trentmkelly/LessWrong-43k huggingface dataset:
Introduction to Introduction to Category Theory
by countedblessings — 2019-10-06T14:43:46.977Z

Category theory is so general in its application that it really feels like everyone, even non-mathematicians, ought to at least conceptually grok that it exists, like how everyone ought to understand the idea of the laws of physics even if they don't know what those laws are.

We expect educated people to know that the Earth is round and the Sun is big, even though those facts don't have any direct relevance to the lives of most people. I think people should know about Yoneda and adjunction in at least the same broad way people are aware of the existence and use of calculus.

But no one outside of mathematics and maybe programming/data science has heard of category theory, and I think a big part of that is because all of the examples in textbooks assume you already know what Sierpinski spaces and abelian groups are.

That is to say: all expositions of category theory assume you know math.

Which makes sense. Category theory is the mathematics of math. Trying to learn category theory without having most of an undergraduate education in math already under your belt is like trying to study Newton's laws without having ever seen an apple fall from a tree. You can...you're just going to have absolutely no intuition to rely on.

Category theory generalizes the things you do in the various fields of mathematics, just like how Newton's laws generalize the things you do when you toss a rock or push yourself off the ground. Except really, category theory generalizes what you do when you generalize with Newton's laws. Category theory generalizes generalizing.

Therefore, without knowing about any specific generalizations, like algebra or topology, it's hard to understand general generalities—which are categories.

As a result, there are no category theory texts (that I know of) that teach category theory to the educated and intelligent but mathematically ignorant person.

Which is a shame, because you totally can.

Sure, if you've never learned topology, plenty of standard examples will fly over your head. But every educated person has encountered the idea of generalization, and they've seen generalizations of generalizations. In fact, category theory is very intuitive, and I don't think it necessarily benefits from relating it all as quickly as possible to more familiar fields of mathematics. Instead, you should grasp the flow of category theory itself, as its own field.

So this is (ten...
What is category theory?
by countedblessings — 2019-10-06T14:33:50.455Z

Category theory is the mathematics of math—specifically, it's a mathematical theory of mathematical structure. It turns out that every kind of mathematics you're likely to encounter in a normal university education is just another kind of category—group theory falls under the category of groups, topology falls under the category of topological spaces, etc.

Specifically, category theory shows that all of the highly diverse mathematical structures that we know of can be broken down into nodes and arrows between nodes. Nodes and arrows define a category in a nutshell—plus something called composition, which basically says that if a bird can fly from Mexico to the USA to Canada, then the bird can also travel "directly" from Mexico to Canada in a way that is equal to the Mexico —> USA —> Canada path. (See "the right to use a name" section.)

Breaking any and every mathematical structure down to nodes and arrows between nodes is a super-general, super-abstract way of studying mathematics. It's like trying to study Shakespeare by breaking down all of his sentences into nouns and verbs. Category theory has a reputation for being painfully abstract—in fact, it's been called "abstract nonsense" by one of its founders. Because of this, it's typically recommended that you have a few mathematical structures under your belt—algebra, groups, topology, etc.—before studying category theory so that you have specific examples to relate the abstractions to. (It would be tough to study verbs if you didn't know about things like running and jumping!)

But while there's only so much to learn about Shakespeare by breaking "to be or not to be" into infinitives, conjunctions, and adverbs, it turns out that the super-general perspective of category theory is incredibly useful in concrete ways. In particular, it turns out that pretty much every cool idea in math is something called an adjoint functor—a special construction that can only be accessed through category theory. A lot of category theorists will tell you that adjoint functors are kind of the point of category theory. Adjoints, or adjunction, generalizes optimization itself.

Then there is the Yoneda lemma, which is as deep as it is elegant and powerful. We will explore it in depth. (If this ...
Advanced Dances
by jefftk — 2019-10-06T11:10:01.810Z

BIDA is hosting its first
advanced dance

this
afternoon, before our regular dance:

I've been thinking a lot about it. If you had asked me ten years ago
whether BIDA would ever do advanced dances I would probably have said
no. A major goal with BIDA is to be welcoming, especially to
newcomers, and a dance where people aren't welcome unless they already
know how to dance seems antithetical. So why do I think having one is
good for our community?

Over time I've gotten a better understanding of the different roles
contra dancing plays in people's lives, and a common pattern is that
someone will start coming, get excited about it, dance a lot for a
while, come less often, and then stop attending, over the course of
about five years. The pattern is not universal, but it is pretty
common, and one driver is no longer finding contra to be as
interesting as before. Some people stop dancing much, others move on
to more complex styles.

