As scientists, we're taught to think in dichotomies; the scientific method requires testable hypotheses, and hypotheses are testable in that they're 'supported' or 'unsupported' by data - we use these terms to be prudent and cautious, since no dataset is complete, but the underlying conceptual framework is that hypotheses are true or false. So: We think about the world in terms of (binary) truth values of poseable hypotheses.
Is this the way the world actually is? Or maybe, less dichotomously: how well does this let us describe the world in its infinite complexity?
Dumb example: There are some flowers in a vase on my desk, that I got for Jess. It's obvious enough, to a casual observer, that the flowers are purple. And a bit yellow - okay, so already a bit of complexity. Ah, and green, too: don't forget the stems. As a scientist, though, I can't just make these wild claims (about the color of the flowers) - instead, I need to come up with some testable hypotheses, and empirically test them. Hypothesis 1 might be: one component of the flowers absorbs EM radiation in the frequency ranges {X} and reflects EM radiation in the frequency ranges {Y} (where X & Y would have actual values if I had a textbook in front of me; I'm lazy). I could then obtain a spectrometer of some kind, isolate a flower in an appropriately controlled environment, and measure the frequencies absorbed & emitted, to test hypothesis 1. Simple enough, right? Okay, but what if I find that according to my spec data, the picture is a little more complicated; absorption and reflection aren't 100% within the ranges X & Y that I specified; they're actually some (relatively) smooth and complicated function - according to my data, at least. Knowing that my data is a little noisy, however, I know I can't make any strong claims about the precise absorption function of the flower, how much it would vary from flower to flower, etc. And even if I could, such a description of the absorption function wouldn't be easily translatable into a linguistic description like "the flowers are purple, yellow, and green."
So where would I have gotten? posted by Miles 11:08 AM
Arrest This Man, He Talks In Maths 
Sunday, May 21, 2006
