up by two
points.]
action: You lookup ramanujan
response: (in your math book)
Srinivasa Ramanujan was one of the most fascinating mathematicians of the early 20th century. Mostly self-taught, and largely working in isolation from the world's mathematical community, he found creative and profoundly original solutions to outstanding problems in number theory and infinite series.

Seeking a greater connection with that community, he sent his discoveries to several British mathematicians, most of whom dismissed his findings or simply returned his work with no comment. However, G. H. Hardy recognized Ramanujan's genius and was eventually able to arrange for Ramanujan to come to Cambridge University. There followed several years of fruitful collaboration with Hardy.

Unfortunately, Ramanujan had health problems during his time in England. He contracted tuberculosis and died at the age of 32, having spent only six years in Britain. The 2015 biographical film The
Man Who Knew Infinity is about Ramanujan.
action: You look at the booth
response: The booth is large enough for you to enter, and there are two buttons inside it. The clear button is labeled "Multiplicative Inversion," and the crystal button is labeled "Grand Hotel."
action: You look at the patch
response: You don't understand much about your surroundings, but something feels different about this small patch of the space here. It's like it's not really there. Yet you could probably reach out your hand and take it.
action: You get it
response: As your hand closes around the patch of nothingness, it begins to transform. Startled, you pull your hand back. The nothingness continues transforming, finally taking on a slightly more corporeal, but still rather insubstantial, form.

Ramanujan says, "You know, you should think carefully about that before you use it."
action: Look around
response: This is more of an abstract space than a physical place. It feels far, far beyond your understanding, though. Even the language needed to describe it seems beyond your comprehension.

The patch of nothingness has transformed into the largest integer.

You can see a large glass booth, about the size of an old telephone box.

You can also see Srinivasa Ramanujan here.
action: You examine the integer
response: The largest integer looks insubstantial, as if it's more of a concept than something physical. Perhaps curiously, it doesn't seem to have a particular numerical value.
action: Greet him
response: Before you can get a word out, Ramanujan jumps in. "Congratulations!" he says. "You made it here. I'm somewhat impressed - enough to give you a little assistance.

"There's a guy in the hotel," Ramanujan gestures in the direction of the glass booth, "who could use some help, too. I can tell you what he needs. Head to the hotel, talk to him, and then come back and speak with me again."
action: You enter the booth
response: You get into the large glass booth.
action: Press hotel
response: You push the crystal button. The glass booth begins to spin, slowly at first, but then faster and faster. When the spinning stops the glass booth is gone, and you find yourself in...

The lobby of this sumptuous 1920s-era hotel dazzles the eye - crystal chandeliers, a marble floor, an ebony front desk complete with harried clerk. A set of glass double doors leads outside to the west, and an elegant staircase spirals down.

The desk clerk points his fountain pen at the guest register and says, "Increment!" Then he runs over to the double doors, opens them just enough to let the next person in line into the lobby, closes them again, and runs back to his desk. The guest wanders off into the depths of the hotel.
action: You greet the clerk
response: You walk over to the desk clerk. He glances up, a frantic look on his face.

"Sorry; we don't have any rooms available." He points at the guest register, where you can see rooms numbered 1, 2, 3, 4, and so on, with a guest name next to each number. "We do have infinitely many rooms in this hotel, but they're all booked." Then he points to the line of people outside. "I've also got infinitely many people lined up outside wanting a room.

"I'm getting rooms for the people outside by incrementing everyone who already has a room to the next higher-numbered room. That leaves Room 1 available for the new guest.

"Since I can only make one room available at a time, though, this is going to take literally forever. At least when my shift is over I can hand the job off to the next clerk.

"Now, if you'll please excuse me, I've got to get back to work."

Once again, the desk clerk points his fountain pen at the guest register and says, "Increment!" Then he runs over to the double doors, opens them just enough to let the next person in line into the lobby, closes them again, and runs back to his desk. The guest wanders off into the depths of the hotel.
action: You go downwards
response: You start down the spiral staircase. It's a long descent, with the staircase spiraling down and further down until you've lost track of how many turns you've made. Eventually you realize that you're turning in space, not standing on anything at all...

This is more of an abstract space than a physical place. It feels far, far beyond your understanding, though. Even the language needed to describe it seems beyond your comprehension.

You can see a large glass booth, about the size of an old telephone box.

You can also see Srinivasa Ramanujan here.
action: You examine the desk
response: (the ebony front desk)
Made of ebony, the front desk complements this sumptuous lobby well.
A guest register sits on the desk.

Once again, the desk clerk points his fountain pen at the guest register and says, "Increment!" Then he runs over to the double doors, opens them just enough to let the next person in line into the lobby, closes them again, and runs back to his desk. The guest wanders off into the depths of the hotel.
action: You look at the register
response: The desk clerk won't let you touch the guest register. However, you can see that the register shows rooms numbered 1, 2, 3, 4, and so on, apparently infinitely many rooms. There is a guest name next to each number, but the clerk won't let you get close enough to read them.

Once again, the desk clerk points his fountain pen at the guest register and says, "Increment!" Then he runs over to the double doors, opens them just enough to let the next person in line into the lobby, closes them again, and runs back to his desk. The guest wanders off into the depths of the hotel.
action: You examine the chandeliers
response: The chandeliers bathe the room in the soft glow of electric light.

Once again, the desk clerk points his fountain pen at the guest register and says, "Increment!" Then he runs over to the double doors, opens them just enough to let the next person in line into the lobby, closes them again, and runs back to his desk. The guest wanders off into the depths of the hotel.

You're beginning to find the clerk's continual "Incrementing" of the guest register rather annoying.
action: You examine the floor
response: (the marble floor)
This floor looks almost too beautiful to step on. Almost.

Once again, the desk clerk points his fountain pen at the guest register and says, "Increment!" Then he runs over to the double doors, opens them just enough to let the next person in line into the lobby, closes them again, and runs back to his desk. The guest wanders off into the depths of the hotel.

You continue to find the clerk's "Incrementing" of the guest register rather annoying.
action: You look at the doors
response: These doors lead outside. Through them you can see a long line of people waiting to enter the hotel. The line appears to have no end.

Once again, the desk clerk points his fountain pen at the guest register and says, "Increment!" Then he runs over to the double doors, opens them just enough to let the next person in line into the lobby, closes them again, and runs back to his desk. The guest wanders off into the depths of the hotel.

You continue to find the clerk's "Incrementing" of the guest register rather annoying.
action: Go west
response: (first opening the glass double doors)
The desk clerk looks up. "Please keep the doors closed. I don't have enough rooms in the hotel to let everyone in."

Once again, the desk clerk points his fountain pen at the guest register and says, "Increment!" Then he runs over to the double doors, opens them just enough to let the next person in line into the lobby, closes them again, and runs back to his desk. The guest wanders off into the depths of the hotel.

You continue to find the clerk's "Incrementing" of the guest register rather annoying.
action: You go downwards
response: You start down the spiral staircase. It's a long descent, with the staircase spiraling down and further down until you've lost track of how many turns you've made. Eventually you realize that you're turning in space, not standing on anything at all...

This is more of an abstract space than a physical place. It feels far, far beyond your understanding, though. Even the language needed to describe it seems beyond your comprehension.

You can see a large glass booth, about the size of an old telephone box.

You can also see Srinivasa Ramanujan here.
action: You greet Ramanujan
response: "As the desk clerk has realized," Ramanujan says, "incrementing each guest's room number over and over is never going to provide rooms for all the people in the line outside.

"I'll tell you what he needs to do, but I want you to prove to me that you have a more subtle understanding of infinity than I think you have so far. Go back to the room with the machine that controls the golden path. There are several combinations of settings for the golden path that will bring you to the manifestation of infinitude surrounding us. I want you to find a path that rises extremely slowly yet still gets here. You'll know it's the right one when you can't tell from the machine room whether the path leads here or not.

"Even if you've already found this path, I want you to prove to me again that you can find it - that the first time wasn't just an accident."
action: Describe the surroundings
response: This is more of an abstract space than a physical place. It feels far, far beyond your understanding, though. Even the language needed to describe it seems beyond your comprehension.

You can see a large glass booth, about the size of an old telephone box.

You can also see Srinivasa Ramanujan here.
action: Go upwards
response: You make your way up.

The dark blue expanse of space now contains a plane that stretches as far as you can see in all directions. It includes both the real axis you are standing on and the imaginary axis you can see off in the distance, and it is filled with starry, twinkling lights.
action: You go east
response: Real Axis: 1
The dark blue expanse of space now contains a plane that stretches as far as you can see in all directions. It includes both the real axis you are standing on and the imaginary axis you can see off in the distance, and it is filled with starry, twinkling lights.
action: You set the dial to reciprocal
response: You turn the dial to "Reciprocal." Some of the numbers on the golden path change. The warning light is still dark.
action: You look up reciprocal
response: (in your math book)
The reciprocal of a number is its multiplicative inverse. For example, the reciprocal of 7 is 1/7.
action: You look at path
response: The path is level with the floor of the room you are currently in. It consists of golden steps that seem to run on forever. Each step has two numbers appearing on it, although from here you can only read the numbers on the six closest steps. The first numbers on the steps are 1, 1/2, 1/3, 1/4, 1/5, and 1/6. The second numbers are 1, 3/2, 11/6, 25/12, 137/60, and 49/20.
action: Go south
response: As you approach the golden path you take another look at it.