This is where I see an occasional advanced dance fitting in: when you
have a hall where everyone already knows how to dance the caller can
choose more interesting dances. Or run more no-walkthroughs and spend
less time teaching. The dancers spend less time helping people around
them learn to dance, and more time coming up with interesting
variations. People also want to be at dances with their friends, and
if you have a pool of people who only want to come a few times a year
they'll normally not see much of each other. But an advanced dance
can bring coordination, where many of them attend at once without a
"how about we all come to this specific dance" discussion. A
community where people stay involved longer is a healthier one,
and helping people maintain ties they formed dancing is good on its
own.

On the other hand, this needs to be a rare event. Not only does it
lose its coordination power if scheduled too frequently, but if
advanced dances started to take the place of regular dances then new
people wouldn't be able to get into contra. The thing where you can
walk in off the street and start dancing, without attending any sort
of lesson, learning entirely as you go, is one of the best things
about the dance; it's really important that we don't lose this. So
for now this is a one-off event, but we may have others if this feels
like it's meeting a need.

Comment via: facebook
Mako's Notes from Skeptoid's 13 Hour 13th Birthday Stream
by mako yass — 2019-10-06T09:43:32.464Z

Recently, the pretty great skeptic podcast, Skeptoid, celebrated its 13th anniversary with a 13 hour-long livestream, in which host and founder Brian Dunning wore a party hat and received video calls from 24 of his dearest friends and peers.

It was a bit of a wreck, and the simultanious viewers never topped 40, but it was also extremely cozy and intimate. It was great seeing Brian interacting with his friends and colleagues and reflecting on their shared projects. It also lined up perfectly with my Aotearoan timezone, so I uh, I actually watched the entire thing... o.o;

But I'm glad I did! I've watched much sillier streamed events! It was actually very informative.

Here are the notes I took.

Comedian Rachel Bloom came by. The video call quality was terrible.

Apparently Sony funded a pilot of a show called Truth Hurts. Where Brian Dunning and Shira Lazar made a fun time of testing woo. It felt a lot like Mythbusters, with a greater focus on, you know, busting myths, and mainly myths that might really matter to someone. I think I would have loved it, but obviously it didn't go into production and I don't think Sony are funding shows any more.
Archaeologist Ken Feder apparently wrote a book about Weird archaeological sites and the eerie stories wooists tell about them. Usually these stories are something along the lines of "old humans couldn't have made these artefacts, so it must have been aliens". Ken notes that this theory is actually kind of racist, the old people were very clever. He then explains the techniques by which the old people did make those artefacts, which tend to be very interesting.
Magician Brian Brushwood seemed to have a really good attitude about promoting rationality. He hosts something called Scam School where, if I've gathered correctly, he teaches people how to commit acts of fooling. He says that only once you've fooled someone yourself will you learn to spot the signs that someone is trying to fool you, and in many cases those signs will be obvious once you know what to look for. He seemed to have a lot of value to say.

On this note, I recommend Penn and Teller's Fool Us. Magic is the study of wrong-seeing, it should be interesting to any aspiring rationalist, and Fool Us is a great place to see it.

Kiki Sanford, host of the extremely long-running science news podcast Scishow, mentioned being

...
[Event] Meeting in Myrhorod, November 16
by Mary Chernyshenko — 2019-10-06T08:45:59.527Z

On November, 16th (Saturday) we go to Myrhorod (Poltava region) and meet with LW readers from Kharkiv and maybe other places, too. The attendance in Kyiv is low enough to do something crazy without worrying too much.

The meetup is at 16.00, unless Intercity is late, near Gogol's statue at the railway station.

We shall go from there somewhere more comfortable. It will be all the more interesting since nobody who's said they'd come knows a comfortable place there. As usual, you can reach me at chernyshenko123@gmail dot com, +38097-667-29-70, Marichka, but if you bring people there, please do everything to help them return home safely and share your own contact information. Given the political situation, be brave. Write me ASAP if you set out from Kyiv and want to come together, I'll be taking a train.

We shall only have several hours and probably some people will have to leave earlier than others, which means we might want to just hang out and introduce ourselves. The coolest outcome I hope for is for Kharkiv to start their own meetup afterwards, but the sky is not the limit. I also have some hopes for Odessa, although not in the near future.

Likely it will be cold, so charge your phones, take enough money to eat at least twice and bundle up. Do not hesitate to tell me directly that you need whatever, whenever it comes up.

And if you think you are not the typical LWer... does it signify so much about you?
Who lacks the qualia of consciousness?
by Richard_Kennaway — 2019-10-05T19:49:52.432Z

Over on Facebook (I don't know if it's possible to link to a Facebook post, but h/t Alexander Kruel) and Twitter, the subject of missing qualia has come up. Some people are color-blind. This deficiency can be objectively demonstrated by tasks such as the Ishihara patterns. Some people cannot smell, and sometimes do not discover this until well into adulthood. Some people cannot form mental imagery, which was undiscovered until Galton wrote of it, but is now well-known enough to have a Wikipedia article. Until they discover that others really do see with the mind's eye, aphantasics take the expression to be some sort of metaphor. But it is not. Some people, I think most, do see things in their mind's eye.

