jsomers.net

Last call

Sun, 07 Mar 2009 16:51:00 GMT

According to my logs there are 18 people still subscribed to this feed. I have moved, though, so please subscribe to the new feed; all you have to do is click here (and click "Subscribe Now" or whatever). Thanks!

Moved

Sat, 28 Feb 2009 13:22:00 GMT

I have moved to an actual blogging engine, because maintaining this feed without one became too much of a hassle. Please subscribe to the new RSS feed at http://jsomers.net/blog.

A Defense of Philosophy (Against Paul Graham)

Mon, 15 Dec 2008 14:22:00 GMT

1. PG's project

In How to Do Philosophy, Paul Graham claims that "judging from their works, most philosophers up to the present have been wasting their time." His point is that philosophy per se is structurally flawed. How?

The trouble began with Aristotle: "he sets as his goal in the Metaphysics the exploration of knowledge that has no practical use. Which means no alarms go off when he takes on grand but vaguely understood questions and ends up getting lost in a sea of words." In other words, because philosophy aims at the most general truths without worrying about how useful they are, it's able to get away with nonsense. Other fields, by contrast, only seek ideas with some practical value---ideas that make it easier to do something useful; if they arrive at general truths, it's only because abstraction usually works: it buys you simpler theories and makes your algorithms faster.

So whatever "philosophy" we're after, PG says, we should get from able specialist non-philosophers who work their way up chains of abstraction until what they know is general enough to apply elsewhere. That way we guarantee (a) that it's useful, since specialist non-philosophers favor the more useful of two rivals, ceteris paribus, and (b) that it's easy to understand, since specialist non-philosophers don't have time for difficult texts (because they are less useful, in general, than easy ones).

2. Something's rotten in the state of Denmark

The simplest flaw in PG's account is its scope: it implicates most philosophers up to the present, which means all one has to do to rebut it is point to a few groups of contemporary philosophers who systematically aren't wasting their time. I take up that task in the next two sections.

This is not to elide the indirect influence, however, of even those thinkers---Kant, for instance---most susceptible to PG's attack. That influence, I'll argue in section 5, should give their critics pause.

Finally, I will defend the value of "doing philosophy"---an argument that I do not think is "like someone in 1500 looking at the lack of results achieved by alchemy and saying its value was as a process," however similar it may sound.

3. Don't mind us philosophers... of mind

What would we lose if, of the 18,460 papers at MindPapers, a "bibliography of the philosophy of mind and the science of consciousness," we removed the 12,500 or so written by philosophers? Let's take a look at the top 100 most cited works for an idea.

The first to go would be Jerry Fodor's 1983 The Modularity of Mind, in which he revived an idea that phrenologists once took for granted, albeit in a perverted form: "that many fundamentally different kinds of psychological mechanisms must be postulated in order to explain the facts of mental life." He argues, in other words, that for our mind to work the way it does there must be vertically integrated components (modules) in our brain---like the "universal grammar" faculty proposed by Chomsky. Fodor's paper cleared up a lot of conceptual misunderstandings, generated testable predictions, and set the stage for decades of cognitive science that has (largely) borne out his view.

We would also lose John Searle's 1980 Minds, brains, and programs, which gave a negative answer to Turing's question, "Can machines think?" As support he introduced his famous Chinese Room thought experiment, which apparently defeats a functional account of intelligence by demonstrating that if understanding Chinese were an algorithm merely "run" on one's brain, then it could be run in similar fashion by a man in a room shuffling about slips of paper; would we then say that the man, or for that matter the room, understands Chinese? If not, then machines can never understand the way that we do---there is something special (he called it "causal power") about our brains.

Searle's paper is important because if he's right then a whole lot of AI researchers trying to make computer programs with "general intelligence" ought to move on to something else. If wrong, then we ought to figure out how he's wrong---because that will be the secret to making machines think the way we do.

We would lose Thomas Nagel's 1974 exploration and articulation of phenomenal experience, What is it like to be a bat?; Daniel Dennett's The Intentional Stance, and all its elegant abstractions; Andy Clark's (and Rodney Brooks's) idea that our minds are fundamentally embedded in the world, and that our inner model of our environment is far sparser than once thought---articulated recently in Being There: Putting Brain, Body, and World Together Again; etc.

What's more, we would lose thousands of articles that clear the ground for, inform, or integrate findings across the brain sciences. Ned Block's influential review, Philosophical issues about consciousness, is a nice recent example.

Perhaps the scariest omission would be the work of one of my intellectual heroes, Douglas Hofstadter. The little-known computer programs produced under his watch by FARG at Indiana---Metacat or Letter Spirit---could stay, and so could his 1976 "Energy levels and wave functions of Bloch electrons in rational and irrational magnetic fields," but Godel, Escher, Bach: An Eternal Golden Braid would have to go: it is too much a search for the most general truths, not enough a work of original, concrete research; there is too much unconstrained philosophizing in there.

If that idea seems troublesome, to keep only some of Hofstadter's work while throwing out the rest (the far more influential stuff, no less), then you have probably begun to appreciate the special relationship between contemporary philosophy of mind and "hard" cognitive science---they are of one mind, sometimes literally. Divorcing the two would probably hurt them both.

What language game?

PG argues that philosophy is, at bottom, a "language-game" in the Wittgensteinian sense. Here's how he puts it:

There are things I know I learned from studying philosophy. The most dramatic I learned immediately, in the first semester of freshman year, in a class taught by Sydney Shoemaker. I learned that I don't exist. I am (and you are) a collection of cells that lurches around driven by various forces, and calls itself I. But there's no central, indivisible thing that your identity goes with. You could conceivably lose half your brain and live. Which means your brain could conceivably be split into two halves and each transplanted into different bodies. Imagine waking up after such an operation. You have to imagine being two people.

