Month: August 2008

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.

Last summer I was at a conference where a colleague referred to herself (only half-seriously) as a “person of gender”. Of course I ended up thinking to myself “well, I’m a person of gender too. Everyone is a person of gender.” And I think that was rather her point.

Today I was at a committee meeting of science professors, gathered around to give an award that was to go to one science professor – who could be in any science discipline. Of course it’s impossible to choose a “best” science professor across disciplines. How would you choose between, say, cell biology and astrophysics? So inevitably such an award becomes a kind of message: Because all the candidates at this level are excellent, ultimately the committee is really deciding what statement it is trying to make through its choice.

Now it happens that a lot more men become science professors in the U.S. than women. And I mean a lot more. The ratio seems to be hovering at around five to one from figures I’ve seen. Yet I know from personal experience in teaching that I get just as many brilliant female students as brilliant male students – there is no gender-based difference that I’ve ever been able to tell. And I can tell you straight out, these days in the sciences all the academic departments I know are actively looking for women faculty. So clearly there is self-selection going on here: Men are choosing to stay in the sciences at this level a lot more than women are.

While I am indeed a “person of gender” (as is everyone) I am also a “person of science”. And speaking as a person of science, the available evidence from that five to one faculty gender ratio tells me that four out of five qualified young women are choosing not to go into the sciences in academia. This constitutes a phenomenally huge portion of our nation’s best talent not finding its way into the sciences!

So when it comes time to confer awards, it’s my identity as a “person of science”, not as a “person of gender”, that encourages me to confer awards upon women, because I want to find ways to help reach that huge portion of our nation’s young people who would benefit from role models.

In short, speaking as a scientist, I find myself more inclined to give awards to a woman in science than to a man, for the benefit of the future of science itself.

Ned and I decided to do an art project that might be called virtual sculpture with mirrors. We took three mirrors, positioned at right angles, as you can see in the picture, viewed from the back (you can see where the mirrors are taped together). This arrangement of mirrors makes it look like there are eight of anything you put in front. That’s because each mirror doubles things (the thing itself plus its reflection) so you get 2 × 2 × 2 of everything, which is eight.

Then we positioned four shapes, each made from clear plastic tubing. The idea was to make shapes that, when placed against the mirror, would create the edges of cool looking virtual regular and semi-regular solids. Below are the four shapes we placed against the mirrors.

Here you see all the shapes together in front of the three mirrors, held together by blue tape. It really does look like a fully rounded object, doesn’t it? We didn’t like the way the blue tape looked, so we redid it all a little more carefully.

Here is the final result, first seen from the side, so that the shapes look almost fully round…

and then finally fully from the front. We lit the whole thing with a spotlight, so it would glow in a really wonderful eery way. Unfortunately the glow was so bright that it burns out the image on the digital camera, so you can’t see all the details in the actual sculpture.

The four nested virtual sculptures are, listing from inside to out, an octahedron, a cube, a cubeoctahedron and a rhombic icosahedron. In the second photo above (the one that shows the inserts lying flat on a blue surface), the corresponding inserts are arranged from bottom to top.

This, in case you were wondering, is what people do when they live in the woods around Santa Cruz. Now you know.

I spent a lovely day today with my friend Ned, at his house deep in the woods near Santa Cruz. Ned builds things for fun, and I suspect he can build just about anything. There’s a big treehouse out back that he built himself, decked out in grand Art Nouveau style, adorned with a print (weatherproof of course) of Mucha’s Zodiac over the lintel. The other night he had one of his famous “heaven and hell” themed costume parties, and at some point in the evening an entire band of angels and devils ended up gathered in the treehouse, sharing drinks and conversation, enjoying the night air under a perfect starlit sky. I’m sure there is a metaphor to be found here, but so far it escapes me.

When you are this far out in the woods, you realize how much we are the visitors here. This afternoon a family of deer crossed our path, a mother and three of her little ones, completely unconcerned by our presence. Mom went about her business finding the choicest places to nibble, and her young ones ambled along behind, more or less, darting here and there the way curious children will, all clearly enjoying the sunny weather on this beautiful summer day.

There is nothing here
We have not seen before now
And not much will change

A moment, some words
A ceremony perhaps
Maybe a few friends

What did we expect?
We are the same, you and I
That’s why it matters