Archive for August, 2008

Circular reasoning

Thursday, August 21st, 2008

I ran into my former student Troy today, and he mentioned the ending to Carl Sagan’s novel Contact in which the main character discovers that at some point the digits of pi, when written out in base 11 and arranged in a square of the right size, form a perfect circle of ones and zeros. And this is taken as a sign from God.

Troy mentioned this because he recalls having felt a sense of awe at this idea. I told him that I vividly remember this plot point (which does not show up on the film), from the time I first read Contact. Troy told me that I am the first other person he’s encountered who remembers the God-in-a-circle ending – and he has talked about this to many people.

But here’s the interesting thing: I recall it as the moment I stopped feeling good about Carl Sagan. Up until then he had been a hero of mine – the guy who got people interested in science, the intellect behind Cosmos, the bridge builder who was able to shine a light on the rarified world of cutting edge research, and show its beauty to the general populace.

But when I read about a God who encodes a circle in the digits of pi, as a kind of shout-out to whatever intelligent race might be listening, my blood ran cold. I think that I can safely say that, on an intellectual level, it was the single most disgusting and repugnant thing I have ever read. Bear with me here…

What Sagan is positing is that a supreme being, creator not merely of the universe but of all possible universes – we know this because the message is encoded in pi, which has the same meaning in all universes – is resorting to a gimmick, a cheap and irrelevant trick, to get our attention.

It’s as though the supreme creator, author of all that is and could ever be, had scrawled the words “Hi mom!” onto the firmament, or maybe held its hands up in Plato’s shadow to make cool shapes like barking dogs and bouncing bunny rabbits.

If there were an intelligent being responsible for the universe, and for the beauty of mathematics, for the sheer loveliness that is logic and symmetry and universal truth, that being would not be resorting to cheap vaudeville tricks to signal its existence.

What it felt like to me, reading the novel’s lame conclusion, was that Sagan had sketched out evidence for God’s existence by arranging for Him to show up on stage in a porkpie hat, pull His pants down and fart.

Would you want to live in such a universe?

Peripheral thinking

Wednesday, August 20th, 2008

If you ask most people “Why is it hot in the summer and cold in the winter?” you get the same nonsensical response: “Because the sun is closer in the summer and further away in the winter.” I know this because I’ve tried asking the question of different people in various different contexts. Some people seem vaguely disturbed while they are answering, because they sort of remember that way back in high school they’d learned it was something else. But they usually can’t really remember what that other explanation was, except that maybe it involved math.

The reason the response is nonsensical (as opposed to simply wrong) is that these same people generally know that places in the southern hemisphere, like Brazil and Australia, have winter during our summer, and summer during our winter. So whatever the answer is, it can’t be about the distance from the earth to the sun. And yet, that’s the answer I hear most often.

What is going on here? I can’t help shaking a sneaking suspicion that something larger is at work. My theory is that we humans, even those highly rational ones who solve problems in their daily lives and are rightly considered highly capable, reserve true rational thought for only a narrow range of problems – a kind of intellectual foveal region. Outside of this narrow region, we resort to a much more primitive kind of peripheral thinking. I suspect that this sort of intellectual economizing probably helps us get through life without overtaxing our brains.

Unfortunately, it may be likely that we humans have a very poor ability to distinguish between these two types of thought. As an obvious example, I have yet to experience a conversation involving candidates for higher office in which somebody did not, at some point, flip over from measured analysis to the kinds of reflexive demonizing that seem to dominate presidential politics in this country. In my experience liberals and conservatives are equally prone to falling into this pattern.

I sometimes wonder where the trigger is that flips our minds from focused and rational engagement to fuzzy non-rational engagement and back again. My theory is that the answer lies in the ways we generally distinguish between ourselves as individuals versus ourselves as part of a large group. We find it easier to rise to the level of true thoughtful engagement when we are involved as individuals, and more difficult when we see ourselves as merely a member of a group.

For example, for most of us, if our child were in physical danger we’d probably find ourseves engaged in some very serious and down-to-earth problem solving to get that child out of harm’s way. Yet when it comes to questions in the general world around us that don’t engage us as an individual, we let things get all fuzzy, even when it comes to questions we think are important, and we resort to the repetition of simple explanations that we’ve heard somewhere.

This also seems to explain the phenomenon of scientific thought: A scientist is someone who has committed – as an individual – to rational engagement with the world. The scientist (when operating as a scientist) seeks rational answers as a matter of self-identity, and so is never speaking as an indistinguishable member of a group. And of course, as we’ve all seen, outside of their particular subject areas scientists can be as fuzzy minded as anybody else.


Tuesday, August 19th, 2008

Every presidential compaign since the era of television campaigning (ie: the Kennedy versus Nixon contest of 1960) has gone to the more charismatic of the two leading candidates. One could argue that the American voter ultimately does not decide on the basis of political affiliation, foreign policy, economic strategy, or any of the ostensible “serious” issues on the table.