The real lesson here is that the concepts we use in everyday life are fuzzy, and break down if pushed too hard.

This is why, apparently, philosophy ends up looking like a "word salad," like a "garbled message"---"hard to understand because the writer was unclear in his own mind" and not "because the ideas it represents are hard to understand."

My response is twofold. For one, the split brain example he gives is, at bottom, about the word "I." Fine. But once you know what the word "I" actually means, you have not just learned that your everyday concept was fuzzy, that it breaks down when you push it too hard---you've developed a richer model of the self, (hopefully) including all of the complicated neural, computational, and functional details.

Thus a petty semantic question---what is the meaning of the word "I"?---can open up a deeper line of inquiry: how do we form an integrated sense of self, why do we even have a word like "I," when our brain is apparently just a soup of meaningless symbols? That is a question that, once articulated properly, can be explored by philosophers and scientists alike. (See Hofstadter's "Who Shoves Whom Around Inside the Careenium?, or, The Meaning of the Word 'I'" for one such exploration.)

This kind of thing happens all over the place. Philosophical debates about "metaphysical necessity" sure sound like wasteful bickering over the names of things, until a murder trial turns on whether someone "could have possibly acted differently"; ethicists may seem like they're in the clouds, except when one of their moral frameworks gets written into a country's constitution; Hilary Putnam's famous paper, The Meaning of "Meaning", feels hopelessly out of touch with reality---we all get along just fine without knowing the first thing about "intension" or "extension"---but it raises questions that figure deeply in language learning and AI. And so on.

It's easy to say that philosophy is one big conversation about the color of the bikeshed. What that misses, though, is that the right question asked in the right way can cause a paradigm shift (a term due, incidentally, to a philosopher):

"What is the meaning of the word 'I'?"
"How can someone ever cross a room?"
"Can machines think?"
"Are meanings in the head?"
"Is the mind organized horizontally or vertically?"
"What constitutes moral responsibility?"
"Are mathematical objects real?"
"Is the mind a blank slate?"
"Do macroscopic objects actually exist?"
"Is the accused to be presumed innocent, or guilty?"

That last one brings me to a brief aside: nearly every legal opinion I've ever read had some linguistic issue at its core. Example: should the blotter paper used to drop acid be counted in its weight, which determines the length of mandatory sentences? The argument comes down to the phrase "mixture or substance containing a detectable amount" (see Chapman v. United States, 500 U.S. 453). Point being, wresting imprecise words out of their natural context and plugging them into a perverted formalism is the law as we know it---it's practically the whole game. We don't attack it, though, because we know that their "language-games" help to draw increasingly fine lines around difficult ideas---to, as it were, measure the coast of Britain. I think the same should be said of philosophy.

My second objection to PG's "word salad" comment is more straightforward: most contemporary philosophers of mind do write well. So well, in fact, that I think one can become a better writer just by reading them. They know their Strunk & White and most would probably appreciate PG's aesthetic. See Eric Lormand's But Momma Never Told Me about Philosophy Papers for evidence (or just look at any of the papers mentioned above).

4. Problematizing a purely syntagmatic critique of postmodern critical theory

PG's biggest enemy here, besides the ancient philosophers, seems to be postmodern critical theorists. Example:

The field of philosophy is still shaken from the fright Wittgenstein gave it. [13] Later in life he spent a lot of time talking about how words worked. Since that seems to be allowed, that's what a lot of philosophers do now. Meanwhile, sensing a vacuum in the metaphysical speculation department, the people who used to do literary criticism have been edging Kantward, under new names like "literary theory," "critical theory," and when they're feeling ambitious, plain "theory." The writing is the familiar word salad:

Gender is not like some of the other grammatical modes which express precisely a mode of conception without any reality that corresponds to the conceptual mode, and consequently do not express precisely something in reality by which the intellect could be moved to conceive a thing the way it does, even where that motive is not something in the thing as such. [14]

Elsewhere, on his Quotes page, we find another jab:

"Simultaneously reifying and challenging hegemonic codes of race, class, gender and regional or national identity, his characters explore the complex and changing postmodern cultural landscape."

Robert Bennett, English professor at Montana State, announcing a panel discussion about Brad Pitt

To a certain extent I'm on board. Bennett's sentence is incredibly vague (though I imagine part of that is just being in an introduction). And I find a lot of the writing done by postmodern critical theorists to be obfuscatory bullshit. This is not to say, however, that all of it is. Nor that if someone writes like an idiot then what they're saying must be fundamentally unimportant in the same way that Kant's musings may have been fundamentally unimportant (more on that later).

I can't help but think that PG is taking a line that a lot of people take, which is to laugh at how these lefty hipster professors put on such a show for something as trivial as Brad Pitt. The idea is that something like "Every connected, locally compact, non trivial group has a non trivial, closed, invariant subgroup" from a math exam is completely unilluminating, but at least we go in expecting not to understand anything; we assume the stuff is way beyond us. But with cultural theory, postmodern theory, etc., the lay reader expects to be able to talk about things like "culture," "literature," and "Brad Pitt" at a pretty high level. So when they see technical phraseology---"complexly situation within", "mutual historicization of", "theorizing the subject", etc.---they can't help but feel hoodwinked, as if something that's supposed to be understandable has been made needlessly complex.

But if we take the operations of language and culture to be as complicated as any other object of study, and if we allow that certain professionals within the field want to use shared tokens (e.g. "historicization") to collapse complex ideas that show up all over their literature, then we can begin to understand why this stuff sounds the way it does. They're not writing for every Joe Intellectual, just for the people who put the time in to be part of their club.

