On Sun, Jun 24, 2012 at 8:29 PM, Robert Munafo <mrob27@gmail.com> wrote:
I've had a lot of trouble grasping what you're getting at too. I get the part about "compute approximately how many patterns have a simple outcome", but am totally lost on this "measure" thing.
So let's back up a bit.
The "measure" seems to be a function that takes a pattern as an argument and returns something. Does it matter if the "measure" is into or onto? Same question for its inverse? It seems that the value of the "measure" function is a scalar, real-valued quantity: or is it an integer, or some kind of vector?
The measure is a function from patterns (or natural numbers, since the patterns are enumerable) to real numbers such that the sum over all patterns is finite. The one Michael Kleber described is a perfectly valid measure. My ideal measure would still assign 2^{-s|p|} or 2^{-s ln(index(p))} to each pattern p, since then I still get a partially random real out at computable s, but the cells would be numbered in a way that makes computing the measure of equivalent patterns relatively easy. Does numbering them in an order traced out by a space-filling curve like a Hilbert curve or a dragon curve give any benefits over using a spiral? -- Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com