No, what the contests between Kennedy/Nixon, Johnson/Goldwater, Nixon/Humphrey, Nixon/McGovern, Carter/Ford, Reagan/Carter, Reagan/Mondale, Bush/Dukakis, Clinton/Bush, Clinton/Dole, Bush/Gore and Bush/Kerry all had in common is this: The one who projected the most charisma during that campaign cycle was the one who got to spend the next four years in the White House.

Of course this may all be mere coincidence…


Monday, August 18th, 2008

We usually think of human bodies as being left/right symmetric, and that architecture reflects that symmetry. A house plan can be reversed left-to-right, and the resulting mirrored house will still be perfectly functional, and not seem out of the ordinary.

But recently, when travelling through Europe, I came upon an exception to this rule. All of the spiral staircases in midieval Europe go up in the same direction. I suspect that you would not be able to find a spiral staircase from the middle ages that spirals up to the left – they all spiral up to the right.

I’m not talking here about modern spiral staircases, such as you find in fashionable lofts and bookstores. No, I’m talking about the real deal – the spiral staircases built into the round towers that guard the castles of the kings and feudal lords of old.

The reason is quite simple: human bodies are, after all, asymmetric, in a crucial way. Almost everyone is right handed. And this means that a warrior will fight better while holding his sword in his right hand. An attacker running up a spiral staircase needs to hold his sword in his left hand, because his right hand will be blocked by the large central column of the staircase. Meanwhile, the castle’s defender is able to wield his opposing sword in his right hand. This confers a considerable advantage upon the defender.

Theoretically it would be possible to build a spiral staircase that goes up the other way, but I suspect such a castle would be overrun rather handily by hostile invaders.

Can anybody think of other instances where assymmetry in the human form has resulted in assymmetry in our architecture?

Secret weapon

Sunday, August 17th, 2008

I happen to be a fan of Tom Wilkinson. The name doesn’t really register to most people. They might think they’ve heard of him somewhere, but they’re not exactly sure where. And yet, it is almost certain that he has deeply affected their movie-going experience through the years. Tom Wilkinson is the kind of actor who makes any movie he is in much better, yet people don’t notice him – he operates by stealth, working on you without you quite realizing how.

He first registered in my consciousness when I saw him as Tom Fowler in In the Bedroom, back in 2001. He was so convincing as a man from New England that I was completely taken by surprise to learn that he is actually British. What could have been an eye-rolling melodrama became, through his subtle treatment of the lead, a deeply effecting study of a good man pushed by extreme events to betray his principles.

And he has a way of making other actors look good. If you’ve seen Batman Begins, you most likely remember Killian Murphy’s Scarecrow as a genuinely disturbing and frightening villian. I would argue that what you are probably actually remembering is the moment when Wilkinson, as the arrogant crime boss Carmine Falcone, is suddenly transformed by the Scarecrow into a hapless psychotic, thrown into an imaginary world of unbounded terror. It is Wilkinson who makes this scene – personally I thought it was the only truly transcendent moment in the entire film.

Going back to the theme of a man betraying his principles, think about Charlie Kaufman’s Eternal Sunshine of the Spotless Mind. One remembers this as a romance starring Jim Carrey and Kate Winslet, but in fact the story is, at its core, a tragedy centered on the character of Wilkinson’s Dr. Howard Mierzwiak, a man trapped by his own faustian manipulations of fate and memory.

Thinking about what Kaufman has written here, I am reminded of Tom Stoppard’s Rosencrantz and Guildenstern are Dead, an absurdist comedy in which the minor courtiers, little more than a footnote in Shakespeare’s Hamlet, are put center stage: The events in Hamlet’s great tragic tale are glimpsed from their oddly limited off-kilter point of view.

Kaufman is up to something similar in Eternal Sunshine, but to more serious purpose. From the somewhat limited viewpoints of Carrey and Winslet’s characters of Joel and Clementine, we witness an immense tragedy, caused by Wilkinson’s doomed Mierzwiak. On paper, the character reads as an unredeemable monster. And yet Wilkinson underplays the part with enormous subtlety and sadness and grace. In the hands of a lesser actor, this character would have been a cardboard villian. But Wilkinson, by playing the role so perfectly, makes you feel the man’s pain, the way he has become trapped by the insane world created by his own misplaced genius.

Nobody thinks of this as a film starring Tom Wilkinson, and yet his performance transforms it, gives it the extra levels of depth it needs to achieve greatness. Kaufman and director Michel Gondry both took home Oscars for this film, and I am sure they both realized what a debt they owe to Tom Wilkinson, its secret weapon.

True story

Saturday, August 16th, 2008

This actually happened: one day a colleague and I were taking a shuttle bus from the airport to a conference on Lifelike Computer Characters. We had a demo the next day, and were still having software problems. We were so deeply immersed in a conversation about our dysfunctional animated demo character that we hardly noticed the two women who shared the shuttle bus with us, listening with rapt attention.

