An Algorithmic Lucidity

"Don't worry, I'm sure it'll all go fine. Just be yourself."

"Of course. But ... how am I supposed to compute that?"

It turns out that I've been doing human psychology wrong, all wrong. My entire life, I've been modeling other people as defective versions of my model of myself, and I just didn't notice that that doesn't work. (Even though I was warned.)

"I miss being a human."

"You miss it? What do you think you are now?"

"A crude, slow, bug-ridden implementation of general intelligence patched into a human brain."

"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."

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.

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.)

"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."

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—

Let's say a set of \(n\) elements \(\{v_j\}_j\) from a vector space \(V\) span the space iff every element \(v\) in the space can be written as a linear combination of elements in the set: \(v = \sum_j c_j v_j\) for some coefficients \(c_j\). Let's also say that a set of vector space elements is linearly independent iff the only way a linear combination of them can be the zero vector is if all the coefficients are zero: \(\sum_j c_j v_j = \vec{0}\) implies \(\forall j\, c_j = 0\). We say a set is a basis if and only if it spans the space and is linearly independent. Bases are important because of the following

Theorem. Every element of a vector space can be written uniquely as a linear combination of basis elements.

Proof. Consider an arbitrary \(v\) in a vector space \(V\) with basis \(\{v_j\}_j\). Because a basis is a spanning set, it follows trivially that we can write \(v\) as a linear combination of basis elements, but we want to show that such a representation is unique. But uniqueness follows from the linear independence of the basis: suppose \(v = \sum_j c_j v_j\) and that \(v = \sum_j d_j v_j\). It turns out that the corresponding \(c\) and \(d\) coefficients have to be the same: \(\sum_j c_j v_j = \sum_j d_j v_j\) implies that \(\sum_j c_j v_j - d_j v_j\) equals the zero vector, which implies that \(\sum_j (c_j - d_j) v_j\) equals the zero vector, which (from linear independence) implies that \(\forall j\, c_j - d_j = 0\) and thus that \(\forall j\, c_j = d_j\), yielding uniqueness, which is what I've been trying to tell you this entire time.

Because (given a particular basis) we have a unique representation of every \(v\) as a linear combination of basis elements, we can use the coefficients of that linear combination as coodinates and treat the vector as a list of numbers ... but that's just our convenience; the coordinates with respect to a different basis would be different, and the vector itself simply is.

"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."

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.

"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!"

"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."

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.

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.

"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."

"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."

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.

Short-Term Career Objective: make money and help people by means of using computers to solve problems

Long-Term Career Objective: make lots of money and help people lots by means of wielding godlike mastery over computational existence to solve important problems

In computing, a fork bomb is a program that recursively spawns instances of itself, rapaciously capturing all available system resources. A similar sort of thing can happen, at least metaphorically, within a human mind, when you get so taken with a particular idea (I expect taken is the right word in more ways than one) that it consumes your conscious thoughts, the arguments and counterarguments and countercounterarguments bubbling up and expanding until you can't do or think about anything else. If that one idea is your lifework, then this is probably a good thing. But if not—if there's something more important you want to do with your life rather than obsess about this one idea—then the cacaphony of cognitive noise is a serious vulnerability, as fatal as entering ":(){ :|: & };:" at a Bash prompt.

Dear reader, you occasionally hear people with conservative tendencies complain that the problem with Society today is that people lack personal responsibility: that the young and the poor need to take charge of themselves and stop mooching off their parents or the government: to shut up, do their homework, and get a job. I lack any sort of conservative tendency and would never say that sort of thing, but I would endorse a related-but-quite-distinct concept that I want to refer to using the same phrase personal responsibility, as long as it's clear from context that I don't mean it in the traditional, conservative way.

The problem with the traditional sense of personal responsibility is that it's not personal; it's an attempt to shame people into doing what the extant social order expects of them. I'm aware that that kind of social pressure often does serve useful purposes—but I think it's possible to do better. The local authorities really don't know everything; the moral rules and social norms you were raised with can actually be mistaken in all sorts of disastrous ways that no one warned you about. So I think people should strive to take personal responsibility for their own affairs not as a burdensome duty to Society, but because it will actually result in better outcomes, both for the individual in question, and for Society.

To the extent that good things actually get done in the world, it's almost always because somewhere along the line, a human mind designed that outcome. Valuable things typically don't grow on trees; fruit does, but in our modern civilization, it's because someone decided to plant that tree there, because a mind (not necessarily consciously, and not necessarily wisely, but all the same) generated a number possible plans, guessed at the probable consequences, and selected one to make real.

If you've been raised to believe that morality consists of obeying your parents or employers or schoolteachers, then it might seem like you don't have the right to make decisions, that decisionmaking (if it happens at all) is something done by committees of distant authority figures, not ordinary people like you, or that your right to decide things comes exclusively in the form of your right to vote, or buy consumer goods, or enroll in school courses. But it's not true; it can't be true; life itself does not emanate outwards from Washington or Wall Street or the Dean's office; with every thought and every breath, you are (implicitly, whether you realize it or not) controlling the tiny fragment of the world which is you, exerting an influence (however faint, however unpredictable) over the history of the universe outward and futureward from that tiny fragment.

Dear reader, I would not be so foolish as to advise you what you should do with this power, because I don't know anything about you or what situation you're in. I can't pretend to know what you should say or do, nor whom you should help, hurt, ignore, obey, or command. I just want to mention—because I wish someone had told me in so many words, this truth which still takes me an intense effort to keep salient—that it is a choice, that it is a responsibility. Not a responsibility to Society, or the moral law, or even to yourself. A responsibility over the outcome, whatever you make of that, or it.