Tuesday, May 21, 2002
Okay, through the first couple of chapters of Wolfram's book. One gripe and one idea so far.
The gripe is that I don't think he's adequately defined "complexity," and complexity seems to be what he's most interested in talking about. Maybe I should revert to Webster's dictionary, but I'd really rather know more exactly what Wolfram means when he says complexity. Maybe he forgot that the reader doesn't necessarily share his context of having worked in matters of complexity previously. (I have my own ideas about what complexity is, but I'm not sure they're the same as Wolfram's. Or, I could just be being somewhat characteristically dense about this one issue.)
The idea is that I'd love to see what his one-dimensional cellular automata look like in one dimension as they evolve over time. Some of them (hey, maybe the less complex ones) are more easily visualized than others in terms of what a single line of pixels would look like as an animation, but for the more wiggledy stuff (complicated?), it's harder to imagine. This should be doable, maybe even with Wolfram's own Mathematica software (plugged prominently in the book).
I'm a big fan of displaying things that evolve in time in proportionate, at least, time. We've all seen so many pictures of sine waves, but do we know what the sinusoidal oscillation of a point bobbing up and down looks like? Okay, so we all almost certainly do. After a little thought. But, if I say "sine wave", most readers will think of a graph on a page or a trace on an oscilloscope, not of one point moving up and down. (One way to see it is to turn off the timebase on a scope with the vertical amplifier hooked up to the sinuosidal output of a function generator.)
Similar issues arise in research of my own, because the output of the mammalian cochlea is the firings of several tens of thousands of nerves. I really don't think the brain has access to frozen collections of those firings over some previous N milliseconds; instead, it has to work with the firings that are coming in right now. Oh, sure, it can average out activity over some past interval, but if there's information in the detailed timing of the firings, that's hard to keep around.
Or why would one even want to keep it around, when the instantaneous spatial distribution of the pattern has lots of the same information in it as the time between firings does? So, why display that information as if time stopped, as if the information over chunks of time was all available at some same time? Instead, let's see the neural firings -- or Wolfram's cells turning on and off -- as they happen.
Again, this is probably easily done in Mathematica.