Apophenia

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It's well-known that it shouldn't actually be that shocking to occasionally encounter seemingly shocking coincidences: the time your friend calls you just as you were about to call them might seem like compelling evidence for psychic powers, but only because you don't remember all the other occasions when an equally improbable coincidence could have happened, but didn't. We tend to see patterns even where none exist, and neglect that million-to-one events happen seven times a day in New York.

I expect this problem to actually get worse as you learn more: if you know n concepts, the number of possible connections between them is O(n2); if your ability to notice patterns grows faster than your sense of what patterns constitute a coincidence worth noticing, then you should expect to encounter more and more shocking coincidences over time.

Actually Trying

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"I'm alright—I'll get through it—I've been through this before. This fear and anxiety—it's a fact about me, not about the world. In early 2007, I spent weeks being terrified of either accidentally commiting plagiarism or being accused thereof. In late 2009, I spent weeks being upset about which form of my name to use in which contexts. In late 2010, I spent some time being deeply upset about having violated copyright law by writing fanfiction. All of those episodes, and the others that I haven't mentioned, seem so silly in retrospect ... so maybe now I'm sufficiently self-aware to pick up the pattern: that my brain just arbitrarily latches onto ideas to feel threatened by, but that this process isn't actually useful, and there are probably learnable techniques to dampen it."

"Sounds good."

"But now that I've returned from madness—relatively speaking—there remains the question of what to do next. I had been angry at the University because it's allegedly a place of learning, but in practice, it's just an obedience test: everyone talks about grades and teachers and classes and degrees and no one says a single goddamned word about grace, beauty, or the true structure of the world beneath the world. I felt betrayed that it turns out that there is such a thing as mathematical beauty and no one had told me, that I needed luck to find out. To the extent that I do have access to recondite magic that my classmates know not, it's not because I'm innately brilliant—I'm not—but because four years ago, I somehow got the idea that I was actually allowed to try. Not just show up and obey instructions, but actually try. I ended up continuing with the college thing because it was easy, because it was the default, because Father was paying for it, all the while hoping that at some point someone would appeciate the beauty that I had worked so hard to uncover—but ..."

"But?"

"But maybe now I'm sufficiently aware to pick up another pattern, which is that no one cares. Ever. I kept expecting arbitrary people to respect me for being 'smart,' and kept getting disappointed when it didn't happen. But isn't that, properly, my problem, not theirs? My internal sense that I'm superior because of my vaunted book-learning is only justified insofar as it actually helps me make better decisions; expecting respect from those who don't respect book-learning, or who read different books, is just inaccurate. So now ... I just need to switch strategies. Now that I've glimpsed a little bit of what it feels like to actually try, as opposed to just subordinating oneself to the local authority figures—what happens if I throw that same energy and intelligence to the problem of how to make money and carve out a life for myself? What does that look like?"

Insight Porn

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"Actually, maybe my father is right. Maybe the social worker is right."

"About what?"

"My insight porn addiction—reading and thinking about the sorts of things we read and think about—is harming me in the same way that drug addictions harm people."

"They think that?"

"Not in those words."

Tradition

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"It's really too bad—while I was in the psych ward, I missed out on my annual Super Bowl Sunday tradition."

"You have a Super Bowl tradition?"

"Not what you're thinking. Since 2008—well, not this year—I've made a point of reading something by Evelyn Fox Keller during the game."

"Awfully specific tradition. How did that happen?"

"On third February 2008, I worked a long closing shift at my job at the supermarket, and during my lunch, the game was on the television in the breakroom, and I sat there trying to ignore it, reading my copy of Reflections on Gender and Science. And, you know, I was really proud of that image—as a symbol of what I am, in contrast to what mainstream American culture expects men to be. So I read from the same book next year. And from Making Sense of Life and the Barbra McClintock biography and The Mirage of a Space Between Nature and Nurture on subsequent Super Bowl Sundays. I'm proud that I remember this, as opposed to remembering the games. Only it's funny."

"What?"

