Sir Mustapha
Group: Musicians
Posts: 2802
Joined: April 2003 |
|
Posted: Jan. 03 2008, 20:19 |
|
Quote (Alan D @ Jan. 03 2008, 16:51) | Obviously any work of art must have a structure of some kind (in order to exist as a conception in the artist's mind), but I don't see why that means it must also be mathematical. For example, a tree has a structure (the same kind of organic structure, perhaps, as many works of art), but I wouldn't want to try to insist that structure of that kind is mathematical. I mean - you CAN attempt to describe the structure of a tree in terms of fractals, statistics, and chaos theory, but all you get when you do that is a pattern that looks vaguely like a generalised tree. It kind of misses the point about the quiddity of this particular tree, somehow: how it got here; the trials it endured; the sheer story of it. The same goes for a work of art. |
Correct me if I miss your point, but there is a difference between finding a viable mathematical model for trees (which would probably result in your suggestion of a generalised tree) and finding an actual mathematical representation of one particular tree. I'm talking hypothetically here, but I don't think it's a stretch to think you can express one tree entirely in mathematical terms. Whether you'd put that to any use, and whether it would be viable, is something else. Eventually you could stumble into a continuous function that stretches towards both infinities, or an infinite series or something, but at least you can model it, whatever may be your criteria. For example, if you want to transport that tree to a computer generated 3D environment, you'll be obliged to express it in terms of equations, vectors and all that; in that way, you'll be limited by the capacity of representation inherent to the computer. The same happens with music, when you record it on any digital media. An entire song is broken down into numbers, and even though what you get in the end is a reconstruction of a sound wave which lose any frequencies above ~22kHz (for CD quality, iirc), it is sufficient for us. But if you're talking in more abstract, theoretical terms, you have the Fourier transform which will give you the entire frequency spectrum of that wave.
I'm walking on rocky terrain here, mind. My "belief" (mind the quotes) is that if something can't be expressed in mathematical terms somehow, then it just defies everything we know. But finding those mathematical methods might be even impossible, in the end, to the point that we fail to even imagine how it will be - thus giving it that air of impossibility. Mathematics is such a wild, absurdly big thing, that we don't even know it very well. There's so much to it that, sometimes, the "limitations" of mathematics are actually limitations of what we think it can do. Or something.
-------------- Check out http://ferniecanto.com.br for all my music, including my latest albums: Don't Stay in the City, Making Amends and Builders of Worlds. Also check my Bandcamp page: http://ferniecanto.bandcamp.com
|