# Presentation: 741970

## Understanding What

***Understanding What***

***Mr. K. NASA/GRC/LTP***
***Edited: Ruth Petersen***

***Numbers Tell Us***

**Notes:**
Understanding What Numbers Tell Us
We find marvels in the most ordinary places! In another presentation, I explore with you the wonders of the calendar. Here we will crack open a number (just one number), much as an archaeologist cracks open a rock or a hidden tomb, and see what it contains inside. Numbers are the essence of modern science. To understand them is to take an important step in understanding the science of today...and tomorrow. So, let’s embark upon a voyage of discovery, an adventure worthy of the best...
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The wind blew dust across the ageless dessert. As the sun set, the evening star mustered and gazed upon the time-worn expanse and its lone occupant. That old pyramid held secrets--secrets known only to the dessert sun, the evening star, and...

## Preliminary Activities:

***Be prepared to do some in-class arithmetic! You are required to know:***
*** ******the speed of light in km/s***
*** ******the earth’s circumference***
*** ******the distance from the earth to the moon, the sun, Pluto, and the next closest star.***
***how to represent a number in scientific notation *****(*****e.g., 1,000 = 10******3 *****).**

**Notes:**
You don’t need much to begin--pencil, paper, and an open mind. Please complete these preliminary activities before going on, as the discoveries made along the way will be far more exciting if you have done some initial spade work on your own.

## Purpose:

***It is important to think carefully about situations and ideas that you encounter in life. This activity is designed to provide practice in thinking carefully.***

**Notes:**
I take it as axiomatic that the greatest wonders the world has to offer are, literally, right beneath our noses. We do not necessarily have to travel to far-off places to seek adventure. We just have to know where to look in our own back yard!

## ??????

***Imagine that you are an explorer in Wonderland, and you have just found a number artifact. . .***

**1,000,000,000**

**,000**

- 1

**??????**

**Notes:**
Imagine that you are an explorer in Wonderland, and you have just found a number artifact. . .
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A line of sultry riders approached on horseback. The heat of the day had taken its toll on everyone. Now the sun was edging its way ever so slowly toward the horizon. Shadows lengthened. The horses seemed intent only on placing one tired foot in front of the other in anticipation of soon coming to a stop.
The expedition had pushed hard toward its destination because time was growing short – they had to make it to the artifact before [...you can choose the bad guys – make them anyone you wish!...] otherwise... (etc. etc. etc.)
“You still think that we’re going to make it before nightfall?” asked the field hardened archaeologist fingering his canteen.
“Yes, sir; it should be just ahead, sir,” said his worthy native guide. Then bringing his horse up abruptly, he pointed:
 “In fact, there it is!” 
Horses and riders stopped in unison. Every head turned toward where the guide was pointing. Suddenly the expedition had forgotten the heat and fatigue of the day. They stared in disbelief.
“Well, I’ll be... ,” said the archaeologist finally. “That old map was right after all...”

## What do you make of this?

***If you were Indiana Jones, what types of questions would you ask at this point?***

***“******Does it have a name?”***

***“******How big is it?”***

***“******Why is it significant?”***

**Notes:**
OK!
Stop here and think about these questions!
Do you have answers? Or do you just come up with more questions?
If we found an artifact on Mars, would you ask the same types of questions?
What sorts of things might you want to know?

## Right !!!!!!

***Imagine that you are an explorer in Wonderland, and you have just found a number artifact. . .***

**1,000,000,000**

**,000**

- 1

**The artifact is the number ****one trillion**** -**

***Right !!!!!!***

**As for the rest... **

**Notes:**
The artifact does indeed  have a name: in the U.S., we call it, “One Trillion.”
But things are never quite that simple. Reference to a good dictionary will reveal that in the U.K., the same number is called, “One Billion.” If you asked someone from the U.K. what ‘one trillion’ meant to them, they would reply, “1,000,000,000,000,000,000.” Their ‘trillion’ is our ‘quintillion.’ If, in turn, they asked YOU what YOU meant by ‘one-billion,’ what would you tell them?
Confused?
Welcome to the world! Anyway, we will use the U.S. system of nomenclature (system of names). As for the rest...

## 1

***First, let’s consider: *****“*****How big is it?”***
***How would ***_***you***_*** ******approach this question?***

**1,000,000,000**

**,000**

**Notes:**
Big and small are relative terms. I am big compared with a pencil, but small compared with a planet. It seems that the question posed above (“How big is it?”) can be answered only by making some kind of comparison between 1,000,000,000,000 and something else. What do you suggest?
Where else in science are comparisons made? Have you ever heard of: Comparative Anatomy? Comparative Planetology?
How does the archaeologist understand an ancient city whose crumbling ruins he/she has just excavated?
How does the paleontologist understand the dinosaur or Ice-Age mammal bones he/she has just unearthed?
We seem to be following a well established process here. Let’s see where it leads!

