Monthly Archives: January 2013

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.

Concreteness

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"I'm not sure that I'm happy that concrete is used as a sort of metonym for anything definite and fixed; there are lots of other hard substances, too, like diamond, steel, or topaz."

"Concrete spends part of its life as a fluid."

"Oh, so it is actually especially good as a verb, concretize or to make concrete, because you're 'hardening' something that previously was not. Thanks!"

Humans Are Mysterious

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"You are mysterious."

"What, really?"

"Well, I can talk with you and guess what you're really like, but that's just me making inferences from your behavior; I could easily be horribly, horribly confused and wrong."

"So I'm not, like, unusually mysterious?"

"No, just ordinarily mysterious. That's still a huge amount of mystery. This is easier to notice when you have first-hand experience of being horribly, horribly confused and wrong about yourself."

Education and Indoctrination Feel the Same From the Inside

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They have to. The psychology of what it feels like to learn something from a book is going to be the same whether or not the things the book says are actually true. The psychology of what it feels like to believe the things your teacher tells you and your peers repeat is going to be the same whether or not the things your teacher says are true. You can't just trust the book or the teacher, you have to use whatever other information you have (from observation and experience, from other books, from other teachers) about the reliability of the processes that produced the book, the reliability of your teacher to have done this same kind of thinking.

After an Epiphany

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I've been so confused in so many ways that I had been specifically warned against dozens of times, in writing and in person, and I still didn't get it! Of course, I was warned about this, too: everyone knows that there are things you don't know that you don't know, and that there's a difference between endorsing a proposition, and integrating its implications into your way of thinking. But it's still such a shock to actually see ... to go so suddenly from hating the local Authorities for not telling you all the true and important things that your friends have been telling you, to noticing that the things that your friends have been telling you can actually be applied to stop being so hurt all the time about how the local Authorities had misled you.

Clearness

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"I somehow feel less bitter today."

"Yay!"

"Naturalistic explanations feel better than hatred; I don't feel outraged and betrayed that Safeway is not a Sacred Shining Beacon of Goodness and Food Provision unto the world or that Goldman Sachs is not a Sacred Shining Beacon of Goodness and Efficient Capital Allocation, so I shouldn't feel outraged and betrayed that college isn't a Sacred Shining Beacon of Goodness and True Education."

"Uh-huh."

"Even when Goldman Sachs causes a global financial system meltdown, I don't say, 'And that's why capitalism is Evil forever!'"

"Yes."

"Alternatively and isomorphically, maybe I should start saying—calmly, without malice or outrage, but just as a fact—that capitalism is Evil forever, with the caveat that I don't actually know how to fix anything myself."

"Why would you bother?"

"Because the insight that our current forms of social organization can't be the best possible, that you're actually allowed to think about them, even if innovations that actually work are hard, is really important and worth emphasizing and communicating. Because if you don't know and you don't think, you just get sucked in by whatever memetic attractor happens to be nearby, which is always suboptimal and often quite bad. I mean, you still get sucked in by whatever attractor happens to be nearby, by definition really, but it's nice to have some inkling of what's happening to you."

Hustle

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"I'm entertaining this daydream of standing in a coffeeshop with a sign saying, 'BUSINESSPEOPLE: TELL ME ABOUT YOUR PROBLEMS; I WILL BUY YOU COFFEE' in the hopes that some of their pain points could be easily solved in software for money. I don't know if this would actually work."

"That sounds inexpensive and high-upside. Do it. If it's boring, stop."

"Not right now; I'm still on Father's dole for another year, which is fine. I'm just musing on the principle of Make Something People Want as opposed to 'get a job.'"

"Why not right now? You are allowed to cut yourself off the dole if you find something else."

"I agree that it's important to appreciate that such things are allowed, but note that the amount that I complain about my social position is more reflective of ideologically-induced madness rather than actual preferences; I really do like having time to study. My constant petulance is a distortion, a mistake."

"Ah."

Mode Lock

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I'm afraid—it seems like (or maybe the weak phrasing seems like is just a form of denial, when the proposition under consideration should actually just be considered obvious) there's this terrible, terrible psychological trade-off, that there are some valuable qualities that you can't have without neglecting other valuable qualities, not just because you don't have enough time to fully develop too many different skills, but because when your brain is specialized in one direction, there are other things you can't learn.

Oftentimes I feel like I don't want or know how to do anything except read and think ... which might be fine if I were independently wealthy and there wasn't any actual work left to do in the world, but in our current situation, it would be nice to make some money and actually accomplish something. There's a Trope for "Shapeshifter Mode Lock" but the cognitive equivalent is arguably more serious as disabilities go.