The path is level with the floor of the room you are currently in. It consists of golden steps that seem to run on forever. Each step has two numbers appearing on it, although from here you can only read the numbers on the six closest steps. The first numbers on the steps are 1, 1/2, 1/3, 1/4, 1/5, and 1/6. The second numbers are 1, 3/2, 11/6, 25/12, 137/60, and 49/20.

Just before you reach the path, though, it shifts: The heights of the steps change. The first step is now up. After that, the path rises very gradually. In fact, it's such a gradual rise that it's hard to tell whether the path is leveling out or continuing to climb.

Then you walk out onto the path. The limit shoes react to the contact with the first step: They propel you to the next step, and the next, and the next - faster and faster. Soon you are moving so fast the path is a blur, and then you can't even see it anymore.

You find yourself hurtling through space, only to land in...
Infinity
This is more of an abstract space than a physical place. It feels far, far beyond your understanding, though. Even the language needed to describe it seems beyond your comprehension.

You can see a large glass booth, about the size of an old telephone box.

You can also see Srinivasa Ramanujan here.

Ramanujan smiles at you. "Well done," he says. "The harmonic series, consisting of the sum of the reciprocals of the positive integers, rises extremely slowly. Yet it does eventually become arbitrarily large, so that we can say its limit is infinity.

"Now, to keep my promise. Tell the desk clerk that he needs to double the room numbers in the register."
action: You talk to clerk
response: "I'm sorry, but I don't have time to chat. I've got to keep incrementing everyone who already has a room to the next higher-numbered room so that a new guest can take Room 1. Now, if you'll please excuse me, I've got to get back to work."

Once again, the desk clerk points his fountain pen at the guest register and says, "Increment!" Then he runs over to the double doors, opens them just enough to let the next person in line into the lobby, closes them again, and runs back to his desk. The guest wanders off into the depths of the hotel.
action: You say double
response: (to the desk clerk)
You walk over to the clerk and suggest that instead of incrementing each guest's room number he should double it.

The clerk stops what he's doing and looks at you quizzically. "Double them?" he asks. "That's not what I was told to do. Why should I do that?"

"Ramanujan suggested it," you reply. "Ramanujan? Really?"
He thinks for a while. "This incrementing is going to take forever. All right. I'll try doubling."

He points his fountain pen at the guest register and says, "Double!" Each guest's room number doubles, so that if a guest has room number n, they now have room number 2n.

"This leaves all the odd-numbered rooms available!" says the clerk. "And since there are infinitely many odd numbers..."

He runs to the double doors and throws them wide open. The line of people comes streaming into the lobby, and each goes off to take a different odd-numbered room. Soon all of the people are gone.

"Nice! And thanks!" says the clerk. "I think I'll take my break now."

He grabs the guest register and walks off into the hotel. It looks like you're now free to go through the double doors to the west.

[Your understanding of Infinity has increased. You estimate
that your score on tomorrow's final has just gone up by two
points.]
action: You go to the west
response: The courtyard, with its flowering trees and carefully-manicured lawns, is just as elegant as the interior of the grand hotel. A set of glass double doors leads east into the hotel.

One of the guests has dropped a short brass rod in the courtyard.
action: You look at the rod
response: This brass rod is short and, for a rod, relatively thick. It has the number 69,105 written on it.
action: You get it
response: (putting Descartes's saying into the set to make room)
Taken.
action: You examine the lawns
response: Keeping these lawns green and trimmed must require a small army of gardeners.
action: You examine the trees
response: They're beautiful - but purely ornamental.
action: Go west
response: From here, the only exit is east.
action: You look around
response: The lobby of this sumptuous 1920s-era hotel dazzles the eye - crystal chandeliers, a marble floor, an ebony front desk. A set of glass double doors leads outside to the west, and an elegant staircase spirals down.
action: You go downwards
response: You start down the spiral staircase. It's a long descent, with the staircase spiraling down and further down until you've lost track of how many turns you've made. Eventually you realize that you're turning in space, not standing on anything at all...

This is more of an abstract space than a physical place. It feels far, far beyond your understanding, though. Even the language needed to describe it seems beyond your comprehension.

You can see a large glass booth, about the size of an old telephone box.

You can also see Srinivasa Ramanujan here.
action: You enter the booth
response: You get into the large glass booth.
action: Go upwards
response: You make your way up.

The dark blue expanse of space now contains a plane that stretches as far as you can see in all directions. It includes both the real axis you are standing on and the imaginary axis you can see off in the distance, and it is filled with starry, twinkling lights.
action: You go east
response: Real Axis: 1
The dark blue expanse of space now contains a plane that stretches as far as you can see in all directions. It includes both the real axis you are standing on and the imaginary axis you can see off in the distance, and it is filled with starry, twinkling lights.
action: You check what you're carrying
response: You are carrying:
a brass rod
the largest integer
Foundations for a General Theory of Functions of a Complex
Variable
a logic scroll
some limit shoes (being worn)
a square root
a set (no longer empty)
Descartes's saying
a printout
a toy mountain range
some correspondence
the trig homework
your math book
action: You put rod in Machine
response: The brass rod slides perfectly into the circular hole. A mechanical voice intones, "Riemann Rearrangement Mode activated."
action: You look up the riemann rearrangement
response: (in your math book)
The Riemann Rearrangement Theorem is one of the more unintuitive theorems in mathematics. It says that for some types of infinite series, if you sum the terms in a different order you can get a different answer. This is emphatically not true with usual arithmetic, where 3 + 5 = 5 + 3. The Riemann Rearrangement Theorem applies only to what are known as conditionally convergent
infinite series.
action: You look up conditionally convergent
response: (in your math book)
A conditionally convergent infinite series has the following properties: (1) It consists of positive and negative numbers added in a series, (2) It sums (converges) to a finite value, and (3) If you make all the negative numbers in the series positive, the resulting series does not converge to a finite value.
action: You examine Machine
response: This machine is just as steampunk as everything else here, although there are several parts to it that look at least somewhat recognizable.

For one, the machine has a switch that can be set to "Sequence" or "Series." It is currently set to "Series," although you could easily move it to the other setting by flipping the switch.

There is a button labeled "Alternate" that is currently pushed off.

The machine also has a dial that can be set to "Constant," "Identity," "Squared," or "Reciprocal." It is currently set to "Reciprocal."

There is a small circular hole near the button. A brass rod has been inserted into it.

Finally, there is a warning light on top of the machine. The warning light is dark.
action: You examine the path
response: The path is level with the floor of the room you are currently in. It consists of golden steps that seem to run on forever. Each step has two numbers appearing on it, although from here you can only read the numbers on the six closest steps. The first numbers on the steps are 1, 1/2, 1/3, 1/4, 1/5, and 1/6. The second numbers are 1, 1/2, 5/6, 7/12, 47/60, and 37/60.
action: You go south
response: As you approach the golden path you take another look at it.

The path is level with the floor of the room you are currently in. It consists of golden steps that seem to run on forever. Each step has two numbers appearing on it, although from here you can only read the numbers on the six closest steps. The first numbers on the steps are 1, 1/2, 1/3, 1/4, 1/5, and 1/6. The second numbers are 1, 1/2, 5/6, 7/12, 47/60, and 37/60.

As you near the path, though, the seventh step swaps places with the fifth step. Then the sixth step swaps places with the ninth step. Other steps swap places with each other, and you stop, watching, as the entire path appears to rearrange itself.

Then a mechanical voice intones, "Rearrangement succeeded."

You move towards the path once more. Just before you reach it, though, it shifts: The heights of the steps change. The first step is now up. After that, some steps are up, and some steps are down, but you cannot discern any sort of pattern to which are up and which are down. Overall, though, the path rises slowly, but it's hard to tell from where you are whether it continues to rise or whether it levels out.

Then you walk out onto the path. The limit shoes react to the contact with the first step: They propel you to the next step, and the next, and the next - faster and faster. Soon you are moving so fast the path is a blur, and then you can't even see it anymore.

You find yourself hurtling through space, only to land in...
69,105
This is more of an abstract space than a physical place. It feels cavernous - large but with walls that you can sense are out of your field of vision. A hole leads up.

A pile of leaves is here.

[Your understanding of Infinity has increased. You estimate
that your score on tomorrow's final has just gone up by two
points.]
action: Count leaves
response: You don't have the patience to count the leaves. However, given where you found them, you have a pretty good guess as to how many there are.
action: You get them
response: You pick up the leaves. There are too many to juggle, so you stuff them all into the set.
action: You look around
response: 69,105
This is more of an abstract space than a physical place. It feels cavernous - large but with walls that you can sense are out of your field of vision. A hole leads up.
action: Inventory
response: You are carrying:
the largest integer
Foundations for a General Theory of Functions of a Complex
Variable
a logic scroll
some limit shoes (being worn)
a square root
a set (no longer empty)
some leaves
Descartes's saying
a printout
a toy mountain range
some correspondence
the trig homework
your math book
action: Go upwards
response: You make your way up.