Compare, for the sake of illustration, two definitions of Stokes' Theorem. One is for a more general audience, like Calc II or first-year physics students:

The curl theorem states

The other, of which the first is just a special case, is for mathematicians:

Let M be an oriented smooth manifold of dimension n and let α be an n-differential form that is compactly supported on M. The integral of α over M is defined as follows: Let {f_i} be a partition of unity associated with a locally finite cover {U_i} of (consistently oriented) coordinate neighborhoods...

The analogy back to critical theory should be apparent. On one level you have concrete, special cases with correspondingly concrete writing. This seems to be the level that PG would be interested in, if any. To get access to it you can look at magazine covers critically, or remark on the homosexual tension in Fight Club, or read something like Introducing Postmodernism or this incisive essay on television and U.S. fiction by David Foster Wallace, who intentionally eschews the standard vocabulary.

On another level is the "deeper" theory or more general framework. A conversation on this level, if you're an outsider, sounds like two people talking about Starcraft if you've never played. But there is more content here, too, just as there's more content in the second formulation above. Perhaps the ratio between the two levels is tighter in critical theory, but I suspect it's far greater than PG thinks.

I say that because I also had strong misgivings about the subject---for its insuperable tomes, hipster followers, and radical political agenda---before finally easing into it via writers like Richard Dyer, Patsy Yeager, Simon Gikandi, and Fredric Jameson. I took a class on culture theory with a professor who found herself "increasingly irritated by the French philosophers," and whose reading selections were recent and down-to-earth; Dani Cavallaro's Critical and Cultural Theory was a fine textbook. After a bit of training, sentences that I once found unreadable (e.g. Foucault's or Barthes's) became just as crisp and insightful as PG's best. I had only to learn the language.

I'm reminded of how chess experts can recall legal board positions with far greater fidelity than someone who doesn't play, but perform about equally when the pieces are arranged in ways they'd never see in a real game. The difference, of course, is that a legal board position means a lot more to the expert than to the lay person---he can consider strategic features like "pawn strength" and "control of the center," and think of scenarios ("Sicilian opening with a queen's gambit") that he's encountered before---whereas a jumble of pieces reduces them both to rote memorization. My point is that if a work of critical theory looks like a "garbled message," it could be that it really is garbled (e.g. Derrida), or it could be that one simply hasn't read enough of the stuff to know.

Good ideas

I fear that I've spent too much of my defense on the language of critical theory and not enough on the actual ideas. But I think that PG attacks these guys because of the language, and could---for all I know---not give a hoot about what they're actually saying. In case that's happened, here are some of their good ideas off the top of my head:

All language is political; capitalism-as-market-system is tremendously good, but capitalism-as-defining-roles-in-terms-of-production is dangerous; there is a causal connection between Cosmopolitan and increased labioplasty among 14 year-olds; the simulacrum; the panopticon; art once made the strange familiar, and now it makes the familiar strange; gays appropriated "queer" and largely defused it---could "nigger" be defused, and how?; television uses self-aware irony to swallow attacks leveled against it; the medium is the message; photography is a special kind of representation because it feels objective; if you don't think Aladdin is racist, then your working definition of "racist" is inadequate; etc.

These are the kind of ideas that satisfy PG's criterion: they "would cause someone who understood them to do something differently."

Interlude: PG and brevity

I think it's worth commenting on PG's apparent preoccupation with brevity. See, for example, his handle (pg), the URLs on paulgraham.com, his comments on writing, and these excerpts from a few of his essays:

One thing hackers like is brevity. Hackers are lazy, in the same way that mathematicians and modernist architects are lazy: they hate anything extraneous.

and

[on developing Arc:] I didn't decide what problems to work on based on how hard they were. Instead I used what might seem a rather mundane test: I worked on things that would make programs shorter.

Why would I do that? Because making programs short is what high level languages are for. It may not be 100% accurate to say the power of a programming language is in inverse proportion to the length of programs written in it, but it's damned close.

I bring it up because I think he may occasionally make sacrifices in the service of his aesthetic. He may elide the complexities of an argument---saying "most philosophers" instead of singling out specific people or schools of thought---to make sure an essay reads well. Or he may ignore what you're saying if you say it poorly, like if you're a critical theorist.

The curious thing about PG's writing is that every sentence sounds... not dispassionate, but not emphatic, either. There are no vicissitudes of character, there is no modulating voice that rises with the important bits and falls with the bits it's not so sure about. There is just a monotone that declares, sentence after sentence, the self-evident truth.

What that means is that something like

Books on philosophy per se are either highly technical stuff that doesn't matter much, or vague concatenations of abstractions their own authors didn't fully understand (e.g. Hegel).

sounds just as vanilla, to the point, and obviously "the way it is" as this:

Embedded languages (or as they now seem to be called, DSLs) are the essence of Lisp hacking.

We're tempted to take his word on the one because we respect his authority on the other, just as Apple fans gawked at the iPhone no less than they did the iPod---because Steve Jobs had the same magical pitch each time.

5. A web of knowledge and a pretty picture

It took several centuries to prove the unsolvability of the quintic by radicals---a result due to Evariste Galois when he was just nineteen. Everyone before him was wrong, and of those, most were hopelessly wrong: they worked in the wrong direction, trying to devise a "quintic formula" instead of proving one couldn't exist.

Were all of these people wasting their time? To say so would vastly oversimplify history.

I'm reminded of the following account of creativity (Koestler 1964, cited here):

The moment of truth, the sudden emergence of a new insight, is an act of intuition. Such intuitions give the appearance of miraculous flashes, or short-circuits of reasoning. In fact they may be likened to an immersed chain, of which only the beginning and the end are visible above the surface of consciousness. The diver vanishes at one end of the chain and comes up at the other end, guided by invisible links.

