Ken’s Blog

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

 

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,

Unending
accidents,
elegant mischance.

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

Are our melodies.
Let us compose
eternally!

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.

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?

One day when I was sixteen I decided that I would learn fifteen digits of pi every day. That afternoon I diligently memorized the first fifteen decimal places of pi. It wasn’t too hard, and I remember thinking that this was a piece of cake. All I would need to do was go through the same ritual every day, until eventually I would … well, I didn’t really have a long term goal, but to my somewhat addled teenage brain learning fifteen digits of pi a day seemed like a worthy idea, one that would eventually lead to untold glory, acclamation from my peers and the admiration of pretty girls everywhere.

Somehow I never made it to the second day. But for years thereafter I could recite those first fifteen decimal places of pi. In a way it was cool – I knew ten decimal places more of pi than the usual 3.14159 – but deep down in my heart of hearts it was something quite different – a moment to the folly of, in Robert Burns’ memorable phrase, “the best laid plans of mice and men”. This abortive monument to adolescent hubris, a string of fifteen digits that I could now rattle off at will, became in its way my short-hand for all of the projects through the years that I had started but never finished. Of which, I am sad to say, there have been many.

In time I came to realize that I am a fifteen digit man – prone to set out on vast and ambitious epic voyages of the mind, which turn out to be day trips. And over time I have learned to operate within this limitation, making a virtue of a vice, by developing a sort of shorthand style of rapid prototyping and experimentation, so that there would always be something interesting to show for even that first day of work. Some of these daily experiments are on my NYU Homepage. And of course this blog is very much in the same spirit.

Recently when my friend Ned was graciously driving me to the San José Airport, it came up in conversation that he knew pi to thirty one decimal places. I confessed to him that I knew only the first fifteen. He challenged me to recite them, which I did without even thinking: 3.141592653589793.

Ned told me he was surprised and impressed. He said that many had told him that they knew multiple digits of pi, but I was the first person who could actually recite them when asked. To me there was nothing surprising about it. Over the years I have come to think of them as old friends, three short groups of familiar strings of digits: 3.14159 followed by 26535 and then 89793. The knowledge has become bittersweet, both my glory and my bane, like the phone numbers written on napkins by beautiful girls who would later turn out to break my heart.

Ned then said: “238462”, giving me the next six digits. In my head I found myself breaking them town into three groups of two, like a phone number: 23 84 62. After a few minutes I had those digits fixed in my mind, and then Ned said “64338”, which I pictured in my head as the two digits 64 followed by the three digits 338. I practiced these for a few minutes more, and then he said “32795”. I pictured this as 32 followed by 795. After about ten minutes we had brought my knowledge out to the same thirty one decimal places that Ned knows.

I’ve practiced reciting them every few days since then, and the other day I checked on the web to make sure I was still getting them right, when I happened to notice that the two next digits are “02”. So now I am up to thirty three decimal places, and I find that I can rattle them all off with ease:

3.141592653589793238462643883279502

Such a sense of power – more than doubling my mastery of pi in a single day! Maybe this is the start of a new era for me. Perhaps from now on I shall learn fifteen new digits a day, gradually build up my range, eventually reach a thousand, two thousand, and why stop there? This could be the beginning for me of an entirely new way of thinking, a powerful shift from mere sketch artist to master of the long-form opus. Perhaps I will follow this triumph by producing a novel, an opera or two, a string of feature films.

But somehow I doubt it.

Sally asked for context for my August 7 post, and I received several other emails as well on the subject. The post was inspired by real events, but not in a direct way. Rather, I was following a chain of internal thoughts, based on contemplation of the responsibilities we each take on when we make a serious emotional commitment.

I was reflecting in my mind that this is a very solemn kind of promise, and that to honor such a promise is not a trivial task. Paradoxically, it requires a certain amount of self-protection – a responsibility to never lose sight of our own core principles and necessary boundaries – in order to guarantee that we have the strength to fulfil the commitment.

I realize I didn’t explain any of this on August 7. Sorry about that – I was focusing on the thought itself, and was also a bit distracted on that day. I am reminded of Sonnet 116, in which our old friend Mr. Shakespeare reminds us to love the other for who they really are, come what may:

Let me not to the marriage of true minds
Admit impediments. Love is not love
Which alters when it alteration finds,
Or bends with the remover to remove:
O no! it is an ever-fixed mark
That looks on tempests and is never shaken;
It is the star to every wandering bark,
Whose worth’s unknown, although his height be taken.
Love’s not Time’s fool, though rosy lips and cheeks
Within his bending sickle’s compass come:
Love alters not with his brief hours and weeks,
But bears it out even to the edge of doom.
      If this be error and upon me proved,
      I never writ, nor no man ever loved.

We are not permitted to define the person we love, and they are not permitted to define us. We can only try to love them for who they are, and insist, as firmly as necessary, that they do the same for us.

Arrived in L.A. today and checked into the wonderfully fun and oddball Figueroa Hotel. I was given a tiny tiny room, no bigger than a monk’s cell, which barely had space for a bed and a little writing desk. And I find myself charmed by this.

I am pretty sure I would not want to dwell in a monk’s cell. And yet there is something comforting, in an unexpected way, in temporarily entering a smaller and simpler world – for a time reducing your personal space to not much more than bed, desk, and a little nook to hang your shirts.

It is a kind of vacation from the large, an affirmation of Thoreau’s observation that “Our life is frittered away by detail… simplify, simplify.” And in a way such a little aesthetic vacation validates what the Zen Buddhists have been saying all along: once you stop focusing on adding objects into your environment, you become more able to wander at will in your mind, unfettered and free.