Real Axis: 69,105
You are in a dark blue expanse of space, standing on a white line that stretches as far as you can see to the west and as far as you can see to the east. The number 69,105 is marked on the line here. There is a hole next to the number large enough for you to climb down into.

The dark blue expanse of space now contains a plane that stretches as far as you can see in all directions. It includes the real axis you are standing on, and it is filled with starry, twinkling lights.
action: Go west
response: You walk along the real axis for a while and see marks for 69,104; 69,103; 69,102; and ever smaller numbers. You find no holes or anything else featured on this part of the real axis, though, and you soon decide return to the 69,105 mark.
action: Go down
response: You clamber down the hole.

69,105
action: Extract root
response: You speak the word of power. It echoes in the space around you, and the square root seems to be absorbing the echoes. Then the square root vibrates quietly. You feel yourself shift.

again. Another space, and then shift. And shift.
Shift.

Irrational: Between 1 and 2
This is more of an abstract space than a physical place, but it feels large beyond your understanding, as if it encompasses infinitely more space than the single-number locations beneath the real axis. A hole leads up to the real axis.
action: Go upwards
response: You make your way up.

As you step onto the real axis, the hole behind you closes. Rather than standing at an unmarked spot between 1 and 2, you head back to 1.

Real Axis: 1
The dark blue expanse of space now contains a plane that stretches as far as you can see in all directions. It includes both the real axis you are standing on and the imaginary axis you can see off in the distance, and it is filled with starry, twinkling lights.
action: You give the leaves to count
response: The Count takes the pile of leaves from you excitedly and places them on the table. "One," he says. "Two." "Three." A smile spreads across his face, and he turns back to you.

"Once again," he says, "thank you! Another gift is appropriate, I think." He produces a small bell from somewhere and rings it. A servant rushes in, and the Count whispers something to him. The servant disappears, but he soon returns, hands a book to the Count, and disappears once more.

The Count gives the book to you. "Please take this," he says, "with my gratitude. It's a copy of Fibonacci's book on counting and calculations."

The Count returns to the leaves, and soon he is lost in numerical ecstasy.
action: Inventory
response: You are carrying:
Liber Abaci
the largest integer
Foundations for a General Theory of Functions of a Complex
Variable
a logic scroll
some limit shoes (being worn)
a square root
a set (no longer empty)
Descartes's saying
a printout
a toy mountain range
some correspondence
the trig homework
your math book
action: You examine the Abaci
response: This is a copy of Liber Abaci, by Leonardo of Pisa (also
known as Fibonacci).
action: Go east
response: As you move east, you feel an electrical impulse course through you. The space around you seems to fold in on itself.

Gray Matter, Level One
action: Go east
response: There are currently five books on the bookcase:
Introduction to the Analysis of the Infinite
Diophantus's Arithmetica
Ars Magna
The Compendious Book on Calculation by Completion and
Balancing
Elements
action: You put the abaci in the shelf
response: You put Liber Abaci on the bookcase. As it slides into place
you hear a faint click. Then you hear the same voice as
before - the one that sounds like Professor Glasser.

The voice says, "This masterpiece on computation techniques by Leonardo of Pisa (more commonly known as Fibonacci) served as Europe's first comprehensive introduction to the algebra of the Islamic world. The famous Fibonacci sequence was also first discussed in this book, in the context of a problem about rabbit breeding."

[Your understanding of Mathematics Texts has increased. You
estimate that your score on tomorrow's final has just gone up by one point.]
action: You put the Foundations in the shelf
response: You put Foundations for a General Theory of Functions of a Complex Variable on the bookcase. As it slides into place you hear a
faint click. Then you hear the same voice as before - the
one that sounds like Professor Glasser.

The voice says, "Riemann's doctoral dissertation is notable for extending our understanding of functions that take on complex values and introducing the idea of a Riemann surface. It has been called 'one of the most important achievements of 19th-century mathematics.'"

[Your understanding of Mathematics Texts has increased. You
estimate that your score on tomorrow's final has just gone up by one point.]
action: You examine the shelf
response: The bookcase looks like it has space for twelve books. There are currently seven books on the bookcase:
Foundations for a General Theory of Functions of a Complex
Variable
Liber Abaci
Introduction to the Analysis of the Infinite
Diophantus's Arithmetica
Ars Magna
The Compendious Book on Calculation by Completion and
Balancing
Elements
action: You go to the west
response: As you move west, you feel an electrical impulse course through you. The space around you seems to fold in on itself.

Gray Matter, Level Two
Off to the side sits a gray storage bin. In the storage bin you see an old coin, a comic strip, a pile of money, a brochure, a piece of paper, a wad of plastic, an x-finder, Archimedes's staff, a
square piece of metal, and a scribbled scroll.

A gray, translucent ghost flits around the storage bin.
action: Go down
response: You make your way down.

The blinding light is completely gone, and you can now see all of this space clearly.

Gray Matter, Level Four
The source of the blinding light appears to have been a book: a copy of Disquisitiones Arithmeticae.
action: You examine the Disquisitiones
response: This is a copy of Gauss's Disquisitiones Arithmeticae.
action: You look around
response: Gray Matter, Level Four
This space is made of the same gray matter as the three above you. There is an inscription on the wall, as well as exits up to Gray Matter, Level Three, north to the Smoky Pub, south to the Window into Oblivion, east to the Machine Room, and west to the Research Lab.
action: Go south
response: You make your way south. As you do, you feel an electrical impulse course through you. You find yourself in...

A tray is attached to the wall next to the window.

Through the window you can see a flat, gray plane. A pile of discarded objects lies a short distance away in the plane. Standing near the pile, rocking back and forth and muttering to himself, is René Descartes.
action: You check what you're carrying
response: You are carrying:
Disquisitiones Arithmeticae
the largest integer
a logic scroll
some limit shoes (being worn)
a square root
a set (no longer empty)
Descartes's saying
a printout
a toy mountain range
some correspondence
the trig homework
your math book
action: You put largest in the tray
response: You place the largest integer on the tray. The tray beeps loudly, and a voice says, "Non-existence detected!"

A door slides open in the wall, and a woman runs in. She's holding a cell phone and is slightly out of breath. The door closes behind her, leaving only a faint outline.

"I'm so sorry," she says. "Between my cell phone constantly ringing and all the cranks on the Internet, I just can't keep up like I used to."

Turning to the tray, she picks up the largest integer. "Hmmm." she says. "This definitely does not exist. How did you acquire it? This was consigned to Oblivion at least by Archimedes's time. Actually, never mind. I bet one of the imps left it somewhere; they're not always reliable. It's enough that we have it back."

She makes a quick call on her cell phone. An imp materializes, takes the largest integer from the woman, rematerializes outside the window, and drops the largest integer onto the pile. Then the imp disappears.

"Where are my manners?" the woman asks. "I'm Hypatia, caretaker of Oblivion."
action: You greet Hypatia
response: "Thank you for returning the largest integer," Hypatia says. "As you likely have already figured out, Oblivion is where we keep everything that doesn't exist. I'm the caretaker. This job was a sort of reward for being one of the few mathematicians martyred.

"If you know of anything else that doesn't exist, please let me know, and I'll take care of it," Hypatia says. "I also field questions about whether things exist." She leans closer and whispers, "Occasionally we even make a mistake and consign something to Oblivion that actually does exist. We don't really like to talk much about that, though."

Hypatia's cell phone rings, and she answers it. "No," Hypatia says. "I don't think there is an odd perfect number, either, but that proof isn't valid. Please try again." She hangs up.
action: You ask about descartes
response: (to Hypatia)
You point through the window at Descartes, who is still rocking back and forth and muttering to himself.

Hypatia's eyebrows rise. "What is he doing there? That's a mistake; surely Descartes actually exists!" She sighs. "I've been too preoccupied."

She thinks for a moment and then comes to a decision. "I bet one of the imps did this, but I don't know which one, and I don't have time right now to sort this out. If you can figure out why someone thought Descartes does not exist I'll do what I can to get him out of Oblivion."

Hypatia's cell phone rings once more, and she answers it. Hypatia listens for a while. Finally, exasperated, she cuts the caller off. "No, no, no! That doesn't work! Besides, do you really think you're going to be the one to prove that there is no nontrivial solution to Riemann's zeta function with real part unequal to 1/2? Far better minds than yours have worked on that and failed!" She ends the call with an emphatic jab of her finger.
action: You show saying to Hypatia
response: (first taking Descartes's saying)
Hypatia takes the saying from you. "This means 'I think; therefore I am.'" She thinks for a moment. "Since the saying is about existence it might have something to do with one of my imps consigning Descartes to Oblivion. But Descartes is deducing that he exists, not that he doesn't exist. There must be more to it than this." She returns the saying.

Hypatia's cell phone rings again, and she answers it. "I'm sorry, but I'm afraid I don't know how to say 'exist' in Old Gywndyngwah," Hypatia says. "I'm not familiar with that language." She ends the call.
action: You greet descartes
response: (René Descartes)
Descartes looks up at you briefly, a request for help in his eyes. Then he grabs his head once more. "I can't think here. I can't think here," he mutters.