## 

****

****

****

**?**

**?**

**Notes:**
We can be pretty arbitrary at first. I chose to use time as a basis for comparison. Is this choice OK? What would YOU have used?
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“Do you have a clock,” the archaeologist asked suddenly. “Mine has stopped working.”
He held up an old timepiece and watched a thin streamer of sand pour out of it.
“You should have retired that old watch years ago,” said the guide with a short laugh.
“I like that old watch...” the archaeologist retorted...

## Let’s do some arithmetic!

_***24***_

_***86,400***_*** s/day***

***s/m X ***

***m/hr X***

***hr/day***

_***60***_

_***60***_

***=***

***Seconds in a Day...***

***Seconds in a Year!!!***
_***86,400***_*** s/day X ***_***365.25***_*** day/yr***
***= ***_***31,557,600***_*** s/yr***

**Notes:**
In order to comprehend the unknown, I must make reference to – comparison with – something known. And... I know a lot about time.

## Are these numbers even close to 1,000,000,000,000?

***What percentage of 1,000,000,000,000 is 31, 557, 600?***

**Notes:**
But, is the comparison any good; i.e., does it teach me anything?
Well, it seems to say that, if I am to use time as a basis for comparison, I will need more than just the number of seconds in a year – much more!!!
Negative results, such as this one, DO give us information; only, we must determine how we are to use it. E.g., I now know that I must find a much larger unit of time if it is to have enough seconds to be comparable to a trillion! This result is a positive result!

## .

**.**

***How about making a comparison with how many seconds we’ve been alive?***

**Notes:**
If one year doesn’t do it, how about a whole lifetime of years?
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“We’ll make camp here,” said the guide. “In the morning, we’ll press on.”
“Seems like I’ve been making camp and pressing on all my life,” said the archaeologist. “When does it ever stop?...” 
“Time, time, time, in a sort of runic rhyme,” said the guide, smiling.
“Since when did you study Poe?” asked the archaeologist, surprised.
“What else have we but time?” the guide returned, cryptically...

## Mr. K. is 50 years old.

***50 yr  X***

***1,577,880,000 sec***

***=***

***31,557,600 s/yr***

**Notes:**
So now, I reveal my age...
Does this work any better?

## What percentage of 1,000,000,000,000 is 1, 577, 880, 000?

***Well, when I say that I’m working on my second billion, I now know what I really mean!***

**Notes:**
A little closer, but still far from the mark!

## .

**.**

***OK, Let’s come at it another way:***
***If I told you that I was a trillion seconds***
*** ******old, what would be my age in years?***

***How well are we doing so far?***

**Notes:**
This time, we’ll reverse the logic. Let’s determine that length of time occupied by 1,000,000,000,000, seconds and see where that leads.
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The fire drew low, and the embers glowed a sullen red.
“I hate snakes,” said the archaeologist.
“Then why do you come to such places as this,”  asked the guide.
“Because time is here,” answered the archaeologist. “I am a student of time. Does that seem so strange to you?”
“Not if you say so,” said the guide yawning.
That night, the archaeologist dreamed of ages past...endless ages extending backward, and then backward still more...until...

## What do you conclude from all this? Does this help you to understand how big a trillion is?

***My age would be...***

**Notes:**
31,558 years ago, the Great Ice Age was still in full swing in the Northern Hemisphere! The glaciers would not retreat for another 10,000-20,000 years. The Neanderthal people were living in the caves of Europe, although their race was already in demise. The Cro Magnon people had ‘recently’ appeared and were beginning to spread throughout Europe and elsewhere.
31,550 years ago, modern Anthropology tells us there were two distinct species of human abroad on the earth: Homo neanderthalensis, and Homo sapiens. This situation is unprecedented by today’s standards: today, H. sapiens is the only human species on earth. We need to think about this idea especially now, whenever we are confronted with issues of cultural diversity!!!
31,550 years ago, no modern cities had yet sprung up, and the best technology was one of stone, wood, and bone tools!!!
31,550 years ago, the great animals whose skeletal remains we see in our local museums were alive and walking the land – in full view of our ancient ancestors.

## Next, let’s consider: Why is this number artifact significant?

**.**

***Next, let’s consider: Why is this number artifact significant?***

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**Notes:**
OK. We should now have the notion that the number 1,000,000,000,000 is immense. All well and good. We’ve certainly learned something. But...
What does it all stack up to mean???
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“If I had a lever of sufficient size, I could move the world,”  said the guide.
“Archimedes,” said the archaeologist. “But could you pay the debt?”
“What person could pay the debt?” asked the guide, feigning philosophical despair, “or measure the light years in the universe, for that matter...”