My friend Gary Marcus recently wrote a delightful book Kluge: The Haphazard Construction of the Human Mind, about how the mind is not so much a machine of logical precision as it is a contraption of string and baling wire – a consequence of how the human brain evolved. Today I had an experience that illustrates his point splendidly.

Yesterday I went out to a formal event, and didn’t really want to carry a bulky wallet in my fancy suit (spoils the look). So I stuffed some twenties and a credit card in the pants pocket of the suit, and left my wallet at home.

Coincidentally, my housekeeper came yesterday for her fortnightly magical rescue of my humble nest from its otherwise sorry state of entropic disaster. Some of this magic involves relocating my various strewn possessions into logical places, presumably so that I can find them more easily. That’s the theory anyway. But as a wise individual once observed: Theory and practice are the same in theory, but different in practice. I confess I have been known to hide things before she comes, as a kind of trovarian insurance policy.

And so it came about that I woke up this morning and realized that I had no clue as to the location of my wallet within the apartment. Of course this happened, as it invariably does, exactly at the moment of my intended egress, which I had timed to the secoond so as not to be late for an important meeting at the University. Needless to say, I not only ended up being late for the meeting, but I also arrived without a wallet, a circumstance that was both awkward and educational. For example, I learned today that guards in lobbies who don’t recognize you will generally not accept your friendly greeting of “oh you must be new here” as a substitute for proper identification, no matter how pleasantly you smile at them while you are saying it.

I came home in the evening determined to find my wallet. I searched, at first with the calmness that comes with certain confidence of success, and then in an increasingly frantic state of mind. I looked everywhere: In closets, through dirty laundry, on top of bookshelves, inside bookshelves, behind bookshelves, even in the kitchen and bathroom (I have no logical excuse for the odder parts of my search – logic doesn’t really come into it).

Finally, having lost all patience with my pesky housekeeper, and determined to get to the bottom of the matter, I stood there indignantly in the middle of my bedroom, my cell phone in hand, and dialed her number. As the phone was ringing, I watched in astonishment as my other hand darted out, opened up my sock drawer, reached all the way to the very back left corner, and pulled out my wallet, from the exact spot where (I now remembered) I had secreted it the day before.

I quickly hit the “hang up” button on the phone – thankfully before anybody had picked up on the other end – put the wallet in my pocket, and headed back out the door, a relieved but chastened man.

So it would seem that Gary is right.

Sometimes we forget that even those we are closest to are separate beings, not extensions of ourselves. The reason they come to us is not the reason we come to them. And so we lull ourselves into thinking that because something makes sense in our own mind, it will also make sense in theirs.

Unfortunately, this is not the way the world works. Not only do we need to understand that our friend is different from us, but we also need to be willing to risk separation from them, by saying: “No, the way you are being toward me does not honor my true self – you must recognize this boundary within me, even if it means little to you”. This is hard, because that level of honesty can drive away those we most wish to be close to.

But in the long run, it is the only way.

Yesterday J. drew our attention to an article by Peter Wood in the Chronicle of Higher Education in which Wood posits that the drive to increase enrollment by women in the sciences is based on a destructive feminist political agenda. This is one of those situations (familiar to anyone observing recent campaigns for the U.S. Presidency) in which a viewpoint is simply dismissed outright as being driven by preconceived doctrine, and therefore devoid of rational merit.

But in this case, it seems to me that cold hard rational science is against Peter Wood. I mentioned this yesterday, but it’s worth spelling it out in more detail, because our nation’s economic well-being is at stake. Let us begin with the myth that women cannot do science. Current secondary level test scores in science show male and female students scoring at an essentially equal level. If there is any bias at all in these numbers due to the long history of girls being told that “girls can’t do science”, these numbers suggest that female students actually have an innately greater facility in these areas than do their male counterparts. But let’s put that aside, and take the current numbers at face value in their message that ability in science has no gender bias.

What then are we to make of the current situation, in which only one out of every six science professors is female? Since the evidence rules out innate ability as the deciding factor, we must conclude that this disparity is due to environmental factors. And that leads us to the following diagram:

If we simply look at the numbers, we see that all of the social, political and economic factors that discourage women from pursuing science careers in higher education are having an enormous – and quantifiable – negative effect on our nation’s productivity. We are only able to utilize 60% of our nation’s top level talent for cutting edge scientific research. This is staggeringly wasteful – like throwing away $40 out of every $100 you earn.

Considering how much of our nation’s wealth depends upon its achievements in the sciences, I would argue, in marked contrast to Peter Wood’s sanguine view, that more resources should go into addressing this problem. Wood makes the following statement:

“A society that worries itself about which chromosomes scientists have isn’t a society that takes science education seriously. In 1900 the mathematician David Hilbert famously drew up a list of 23 unsolved problems in mathematics; 18 have now been solved.”

The assertion that 18 of Hilbert’s problems have been resolved is rather simplistic. But setting this point aside, it is quite reasonable to assert that, had we been able to utilize that 40% of potential top mathematicians who have gone into other fields, we might also by now have a solution to problem 8 (the Reimann Hypothesis) and problem 12, as well as full solutions to problems 9, 11 and 15.

Often those who point fingers and cry “politics” are themselves unwittingly following a doctrinaire agenda. Politics aside, a nation operating at only 60% efficiency in scientific research in a competitive global economy is in a state of crisis. All of us, no matter our gender, need to recognize this state of crisis and address it.