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.
“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.
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.
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.