More concretely,

There is a tendency to completely overlook the power of brain algorithms, because they are invisible to introspection. It took a long time historically for people to realize that there was such a thing as a cognitive algorithm that could underlie thinking. (link)

I think the description serves equally well for innovation, where lots of unseen activity occasionally generates a good idea. Our tendency, of course, is to focus on the ends---that is usually all that we can see. Think of Marconi getting credit for the radio, or, on the other side, "the strong 'first-mover' effect under which the first papers in a field will, essentially regardless of content, receive citations at a rate enormously higher than papers published later" (arXiv:0809.0522v1).

This is not to advocate for some kind of "butterfly effect" whereby we should recognize everyone's mysterious role in a delicate chain of influence. But there is a chain of influence, and we should be careful not to ignore large swaths of it.

That includes all those people who were wrong, or whose "programs" were fundamentally misguided---because I don't think we could confidently say we'd be better off without them. See, for example, Immanuel Kant, a philosopher who on PG's account basically wasted his time, but whose influence extends by way of second- and third-degree connections through all kinds of treasured scientists, sociologists, philosophers, authors, painters, etc.:

The image shows three levels of "Influenced" infobox links from Wikipedia; click for full version [pdf]. (Download source.)

Would it really be fair to say he "wasted his time"? Or did his work set the stage---even if only as a guide to what not to do---for the kind of "miraculous flashes" we now take for granted?

6. Philosophy is my favorite class

From a footnote to PG's essay:

Some introductions to philosophy now take the line that philosophy is worth studying as a process rather than for any particular truths you'll learn. The philosophers whose works they cover would be rolling in their graves at that. They hoped they were doing more than serving as examples of how to argue: they hoped they were getting results. Most were wrong, but it doesn't seem an impossible hope.

This argument seems to me like someone in 1500 looking at the lack of results achieved by alchemy and saying its value was as a process. No, they were going about it wrong. It turns out it is possible to transmute lead into gold (though not economically at current energy prices), but the route to that knowledge was to backtrack and try another approach.

If everything you learned in philosophy class was useless, and other classes, in addition to teaching you valuable truths, also used the same "process" as philosophy, then it'd probably be Pareto optimal to jump ship. But I don't think that's the case.

For one, there are plenty of valuable truths to be learned in philosophy---that has been the burden of the rest of this essay, and I hope we can dispense with it now.

But I'd also argue that (good) philosophy classes are special:

Philosophy professors are very smart. Say what you will about the material, but it tends to attract sharp thinkers. On its own that wouldn't mean much, except that...

There's a lot of action in a philosophy class. My smartest professors have been math and computer science guys, but I only know that by reading about them---there is unfortunately not a lot of back-and-forth in math class, even though there could be. In philosophy, though, that's all there is: someone presents an objection to the reading, and---if nobody else will---the professor chips away. There is tons of dialogue, and not the kind of noise that you find in a lot of English classes: in philosophy, as in math, there is a wrong answer (or at least a poorly argued one).

It's hard to argue well. You learn a lot of the same stuff in philosophy as you do in a proof-based math class, which basically comes down to:

how to solve hard problems
- break it down,
- work through examples,
- think extremes,
- etc.
how to express your solution (writing proofs, mostly)

Trouble is, because there is so little talking in math classes, most of this stuff happens on your own in a room somewhere; you don't have to construct or destroy an argument on the spot. If nothing else, a few hours of good philosophy talk among people much smarter than you teaches you that it's a lot harder than it looks to (a) defeat even the dumbest-sounding arguments, (b) construct a solid argument of your own, and (c) respond to attacks, all in real-time.

Philosophy papers != English papers. In my experience you can write your way out of an English paper, which is to say, you can think (somewhat) poorly, write well, and get an A. Not so in philosophy. I think this has to do with literary analysis in general; see PG's essay on essays.

Good philosophy articles are like squash videos. Squash is one of those sports where, if you're at my level at least, just watching professionals play can noticeably improve your game. The same seems to be true of good philosophy articles. (And it might be true of good math articles, but most mortals aren't able to read those until grad school; but that's another essay...)

Of course, this could all have to do with the special mix of classes that I've taken. But I have found that contemporary analytic philosophy offers excellent intellectual training.

7. Conclusion

There has been a lot of "bad" philosophy... maybe even most of it. But the subject came clean on that point a long time ago (say, the 1960s) and has been recovering since.

I've tried to give a picture of what I take to be the good stuff, and I can only hope that it is not offensively incomplete.

Intelligence and the World

Mon, 15 Dec 2008 14:19:00 GMT

Alva Noe, a philosopher of mind, talks over at edge.org about the problem of consciousness. He argues that the old "input-output" model—where "perception is input from the world to the mind, action is output from the mind to the world, and cognition and consciousness is what happens inside the head to relate those two"—is wrong. Instead, he says, consciousness is "something we do." Like a dance, it is "locked into an environment"—it is as much in the world as it is in our heads. Divorcing the two would produce "only very impoverished experiences."

I'm reminded of the 1987 paper, "Intelligence without representation [pdf]," by Rodney Brooks (inventor of the Roomba), in which he develops his famous subsumption architecture. His key insight is to "use the world as its own model." No central processor, no ontologies, no "representations."

Instead, his robots have independent modules that each do their own low-level sensing, processing, and actuating; the system's intelligence comes from the suppression of one by another. So, for example, a robot might have two modules: "avoid objects" and "go towards the light." They don't talk—the high-level light seeker doesn't care about avoiding objects, and the low-level collision detector doesn't care about the light. But the bot's behavior looks coordinated: it will go towards the light while it avoids objects. How?