"That I should feel proud of being ignorant of something. Nerds being proud that they don't know what jocks know, and jocks being proud that they don't know what nerds know, are both expressions of the same underlying psychology, just anchored on different subcultures. If I really wanted to show what a special snowflake I am, I'd find some delightfully quirky way to break the symmetry."

Religious

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"Childlike ... or maybe religious. I've been part of this subculture where people spend a lot of time speculating about future machine superintelligences, and give credence to the idea that we're already living in a simulation. During my recent psychotic episode ... I don't want to go into the details of what I was thinking, but it was as if those ideas started hitting the God-shaped hole in my psychology really hard, a hole that I had previously managed to leave blissfully empty."

"'God-shaped hole'?"

"You know, like ... these ideas were tapping into the same flaws in primate psychology that make people fear God even though there's no evidence for one, and so I shouldn't blame the ideas for what happened to me, because someone from a different subculture but otherwise similar to me would have had a similar episode, except instead of science-fictional- and futurist-themed delusions, they'd be afraid of demons, or the CIA, or whatever."

"I know you said you don't want to talk about it, but could you give me an example of one of your delusions?"

"Like ... at some point I decided that there must be a conservation law constraining the net power of any optimization process to be zero, and that therefore everything good in life had to be paid for by something correspondingly bad, and that therefore I should be afraid to sleep because I would have horrible torture nightmares."

"What?"

"Yeah, I know. My friend Anna was able to talk me out of it by pointing out that most possible conservation laws are false. Like, conservation of blue: do blue things necessarily come from other blue things? Well, no: there are chemistry experiments where they combine two transparent liquids to make a liquid of a different color. But I'm worried."

"Worried how?"

"Worried about losing my mind for real. My mother's brother got a postmortem diagnosis of schizophrenia after suiciding. I'm pretty good at metacognition, mostly able to notice when my thoughts are failing checksums, sometimes able to correct for it with explicit Bayesian reasoning, of all things ... but for how long will that continue to be true?"

A Possible Future

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I just saw a film first conceived near the kiln
At the school by a woman called Nora,
Near the pots and the wheels near the streets near the fields
Filled with Santa Cruz fauna and flora.

The seat wasn't cheap, and the popcorn was stale,
And yet bumps on my arms fomed subtitles in Braille,
For this art was apart from all that I had seen,
As each line and each part and each act and each scene
Put soul to the surface, a window now cleaned
Or made silver, though only a screen.

And now cats in the street seem to meow as if pleased
By the film by the woman called Nora,
And I know it's just me, for the cats are just pleased
At a mouse that they've caught, or yet for a
Sense that they get from the footfalls that hit
On the ground from those leaving the theater?
Could cats know higher art from reactions they sense
In the human filmgoer or reader?

No—cats do not follow clues, so these mews know no Muse,
They are meaningless, yes, in the worst way ...
And yet—wish the artist happy birthday?

Childlike

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"I think the best term to describe how I feel is childlike. That also explains the delusions I was having: children can't tell the difference between fantasy and reality as adults judge such things, and neither can people having or immediately recovering from a psychotic episode."

"I wonder why it resolves itself so much more calmly in children."

"I've been taking the whole evolution thing much more seriously lately, so my guess is that children are 'supposed' to think like children, but when it happens in adults, it's a biological dysfunction. But, you know, the morally valuable kind of dysfunction, like exclusive homosexuality, not the kind of dysfunction everyone hates, like cancer."

Group Introduction

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"Hey, I'm Kevin. I'm a junior majoring in marketing. I live in San Leandro, and my favorite teacher was my high school English teacher Mr. Wheeler."

"Hi, I'm Jody. I'm a kineseology major in my fourth year, and I live in Daly City. And my favorite teacher's name is Kelly Schmidt."

"Why, hello there. My name is Zack M. Davis. As far as this whole 'college' business goes, I have accumulated ninety-four credits towards a Bachelor of Arts in mathematics. I live on an island of guesswork, storytelling, and noise, and my favorite teachers are grace, beauty, and the true structure of the world beneath the world."

