a blog
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.
I keep feeling like I need to study Bayes nets in order to clarify my thinking about society. (This is probably not standard advice given to aspiring young sociologists, but I'm trying not to care about that.) Ordinary political speech is full of claims about causality ("Policy X causes Y, which is bad!" "Of course Y is bad, but don't you see?—the real cause of Y is Z, and if you hadn't been brainwashed by the System, you'd see that!"), but human intuitions about causality are probably confused (and would be clarified by Pearl) much like our intuitions about evidence are confused (and are clarified by Bayes).
Almost every policy proposal is, implicitly, a counterfactual conditional. "We need to implement Policy A in order to protect B" means that if Policy A were implemented, then it would have beneficial effects on B. But most people with policy opinions aren't actually in a position to implement the changes they talk about. Insofar as you construe the function of thought as to select actions in order to optimize the world with respect to some preference ordering, having passionate opinions about issues you can't affect is kind of puzzling. In a small group, an individual voice can change the outcome: if I argue that our party of five should dine at this restaurant rather than that one, then my voice may well carry the day. But people often argue about priorities for an entire country of millions of people, vast and diverse beyond any individual's comprehension! What's that about?
(To be sure, you can come up with reasonable arguments why someone should concern themselves with large-scale politics: every collective effort requires the actions of many, so one might cooperate with a group rather than defect, precisely because bad things would happen if everyone defected; or, maybe some particular individual is exceptionally well-positioned to make a difference through their own actions; or, a tiny probability of having a large effect might be worthwhile in expectation; or, ... &c. Whether or not these are good arguments, I don't think they're an adequate explanation of what's actually going on inside most people's heads.)
I often find myself feeling angry and upset that the mainstream society around me doesn't reflect my values; I spend hours composing rhetoric and slogans about how our dominant forms of social organization are systematically flawed in knowable ways. I imagine the world being different—and only in brief moments of lucidity do I realize that what I'm doing is daydreaming, fantasizing. Thinking about social change doesn't feel like a mere fantasy in the way that thinking about how great it would be to have magical superpowers is obviously fantasy, but it is: thinking about good outcomes in the absence of actual planning about how to achieve those outcomes from the present state is wasted cognition except insofar as the thinking-about-good-outcomes is valuable for its own sake. Fantasy is a fine thing in moderation; it's not being able to reliably tell the difference between fantasy and reality that's dangerous. In the case of magical superpowers, the difference is obvious. In the case of the mainstream magically adopting my priorities, it's somehow not obvious; somehow I find it hard to stop thinking about worlds that are not my own. Why?
It's easy to tell an evolutionary psychology just-so story: precisely because arguing about politics actually is important in small groups like the ones our ancestors lived in during the environment of evolutionary adaptedness, I can't bring my brain to notice that things don't work the same way when you're one voice among three-times-ten-to-the-eighth. Whereas obviously-fantastical fantasy is just wireheading in the sense that it's a byproduct of imagination and preferring-certain-experiences, both of which are adaptive in themselves, but which together result in non-adaptive daydreaming; since this has a different etiology than political daydreaming, it's not surprising that it would have a different character ...
But that's just a story I made up; I'm not claiming it's actually true; most of the stories people make up aren't actually true.
Loopy is slang for "crazy", but I think it should be repurposed to refer to the quality of thinking the same sorts of thoughts over and over again, never breaking patterns, being stuck indefinitely at the same stage of intellectual development. You could argue that this is a form of craziness compared how an ideal agent would allocate cognitive resources, but I think it's pretty normal and common in our world, not the kind of craziness generally recognized as crazy.
Of course, the traditional beverage of Newtonmas is bleggnog.
I'm not sure I like how when we want to prove that two statements are equivalent, we typically say "A if and only if B" and we prove it by separately proving "both directions" A ⇒ B and B ⇒ A, but when we want to prove three or more statements are equivalent, we typically say "The following are equivalent" and prove a "circular chain" of conditionals (1) ⇒ (2) ⇒ [...] ⇒ (n) ⇒ (1), as if these were different proof strategies. Because really, the "both directions" business is just a special case of the chain-of-conditionals idea: (1) ⇒ (2) ⇒ (1). At the very least, one of my books ought to have mentioned this.