Hypatia's cell phone rings again, and she answers it. "God?!"
Hypatia flashes a grin at you. "Lots of people have tried, but as yet there is no conclusive proof that God does not exist." She hangs up and turns to you conspiratorially. "Don't tell anyone, but who do you think gave me this job?"
action: Inventory
response: You are carrying:
Descartes's saying
Disquisitiones Arithmeticae
a logic scroll
some limit shoes (being worn)
a square root
a set (no longer empty)
a printout
a toy mountain range
some correspondence
the trig homework
your math book

Hypatia's cell phone rings again, and she answers it. "No," Hypatia says. "You're likely right, but there's no proof yet that there is no polynomial-time algorithm for finding Hamiltonian cycles." She hangs up.
action: You show scroll to Hypatia
response: Hypatia replies, "Yes, these are two well-known logical fallacies. What do they have to do with Descartes being consigned to Oblivion?"

Hypatia's cell phone rings once more, and she answers it. Hypatia listens for a while. "No," she says. "There are some intelligent and thoughtful people in the other political party." She holds the phone away from her ear, and you hear angry ranting on the other end. Hypatia lets it go on for a while before she breaks in with "You might try spending less time on social media," before hanging up. She turns to you. "It seems like that has been getting worse lately."
action: You show saying to Hypatia
response: "Descartes's saying 'I think; therefore I am,' might have something to do with one of my imps consigning Descartes to Oblivion. But Descartes is deducing that he exists, not that he doesn't exist.
There must be more to it than this."

Hypatia's cell phone rings again, and she answers it. "Just because we haven't found life on other planets yet doesn't mean it doesn't exist," Hypatia says. "Absence of evidence isn't evidence of absence." She ends the call.
action: Show descartes to Hypatia
response: (Descartes's saying to Hypatia)
"Descartes's saying 'I think; therefore I am,' might have something to do with one of my imps consigning Descartes to Oblivion. But Descartes is deducing that he exists, not that he doesn't exist.
There must be more to it than this."

Hypatia's cell phone rings once more, and she answers it. "No," Hypatia says. "I sympathize, but there are some honest lawyers." She hangs up.
action: You show correspondence to Hypatia
response: (first taking the correspondence)
Hypatia takes the correspondence from you and reads through it. "This is interesting! It appears the last thing Descartes did was write this letter to Fermat. Perhaps it has something to do with why one of my imps consigned Descartes to Oblivion. But why?" She returns the correspondence.

"Wait a minute..." Hypatia stops herself. "'I think; therefore I am.' That's Descartes's famous saying. What was that last phrase in Descartes's correspondence? 'I think not...' Oh, no!" She buries her face in her hands.

When Hypatia raises her head again she has an exasperated look on her face. "I think we both know what happened here," she says. "I could order my imps to set Descartes free now, but there's no guarantee that they won't make this kind of mistake again.

"I hate to ask you for something else, but I really need some evidence to show my imps that 'I think; therefore I am,' and 'I think not,' do not together imply 'I am not.' If you can bring some evidence like that to me, I'll feel comfortable letting Descartes go."

Hypatia's cell phone rings once more, and she answers it. Hypatia listens for only a moment before she says, "Wait a minute. You state that truth does not exist. Yet that claim itself is a truth claim. You're assuming the existence of the very concept you claim doesn't exist!" She hangs up emphatically and says to you, "I'll be so glad when the postmodernism fad passes."
action: You show scroll to Hypatia
response: Hypatia takes the logic scroll from you. "Yes, these are two well-known logical fallacies. And denying the antecedent is exactly the mistake that my imps made. Well done!"

Hypatia makes a call on her cell phone, and an imp materializes. "One of you idiots consigned Descartes to Oblivion just because he said, 'I think not'!" Hypatia yells. "Don't you fools even know basic logic?!"

She hands the imp the logic scroll and begins tapping her foot. The imp reads through the scroll. He blanches.

"Get Descartes out of there, now!" Hypatia orders.

The imp disappears and then rematerializes on the other side of the window. He grabs Descartes by the arm, and they both vanish.

Hypatia turns back to you. "Thank you for straightening that out," she says. "My imp will be returning Descartes to wherever he was before. Hopefully we won't be seeing that kind of mistake again.

"If you don't mind, though, I probably should get back to my computer." She sighs. "The Internet has brought out all of the cranks from whatever holes they normally hide in.

"Speaking of which..." She hands you a small object. "People keep giving me these as gag gifts. You might it useful. Also, if you mess it up, bring it back, and I'll give you a new one. Just knock on the door to get my attention."

Hypatia presses a button on her phone, and the door in the west wall slides open. She walks through it. As the door closes behind her, she calls out, "You might want to check on Descartes; he will probably be grateful for what you've done!"

[Your understanding of Logic has increased. You estimate that
your score on tomorrow's final has just gone up by four
points.]
action: You check your inventory
response: You are carrying:
a small crank
some correspondence
Descartes's saying
Disquisitiones Arithmeticae
some limit shoes (being worn)
a square root
a set (no longer empty)
a printout
a toy mountain range
the trig homework
your math book
action: You examine the crank
response: This crank is made of lead. It has threads that are oriented clockwise.
action: You go to the north
response: As you move north, you feel an electrical impulse course through you. The space around you seems to fold in on itself.

Gray Matter, Level Four
action: Go upwards
response: You make your way up.

Gray Matter, Level Three
action: You go south
response: You make your way south. As you do, you feel an electrical impulse course through you. You find yourself in...
action: You go east
response: Descartes has left you a copy of his La Géométrie here.

A display is set into the wall, with a slot next to it.

You can also see a thin card here.
action: Go east
response: From here, the only exit is west.
action: Look around
response: You stand at the entrance to a huge roller coaster, which sprawls above and around you in every direction - even into the river below.
A new notice hangs nearby. You could climb up to the boarding platform above you. The operator's office is to the east, and you can exit the roller coaster area to the north.
action: You look at notice
response: The new notice reads, "Descartes is recuperating at home. Shortly after returning from his mysterious disappearance, he stepped in front of a carriage and was run over." Underneath it someone has written, "You shouldn't put Descartes before the horse!"
action: You go east
response: There are currently seven books on the bookcase:
Foundations for a General Theory of Functions of a Complex
Variable
Liber Abaci
Introduction to the Analysis of the Infinite
Diophantus's Arithmetica
Ars Magna
The Compendious Book on Calculation by Completion and
Balancing
Elements
action: You put la in shelf
response: You put La Géométrie on the bookcase. As it slides into
place you hear a faint click. Then you hear the same voice
as before - the one that sounds like Professor Glasser.

The voice says, "An appendix to Descartes's Discourse on
Method, itself one of the most important works in the history of philosophy, La Géométrie features the representation of
algebraic equations as geometric curves. This synthesis of algebra and geometry has become known as analytic geometry; it soon
led to the development of calculus by Newton and Leibniz. The Cartesian coordinate plane, used in the representation of equations as curves, is named after Descartes."

[Your understanding of Mathematics Texts has increased. You
estimate that your score on tomorrow's final has just gone up by one point.]
action: You check your inventory
response: You are carrying:
a small crank
some correspondence
Descartes's saying
Disquisitiones Arithmeticae
some limit shoes (being worn)
a set (no longer empty)
a square root
a printout
a toy mountain range
the trig homework
your math book
action: You put the Disquisitiones in the shelf
response: You put Disquisitiones Arithmeticae on the bookcase. As it
slides into place you hear a faint click. Then you hear the
same voice as before - the one that sounds like Professor Glasser.

The voice says, "Gauss's Disquisitiones Arithmeticae,
published when he was 24, synthesized much of what was known at the time in the field of number theory while also featuring many of Gauss's own discoveries. Its most famous result is probably the first proof of the quadratic reciprocity theorem."

[Your understanding of Mathematics Texts has increased. You
estimate that your score on tomorrow's final has just gone up by one point.]
action: You show saying to the ghost
response: The gray lady looks carefully at Descartes's saying. Then she says, "I'm not sure you'll have any more use for that." She takes Descartes's saying from you and places it in the gray storage bin.
"If you ever want it back, though, feel free to just take it," she adds. "I might be wrong."
action: You show correspondence to the ghost
response: The gray lady looks carefully at the correspondence. Then she says, "I'm not sure you'll have any more use for that." She takes the correspondence from you and places it in the gray storage bin. "If you ever want it back, though, feel free to just take it," she adds. "I might be wrong."
action: You show the range to the ghost
response: (first taking the toy mountain range)
The gray lady looks carefully at the toy mountain range. Then she says, "I think you may still find some use for that. You never know, though," she adds. "I might be wrong."
action: Go west
response: You make your way west. As you do, you feel an electrical impulse course through you. You find yourself in...

Not all of the experiments are gone; near the west door is a platform, raised slightly off the floor. A control panel is attached to the wall near the platform.

There is also a large fan set into the east wall.
action: Switch fan
response: You switch on the wall fan. A strong breeze begins to blow through the lab.

The breeze ruffles the printout.
action: You examine the printout
response: The note is a printout of an email. It reads, "To my graduate students: Greetings from Hawaii! I'm having a great time at the conference. It's too bad none of you could come.

"Unfortunately, I have some bad news. Most of my funding has run out. While I have enough to support myself, I do not have enough left to support any of you anymore. Thus, all of your current projects are hereby cancelled. If you want to finish your degrees you'll need to find another adviser."