Three Problems With Unsolicited Advice

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First, it's patronizing. The natural reaction of the one being advised is to feel indignant: how arrogant of someone to think that they know better than me how to run my own life! And so, whether the advice is good or not, the resentment of being talked down to is often enough to ensure that the advice will be ignored. Which isn't so bad, really, because—

Second, the advice is usually wrong. People don't know how much they don't know, but they think they know, and think they can help others by telling them what they think they know. It's tempting to think that once you've been told about this tendency, you can correct for it, and give genuinely good advice that takes into account what you don't know, but you're probably mistaken about that, because—

Third, telling people things mostly doesn't work. Natural language is the only means we have to communicate thoughts with each other, but it doesn't necessarily work very well on an absolute scale. You can try to sum over what you've experienced and package it in a few natural language sentences of advice, but the words are going to be interpreted in the context of the listener's experiences, not the context in which you generated them; it takes years of study and practice to transform verbal lessons into usable, actionable knowledge. Get what I'm saying? That's right: probably not.

Don't Try to Be Clever

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The great Brian Kernighan wrote, "Everyone knows that debugging is twice as hard as writing a program in the first place. So if you're as clever as you can be when you write it, how will you ever debug it?"

It's not just good advice for programmers. The same principle applies to any sort of planning and any sort of reasoning: the most intricate, sophisticated thoughts you can think, the thoughts at the very edge of your current abilities, are going to be less reliable than simpler thoughts that you can not only conceive of, but also understand in detail exactly why they're correct. Thus, insofar as you're thinking to achieve an outcome in the world, insofar as you actually care about your plan working, then (other things being equal) simple plans are preferable.

(On the other hand, if what you really want to do is show off how smart you are, then you should think and say complicated things. At the meta level, this is itself a simple plan, as contrasted to complicated and nonobvious schemes to achieve the outcome of looking smart.)

Identity Secrets

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"You know secrets."

"Do I?"

"For example, you possess the True Secret of What It Feels Like to Be You, except you'll never tell, due to the best secret-keeping method of all, far stronger than any vow or oath ... namely, the lack of a language in which this secret can be expressed."

"Yeah."

"Actually, no, come to think of it, we might already have cryptography better than that. Unraveling the secrets of how the brain generates subjective experience is a monstrously difficult cognitive science problem, but it doesn't provably require unphysically large amounts of computation."

Epiphenomenal Coordinates

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In the study of elementary linear algebra, unwary novices are often inclined to think of a vector as an ordered list of real numbers; to them, linear algebra is then conceived of as the study of multiplying matrices with column vectors. But this is a horribly impoverished perspective; we can do so much better for ourselves with a bit of abstraction and generality.

You can think of arrows or lists of numbers if you want or if you must, but the true, ultimate meaning of a vector space is ... well, anything that satisfies the vector space axioms. If you have things that you can "add" (meaning that we have an associative, commutative binary operation and we have inverse elements and an identity element with respect to this operation), and you can "multiply" these things by other things that come from a field (the "vectors" in the space and the "scalars" from the field play nicely together in a way that is distributive &c.), then these things you that you have are a vector space over that field, and any of the theorems that we prove about vector spaces in general apply in full force to the things you have, which don't have to be lists of real numbers; they could be matrices or polynomials or functions or whatever.

Okay, so it turns out that n-dimensional vector spaces are isomorphic to lists of n numbers (elements of the appropriate field), but that's not part of our fundamental notion of vectorness; it's something we can prove—

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Silent Theories

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"I like adherents of Ideology X; I really do. Wonderful people with noble goals. It's just genuinely hard to communicate with most of them, because I assign a fairly high probability to hypotheses that they consider unthinkable—not even that; the problem with unthinkable hypotheses is that you can't consider them."

Missing Books I

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Someone should write a combined novel/textbook about a mathematician-princess's quest to understand the true nature of continuity and change. When her father dies, she'll have the opportunity to be Queen regnant, but she'll quickly marry some guy instead so she can be a Queen consort and continue her research without being distracted with boring politics.