The bot's primary directive is to seek light. But the collision detector is always working. So when the light-seeker chooses to move in a way that would cause a collision, the lower-level module kicks in and suppresses its parent. It's that simple.

Since the only interconnections in this model are inhibitory side-taps (which are trivial to implement), each module can devote almost all of its computational resources to a single task, instead of passing and processing messages. And that buys you a very tight loop with the environment, because there's no delay caused by a central intelligent symbol-cruncher. Sound familiar?

Brooks, like Noe, thinks intelligence comes from interaction with the world, not some intricate calculator within a mind. They both eschew "representation" in favor of a different kind of dance between your brain and the environment. (Mind you, Noe's never quite clear—in this talk at least—about what this "dance" entails.)

It turns out they're both off. Brooks, in fact, anticipates the critical flaws with the approach in two questions near the end of his paper:

How many layers can be built in the subsumption architecture before the interactions between layers become too complex to continue?
How complex can the behaviors be that are developed without the aid of central representations?

Here's a good answer to the first question. I'll leave it to Arnold Trehub, who wrote a response to Noe's talk, to take a shot at the second:

The rich and constantly changing content of your phenomenal world cannot exist outside of your phenomenal 3D space that encompasses it. Whatever your conscious experience, it must be an experience of something somewhere in your egocentric phenomenal world. The problem is that humans have no sensory transducers by which to detect and represent the extended coherent 3D space of the world we live in. This means that the brain must have an innate system of biological mechanisms (most likely neuronal) that provide us with a transparent representation of the world from our privileged egocentric perspective.

And as he points out later in that response, recent research has quite convincingly identified (some of) the neural correlates of phenomenal experience. Your brain does represent the world. It does crunch symbols intelligently.

Of course, we would be remiss to claim that either Noe or Brooks is wrong for thinking that intelligence is a feature of both the brain and the environment. It is. It's just that the brain creates its own world—maybe not a complete representation of reality, but something close.

How to Write Readable E-mails

Mon, 15 Dec 2008 14:14:00 GMT

Strunk & White. Write crisply, punctuate, and capitalize. Don't make mistakes.
Cover one topic per e-mail. If you have lots to say, break it up.
Use the subject line to articulate your main idea, question, or action item. Your recipient should know exactly what they're getting before they read the message body. It might help to write this last.
Favor lists. Lists are easier to write than paragraphs, and easier to parse. They also encourage inline replies. If you have to use paragraphs, make them absurdly short: one or two sentences each.
Reply inline if possible. It's faster to address each of your correspondent's points in turn than it is to compose a coherent reply to all of them; inline replies are also easier to read, because they're right beside their referents.
Paste whatever you can. Attachments are clumsy—they must be virus-scanned, downloaded, and opened (and Microsoft Word takes a while to launch).
Respond within 24 hours, if only to say "I'll get to this later." But be sure to give a conservative time frame for your more thorough reply.

[If you're writing a long, letterish e-mail, then to hell with it all (except #1, of course)—these are so rare that no one will begrudge you if you write with abandon.]

Leaving the Bikeshed

Fri, 6 Jun 2008 11:20:22 GMT

There's a lot of contrarianism in college, and I think it's because agreeing seems lazy. When you don't challenge something, one's liable to think you haven't thought it through. After all, scholarship is about critical thinking---falsifying hypotheses and questioning authority; you hear academics saying all the time that doubt is the foundation of intellectual progress. And since college students like to sound smart (I would know), it's no wonder they tend to err on the side of negativity.

I think that's how "the cynical college student" became such a cliche. When kids are finally allowed (and encouraged) to think for themselves, they jump from too much "yes" to too much "no"; they get wrapped up in the sound of skepticism instead of its substance.

It's the same kind of thing when two grad students, arguing some difficult philosophy, walk into a coffee shop hoping to be overheard. Or when you steer a conversation to familiar ground so that you can speak with authority. Or when someone tilts an impressive book so passersby can see the cover. Etc.

It's nice to think of how learned you are, to hear yourself picking points apart, opining with such casual confidence. It's also easy, and that's what makes it dangerous. Do it enough and you start to think you actually know something; instead of tirelessly hunting for reasons you may be wrong, you wallow in your rightness. You get comfortable with weak ideas. And there's nothing more poisonous than comfort, at least to the critical mind.

This is why communities scare me. No matter how fragmented, they always have their mores, their shared preoccupations and quirks. It's easy to get sucked in: you learn what works, how to get attention. There's no need to think anymore. You learn to love the group for what it is: your personal confirmation pit, intellectual theater where the actors are the audience.

It's almost worse than television, which a lot of smart people watch just to criticize. At least nobody gives you credit for sitting in front of the TV, except maybe the few friends who enjoy your spot-on sarcastic quips about how absurd it all is. But communities reward participation---online, they even give you points for it! So there are incentives---social self-consciousness and ego, mostly (the really strong ones)---to fuel the fire, to pump out easy ideas that are well received.

And the ideas are usually easy, because hard problems require hard work. Not everyone can have an opinion about something technically difficult, but we can all fight for days about what to call it (i.e., the color of the bikeshed phenomenon). So that's what you get, vociferous battles over the names of things.

Really what we should all do is push our egos aside and toil nobly, in the name of nothing but the hard-fought prize of truth. Or, at the very least, we should be wary of our own assertions, of the company we keep and their priorities; we should be afraid to get comfortable and embrace the right kind of doubt---not showy skepticism but its bolder cousin, independence. We should have no allies, no easy audiences and no safe ideas.

The Ro-ad Phenomenon

Fri, 25 Apr 2008 04:02:22 GMT

There is a scene in Black Sheep where David Spade becomes fascinated by the simple word "roads."