Underneath someone has written an unprintable commentary on the contents of the email.

The breeze ruffles the trig homework.
action: Switch fan
response: You switch off the wall fan, and the breeze dies down.
action: You examine the panel
response: The control panel is labeled "Transformation Matrix Prototype." It features numbers in a 3 by 3 matrix. Each number in the top row has a slider above it that controls the setting of that number. The numbers in the second and third rows, though, seem to be fixed. A button is next to the 3 by 3 matrix.

The matrix currently looks like this:
0  -1   0
1   0   0
0   0   1
action: You put crank on the platform
response: You put the small crank on the platform.
action: You press the button
response: You push the button, and a shimmering light envelops the platform.
The small crank transforms, so that it is now rotated 90 degrees counterclockwise.
action: You examine the crank
response: This crank is made of lead. It has threads that are oriented clockwise.
action: You examine the second slider
response: The second slider can be turned to -1, 0, or 1 to set the value of the second entry in the top row. The second slider is currently set to -1.
action: You set second to 1
response: You set the second slider to 1. Now the matrix looks like this:
0   1   0
1   0   0
0   0   1
action: You examine the first slider
response: The first slider can be turned to -1, 0, or 1 to set the value of the first entry in the top row. The first slider is currently set to 0.
action: You look at the third slider
response: The third slider can be turned to -1, 0, or 1 to set the value of the third entry in the top row. The third slider is currently set to 0.
action: You examine crank
response: This crank is made of lead. It has threads that are oriented counterclockwise.
action: You go east
response: As you move east, you feel an electrical impulse course through you. The space around you seems to fold in on itself.

Gray Matter, Level Four
action: Go upwards
response: You make your way up.

Gray Matter, Level Two
Off to the side sits a gray storage bin. In the storage bin you see some correspondence, Descartes's saying, an old coin, a comic strip, a pile of money, a brochure, a piece of paper, a wad of plastic, an x-finder, Archimedes's staff, a square piece of metal, and a
scribbled scroll.

A gray, translucent ghost flits around the storage bin.
action: You put crank in the mailbox
response: You screw the small crank into the hole in the mailbox.
action: You open the mailbox
response: You turn the crank. The mailbox opens, revealing a brown paper package.
action: You look at it
response: Judging by its size and shape, it probably contains a book. It is not, you note, tied up with string.
action: You open the package
response: You open the package, wadding up the paper in the process. Inside is a copy of The Art of Computer Programming, by Donald Knuth,
which you take.
action: You examine Art
response: Programming "The Bible of Computer Science." This is just Volume
I, though. Flipping through it, the first section seems to be mostly mathematics.
action: You read it
response: Programming "The Bible of Computer Science." This is just Volume
I, though. Flipping through it, the first section seems to be mostly mathematics.

material to read through.
action: Go east
response: There are currently nine books on the bookcase:
Disquisitiones Arithmeticae
La Géométrie
Foundations for a General Theory of Functions of a Complex
Variable
Liber Abaci
Introduction to the Analysis of the Infinite
Diophantus's Arithmetica
Ars Magna
The Compendious Book on Calculation by Completion and
Balancing
Elements
action: You put Art on the shelf
response: You put The Art of Computer Programming on the bookcase. As
it slides into place you hear a faint click. Then you hear
the same voice as before - the one that sounds like Professor Glasser.

The voice says, "Computer science was originally a branch of mathematics, and there is still much overlap between the two disciplines. Donald Knuth's Art of Computer Programming has
been called 'The Bible of Computer Science,' and it contains some sophisticated mathematics, particularly those parts of mathematics needed for the analysis of algorithms."

[Your understanding of Mathematics Texts has increased. You
estimate that your score on tomorrow's final has just gone up by one point.]
action: You check your inventory
response: You are carrying:
a wad of brown paper
a toy mountain range
some limit shoes (being worn)
a set (no longer empty)
a square root
a printout
the trig homework
your math book
action: Go west
response: There is a small mailbox here, with a crank attached to it.
action: Go west
response: As you move west, you feel an electrical impulse course through you. The space around you seems to fold in on itself.

Gray Matter, Level Two
Off to the side sits a gray storage bin. In the storage bin you see some correspondence, Descartes's saying, an old coin, a comic strip, a pile of money, a brochure, a piece of paper, a wad of plastic, an x-finder, Archimedes's staff, a square piece of metal, and a
scribbled scroll.

A gray, translucent ghost flits around the storage bin.
action: You show the wad of the paper to the ghost
response: The gray lady looks carefully at the wad of brown paper. Then she says, "I'm not sure you'll have any more use for that." She takes the wad of brown paper from you and places it in the gray storage bin.
"If you ever want it back, though, feel free to just take it," she adds. "I might be wrong."
action: Go west
response: You make your way west. As you do, you feel an electrical impulse course through you. You find yourself in...

A gaming machine is here.
action: Go east
response: As you move east, you feel an electrical impulse course through you. The space around you seems to fold in on itself.

Gray Matter, Level Two
Off to the side sits a gray storage bin. In the storage bin you see a wad of brown paper, some correspondence, Descartes's saying, an old coin, a comic strip, a pile of money, a brochure, a piece of paper, a wad of plastic, an x-finder, Archimedes's staff, a square
piece of metal, and a scribbled scroll.

A gray, translucent ghost flits around the storage bin.
action: You go to the north
response: At the west end of the chapel stands a statue of Isaac Newton.

A beam of light shines through a window and forms a circle on the floor.

You can also see a sphere here.
action: You look in it
response: This beautiful translucent sphere seems to sparkle as you look into it.
action: You put the sphere in the circle
response: (first taking the sphere)
You place the sphere into the circle of light. The beam of light passes through the surface of the sphere, refracting into a beautiful rainbow that shines across the statue of Newton.

Once again, the statue grins at you, steps down off its plinth, and takes your hand.

The chapel slowly fades from view, and you find yourself on...

You stand on the broad shoulder of a giant. From this location you have a sweeping view of the surrounding landscape - a valley below with a lake in its center, surrounded by a forest.

Sir Isaac Newton is here, gazing out over the landscape.
action: You give the range to Newton
response: "Thank you," Newton says, as he takes the toy mountain range from you. He stretches out his arm, and the toy mountain range flies out of his hand, speeding away from the two of you. You blink, and the when you look again you can see the snow-capped mountain range once more off in the distance.

"I have one more thing for you," Newton says. "You may find this useful." Newton hands you a copy of his Principia
Mathematica.
action: You jump
response: You jump off the giant's shoulder and hurtle toward the ground. It's a long fall. You're falling, and falling, and falling...
a long fall. You're falling, and falling, and falling...And you hit the ground back in the chapel of Trinity College.

You stand in the magnificent chapel of Trinity College. You make a mental note to visit this place sometime when you're truly awake. The exit is to the south.

At the west end of the chapel stands a statue of Isaac Newton.

A beam of light shines through a window and forms a circle on the floor.

You can also see a sphere here.
action: You go east
response: As you move east, you feel an electrical impulse course through you. The space around you seems to fold in on itself.

Gray Matter, Level Three
action: You go upward
response: You make your way up.

Gray Matter, Level Two
Off to the side sits a gray storage bin. In the storage bin you see a wad of brown paper, some correspondence, Descartes's saying, an old coin, a comic strip, a pile of money, a brochure, a piece of paper, a wad of plastic, an x-finder, Archimedes's staff, a square
piece of metal, and a scribbled scroll.

A gray, translucent ghost flits around the storage bin.
action: You show the sphere to the ghost
response: The gray lady looks carefully at the sphere. Then she says, "I'm not sure you'll have any more use for that." She takes the sphere from you and places it in the gray storage bin. "If you ever want it back, though, feel free to just take it," she adds. "I might be wrong."
action: Inventory
response: You are carrying:
Principia Mathematica
some limit shoes (being worn)
a set (no longer empty)
a square root
a printout
the trig homework
your math book
action: You go east
response: You make your way east. As you do, you feel an electrical impulse course through you. You find yourself in...

There is a small mailbox here, with a crank attached to it.
action: You go east
response: There are currently ten books on the bookcase:
The Art of Computer Programming
Disquisitiones Arithmeticae
La Géométrie
Foundations for a General Theory of Functions of a Complex
Variable
Liber Abaci
Introduction to the Analysis of the Infinite
Diophantus's Arithmetica
Ars Magna
The Compendious Book on Calculation by Completion and
Balancing
Elements
action: You put Principia in the shelf
response: You put Principia Mathematica on the bookcase. As it slides
into place you hear a faint click. Then you hear the same
voice as before - the one that sounds like Professor Glasser.

The voice says, "Newton's Principia Mathematica is one of the
most important books on science ever written. Its specific contributions include Newton's three laws of motion, his law of universal gravitation, and a derivation of Kepler's laws of planetary motion. Perhaps even more important, though, is Newton's stunning demonstration of the power of mathematics in describing natural phenomena. While the arguments presented in the Principia
tend to be geometric, Newton did use many of the ideas of calculus (which he also invented) in order to derive his results."

[Your understanding of Mathematics Texts has increased. You
estimate that your score on tomorrow's final has just gone up by one point.]
action: Go west
response: As you move west, you feel an electrical impulse course through you. The space around you seems to fold in on itself.

