jsomers.net

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.