My colleague and I ran down the list of problems the character was having balancing properly, reaching for things, and tracking the position of moving objects with his gaze. The two women were nodding silently, completely absorbed in our discussion. Then my colleague mentioned one persistent problem with our demo character: Under certain conditions his head would pop off and float in the air about two head lengths above his body.

As he said this, both of the women seemed to jump in their seats, looking completely startled and alarmed. Then they just sat there, obviously very upset, and stared at the two of us as though we were both out of our minds. We stared back, and there were a few moments of uncomfortable silence.

Finally I asked “are you here for the conference on lifelike computer characters?”

The women looked at each other and laughed, obviously immensely relieved. “No,” one of them said, “we’re here for the conference on child autism.”

All the songs ever written, and one song

Friday, August 15th, 2008

Manooh and I have had all kinds of conversations about pi. Actually I wrote the song lyrics that I posted yesterday because she and I had been discussing the fact that pi contains, somewhere in its digits, all the melodies that have ever been written or ever will be written.

It’s true for poems too. For example if you write A as 01, B as 02, all the way up to Z as 26, space as 27 and so on for other punctuation, then any poem you can think of (as well as all the poems you can’t think of) will show up sooner or later as a string of digits in pi, if you go out far enough (2515212701180527031205220518). And if you write music as a string of digits, then you can also find all the melodies.

Manooh, quite rightly, felt that a song needs music. Since I had used the first thirty one digits for the lyrics of my little tribute to pi, she responded by using the digits immediately after those for the melody. The result was the following lovely song, which she promptly recorded and posted, and has now graciously given me permission to link to here, for your listening pleasure:

A song regarding pi


More servings of pi

Thursday, August 14th, 2008

Returning to the theme of the digits of pi… A while back, just for fun, I wrote a poem regarding the digits of pi for my friend Manooh. The gimmick was that if you count the number of letters in each successive word of the poem, you get 3.141592653589793238462643383279. But what’s reall amazing is the way she responded, and that will be the subject of tomorrow’s post.

Hey, a song I wrote
regarding pi:
Digits weave and dance,

elegant mischance.

Yet in the serenade
deep within it,
lovely, free,

Are our melodies.
Let us compose

Computer graphics

Wednesday, August 13th, 2008

Two days ago I received the annual ACM/SIGGRAPH Computer Graphics Achievement Award. I wouldn’t have mentioned it here, but quite a few people have been asking me to put my acceptance speech on-line. Here it is:

I am going to tell you why I think this is such an unbelievable honor. Because computer graphics is important. Until us the only human medium capable of absolutely infinite possibility was the written word: Shakespeare, Molière, Cervantes, Goethe, Austen. But as Lance Williams has said: “Computer graphics is limited only by your imagination.” Only we have the power to enable people to actually see their dreams come alive. And to do this has required a new way of thinking.

The late Rich Gold spoke of the four kinds of creator: Artist, Scientist, Engineer, and Designer. Most of the world foolishly believes these are different people. But everyone in this room knows better: each of us must learn to be a synthesis of all of them. And those of us who know this, recognize each other.

I think that’s why this field is built on generosity. From the beginning, I had many teachers and mentors, giants who recognized in me, a skinny kid from New York still wet behind the ears, this shared passion to fuse mathematics with art, the beauty of science with the science of beauty.

Great visionaries like Jim Blinn, Turner Whitted, Frank Crow, my thesis advisor David Lowe, my mentor at NYU Jack Schwartz, and so many others, who went out of their way, took the time to help and encourage me to see a universe in a marble vase, all for the sake of this shared belief in infinite possibility. I learned from them that it’s important not only to live this synthesis, but to teach it, to inspire and encourage those who come after.

So here is what I would like to ask each of you, the young men and women of computer graphics: To make wise use of your extraordinary power to bring dreams to life, to fight against the world’s foolish belief that art and science are irreconcilable disciplines, and to always aim to teach and inspire the next generation, with everything you do. For, as Arthur O’Shaughnessy said: We are the music makers, and we are the dreamers of dreams.

Thank you.

Spoiler alert

Tuesday, August 12th, 2008

OK, this one is just for fun. Each of the following is the essence of a surprise ending to a well known movie. Please don’t post a comment here saying what those movies are – you wouldn’t want to spoil the movie for anyone else, would you?

Here’s what I want to know: Are there any important surprise movie endings that I’ve missed?

He’s really his dad.
He’s actually dead.
She’s actually dead.
They’re all actually dead.
She’s really a guy.
She’s really him, and he’s really her.
They are actually brother and sister.
Her daughter is actually her sister.
His mother is actually him.
The happy ending was actually a dream.
The entire story was actually a dream.
He was just pretending to be crazy.
He was making the whole thing up.
One of them was actually a figment of the other’s imagination.
It’s the sled.

Which brings up an interesting question: If nobody tells you where it’s from, is it still a spoiler?