# Nisan comments on What are you counting? - Less Wrong Discussion

-14 18 July 2012 03:22PM

You are viewing a comment permalink. View the original post to see all comments and the full post content.

Sort By: Best

Comment author: 18 July 2012 07:59:49PM 1 point [-]

I'm not sure what you mean by "an AI which isn't constrained by the same biases inherent to the human perspective"; I know what I mean when I say that but it might not be what you mean.

If by "realize that arithmetic in itself is derived from a bias inherent to the human perspective" you mean "realize that an alien might say that 1 + 1 = 1.3" then I don't see how that would help you build anything.

Comment author: 18 July 2012 09:33:44PM 0 points [-]

1.3 may be a more useful answer than 2.

I responded elsewhere with this:

"One of my biggest revelations in mathematics was in statistics, when, after the class (including me) worked unsuccessfully for a couple of hours to integrate an equation, the instructor (who I'm sure was laughing at us) walked up to the board, converted into a different coordinate system, and integrated the now very easily integrated equation in about thirty seconds."

Imagine you're an alien, for a moment, whose mathematics don't have any of the trigonometric functions - no sine, no cosine, no tangent. Whenever they're called for in their mathematics, they do a fourier transform of an infinite series of aperiodic waves, although they would never understand them -as- aperiodic waves, but as simple equations. This is an equally valid way of representing the trigonometric functions - but there would be a lot of very intractable mathematical problems.

Before you call that ridiculous, we didn't have set theory until the 19th century; it permitted the solution of a lot of mathematical problems we had, until then, been struggling with. Set theory overcame a lot of the problems arithmetic had struggled with. New mathematical models have arisen since then, such as category theory.

It's useful, therefore, to recognize arithmetic as a model, and one we may have a bias for, in consideration that another model might be more useful. More specifically, it's useful, when building AI for example, not to build into it a requisite bias for a particular model, if your goal is to permit it to solve problems which we have thus found far intractable; you may be building into it the very structural problems which have made it intractable for us.