Gray Matter, Level Two
Off to the side sits a gray storage bin. In the storage bin you see a sphere, a wad of brown paper, some correspondence, Descartes's saying, an old coin, a comic strip, a pile of money, a brochure, a piece of paper, a wad of plastic, an x-finder, Archimedes's staff, a
square piece of metal, and a scribbled scroll.

A gray, translucent ghost flits around the storage bin.
action: Go downwards
response: You make your way down.

Gray Matter, Level Two
Off to the side sits a gray storage bin. In the storage bin you see a sphere, a wad of brown paper, some correspondence, Descartes's saying, an old coin, a comic strip, a pile of money, a brochure, a piece of paper, a wad of plastic, an x-finder, Archimedes's staff, a
square piece of metal, and a scribbled scroll.

A gray, translucent ghost flits around the storage bin.
action: Go south
response: You make your way south. As you do, you feel an electrical impulse course through you. You find yourself in...

A tray is attached to the wall next to the window.

Through the window you can see a flat, gray plane. A pile of discarded objects lies a short distance away in the plane.
action: Inventory
response: You are carrying:
some limit shoes (being worn)
a set (no longer empty)
a square root
a printout
the trig homework
your math book
action: You examine the trig
response: The homework is covered with equations involving sines, cosines, and tangents. There are also a couple of graphs drawn on the homework, labeled "sin x" and "cos x." Each graph consists of
a wavy line that switches from positive to negative every Pi units. Circled at the top of the homework is the phrase "Review Logarithms!!!"
action: You go to the north
response: As you move north, you feel an electrical impulse course through you. The space around you seems to fold in on itself.

Gray Matter, Level Four
action: Go west
response: You make your way west. As you do, you feel an electrical impulse course through you. You find yourself in...

Not all of the experiments are gone; near the west door is a platform, raised slightly off the floor. A control panel is attached to the wall near the platform.

There is also a large fan set into the east wall.
action: You examine the fan
response: This is a large, industrial-strength wall fan. You wonder what experiments it was used for.

The wall fan is currently switched off.
action: Switch fan
response: You switch on the wall fan. A strong breeze begins to blow through the lab.

The breeze ruffles the printout.
action: You go east
response: As you move east, you feel an electrical impulse course through you. The space around you seems to fold in on itself.

Gray Matter, Level Four
action: Go west
response: You make your way west. As you do, you feel an electrical impulse course through you. You find yourself in...

Not all of the experiments are gone; near the west door is a platform, raised slightly off the floor. A control panel is attached to the wall near the platform.

There is also a large fan set into the east wall. The fan is on, and a strong breeze is blowing through the lab.

The breeze ruffles the trig homework.
action: You open Window
response: You open the window.
action: You go north
response: Not all of the experiments are gone; near the west door is a platform, raised slightly off the floor. A control panel is attached to the wall near the platform.

There is also a large fan set into the east wall. The fan is on, and a strong breeze is blowing through the lab.

The breeze ruffles the trig homework.
action: Go north
response: On the seminar table are some presentation slides.
action: You look out Window
response: This window overlooks a small courtyard.
action: You look at the courtyard
response: The courtyard is a rather sad, neglected affair. At least the view is better than the one from the graduate student office.
action: Go north
response: You're too high up. There is no way you would survive the drop to the hard ground below.
action: Go south
response: Not all of the experiments are gone; near the west door is a platform, raised slightly off the floor. A control panel is attached to the wall near the platform.

There is also a large fan set into the east wall. The fan is on, and a strong breeze is blowing through the lab.

The breeze ruffles the trig homework.
action: You look at your surroundings
response: Wires and pieces of metal indicate that highly complex experiments must have once been performed in this room. Now, though, they lie scattered haphazardly here and there: Someone has cleared this place out. There are open doors to the north and south, and the exit to the lab lies east. A door to the west is closed.

Not all of the experiments are gone; near the west door is a platform, raised slightly off the floor. A control panel is attached to the wall near the platform.

There is also a large fan set into the east wall. The fan is on, and a strong breeze is blowing through the lab.

The breeze ruffles the trig homework.
action: You go east
response: As you move east, you feel an electrical impulse course through you. The space around you seems to fold in on itself.

Gray Matter, Level Four
action: You examine Machine
response: This machine is just as steampunk as everything else here, although there are several parts to it that look at least somewhat recognizable.

For one, the machine has a switch that can be set to "Sequence" or "Series." It is currently set to "Series," although you could easily move it to the other setting by flipping the switch.

There is a button labeled "Alternate" that is currently pushed on.

The machine also has a dial that can be set to "Constant," "Identity," "Squared," or "Reciprocal." It is currently set to "Reciprocal."

There is a small circular hole near the button. A brass rod has been inserted into it.

Finally, there is a warning light on top of the machine. The warning light is dark.
action: You look at the rod
response: This brass rod is short and, for a rod, relatively thick. It has the number 69,105 written on it.
action: You switch the switch
response: You flip the switch to "Sequence." Some of the numbers on the golden path change. The warning light is still dark.
action: You examine the path
response: The path is level with the floor of the room you are currently in. It consists of golden steps that seem to run on forever. Each step has two numbers appearing on it, although from here you can only read the numbers on the six closest steps. The first numbers on the steps are 1, 1/2, 1/3, 1/4, 1/5, and 1/6. The second numbers are 1, -1/2, 1/3, -1/4, 1/5, and -1/6.
action: You go south
response: As you approach the golden path you take another look at it.

The path is level with the floor of the room you are currently in. It consists of golden steps that seem to run on forever. Each step has two numbers appearing on it, although from here you can only read the numbers on the six closest steps. The first numbers on the steps are 1, 1/2, 1/3, 1/4, 1/5, and 1/6. The second numbers are 1, -1/2, 1/3, -1/4, 1/5, and -1/6.

As you near the path, though, the second step swaps places with the fifth step. Then the sixth step swaps places with the first step. Other steps swap places with each other, and you stop, watching, as the entire path appears to rearrange itself.

Then a mechanical voice intones, "Rearrangement failed." The steps continue to swap places with each other for a while. When they finish you realize from their numbers that they are back in their initial order.

You move towards the path once more. Just before you reach it, though, it shifts: The heights of the steps change. The first step is now up. After that, the second step is down, the third step is up, the fourth is down again, and so on, up, down, up, down... for as far as you can see. Each down step looks like it goes below the level of the floor of this room, and each up step looks like it is above that level. However, each down step isn't quite as far down as the one before, and each up step isn't quite as far up as the one before. After a while, despite the up and down steps, the path looks almost flat.

Then you walk out onto the path. The limit shoes react to the contact with the first step: They propel you to the next step, and the next, and the next - faster and faster. Soon you are moving so fast the path is a blur, and then you can't even see it anymore.

You find yourself hurtling through space, only to land in...
Zero
This is more of an abstract space than a physical place. Besides the hole leading back up to the real axis, you sense nothing here.
action: Go upwards
response: You make your way up.

The dark blue expanse of space now contains a plane that stretches as far as you can see in all directions. It includes both the real axis you are standing on and the imaginary axis you can see off in the distance, and it is filled with starry, twinkling lights.
action: You look at Machine
response: This machine is just as steampunk as everything else here, although there are several parts to it that look at least somewhat recognizable.

For one, the machine has a switch that can be set to "Sequence" or "Series." It is currently set to "Sequence," although you could easily move it to the other setting by flipping the switch.

There is a button labeled "Alternate" that is currently pushed on.

The machine also has a dial that can be set to "Constant," "Identity," "Squared," or "Reciprocal." It is currently set to "Reciprocal."

There is a small circular hole near the button. A brass rod has been inserted into it.

Finally, there is a warning light on top of the machine. The warning light is dark.
action: You get the rod
response: You remove the brass rod from the circular hole. A mechanical voice intones, "Riemann Rearrangement Mode deactivated."
action: You set the dial to the identity
response: You turn the dial to "Identity." Some of the numbers on the golden path change. The warning light is now glowing.
action: You look at the path
response: The path is level with the floor of the room you are currently in. It consists of golden steps that seem to run on forever. Each step has two numbers appearing on it, although from here you can only read the numbers on the six closest steps. The first numbers on the steps are 1, 2, 3, 4, 5, and 6. The second numbers are 1, -2, 3, -4, 5, and -6.
action: You set the dial to constant
response: You turn the dial to "Constant." Some of the numbers on the golden path change. The warning light is still glowing.
action: You examine the path
response: The path is level with the floor of the room you are currently in. It consists of golden steps that seem to run on forever. Each step has two numbers appearing on it, although from here you can only read the numbers on the six closest steps. The first numbers on the steps are all the same: 1, 1, 1, 1, 1, and 1. The second numbers are 1, -1, 1, -1, 1, and -1.
action: Continue
response: You push the button on. Some of the numbers on the golden path change. The warning light is now glowing.
action: You set the dial to squared
response: You turn the dial to "Squared." Some of the numbers on the golden path change. The warning light is still glowing.
action: You examine the path
response: The path is level with the floor of the room you are currently in. It consists of golden steps that seem to run on forever. Each step has two numbers appearing on it, although from here you can only read the numbers on the six closest steps. The first numbers on the steps are 1, 4, 9, 16, 25, and 36. The second numbers are 1, -4, 9, -16, 25, and -36.
action: You examine Machine
response: This machine is just as steampunk as everything else here, although there are several parts to it that look at least somewhat recognizable.

