Author: admin

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

This evening over dinner the conversation turned to whether people are capable of visualizing in more than three dimensions, a topic that I have found endlessly fascinating for years. There are some four dimensional shapes that are very easy to think about intellectually, but nonetheless there is a gap between intellectual understanding to intuitive seeing. For example, it is very easy to think about a hypercube. Just as you can place two squares apart in a third dimension and draw four lines to connect them to make a cube, you can place two cubes apart in a fourth dimension and draw eight lines to connect them to make a hypercube. Very easy to describe and to understand, but understanding is not seeing.

When I talk about understanding in four dimensions, I mean something very specific, which I can describe by analogy. If you were a character in Abbott’s novel Flatland, living your whole life within a two dimensional plane, you might develop a great facility for manipulating the ever-changing two dimensional shape formed by the shadow of a wire-frame cube onto your planar world. You could “rotate” these twelve lines that connect eight points into all kinds of shapes: a square within a square, two connected parallelograms, a hexagon surrounding a point, and so on.

But you might play with this shape all day and never see it as a cube the way we think of a cube. For example, you might never be able to envision filling the cube with smaller boxes, stacking those little boxes up, laying them side by side, or other tasks that are quite easy to us three dimensional folks to visualize. But then again you might. It would be pretty easy to design a test to find out. I would argue that you could design a similar test to see whether somebody can really make their way around a four dimensional hypercube.

To me the question of whether people can visualize in four dimensions is intriguing because it’s really part of a larger question: Have our brains evolved through the millenia to deal specifically with three dimensional spaces, or have they evolved to be general purpose problem solvers, which only become attuned to three dimensional space after we are born, in response to the experiences of our senses? The answer to this question could shed light on just how general purpose are these problem solving devices we carry around in our skulls.

There have been studies that illustrate that our intuitive understanding of three dimensional space is a facility that we develop after having directly manipulated objects with our hands as infants. In fact, comparative studies have shown that children who are raised in orphanages where they are not given toys to play with will grow up with diminished capacity for three dimensional reasoning. Apparently, as with spoken language, there is a general window in our development during which we need to be exposed to certain experiences. If we are not exposed to those experiences during those windows, then we end up having diminished skills as adults.

Perhaps it would be possible for an eccentric uncle – or aunt – who happens to be an inventor, to give a toy to a young niece or nephew. You could hold this toy in your hand, manipulate it, turn it around in various ways, and it would behave exactly like a normal four dimensional object. I’m not saying I know how to do this, I’m just thinking out loud here. As we know, technology often ends up providing a way to do things once we know we want to do them. But first we need to think to ask.

I wonder whether that child would end up developing the sorts of physical intuitions about four dimensional space that we have about three dimensions. It would sure be interesting to try, wouldn’t it?

Today I travelled from Seattle down to Santa Cruz to visit my friend Ned in his house in the woods. In the evening we went to see a one-man-band – a guy who creates an entire musical experience out of nothing but his voice, a banjo, a tambourine strapped to his left foot, and a base drum that he plays by stepping on a pedal with his right foot. Out of these limited tools this one musician proceeded to create an entire musical world.

But I was also struck by how he was dressed. It was all very precisely calibrated. Brown shoes, black socks, brown slacks, a dark grey vest over a light colored button-down shirt with the sleeves rolled up. And to top it all off a porkpie hat. Everything about him said that we were back in the great American depression of seventy years ago, the vast dustbowl, and here was an iterant musician travelling through our little midwestern town, a young man fallen on hard times, but armed with a banjo and a fistful of tunes and tall tales. I suddenly realized how rich a tradition this is – how precise the image, and how powerful.

The Harlequin figure – God’s holy fool and trickster – has been merged over time with Pierrot the sad lover to create the endearingly seductive troubadour, and we recognize and welcome him wherever he goes. He shows up as Nanki Poo in Gilbert and Sullivan’s The Mikado playing his lute while singing “A wandering minstrel I — A thing of shreds and patches, Of ballads, songs and snatches…” Or as Jason Robards in A Thousand Clowns, porkpie hat fixed firmly on his head as he strums his banjo and sings Yes sir, that’s my baby to win the girl’s heart. Or practically any role played by Danny Kaye or by Jack Lemmon early in his career. Or as Ryan O’Neal in Paper Moon. Or as John Cussack in Say Anything, the harlequin outfit changed for a long coat, the lute/banjo replaced by a boombox held high over his head as he stands out in the rain to win the love of Ione Skye.

The one-two punch of Arthur Penn taking Warren Beatty from Mickey One to Bonnie and Clyde was all about exploring this character – the fast-talking joker in the porkpie hat as sympathetic antihero. We know he’s a loser, we don’t believe his patter for a moment, but we love him all the same, because we understand that beneath the fast talk is a sweet boy-man who is simply in need of love.

What’s fascinating to me about this character is the way he distills the archetype of the sensitive dreamer as romantic hero – the non-alpha male who invariably wins our hearts. Johnny Depp as Captain Jack Sparrow channels him, every Judd Apatow film is built around him, and Joss Whedon’s delightful new web-movie Dr. Horrible even dares to turn the evil arch-villain into the sensitive harlequin/peirrot figure, a complete reversal of genre roles which depends entirely for its success upon our automatic acceptance of this archetype.

I wrote recently about Heath Ledger’s deeply powerful and disturbing turn as The Joker. It is now clear to me that in this performance Ledger was playing this psychotic monster as depression-era troubadour – fast-talking, oddly endearing, the adorable one-man-band, but in this case transformed into your ultimate nightmare. And it is partly because of this archetype – because we recognize the vulnerable harlequin/peirrot archetype and automatically turn our full attention and love toward him – that Ledger was able to steal the film away from its ostensible hero. In the battle for our affections the Dark Knight never had a chance, for his nemesis was a harlequin in a porkpie hat.

Have you ever noticed that there is an odd sort of duality about a day? On the one hand, a day is quite short – sometimes it seems as though mere minutes have elapsed from the time you woke up in the morning until the evening when you find yourself getting ready for bed. And in moments like these, it can seem as though life itself is flitting by, the days blurring alarmingly together, one into the other.

On the other hand, so much can happen in a day. We have all seen that vast changes can occur in a moment, and individual encounters and experiences can take place that alter the course of your life. Taken minute by minute, the course of a day is an incredibly long and rich event.

Of course this is because we are talking about the same object seen from different points of view: Introspection tends to lead to Proustian discovery, and to look into one’s own experience of life is to uncover vast undiscovered uncharted spaces in even the smallest room. As Walt Whitman said “I am large. I contain multitudes.”

I have a cousin who meditates for an hour at the start of each day, as a spiritual practice. I think this helps him to realize the power of each moment that goes by, the importance of paying attention to each drawn breath, and to remain mindful not to take the moment of that breath for granted.

Keeping this blog helps me to do that. Perhaps it is a newfangled form of meditation.