todd

Theoretical Coffee Break

I've been shoving my nose into matrix calculations, vector addition, and quaternions for a while now, so I just needed to stop and have a break, and talk about some of the actual ideas I want to be pursuing (not just linear algebra). These will be some of the issues I'll be exploring for my semester project, and potentially my final.

I've been fascinated by what I call the "digitally complete library" entity. Basically, for any finite list, there are a finite, if extremely large number of combinations. Cycling through every sequence of five letters, for instance, from AAAAA to ZZZZZ will net every five letter word in the english language, as well as a lot of gibberish.

The gibberish the key problem, of course. This is also known as the "monkeys and typewriters" problem. The classic example is that, given enough time, enough monkeys (or computers) will output the complete works of William Shakespeare.

What I'm interested in, though, is what other novels these monkeys might write in the meantime (and heck, afterwards). Again, there's a lot of text to look through (and doing so would probably take longer than the predicted lifespan of the universe). Being able to hunt through this "noise" is where things begin to get interesting.

While cycling through every sequence of five letters will net mostly gibberish (with a few bona fide words here and there), there are sequences of letters that make grammatical sense, even if they currently don't have meaning.

This could also apply to images, sculpture, or, in my case, virtual enviornments.

In any of these cases, you need an "alphabet", or atoms of the system (pixels for digital images, letters for language). You also need a grammar, for how the alphabet fits together.

In the case of a virtual environment, the "alphabet" could be a bitmapped tile, or a polygon. Above that, you'd have polygonal meshes, or groups of tiles. The "grammar" would be extremely dependent on the abilities of the user to navigate the space. If you want a user to navigate from point A to point B, sticking them inside a cement block with no doors (while possible using an "alphabet") would not jive with the grammar or rules of the space.

The next step is to build an algorithm, or method of using such a grammar so that the resulting environment is interesting. If I were producing a digital photograph from an arbitrary set of digital noise, I suppose I'd outline colors I wanted, shapes, etc. Chaotic systems, things like cellular automata and other forms of AL provide some potential for acting as systems to "cull the noise" so to speak.

Indeed, one can argue that digital creation is actuall a method of focusing, a process of removal. Just as a sculpture chisels away pieces of marble, a digital artist starts with every potential combination of a system, and using various tools (programming algorithms, keyboards, wacom tablets) decides on a single instance of that system above all others.

Related Texts and Pieces:
Library of Babel, by Jorge Luis Borges
9 Billion Names of God, by Arthur C. Clarke

Every Icon- John Simon, Jr.

P.S. It should also be noted that the Halt Checker problem in Computer Science, proven to be impossible, is indeed possible for any finite case. That is, if you know how large the machine will be (in terms of say, memory), all you need to make the halt checker work is a stopwatch. In order to see if the program will run indefinitely, simply run the program and look at the stopwatch. In time, the computer will either (a) cycle through every possible state or (b) recieve the same state twice, meaning that it will cycle through that same state again forever.

While it seemes rather inefficient, this is kinda how most people debug a program that may have this issue: It runs until you're pretty sure it's gonna keep running.

Enough ramblin'...back to transformation matrices...