For one, the machine has a switch that can be set to "Sequence" or "Series." It is currently set to "Sequence," although you could easily move it to the other setting by flipping the switch.

There is a button labeled "Alternate" that is currently pushed on.

The machine also has a dial that can be set to "Constant," "Identity," "Squared," or "Reciprocal." It is currently set to "Squared."

There is a small circular hole near the button.

Finally, there is a warning light on top of the machine. The warning light is glowing.
action: You switch the switch
response: You flip the switch to "Series." Some of the numbers on the golden path change. The warning light is still glowing.
action: You examine the path
response: The path is level with the floor of the room you are currently in. It consists of golden steps that seem to run on forever. Each step has two numbers appearing on it, although from here you can only read the numbers on the six closest steps. The first numbers on the steps are 1, 4, 9, 16, 25, and 36. The second numbers are 1, -3, 6, -10, 15, and -21.
action: You set the dial to reciprocal
response: You turn the dial to "Reciprocal." Some of the numbers on the golden path change. The warning light is now dark.
action: You examine the path
response: The path is level with the floor of the room you are currently in. It consists of golden steps that seem to run on forever. Each step has two numbers appearing on it, although from here you can only read the numbers on the six closest steps. The first numbers on the steps are 1, 1/2, 1/3, 1/4, 1/5, and 1/6. The second numbers are 1, 1/2, 5/6, 7/12, 47/60, and 37/60.
action: You put the rod in the hole
response: The brass rod slides perfectly into the circular hole. A mechanical voice intones, "Riemann Rearrangement Mode activated."
action: You set the dial to squared
response: You turn the dial to "Squared." Some of the numbers on the golden path change. The warning light is now glowing.
action: You switch the switch
response: You flip the switch to "Sequence." Some of the numbers on the golden path change. The warning light is still glowing.
action: You examine the path
response: The path is level with the floor of the room you are currently in. It consists of golden steps that seem to run on forever. Each step has two numbers appearing on it, although from here you can only read the numbers on the six closest steps. The first numbers on the steps are 1, 4, 9, 16, 25, and 36. The second numbers are 1, -4, 9, -16, 25, and -36.
action: You set the dial to constant
response: You turn the dial to "Constant." Some of the numbers on the golden path change. The warning light is still dark.
action: You look at the path
response: The path is level with the floor of the room you are currently in. It consists of golden steps that seem to run on forever. Each step has two numbers appearing on it, although from here you can only read the numbers on the six closest steps. The first numbers on the steps are all the same: 1, 1, 1, 1, 1, and 1. The second numbers are the same as the first numbers: 1, 1, 1, 1, 1, and 1.
action: Go west
response: As you move west, you feel an electrical impulse course through you. The space around you seems to fold in on itself.

Gray Matter, Level Four
action: Inventory
response: You are carrying:
a brass rod
some limit shoes (being worn)
a set (no longer empty)
a square root
a printout
the trig homework
your math book
action: You look around
response: Gray Matter, Level Four
This space is made of the same gray matter as the three above you. There is an inscription on the wall, as well as exits up to Gray Matter, Level Three, north to the Smoky Pub, south to the Window into Oblivion, east to the Machine Room, and west to the Research Lab.
action: Go west
response: You make your way west. As you do, you feel an electrical impulse course through you. You find yourself in...

Not all of the experiments are gone; near the west door is a platform, raised slightly off the floor. A control panel is attached to the wall near the platform.

There is also a large fan set into the east wall. The fan is on, and a strong breeze is blowing through the lab.

The breeze ruffles the printout.
action: Go north
response: On the seminar table are some presentation slides.
action: You read the page 7
response: The final page mentions that combinations of these effects as well as other effects can be achieved by using different matrices. A three-dimensional object can even be turned into a two-dimensional or even a one-dimensional object by using the appropriate transformation matrix.

At the end of the final page is a brief description of one of the graduate student experiments involving transformation matrices. Thus far the student has constructed a prototype that allows one to apply a transformation matrix to a physical object. For the prototype the transformations that produce the y and z coordinates
are hard-coded; the user can only affect the transformations for the
x coordinates of the new object. In addition, only a few
choices have thus far been implemented for the top row of the matrix. Finally, the transformation effect is thus far permanent only for objects made of lead. Even for lead objects, though, the process seems to be permanent only once; subsequent transformations on a transformed lead object have so far only been temporary. The current hypothesis is that the transformation process changes something about the lead object at the atomic level.
action: Go south
response: Not all of the experiments are gone; near the west door is a platform, raised slightly off the floor. A control panel is attached to the wall near the platform.

There is also a large fan set into the east wall. The fan is on, and a strong breeze is blowing through the lab.

The breeze ruffles the printout.
action: You check your inventory
response: You are carrying:
a brass rod
some limit shoes (being worn)
a set (no longer empty)
a square root
a printout
the trig homework
your math book

The breeze ruffles the trig homework.
action: You enter the platform
response: You get onto the platform.

The breeze ruffles the printout.
action: You stand
response: You get off the platform.

Not all of the experiments are gone; near the west door is a platform, raised slightly off the floor. A control panel is attached to the wall near the platform.

There is also a large fan set into the east wall. The fan is on, and a strong breeze is blowing through the lab.

The breeze ruffles the trig homework.
action: You look at the printout
response: The note is a printout of an email. It reads, "To my graduate students: Greetings from Hawaii! I'm having a great time at the conference. It's too bad none of you could come.

"Unfortunately, I have some bad news. Most of my funding has run out. While I have enough to support myself, I do not have enough left to support any of you anymore. Thus, all of your current projects are hereby cancelled. If you want to finish your degrees you'll need to find another adviser."

Underneath someone has written an unprintable commentary on the contents of the email.

The breeze ruffles the printout.
action: You drop the homework
response: (first taking the trig homework from the set)
Dropped.

The breeze picks up the trig homework and blows it across the room, where it slides under the door to the west.
action: Go west
response: (first opening the west door)
(first unlocking the west door)
You lack a key that fits the west door.

The breeze ruffles the printout.
action: Switch fan
response: You switch off the wall fan, and the breeze dies down.
action: You examine door
response: (the west door)
The west door appears to be locked. There is a very thin space between the bottom of the door and the floor.
action: You examine the space
response: The west door appears to be locked. There is a very thin space between the bottom of the door and the floor.
action: Inventory
response: You are carrying:
a brass rod
some limit shoes (being worn)
a set (no longer empty)
a square root
a printout
your math book
action: You put the rod in door
response: (the west door)
That can't contain things.
action: Go north
response: On the seminar table are some presentation slides.
action: You look out Window
response: This open window overlooks a small courtyard.
action: You look at the courtyard
response: The courtyard is a rather sad, neglected affair. At least the view is better than the one from the graduate student office.
action: You go south
response: Not all of the experiments are gone; near the west door is a platform, raised slightly off the floor. A control panel is attached to the wall near the platform.

There is also a large fan set into the east wall.
action: Look around
response: This office is small and cramped, although that hasn't prevented someone from squeezing several desks in here. A door leads north, back into the lab. An open window in the south wall looks out onto a dingy part of campus.
action: You examine the desks
response: The desks have all been cleaned out.
action: You look under the desks
response: The empty desks are a sad testament to the graduate students who used to work here. They're not worth bothering with.
action: You look at the door
response: The  door is open.
action: You look at the building
response: The building reflects the uninspired architecture of the 1960s. It's probably an engineering building.
action: You close door
response: You close the door.
action: You look at the door
response: The  door is closed.
action: You sit at the desk
response: I didn't understand that. The first word or two on their own might suffice, though; perhaps it would work to just sit.
action: Describe the surroundings
response: This office is small and cramped, although that hasn't prevented someone from squeezing several desks in here. A closed door leads north, back into the lab. An open window in the south wall looks out onto a dingy part of campus.
action: Close Window
response: You close the window.
action: Go north
response: (first opening the door)

Not all of the experiments are gone; near the west door is a platform, raised slightly off the floor. A control panel is attached to the wall near the platform.

There is also a large fan set into the east wall.
action: You look around
response: The seminar room is dominated by the large table running the length of it. An open window in the north wall looks out onto a courtyard, and a door leads south back into the lab.
action: You go south
response: Not all of the experiments are gone; near the west door is a platform, raised slightly off the floor. A control panel is attached to the wall near the platform.

There is also a large fan set into the east wall.
action: You examine door
response: (the west door)
The west door appears to be locked. There is a very thin space between the bottom of the door and the floor.
action: Inventory
response: You are carrying:
some presentation slides
a brass rod
some limit shoes (being worn)
a set (no longer empty)
a square root
a printout
your math book
action: You examine the panel
response: The control panel is labeled "Transformation Matrix Prototype." It features numbers in a 3 by 3 matrix. Each number in the top row has a slider above it that controls the setting of that number. The numbers in the second and third rows, though, seem to be fixed. A button is next to the 3 by 3 matrix.