More recently of note is that some people lack the qualia of long-term memory (see section 1.4): they can know that things involving them happened, but not re-experience them as a participant.

I want to put the following question: Does anyone here lack the qualia of consciousness?

If you do lack this then you won't know what I'm talking about. So I shall try to describe the experience. I have a vivid sensation of my own presence, my own self. This is the thing I am pointing at when I say that I am conscious. Whether I sit in meditation or in the midst of life, there I am. Indeed, more vividly in meditation, because then, that is where I direct my attention. But only in dreamless sleep is it absent.

Some people claim by meditation to have seen through what they claim is the illusion of consciousness. I am uncertain whether they have self-modified to ablate the faculty of having this experience, or merely philosophised themselves into believing there can't be any such thing, and insisting that they are not experiencing what they are experiencing.

But there may be some people out there who have never had any experience of themselves such as I have described. In effect, almost p-zombies. The original p-zombies are by definition indistinguishable in behaviour from everyone else, including talk about consciousness. But people without this experience of self, quasi-p-zombies, or q-zombies for short, may imitate the discourse as aphantasics or anosmics may, but without real understanding. I invite anyone who recognises themselves to be a q-zombie to put their hand up. Note that this is a question about whether you actually have this exp...
Eight O'Clock is Relative
by jefftk — 2019-10-05T16:20:01.445Z

When Lily was little we used an

analog rotary timer
outlet to turn on a light so she would know when it was ok to get
up. The goal wasn't to wake her, but to let her know when it was ok
to come downstairs. This worked ok, but it wasn't very precise. It
was good to maybe the nearest 15min, and would drift.

As she got better at reading we switched to a clock, and taught her
that when the first digit was "8" she could get up:

pictured: a clock that is not saying "time to get up"

This worked pretty well, but as she got close to starting kindergarten
we needed to move her bedtime and waketime earlier. We did this
gradually, about 15min at a time, over the course of a couple weeks.
Since she can't tell time yet and was only reading the most
significant digit she wasn't going to be able to learn that 7:45, then
7:30, then 7:15, etc meant time to get up. So I did the easy thing,
and started setting her clock early. First fifteen minutes fast, then
thirty minutes fast, until eventually it was an hour fast.

It's now the first week of school and her clock reads "8:00" at 7am.
At this point switching it to the correct time and teaching her she
can get up if it is "7:??" would have made sense, but there was enough
going on that we didn't get to it.

Now we're a month in, she's gotten faster with her morning routine,
and she could be sleeping later. So I've pushed her clock to only be
48 minutes fast instead of an hour, and it reads "8:00" at 7:12am.

All of this is pretty silly: she's pretty close to learning to tell
time, and having one clock in the house that doesn't match the others
is going to start confusing her. And it already confuses adults
sometimes (mostly me) since who expects a clock to be 48min fast?

On the other hand I'm not sure where to go next. I could just leave
things alone until she points out that it's weird, at which point
she'll know time well enough that I can set it correctly and suggest
she not get up before 7:12am. Or I could get a more
accurate outlet timer, which would have the benefit of also
working for our younger daughter? Not sure yet.

(When we were little we had analog clocks in the house, and my dad
made a wooden demonstration clock for us. When the hands on the real
clock matched the hands on the wooden clock, it was time to get up. I
think this worked well, though I remember one weekend when m...
What empirical work has been done that bears on the 'freebit picture' of free will?
by DanielFilan — 2019-10-04T23:11:27.328Z

This picture was described in Scott Aaronson's essay The Ghost in the Quantum Turing Machine in 2013, and claims that human free will is related to our choices being caused by (and/or causing) quantum bits from the initial state of the universe that first have macroscopic effects inside our brains, where all other observers must have purely Knightian uncertainty over such bits[*]. For it to be plausible, a few facts have to be true about human brain biology and cosmic background radiation:

"Quantum uncertainty—for example, in the opening and closing of sodium-ion channels—can not only get chaotically amplified by brain activity, but can do so “surgically” and on “reasonable” timescales."

All photons that impinge on human brains have quantum states that could not "be altered, maintaining a spacetime history consistent with the laws of physics, without also altering classical degrees of freedom in the photons’ causal past".

Have these questions been studied in the intervening years, and what have the results been? Note that the plausibility of the picture has been discussed before on LW, and I'm not interested in further discussing whether a priori it seems at all promising to link free will and Knightian uncertainty.

[*] This is a poor summary, I recommend reading the paper if you have time.
Ideal Number of Parents
by jefftk — 2019-10-04T20:00:01.371Z

I'll often hear people say with varying levels of seriousness that the
ideal number of parents to have is something large, like maybe
five. Children, especially
infants, can be an enormous amount of work, which is certainly
easier spread out among more people. Kids also like getting a lot of
attention, can require a lot of money, and, since different adults are
good with kids in different ways, can benefit from having a range of
adults in their lives. But while having many people involved in
taking care of the kids is great, I'm not sure having all of them be
co-equal parents is a good approach.

