space and games

January 27, 2007

Filed under: General — Peter de Blanc @ 11:52 pm

Numbers 1 to 100

The natural numbers 1 to 100, just hanging out. These numbers prefer to be near their divisors.

Comments (3)

Could you define “hanging out” and “prefer”?
I’d guess you’ve (locally) minimized some energy defined by those two phrases, but I can imagine other models, often easier.

Comment by Douglas Knight — February 11, 2007 @ 12:08 pm
The prior probability distribution for the location of each number is a Gaussian. The likelihood of one number being a divisor of another is a (Gaussian) function of their distance (in 2-space). This is a (local) maximum-posterior probability model.

Comment by Peter de Blanc — February 15, 2007 @ 1:16 am
Thanks!
I’m really happy you answered, because it wasn’t my guess of energy, although probably one can transform between the two models, at least one way.

Comment by Douglas Knight — February 16, 2007 @ 12:04 am