WEEKLY WHINE

A universe of numbers

Now that classes for the third term have ended here at Caltech, it's getting close to a major upheaval time for all of us here. Things will be different soon, so before they are, I figured I should let you know the way that they were.

Ditch Day occurred on Monday of Week 8 this term, having been followed by two fakes. Since one had been the previous Friday, it threw nearly everyone off. Stacks in Ricketts Hovse ranged from Jason Briceño's "Ghetto Life" to Cynthia Gong's "The Wall" to a quadruple stack put together by Mike Astle, Andrea Hasenstaub, Chris Britchford, and Steve McCoy. At about 11:00 PDT, the various stacks met in the courtyard for an immense water fight that took several days to complete. This was followed by lunch, which directly resulted in the head of a pig making its way to the Ricketts courtyard. A reporter asked us what the pig's head was for. We told her that it was completely unrelated to the stack. I don't know whether that particular bit of information made its way into the newspaper.

Here are some highlights of this term, starting with one by Professor Dinakar Ramakrishnan, lecturer in Ma1c Analytic: "If you put a boat in a vector field F that has curl, the boat will turn and go somewhere you don't want it to go. That's why remote control was invented."

Professor Andrew Lange, lecturer in Ph1c Analytic: "What do physicists do when they get really confused? They do energy conservation."

Professor Simon Wilkie, lecturer in Ec11: "Does economics make you more productive? No! It does nothing! All it does is make you miserable!"

Eugene Ha, TA in Ma1c Analytic, explaining how to multiply matrixes: "Well, you take this row, and you kinda hit it on that column."

Lange: "You know, when I'm giving these lectures, I can just imagine Barry Simon in the back row grimacing."

Professer Dave Stevenson, lecturer in Ge1: "There are dinosaur bones down there and none up here. It's that simple. Actually, it's not that simple."

Ramakrishnan: "It's very hard to picture a bad Jordan curve." [class laughs] "Well, it is."

Lange, as he turns off the lights for a demo: "If I don't say anything for a few minutes, you should come up and check on me."

Ha: "Who the hell cares about this problem? No one!"

Wilkie: "The more wasteful the ad is, the better."

One thing that I should point out is that once in lecture, Prof Ramakrishnan told us that it's not possible to formulate a commutative, non-trivial vector product. He told us that there is a vector product in three dimensions, the cross product, but it's not commutative, ie, u × v = -(v × u). But, of course, I couldn't just let him go and say this. I had to try it for myself. And you know what? I found a commutative, non-trivial vector product. What is more, it exists in any space of at least two dimensions.

I call it the "diamond product", defined as follows: If θ is the angle between vectors u and v, and â is the unit vector in the direction of the bisector of θ, then we have u ⋄ v = ||u|| ||v|| sin θ â. In other words, it's in the direction of the bisector between them, and its magnitude is equal to the products of the magnitudes of u and v times the sine of the angle between them.

The advantage of this definition is, as I mentioned, that it is commutative and it exists in any space of two or more dimensions. In addition, its magnitude is equal to that of the cross product in three dimensions that we all know and love, so, for example, u ⋄ u = 0. Unfortunately, it has a couple of disadvantages. One is that (-u) ⋄ v ≠ -(u ⋄ v). Instead, negativinising either u or v rotates the diamond product by π/2, so that (-u) ⋄ (-v) = -(u ⋄ v).

So that's what I've been doing lately. Have a pleasant summer, and be sure not to miss us, because within a month or so, I'll have an entirely new look for GoobNet. I guarantee that it will be more interesting. Cheers.