First, a question: why are people excited about putting so much of
themselves into parenting, when if you wanted to pay for similar
levels of childcare it would be incredibly expensive? Not to suggest
that parenting is simply unpaid childcare; thinking about what why
these superficially similar situations lead to such different levels
of desire helps illuminate what's important about parenting.

Answers will, of course, vary based on individual perspectives and
drives. For some people the answer is "I'm not excited about this,
which is why I don't want kids", but for people who do want to be a
parent I think it's common for things to trace back through two
points:

Having a substantial say in how the child is raised.

Knowing that this is a life-long relationship.

For the first point, the more people you have co-parenting the less
say each one has and the harder it is to reach agreement. Parents can
have different ideas on what is safe, how discipline should work, how
much help to give, how to do food, value of different kinds of
toys/screens/games, co-sleeping, night training, potty training, is it ok to microwave baby milk, what rules
to have for sharing, how structured the
day should be, when they're ready to go outside
alone, how to do money, what to do for childcare, when bedtime should be, what's
important in schooling, how important is predictability, how to handle
various unique challenges most kids have in some form, how to do presents, when to let them try a thing, what medical treatments
make sense, how much to let them make their own
decisions, whether to let them ask
people for things when it's kind of rude, how much to push them,
when to encourage an interest, how to
build responsibility, and how to balance all kinds of tricky
trad...
13 Causes of Bad Science (Novum Organum Book 1: 69-92)
by Francis Bacon — 2019-10-04T19:52:13.700Z

This is the sixth post in the Novum Organum sequence. For context, see the sequence introduction.

We have used Francis Bacon's Novum Organum in the version presented at www.earlymoderntexts.com. Translated by and copyright to Jonathan Bennett. Prepared for LessWrong by Ruby.

Ruby's Reading Guide

Novum Organum is organized as two books each containing numbered "aphorisms." These vary in length from three lines to sixteen pages. Bracketed titles of posts in this sequence, e.g. Idols of the Mind Pt. 1, are my own and do not appear in the original.

While the translator, Bennett, encloses his editorial remarks in a single pair of [brackets], I have enclosed mine in a [[double pair of brackets]].

Bennett's Reading Guide

[Brackets] enclose editorial explanations. Small ·dots· enclose material that has been added, but can be read as though it were part of the original text. Occasional •bullets, and also indenting of passages that are not quotations, are meant as aids to grasping the structure of a sentence or a thought. Every four-point ellipsis . . . . indicates the omission of a brief passage that seems to present more difficulty than it is worth. Longer omissions are reported between brackets in normal-sized type.

Aphorism Concerning the Interpretation of Nature: Book 1: 69–92

by Francis Bacon

[[Bacon continues on from the discussion of Idols of the Mind. Demonstration might be interpreted simply as experiment, but is likely closer to meaning of Aristotle's demonstrations: a scientific deduction where one moves from premises in which one has high confidence to new conclusions.]]

69. But the idols have defences and strongholds, namely defective demonstrations; and the demonstrations we have in dialectics do little except make •the world a slave to •human thought, and make human thought a slave to •words. Demonstrations are indeed incipient philosophies and sciences: how good or bad a demonstration is determines how good or bad will be the system of philosophy and the thoughts that follow it. Now the demonstrations that we use in our whole process of getting from the •senses and •things to •axioms and conclusions are defective and inappropriate. This process has four parts, with a fault in each of them. (1) The impressions of the senses itself are faulty, for the senses omit things and deceive us. Their omissions should be made up for, and their deceptions corrected. (2) Not...
What are your strategies for avoiding micro-mistakes?
by  — 2019-10-04T18:42:48.777Z

I've recently been spending more time doing things that involve algebra and/or symbol manipulation (after a while not doing these things by hand that often) and have noticed that small mistakes cost me a lot of time. Specifically, I can usually catch such mistakes by double-checking my work, but the cost of not being able to trust my initial results and redo steps is very high. High enough that I'm willing to spend time working to reduce the number of such mistakes I make even if it means slowing down quite a bit or adopting some other costly process.

If you've either developed such strategies for avoiding making such mistakes or would good at it in the first place, what do you do?

Two notes on the type of answers I'm looking for:

1. I should note that one answer is just to use something like WolframAlpha or Mathematica, which I do. That said, I'm still interested in not having to rely on such tools for things in the general symbol manipulation reference class as I don't like relying on my computer being present to do these sorts of things.

2. I did do some looking around for work addressing this (found this for example), but most of it suggested basic strategies that I already implement like being neat and checking your work.