## Tuesday, February 27, 2007

### Would it help if I drew a flow chart?

Such great things come out of MIT's media lab: one of their visitors has built a water-based computer.

This could come in handy in the event of a massive electromagnetic pulse. However, I suspect most people would have other matters on their mind at that point.

In all seriousness, this is a wonderful project. Like other mechanical algorithm devices, it allows the fundamental procedures of computation to be animated in space, relieving the burden of mental modeling from the executor.

But remember, if you're seated in the first six rows, you may get wet during this subroutine.

## Tuesday, February 20, 2007

### Gang sines

R. Stevens models his forthcoming design, featuring both a transcendental number and an earthly delight:

With right thumb and left ring finger extended, he'd be repping the circle with proper digits.

## Sunday, February 18, 2007

### Hyperbolic frolic

I had the tremendous pleasure today to attend an exhibit of works by M. C. Escher in my hometown. It was an incredible treat to see so many familiar images, a few of which have adorned my walls, in one place. There were a number of surprises, too: lovingly crafted scenes of Italian buildings and staircases, and a series of early woodcuts with biblical subjects. One of these even had the reversed initials so common to an artist's early ink prints.

I was most struck by the technical prowess that went into his prints. Take "Circle Limit IV", which not only illustrates the peculiar geometry of the hyperbolic plane, but does so with a thought-provoking two-color woodcut. Few in history had the exacting vision required to create interlocking patterns with such precision, while at the same time communicating so much personality. The exhibit includes two "segment proofs", prints of one third of the work. Taken out of the context of its two triplet siblings, the details that Escher chose to omit as he moves toward infinity are brought into sharper relief, making his genius all the more apparent.

Also consider the hauntingly evocative "Rippled Surface", the studies for which include perspective drawings of concentric red and black circles to indicate the local maxima and minima of the wave as it propagates across the water.

Rhythm of Illusion remains at the San Jose Museum of Art through Sunday, April 22, 2007. If you are anywhere near the south bay before then, I urge you to attend.

## Monday, February 12, 2007

### Over my head

I looked up, stretching my neck, and saw this lovely ornament hanging above my cubicle.

## Friday, February 02, 2007

### I thought this one goes up to eleven

One of the more intelligent sorts of mathematical questions I've been asked are those on the nature of higher dimensions. Somewhere in our pop history it was decided that since we lived in the third dimension, there should be others, like so many arrondissement. These are usually just three-dimensional spaces where things are wacky, not the fundamentally larger spaces they ought to be. In fact, some authors believed they could exchange dimensions for vowels.

It's at once refreshing and disappointing to see an exposition such as this. The animation and sound are lovely, and a rather decent volley is made at the concepts of "splits" and "folds", even if the subtle beauty in the relationship and differences between these is largely ignored. However, the narrator suggests that each "dimension" has some inherent parameters defining it, such as "the seventh dimension" being the space of all possible outcomes from the origin of the universe, and similarly pinning the notion of "split" and "fold" only to certain dimensions.

Do you want to see ten-dimensional space? Here it is:

$(x_0,x_1,x_2,x_3,x_4,x_5,x_6,x_7,x_8,x_9)\;:\;x_i\in\mathbb{F}$

Anyway, isn't supersymmetry supposed to be eleven-dimensional? Or does 11-D SUSY refer to a women named Susan with an impossibly small ribcage?