The matrix currently looks like this:
0   1   0
1   0   0
0   0   1
action: You set second to 0
response: Which do you mean, the second slider or the second page?
action: Slider
response: You set the second slider to 0. Now the matrix looks like this:
0   0   0
1   0   0
0   0   1
action: Switch fan
response: You switch on the wall fan. A strong breeze begins to blow through the lab.

The breeze ruffles the printout.
action: You enter the platform
response: You get onto the platform.

The breeze ruffles the presentation slides.
action: You open the drawer
response: You open the drawer, revealing a spare key.
action: You look at Window
response: You can see most of a university campus laid out before you from the window. It's a stunning view.
action: You look at the campus
response: Most of the campus is laid out before you from the window. It is quite the sight.
action: You enter Window
response: There appears to be no way to open the bay window. Even if you could find a way to open it, though, you would never survive the drop.
action: You get all
response: trig homework: Taken.
action: You go to the east
response: (first opening the door)
(first unlocking the door)
(with the spare key)

Not all of the experiments are gone; near the west door is a platform, raised slightly off the floor. A control panel is attached to the wall near the platform.

There is also a large fan set into the east wall. The fan is on, and a strong breeze is blowing through the lab.

The breeze ruffles the presentation slides.
action: Go west
action: You examine the desk
response: Solid and expensive-looking, the desk contributes to the air of authority in this room. It has a single drawer.
action: You look at what you're carrying with you
response: You are carrying:
the trig homework
a spare key
Finite-Dimensional Vector Spaces
some presentation slides
a brass rod
some limit shoes (being worn)
a set (no longer empty)
a square root
a printout
your math book
action: You go east
response: Not all of the experiments are gone; near the west door is a platform, raised slightly off the floor. A control panel is attached to the wall near the platform.

There is also a large fan set into the east wall. The fan is on, and a strong breeze is blowing through the lab.

The breeze ruffles the presentation slides.
action: Go upwards
response: You make your way up.

Gray Matter, Level Two
Off to the side sits a gray storage bin. In the storage bin you see a sphere, a wad of brown paper, some correspondence, Descartes's saying, an old coin, a comic strip, a pile of money, a brochure, a piece of paper, a wad of plastic, an x-finder, Archimedes's staff, a
square piece of metal, and a scribbled scroll.

A gray, translucent ghost flits around the storage bin.
action: Go east
response: There are currently eleven books on the bookcase:
Principia Mathematica
The Art of Computer Programming
Disquisitiones Arithmeticae
La Géométrie
Foundations for a General Theory of Functions of a Complex
Variable
Liber Abaci
Introduction to the Analysis of the Infinite
Diophantus's Arithmetica
Ars Magna
The Compendious Book on Calculation by Completion and
Balancing
Elements
action: You put the vector in the shelf
response: You put Finite-Dimensional Vector Spaces on the bookcase. As
it slides into place you hear a faint click. Then you hear
the same voice as before - the one that sounds like Professor Glasser.

The voice says, "Highly readable and featuring an axiomatic approach, Paul Halmos's famous text was the first introductory book on linear algebra."

An almost inaudible voice whispers in your ear, "Look to your books for the final text."

[Your understanding of Mathematics Texts has increased. You
estimate that your score on tomorrow's final has just gone up by one point.]
action: You look around
response: This is the living room of the white house, and it looks to be the only room still intact. A sofa sits against one wall, and a bookcase stands against another. The sole unblocked exit is through the front door to the west.

There are currently thirteen books on the bookcase:
Fractals (glowing)
Finite-Dimensional Vector Spaces
Principia Mathematica
The Art of Computer Programming
Disquisitiones Arithmeticae
La Géométrie
Foundations for a General Theory of Functions of a Complex
Variable
Liber Abaci
Introduction to the Analysis of the Infinite
Diophantus's Arithmetica
Ars Magna
The Compendious Book on Calculation by Completion and
Balancing
Elements
action: You look at Fractals
response: This is a copy of Fractals, by Benoît Mandelbrot. The book
is emitting a soft glow.
action: You read it
response: You open Fractals, and light bursts forth from it. The light
circles you several times. Then, with a loud "whoosh," it returns to the book, which slams shut.
action: Inventory
response: You are carrying:
Fractals (glowing)
the trig homework
a spare key
some presentation slides
a brass rod
some limit shoes (being worn)
a set (no longer empty)
a square root
a printout
your math book
action: You put the Fractals in shelf
response: You put Fractals on the bookcase. As it slides into place
you hear a faint click. Then you hear the same voice as
before - the one that sounds like Professor Glasser.

The voice says, "Fractals have yet to be defined precisely - even by Benoît Mandelbrot, the author of Fractals and the originator
of the concept. They tend to be characterized, though, by attributes like self-similarity: Changing the scale on a fractal object often results in the same or a similar pattern being repeated over and over. Fractal images are frequently created by iterating a function over the complex plane and assigning colors based on how rapidly the function diverges."
action: About yourself
response: You're asleep. But this is the most vivid dream you've ever had.
action: You go upward
response: You make your way up.

Real Axis: 1
The dark blue expanse of space now contains a plane that stretches as far as you can see in all directions. It includes both the real axis you are standing on and the imaginary axis you can see off in the distance, and it is filled with starry, twinkling lights.
action: You go west
response: The dark blue expanse of space now contains a plane that stretches as far as you can see in all directions. It includes both the real axis you are standing on and the imaginary axis you can see off in the distance, and it is filled with starry, twinkling lights.
action: You go north
response: Imaginary Axis: i
The dark blue expanse of space now contains a plane that stretches as far as you can see in all directions. It includes the imaginary axis you are standing on and the real axis you can see off in the distance, and it is filled with starry, twinkling lights.
action: Extract root
response: The root vibrates quietly, as it extracts the square root of the essence of the space around it. You feel yourself rotate
clockwise, swinging in an arc that takes you halfway back to the positive part of the real axis.

Complex: Modulus 1 and Acute Angle
This is more of an abstract space than a physical place. It strikes you, somehow, as a mixture of both the real and the imaginary spaces you have visited. It also feels large beyond your understanding, but not any more so than the irrational space you've already seen. A hole leads up.
action: You open Fractals
response: You open Fractals, and light bursts forth from it. The light
circles you several times. Then, with a loud "whoosh," it returns to the book, which slams shut.
action: Go upwards
response: You make your way up.

As soon as you climb through the hole, it closes behind you. A curve appears once more, lighting a path for you in the shape of an arc of a perfect circle - through the stars and back to the number 1 on the real axis. You follow the arc. As you step onto the real axis, the arc disappears.

Real Axis: 1
The dark blue expanse of space now contains a plane that stretches as far as you can see in all directions. It includes both the real axis you are standing on and the imaginary axis you can see off in the distance, and it is filled with starry, twinkling lights.
action: You read it
response: You open Fractals, and light bursts forth from it. The light
circles you once, twice, three times, and then it splinters, spinning away in all directions.

Each splinter of light seeks out one of the twinkling stars in the complex plane. The starry lights absorb the splintered ones and begin to pulse: blue, white, blue, white, blue, white...

The pulsing ceases with each point in the complex plane settling on a color from midnight blue to the purest white. Together they form a fractal pattern of infinite complexity, containing spirals throwing out tendrils that themselves contain spirals with tendrils... on and on.

The fractal is blindingly, indescribably, painfully beautiful.
From somewhere you hear - but only in your mind - words once spoken by another:

"Così la mente mia, tutta sospesa
mirava fissa, immobile e attenta,
e sempre di mirar faceasi accesa...

"Oh quanto è corto il dire e come fioco
al mio concetto! e questo, a quel ch'i' vidi,
è tanto, che non basta a dicer 'poco'...

"Qual è 'l geomètra che tutto s'affige
per misurar lo cerchio, e non ritrova,
pensando, quel principio ond' elli indige,

"tal era io a quella vista nova...
"A l'alta fantasia qui mancò possa."

"Thus all my mind, absorbed,
was gazing, fixed, unmoving and intent,
becoming more enraptured in its gazing...

"O how scant is speech, too weak to frame my thoughts.
Compared to what I still recall my words are faint -
to call them little is to praise them much...

"Like the geometer who fully applies himself
to square the circle and, for all his thought,
cannot discover the principle he lacks,

"such was I at that strange new sight...
Here my exalted vision lost its power."
And you wake up. You lie in bed for a while, thinking about what you've learned.
In the morning you get up and make your way to the exam.

You walk into the classroom feeling supremely confident about your understanding of the material. As the exam proceeds, the look on Professor Glasser's face goes from resignation to surprise to shock and finally to bemusement. By the end you have answered every single question correctly. Professor Glasser shakes your hand. "I have never had a student earn a perfect score on one of my final exams," she says, "much less one who skipped most of the class sessions!" She pauses for a moment, thinking. "You know," she says, "I could use a research assistant this summer. I don't normally have undergraduates work with me, but since you did so well in my class... Just think about it."

A couple of weeks later you check your grades...

You owe your roommate an apology about those study pills.
action: MATH
response: Balance scales
Pascal's triangle
Achilles and Zeno's paradoxes
Euclid, his fifth postulate, and non-Euclidean geometry
Top Two game
Farmer's problem, calculus, the roller coaster, and Pennings
Laser bike game
Transformation matrix and determinants
Harmonic series and alternating harmonic series
Grand hotel guest problem