(giggling) Roads! Ro-ads. Ro-ods.

We could write it off as the consequence of nitrous oxide exposure (he was really high at the time), except that we have all had this happen to our perfectly sober selves, which is precisely what makes the scene so funny.

But why do common words, so examined, seem completely ridiculous? The cognitive scientist Marvin Minsky imagined that the brain has different agents for different tasks, like, say, listening to music [1]. Searchers at the lowest level collect data, like notes, peaks, or pulses; above them, Difference-Finders discern objects, separating figure from ground; and at the top, Structure Builders try to make sense of all the lower levels (perhaps identifying a "sequence" or "polyphony"). All of these guys are highly nested, and at each level agents compete to have their "interpretation" heard. So what happens when there's not much going on?

When none of them has any solid evidence for long enough, then agents change at random, or take turns. Thus, anything gets interesting -- in a way -- if monotonous enough! We all know how, when word or phrase is oft enough repeated, it -- or we -- begin to change; because the restless Searchers start to amplify minutiae, interpret noise as structure.

Thus features that are normally discarded, like the potential syllabic split in "road," are amplified if we press hard enough. It's just that usually (like when we're not high on N₂O), we're too busy for the engrossing details. Imagine if every time you got a cup of coffee you pondered its role in the agrarian history of Ethiopia, compared its color to your professor's pants, and really smelled it; you would piss off everyone behind you in line. Like any other heuristic, we "take stuff for granted" because it helps us get on with our lives.

Yet all kinds of illuminating possibilities avail when you take a closer look, though you might seem like a pothead for trying:

They call 'em fingers, but I've never seen them fing. --Otto, The Simpsons.

For instance, I had generally ignored trees until I began to see them as complex machines (and not just quaint scenery); the same goes for eyelids, ear wax, and avalanches -- each is incredibly rich when you think about it. More concretely, I had until yesterday taken for granted the way .jpeg files were generated, when I had a friend explain the process; now I know a little about bitmaps, old assembler code, and the limitations of the human eye.

I suppose I am suggesting that there is an alternative to regular drug use for finding a "new perspective," and it need not be as silly as RO-AD or cliched as being awed by nature. What's more, the process reveals a kind of "bug" in our sub-cognitive machinery that can illuminate the way we think when we're not engrossed in something, i.e., when things are completely normal. It suggests, even, that we can take a crack at "normalcy" itself.

1. Minsky, Marvin, Music, Mind, and Meaning, (A.I. Memo No. 616, MIT Artificial Intelligence Laboratory, February 1981), pp. 11, 12, 19.

Douglas Hofstadter's Innumeracy Exercises

Sun, 20 Apr 2008 07:48:22 GMT

The following fun exercises appeared on p. 134 of Hofstadter's Metamagical Themas, a collection of his Scientific American articles from the early 1980s (the title is a play on Martin Gardner's column, "Mathematical Games").

I have not sought permission to reprint them here, although I doubt he would be upset if more people explored, and became fluent with, really big numbers. Of course, I encourage you to buy the book, which has the same elan vitale that made GEB a classic.

Note: In case anyone is interested, I have posted my "solutions." Or you can view my results as a list of tuples for easy processing; it might be interesting to aggregate people's answers.

I would suggest to interested readers that they attempt to build up their own numeracy in a very simple way. All they need to do is to get a sheet of paper and write down on it the numbers 1 to 20. Then they should proceed to think a bit about some large numbers that seem of interest to them, and try to estimate them within one order of magnitude (or two, for the larger ones). By "estimate" here, I mean actually do a back-of-the-envelope (or mental) calculation, ignoring all but factors of ten. Then they should attach the idea to the computed number. Here are some samples of large numbers:

What's the gross state product of California?
How many people die per day on Earth?
How many traffic lights are there in New York City?
How many Chinese restaurants are there in the U.S.?
How many passenger-miles are flown each day in the U.S.?
How many volumes are there in the Library of Congress?
How many notes are played in the full career of a concert pianist?
How many square miles are there in the U.S.? How many of them have you been in?
How many syllables have been uttered by humans since 1400 A.D.?
How many "300" games are bowled in the U.S. per year?
How many stitches are there in a stocking?
How many characters does one need to know to read a Chinese newspaper?
How many sperms are there per ejaculate?
How many condors remain in the U.S.?
How many moving parts are in the Columbia space shuttle?
How many people in the U.S. are called "Michael Jackson"? "Naomi Hunt"?
What volume of oil is removed from the earth each year?
How many barrels of oil are left in the world?
How much carbon monoxide enters the atmosphere each year in auto exhaust fumes?
How many meaningful, grammatical, ten-word sentences are there in English?
How long did it take the 200-inch mirror of the Palomar telescope to cool down?
What angle does the earth's orbit subtend, as seen from Sirius?
What angle does the Andromeda galaxy subtend, as seen from earth?
How many heartbeats does a typical creature live?
How many insects (of how many species) are now alive?
How many giraffes are now alive? Tigers? Ostriches? Horseshoe crabs? Jellyfish?
What are the pressure and temperature at the bottom of the ocean?
How many tons of garbage does New York City put out each week?
How many letters did Oscar Wilde write in his lifetime?
How many typefaces have been designed for the Latin alphabet?
How fast do meteorites move through the atmosphere?
How many digits are in 720 factorial?
How much is a brick of gold worth?
How many gold bricks are there in Fort Knox? How much is it worth?
How fast do your wisdom teeth grow (in miles per hour, say)?
How fast does your hair grow (again in miles per hour)?\
How fast is Venice sinking?
How far is a million feet? A billion inches?
What is the weight of the Empire State Building? Of Hoover Dam? Of a fully loaded jumbo jet?
How many commercial airline takeoffs occur each year in the world?
These or similar questions will do. The main thing is to attach some concreteness to those numbers from 1 to 20, seen as exponents. They are like dates in history. At first, a date like "1685" may be utterly meaningless to you, but if you love music and find out that Bach was born that year, all of a sudden it sticks. Likewise with the secondary meaning for small numbers. I can't guarantee it will work miracles, but you may increase your own numeracy and you may help to increase others'. Merry numbers!

