J-Soft Blog

Thursday, October 30, 2003

I've been taken by Stravinski's Histoire du Soldat. .....No, don't come to my rescue just yet.
posted by Jesse at 8:34 PM #


Wednesday, October 29, 2003

I don't sense either: see Attentive


This is a whole lot about nothing. I have written a purposeless self defining entity. Although, some might see a human being as a purposeless self defining entity. In any case, the entity in question here is a letter. Why a letter? I don't know, it just seemed to fit. Letters tend to have a fairly clear and obvious purpose. Though, so I suppose, do a lot of things. The word letter is less awkward than paragraph, blog entry, or bunch of words, more formal than email, less vague than thing, more corporeal than idea. Besides, ideas can be purposeless. Writing a purposeless letter is an idea. I started with "This is a letter without a purpose", and then just wrote down whatever nonsense flew into my head.


This is a letter without a purpose. That is to say, it has the outward appearance of purposelessness. So far it appears only to be a description of itself, an apparently purposeless letter. Perhaps that is its purpose, to describe itself, the purposeless letter. Lets just say for the moment that a purposeless letter that describes itself is by definition purposeless. But, this apparently purposeless letter does have a definite purpose. However it is not meant to be known, or at least obvious. If it were, that would give it purpose, and it would no longer be a purposeless letter. Its purpose, though still hidden, is not veiled by some pretense. Besides no purpose at all, there is no purpose to mask its true purpose. No, its purpose is not masked, just very well hidden. But perhaps purposelessness is as much a pretense as is a pretense. This letter also has far too many instances of the word purpose.
posted by Jesse at 5:12 PM #


Monday, October 06, 2003

Dunce

On saturday I was visiting a friend in residence and noticed a 4-dimensional cube(or hypercube) on his monitor(it was made with pipe cleaners). This reminded me of my attempts to draw such an object on the bus in Europe this past summer. Another trumpet player in the band had drawn a 4-d cube as a cube within a cube. This is correct, and I think is the most common way it is drawn. At the time it didn't seem right to me. I tried to find some systematic way to go about drawing a 4-d cube. What I did was start with a basis for the space in which the cube exists, and then try to connect all the basis vectors orthogonally. We both ended up concluding that we were drawing the same thing from different perspectives. His was a head on view, and mine was a side angle view, but mine never came out right. Seeing the hypercube on the monitor prompted me to try again. I looked at my original drawings. They were definitely wrong, but I was certain my reasoning was sound. I began again by comming up with a rigid definition of a general cube. Here's my definition:

A cube is a closed object which has 2^n vertices, each of which forms a basis for the n-dimensional space in which the cube exists.

I then noted that that this definition lends itself to an algorithm for drawing an n-dimensional cube.

1. draw a basis for an n-dimensional space
2. at each vertex or end point draw any basis vectors that are not present(keep them short)
3. extend each vector until it intersects with another vector, or a vertex
4. loop steps 2 and 3 until you have 2^n vertices



This algorithm is easily verified for 3-dimensions. I used it to draw a 4-dimensional cube. What I ended up with looks like two overlapping cubes, joined at the corners. It's exactly the same thing as the cube within a cube, but rotated slightly. The cube within a cube is a head on view. Thinking about this I then realized that if you rotate a 3-d cube to view it head on you end up with what looks like a square within a square. I had just wasted a whole bunch of time and effort to come up with the most convoluted way to draw a 4-d cube, but at least it works.
posted by Jesse at 9:55 AM #