## Well, the U.S. National debt is $6 Trillion!

***At $1 per second, how long would it take to count? *****(*****Take a minute to work it out!***** )**

**Notes:**
We all understand money. And we all know that the U.S. National Debt is/was HUGE. But did you know that it was THIS HUGE???
Here’s another lesson in scale for you to try. Please run a quick calculation before you turn the page!

## 6

**X**

***31,558 years***

***=***

***189,348 years!***

**Notes:**
189,348 years ago...
No. YOU look it all up this time!!!
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“C’mon,” said the archaeologist. “You were doing so well. Work it out!!!”
The guide just dropped his hands at his side.
“It will take time,” he said at last. “But I WILL do it, you’ll see!”
“Sure, sure,” said the archaeologist smiling.
The guide caught the glint in his eye and smiled back.
“You’ll see,” he said again.

## From your knowledge of the speed of light, can you determine how many kms there are in a light year?

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***And not only that, the number of kms in a light year are... ***

***Wait!***
***From your knowledge of the speed of light, can ***_***you***_*** determine how many kms there are in a light year?***

**(*****Hint: A light year is the distance that light travels in one year*****.)**

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**Notes:**
(I’ll give a hint on this one: we’ve just been looking at a similar magnitude...)
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“...or measure the light years...”

## In your pre-conference activities, you should have found that

***c = 300,000 km/s***
***You also probably know that distance S is speed *****X***** time:***
***S = c *****X *****t***

**Notes:**
Time to get out that pre-conference material! I will not offer text notes for a few pages now. The charts pretty well explain themselves...

## So...How far does light travel in:

***1 second?***
***1 minute?***
***1 hour?***
***1 day?***
***1 year?***
**(*****Show results in scientific notation where appropriate. *****)**

## Answer:

***In 1 second:***
***s = 300,000 km***
***In 1 minute:***
***s = 18,000,000 km***
***In 1 hour:***
***s = 1,080,000,000 km***
***In 1 day:***
***s = 2.6 X 10******10****** km***
***In 1 year:***
***s = 9.5 X 10******12****** km***

***What can you say about the last number on the last page???***

## Now, compare these distances to the distances you already found in your pre-conference activities:

***The Earth’s circumference***
***The distance to the moon***
***The distance to the sun***
***The distance to Pluto***
***The distance to the next nearest star***
***State these distances in appropriate light units *****(*****light-second, light-minute, and so on*****)*****. You have five minutes to do this work in class.***

## The earth’s circumference is 0.125 light seconds.

***The moon is 1.3 light seconds away.***
***The sun is 8.3 light minutes away.***
***Pluto is over 5 light hours away.***
***The nearest star is 4.3 light years away!***

***Factoid!!!***
***With NASA’s Hubble Telescope, we can see out to about 10 billion light years!!***

**Notes:**
OK. Here are some numbers --- and an interesting factoid!

## What does this tell you about the cosmos? Did you ever think about the cosmos the way you are thinking about it right now?

**Notes:**
To summarize, we’ve moved from an unknown number artifact, through a system of comparative study, into the National News, and, finally, into astronomy. Now, we seem to have embraced the entire cosmos! Does this exercise tell you anything about how to think about YOUR everyday encounters?
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“Time to go,” said the guide.
The archaeologist look up at him.
“You’re right,” he said. “But what will I tell the museum? What will I say that I have found? We’ve uncovered so much: I can’t possibly bring it all back!” 
“Illumination,” said the guide. And the archaeologist glimpsed a wisdom in his friend that he had not known before. “Illumination,” he said again.
They mounted up and began to ride. The archaeologist paused for just a moment to look back. The sun glinted sharply from behind the pyramid with its mysterious artifact. In another moment or two, it would be full day.
“Illumination...” he muttered to himself.
He turned and, with a “YAH!” to his horse, set off to catch up with the other riders...

## Follow-up Activity:

***With NASA’s Hubble Telescope, we can see out to about 10 billion light years. We now estimate (very roughly) that there may be on the order of 5 sextillion stars in the observable universe. So...***

## 1. Look up “sextillion” in your dictionary, express it in scientific notation, then compare it to other large numbers that you might have learned in school such as Avogadro’s number.

***2. ******Are there more: (1) stars in the observable universe or (2) molecules in a mole of water?***
***3.****** How many cubic centimeters IS a mole of water?***

**Notes:**
Please give these a try. If you wish to ask questions, feel fee to e-mail me at NASA. My address is on the last page!

Ciao!!!

## joseph.c.kolecki@grc.nasa.gov