Tracking Tiger Woods (Using Python)

Sat, 12 Apr 2008 03:19:30 GMT

As much as I enjoy it, I can't always spend an afternoon watching the Masters. So I've rolled a little Python script to keep track of the leaderboard: anytime Tiger Woods moves relative to par, I get a text message telling me.

To convert the raw HTML leaderboard into a friendly list of tuples I just used regular expressions, since speed and reusability didn't seem all that important. From there I grab Tiger's score, check if something has changed, and shoot out an e-mail using smtplib and Gmail.

Hopefully, the last message I get tomorrow will say "Tiger is leading the Masters."

Overactive Structure Sets

Tue, 08 Apr 2008 00:06:34 GMT

I think of my brain¹ as hosting a zoo of deeply nested structures that clump together in response to action in the world. When I encounter something new, whatever is in charge works quickly to find an appropriate structure; in fact, this is where it shines. The tool it uses to go from new to old--the glue that builds and connects structures--is analogies. These tend to be less the SAT Verbal variety (Fish:School::) and more like metaphors:

"Sam is a funnier John"
"This is the play we saw in practice, except for that move"
"R³ is an infinite stack of infinitely large sheets of paper"
etc.

Analogies appear all over the place in more veiled forms. A good example is our everyday working assumption that other people think the way we do. Anytime we read a facial expression, we're implicitly mapping our world onto someone else's; to understand them we consult the best reference we have, namely, the huge store of structural information about our own behavior built from years of self-absorption.

And all kinds of familiar problems, like finding the men's room at a new restaurant, making small talk, or parsing the news can be solved by reference to well-known patterns. That way we avoid all kinds of redundant work, in much the same way that the eye works efficiently by (a) ignoring most of the picture and (b) locking onto movement.

This is not to mention, of course, the critical role of analogy in language. Turns of phrase, puns, cliches, transitions, etc., all exploit ready-made structures to help get an idea across. Like the phrase "get an idea across."

Yet as indispensable as it is, analogical reasoning has a major kink. Each of us has a limited set of things to make analogies to that depends critically on which structures were active most recently; consider how different the world looks after a good laugh or bad grade. The way we think, then, is necessarily shaped by what's in the cache at any given moment. This helps explain the kind of inertia that keeps people from thinking creatively or climbing out of a bad mood.

It also explains why people so often claim to be "streaky" or that they "either failed or aced the exam": interesting edge cases crowd out more frequent--but also more forgettable--scenarios. The brain is easily fooled by the illusion of structure. Just think of religion, racism, conspiracy theories, or rhetoric.

In fact, nearly every kind of evil can be seen in that light, as the byproduct of a particularly overactive structure set.

1. Thanks to Douglas Hofstadter.

Ulysses Haikus

Fri, 04 Apr 2008 21:58:00 GMT

I have discovered a very simple algorithm for generating passable English poetry: grab random sentences from the greatest novel ever written and plug them into the most primitive template you can find. I call this project "Ulysses haikus."

To start we need the text itself and a few lines of Python code to parse it, which should leave us with a list of every sentence in the book. From there we can make two sub-lists containing nothing but five- and seven-syllable sentences (for the 5-7-5 haiku pattern) and use those to randomly generate our poems. You can find the full code, including a cute function for the syllable counts by Danny O'Brien, on this page.

Of the one hundred poems I generated in my first trial, about half ended up being readable, which says something both about Joyce's facility with words and the integrity of haikus. Ten, in particular, were actually quite striking:

					He waits while you wait 
					Moonlight silver effulgence 
					He is young Leopold 

					Hhhn: burst sideways 
					His gun rusty from the dew 
					Breakfast is ready 

					I'll flay him alive 
					Uncertainly he waited 
					Heavy of the past 

					Holohan told me 
					WHAT'S WRONG WITH HIM? I said 
					No security 

					Watching his water 
					Wonder where it is really 
					where the tide ebbs .. 

					You are cautioned 
					Beware of imitations 
					History to blame 

					Must be his deathday 
					Known as Koch's preparation 
					And the rest nowhere 

					Serum and virus 
					Dreadful life sailors have too 
					I needn't tell you 

					ALLELUIA 
					Wonder how he looks at life 
					Probably neuter 

					Repentance skindeep 
					 --Yes, sir, the chemist said 
					Where I come in

In any case I was pleased with the results, though I encourage more experiments as I'm sure there are plenty of gems yet uncovered. Send your best to haikus AT jsomers.net.

Inconceivable Things

Fri, 04 Apr 2008 20:58:00 GMT

Let's say you just got a job as Enumerator at a company that sells integers, and not more than an hour into your first day the vice president of Evens (Mr. Parity) tells you "We need something completely new. People like the product, they're comfortable with it, but you sit on your ass in this business and you end up like the roman numeral guys. I want an integer that no one's even thought of before, and I want it yesterday.''

For a moment you might panic. Now that you think about it, there really are a lot of integers "in circulation,'' especially with all those computers out there. Every transaction, web search, and algorithm is full of them! You fume: "if only someone kept track of these things I could just use an Inducto-tron..."

Soon enough you'd settle down and realize that with a little ingenuity a solution is not so hard to come by. One just needs a suitably large number (say, > ((100!)!)!) constructed somewhat haphazardly. In no time you'd have a candidate impressive enough for Parity. (In fact, why not try it before reading on?)

