Comment by Dominic on Expecting Beauty · 2008-01-13T09:13:36.000Z · LW · GW

Michael: do you think we should decide that the simplest formula is the best?

But then how do we define simple? What do you mean by 'communicating' and 'bits'? Do we assign arbitrary complexity points to the operators? What would be the relative complexity of a power operation as compared to a multiplication? And what of my pet operator I just invented that lets me replace "(n - 1) (n - 2) (n - 3) (n - 4) (n - 5)" with "5##" or something similarly silly?

Ask yourself, how can we be sure we have the simplest explanation? What is the simplest formula for the sequence {1, 2, ...}? Is it the powers of two or the natural numbers? What about the sequence {1, ...}? Is it really sensible to ask such questions?

Comment by Dominic on Expecting Beauty · 2008-01-12T09:40:22.000Z · LW · GW

Given the set: {1, 4, 9, 16, 25, ...} And asked to identify the next number, the answer is: 156 For the sequence is obviously generated by the following formula: ((n - 1) (n - 2) (n - 3) (n - 4) (n - 5)) + (n ^ 2)

It is left to the reader to manipulate the formula into an unreadable form, so that it's hard to see how it works. Especially fun is adding an irrational multiplier to the '(n - 1) ... (n - 5)' part.

And notice this method works for any sequence given to a finite number of elements, for, indeed, there are an infinite number of fully-specified sequences that fit.

That's what I call beauty.