Maybe self-esteem makes sense for deontologists who think that being a good person is a matter of obeying some knowable set of rules, but I think that the goodness of a person is a real number, probably bounded but with no known upper bound. Saying "I'm a good enough person just the way I am; I deserve self-esteem" isn't bad so much as it is meaningless: once you know what you've done and how close the results were to (your current estimate of) what the results should have been, then there's nothing left to describe, no further question to be answered.
We need a word that means almost the same thing as sellout (in the sense of "a person who compromises their principles for financial gain"), but conveys the idea that the problem is not selling out, but selling out for too low of a price. We all have to make trade-offs; there isn't any one principle that takes lexical priority over every other valuable thing in life: sometimes it makes sense to compromise your ideals in exchange for money or power or fame or fitting in.
But you could at least haggle!
"Some of my Facebook 'friends'—that is, distant acquaintances—are political radicals: here's a picture of the words 'KILL COPS' spraypainted on the ground, with five 'Likes.' It would be psychologically interesting to know what that feels like."
"Huh."
"'Weird' really isn't as useful of a category as I typically think it is. These radicals are outcasts from the society that they want to remake, whereas lots of people in our crowd have mainstream jobs and power. And yet I'm usually inclined to think of us as 'weirder,' because destroying capitalism and the corporate state is comparatively easier to explain."
"Is it more common?"
"That probably depends on exactly where we draw the boundaries around social circles? Our group of core supporters is tiny, but the group of people who've read Ray Kurzweil and approved is pretty big. And no doubt I don't have a good model of what the smartest and most serious radicals believe, just as they have no idea what we believe."
"Yeah."
"Smashing capitalism also looks more straightforward; it's not clear what a transhumanist analogue of the Occupy movement would do exactly. 'Let's all go spend eight years studying bioinformatics! Death to itself!'"
If you shouldn't make lemonade, then life hasn't given you lemons.
Do you ever have trouble reconciling your social role of "ordinary college student at a mediocre state university" with your secret identity as junior member of an elite conspiracy to take over the world?
Yeah, me neither.
"But it's kind of funny how my current idea of morality is so different and so much improved from what I picked up in childhood."
"Is it?"
"Well, funny is the wrong word; maybe it's better to say notable when what I really want is just to note it, just to make it salient, maybe eventually salient enough such that I can actually start to be moral for once, instead of continuing to sit and cry about how I was betrayed."
For five years I've known that at some point I need to stop shouting, "the Authorities lied to me; why why why why did they lie to me?!" and start saying, "Okay, so extant social institutions are flawed in knowable ways, and my parents and teachers didn't tell me. Given my current state of information, this shouldn't actually be surprising, so let's stop crying about it and get on with the whole world optimization thing."
But I don't know how to make the switch; after five years, I still don't know how to break clean. It's so much easier to wallow in the pain. Maybe some amount of wallowing was even justified, this time five years ago. But now, I clearly have much better things to do with my life.
Hard Truths from Soft Cats opines that
Your flaws don't make you beautiful or unique. They make you flawed.
While I agree re beauty, technically, your flaws actually do make you unique: the number of ways in which one can be flawed is vastly larger than the number of ways in which one can be perfect; the probability that someone else would turn out to be damaged in exactly the same way you are, is negligible.
It's just that uniqueness is overrated.
The other day while rehearsing my arguments about how currently-existing social institutions are obviously insane, it became more salient that there's also no clear way to fix anything on a large scale. My perspective on How to Do Things Better is the idiosyncratic result of five years of my thinking; even if my vision is in the 99th percentile of Arbitrary People's Idiosyncratic Visions of How to Do Things Better (and everyone thinks that about herself, so don't take my word for it), it's not very transferable.
ur gr(8+ε) for arbitrary ε > 0
I think there needs to be a movie about a woman who has two jobs: artificial general intelligence programmer by day, prostitute by night. I say this mostly because I have a great idea for the tagline to go on the posters: "The oldest profession ... and the last."