I hope you agree that writing out an integer no one's ever seen is at first a bit exhilarating, like skiing through fresh snow. But I think we both know it gets old fast: Z is inexhaustible, and you could conceivably churn out newfangled numbers forever.

Perhaps a more interesting exercise is to think of numbers that have not only never been seen but never could be: the square root of 2, for example. In fact, any irrational number will do since by definition they all have infinite decimal expansions (so you'll never catch a glimpse of their last digit). We can take it one step further with the transcendental numbers first defined by Euler. They're irrational, too, which makes them "unseeable" in that way, but we also know that despite there being infinitely many, mathematicians have only ever found a handful (e, pi, and a few others) "in the wild.'' Spotting a transcendental -- and then proving your find -- is a lot like finding a needle in a haystack filled with spiders: it's very difficult.

So now we have two classes: the set of "unseen" numbers and the "transcendental" ones. Both are slippery -- the former because anytime we put our finger on one it no longer qualifies, and the latter because we can't seem to think of any.

What if we took the worst of both worlds: a set of things such that (a) even finding one is a real achievement and (b) once you find one, you have to throw it out. Can you even conceive of such a set?

Sure: let's call it "the set of inconceivable things." In it is all the stuff that can never be observed, deduced, or imagined. Even things we cannot know, like the last digit of pi, or whether porcupines would work better in C++ or Python, or which eigenvalue will pop out when a wave function collapses, are at least thinkable.

Yet I have a very strong hunch that there are plenty of things that aren't, things we cannot even think of thinking about. What's more, there could be far more of them than their conceivable counterparts! The question is, how important are they?

Wall Street Stole My Smart Friends

Thu, 03 Apr 2008 19:58:00 GMT

Investment banks are machines for turning undergraduates into money. They're a talent vortex, a recruiting machine so well adapted that an entire school system has sprung up to feed it.

Banks take advantage of smart kids who think it's time for an impressive job but aren't sure what to do. They show up with cash in hand, practically pissing prestige, and offer a position guaranteed to keep the "complete fuck-up" scenario at bay. Soon enough you're 45, rich, tired, and anxious about the Nikkei.

It helps that investment banking has a low barrier to entry, because that way the applicant pool grows from a handful of specialists to anyone who can think and talk at a high level. Search costs are minimal: send a recruiter to each of the top schools and cherry pick their best programs. Take care of the rest in a rigorous internal training program.

It also helps that corporations are easily wooed by financial services, that markets are full of losers, and that money makes boring problems interesting.

But I think Wall Street earns the would-be academics, teachers, journalists, and thinkers it employs; it is not just money or "the nature of the industry" that does it. While everybody else waits by the phone for the right girl to call, these guys are out there dancing.

What we're left with is an imbalance: talent leaning towards finance at the expense of everything else. Of course, the job market is precisely that --; a market --; and anyone who's taken Econ 101 knows not to begrudge an equilibrium. But I'm left to ask: is a society that sends so many of its brightest college graduates into a capital markets monkey pit maximizing welfare?

Being Productive

Thu, 03 Apr 2008 12:58:00 GMT

A common narrative these days says we're inundated with data, communicating in increasingly compact forms and living our lives at an ever more frantic pace. Raw bits hop across the network in millisecond bursts. Synthesis is automatic at the edges--we route and index and discard information with cold algorithmic precision. "I" is a syndicate: a reader, writer, hacker. We can't stop typing lest we let the cursor blink.

In any case, that's the narrative. It sounds like bullshit because it probably is. I, for one, struggle with the opposite problem. I lose whole weeks to coffee breaks, DVDs, and languid conversation. "Technology" hasn't ramped anything up--it's made sitting around more fulfilling.

I shouldn't be so hard on myself. Occasionally I operate at full speed: I'll read a ton, write, do homework, solve difficult problems, and work out. It's not like I'm on my ass the rest of the time, just leaning back instead of forward.

Naturally I've tried to discover how "high gear" operates--what kicks it off, how it is sustained, why it ends.

Just as wealth begets wealth and snowballs snowball, getting things done is about inertia. Not a very brilliant revelation, but true. Once you have momentum--you've gone for a run and read two papers already--you're hard to stop. Your brain works on short time scales; it will learn how to be productive quickly. The "turbo" mentality can be jump-started even in those moments when you seem least capable of it, and the rate at which you learn to operate efficiently will itself accelerate.

At worst this theory explains why energetic people are so energetic. And at best it will get me pumped for the new semester.

Before the Water Freezes

Thu, 03 Apr 2008 09:58:00 GMT

I want to write about the net effect of making something clear.

To start I might mention the writing process itself, and talk about how a blank page simultaneously reflects the mind's uncertain, analog intuitions and demands crisper forms. How putting pen to paper can tease out a subtle idea or, perhaps as often, leave the nuance behind.

I'd probably suggest that the operating principle is the same when the wave function collapses and a "perfectly normal cloud of complex amplitude in configuration space" becomes amenable to classical analysis. I'd evaluate the information gained and lost by compacting a set of diffuse possibilities.

What of the endless chase through the digits of pi, I'd then ask rhetorically. What good is arbitrary precision when there's always something left over? How long is the coast of Britain?

I'd change gears, maybe, and poke fun at myself for always losing arguments. I'd break down the simple rhetorical gambits that leave me vehemently defending a position I never believed in, and report on the difficulty of simply claiming ignorance. Again I'd draw a parallel: an assertion forced is kind of like a word chosen or a wave collapsed. I'd have some pithy conclusion.

But unfortunately all I have is this title "Before the Water Freezes" and some vague impressions.