What makes a true story inspirational? I think people usually use that word to describe happy stories, stories that make us think that the world is a better place than we previously thought. But sometimes I want to use it to describe sad stories that remind us that the world is far worse than just the parts of it we're used to seeing firsthand, stories about innocent people being hurt by arbitrary causes. It's inspirational in the sense of a call to action, a reminder that there's still important work to be done in the world: I can't solve this particular problem, but there's a reference class of people containing me (reasonably intelligent, reasonably ambitious people, striving to become more effective) who can help fix a reference class of problems including this one—and that is a sacred responsibility that must not be betrayed. Or however you translate folderol like "sacred responsibility" and "must not be betrayed" into something more basic (Bayes-ic?).
There are a lot of really important concepts that aren't easy to talk about, because we don't have standard words for them.
Like, there needs to be a word designating the skill or quality of possessing independent judgement—the ability to make decisions without getting distracted worrying about how to explain yourself to people who won't understand. Part of me wants to just call it sociopathy, but that's clearly not the right word.
The problem is endemic. Friend of the blog Mike Blume once lamented that we don't have a gender-neutral equivalent of gentlemanly. And we don't have an atheist equivalent of doing God's work, either.
Shut up! Shut up and leave me alone with my books!
Dear [name redacted]:
So, I'm trying (mostly unsuccessfully) to stop being bitter, because I'm powerless to change anything, and so being bitter is a waste of time when I could be doing something useful instead, but I still don't understand how a good person like you can actually think our so-called educational system is actually a good idea. I can totally understand being practical and choosing to work within the system because it's all we've got; there's nothing wrong with selling out as long as you get a good price. If you think you're actually helping your students become better thinkers and writers, then that's great, and you should be praised for having more patience than me. But I don't understand how you can unambiguously say that this gargantuan soul-destroying engine of mediocrity deserves more tax money without at least displaying a little bit of uncertainty!
You said in a previous message that a lot of your students are sheep-like, that they'll never do anything valuable that they're not told to do—but doesn't it seem likely that the system's bureaucratic, anti-intellectual, anti-curiosity culture of death has made them that way? I'm finishing my math degree at SF State (because I'm a coward, because people expect it, because my father is paying tuition and it's easier than getting a real job), and trying to talk to my fellow "math majors" is a source of constant heartbreak, because as far as I can tell, it has never occurred to most of them that knowledge and skills are useful for anything other than pleasing local authority figures. You try to tell them about some new idea you've been working on (see my posts at http://zackmdavis.net/blog/category/mathematics/ for examples of the sorts of things math people think about), and they just stare at you blankly and say, "What class is this for?"
You can't think of a polite answer to that, so you say to them: "Well, what have you been thinking about lately?"
Another blank stare. "Nothing."
"Well, what have you been doing, then? "
"Homework."
"Okay, but presumably the homework was about something ..."
"Calculus three."
"But what particular topi—you know, with respect, I don't think you understand what I'm trying to do here."
Quite often, to my horror (but not shock), it turns out that my interlocutor is planning on becoming a high-school teacher.
But people have been complaining about the incompetence and bad morals of youth for millennia—that's nothing new. Surely at least the University itself is designed to help young minds aspiring to something greater than earning a goddamned piece of paper?
Well, no. They don't give a fuck. They don't even pretend to give a fuck. (Individual professors are wonderful people, but you can't just directly pay them for tutoring; everything goes through the institution.) Earlier this year, after having wasted two years taking mostly worthless so-called "general education" classes at Diablo Valley College (including one in which we spent two class periods watching The Wizard of Oz, including one in which we were instructed to use colored pencils to indicate on a map which states belonged to the Union and which to the Confederacy), it seemed clear to me that the next step in my mathematical development was to study real analysis—the rigorous underpinnings of the differential and integral calculus which all educated people are familiar with. (Right?) But there's a mandatory prerequisite. I asked if I could take the prerequisite course concurrently with real analysis. Two different professors told me that I could not. I emailed the professor scheduled to teach real analysis, attaching a little paper I had written (admittedly rather trivial, but not bad for a mere undergraduate, I thought) about analogues of pi in the \(L^p\) spaces over \(\mathbb{R}^n\). I did not receive a reply.
Oh, well, I thought, my proof skills aren't actually that great; maybe it's for the best. I show up to the prerequisite class, and what's the first topic? Basic propositional logic, something I have known for five years. What's the last topic, in these final weeks of the course? The uncountability of the reals, something I have known for six years. And I am expected to sit there and obey, even though it is completely obvious to everyone in the room that I am not drawn from the same distribution as the other students, because large hierarchical organizations are structurally incapable of nurturing individual minds; all they can do is shove people around and treat them as fungible cogs.
And this is what passes for "education"? This is the system that everyone has to go through in order to be respected as "college educated"? This is the beneficiary of the endless stream of blatantly self-serving propaganda I had to endure this fall (on Facebook, on campus), which the voters (most of whom are monstrous hypocrites who have never voluntarily picked up a textbook in their entire lives) actually fell for, raising California's already-high taxes even more, and for what? Taxes are great if they're being used for something that will actually help people, like roads or libraries or a guaranteed minimum income—but to have this hugely expensive system just to pointlessly boss around young adults who (presumably) already know how to read? Pardon me while I puke, [name redacted].
I realize that I'm being a complete jerk to you by actually sending this [n.b., I did not actually send it]; you have no reason to bother enduring such a bitter screed from one of your former students [...] But, you know—it was only by the sheer luck of happening to read the right blog at the right time that I managed to avoid being permanently intellectually crippled by this credential-mad society, and sometimes, in a moment of pain, I actually feel entitled to be angry. Terribly selfish, I know. Am I morally justified in sending this to you, who have nothing but good intentions? Is it right for me to complain about something so trivial as sitting through a few classes, when I'm so incredibly privileged in so many other ways? Probably not; I think I'm just being a villain. But you know, I'm really not sure I care about that anymore. Really, I need to learn the skill of not paying any attention to mainstream society. My plan is to keep studying and hopefully (and finally, after having wasted so much time) make some money writing software that will actually help people. If the entire civilized world considers it their duty to crush all intellectual initiative out of its children, then it's really not my business. I wish you well, and hope that [names redacted] are also well, and I remain,
Faithfully yours,
Zack M. Davis
Say we have a linear transformation \(A\) and some nonzero vector \(\vec{v}\), and suppose that \(A\vec{v} = \lambda\vec{v}\) for some scalar λ. This is a very special situation; we say that λ is an eigenvalue of A corresponding to the eigenvector \(\vec{v}\).
How can we find eigenvalues? Here's one criterion. If \(A\vec{v} = \lambda\vec{v}\) for some unknown λ, we at least know that \(A\vec{v} - \lambda\vec{v}\) equals the zero vector, which implies that the linear transformation \((A - \lambda I)\) maps \(\vec{v}\) to zero. If \((A - \lambda I)\) maps \(\vec{v}\) to zero, then it must have a nontrivial kernel, which is to say that it can't be invertible, and this happens exactly when its determinant is zero, because the determinant measures how the linear transformation distorts (signed) areas (volumes, 4-hypervolumes, &c.), so if the determinant is zero, it means you've lost a dimension; the space has been smashed infinitely thin. But \(\det(A - \lambda I)\) is a polynomial in λ, and so the roots of that polynomial are exactly the eigenvalues of \(A\).
I agree that it would be wildly out of character to learn JavaScript before Haskell, but life is not a story.
"Gee, Brain, what do you want to do tonight?"
"The same thing we do every night, Pinky—the Right Thing to Do Given Current Info and Preferences!"