[dlgn]

Eah—it is most definitely possible to program "imagination" into a computer, even if we don't know how yet. After all, computers and the brain work pretty much the same, on some level. The big question is whether it's possible to build mathematical intuition into a computer without programming some sort of mind into it, and that isn't something we have the answer to, yet. (Tierra seems fascinating, by the way.)

Do you think you could clarify what you mean about math being asymmetric? It seems to me that it has an underlying simplicity which expresses itself in a myriad of different ways, if that makes any sense.

On a completely unrelated note:



~dlgn

[eah]

I mean math is so dynamic. People are always finding new foundations and new theorems. It doesn't have a pattern. It's actually like a computer simulation in this way -- You give the computer a set of rules to perform on, but you can't know the exact outcome without performing the simulation. Math follows very basic rules of logic and math is all of the theorems and theorems of theorems we derive from these rules. We still have yet to derive it all. We do not know the final outcome.

There are some examples of what I mean by asymmetry. We can know the exact roots of some complex polynomials through a equation, while other complex polynomials we can not. There is no antiderivative of e^(x^x). And many others I'm sure. I realize there are reasons for this, but it's certainly not as friendly as the root symmetric logic it comes from.

This is probably what you mean by an "underlying simplicity which expresses itself in a myriad of different ways."

[dlgn]

We can know the exact roots of some complex polynomials through a equation, while other complex polynomials we can not.

Huh? I'm pretty sure that all polynomials have a number of roots equal to their degree. The asymmetry you mention disappears once you widen your domain to complex numbers.

[eah]

We can know the exact roots of some complex polynomials through a equation, while other complex polynomials we can not.

Huh? I'm pretty sure that all polynomials have a number of roots equal to their degree. The asymmetry you mention disappears once you widen your domain to complex numbers.

http://en.wikipedia.org/wiki/Abel-Ruffini_theorem

I should have said formula instead of equation and higher degree instead of complex.

[dlgn]

All that theorem states is that higher-degree polynomials can't be solved via standard arithmetic operations and radicals. In fact, the Wikipedia article specifically says that

Every non-constant polynomial equation in one unknown, with real or complex coefficients, has at least one complex number as a solution; this is the fundamental theorem of algebra...the theorem only concerns the form that such a solution must take.

~dlgn

[eah]

All that theorem states is that higher-degree polynomials can't be solved via standard arithmetic operations and radicals. In fact, the Wikipedia article specifically says that

Every non-constant polynomial equation in one unknown, with real or complex coefficients, has at least one complex number as a solution; this is the fundamental theorem of algebra...the theorem only concerns the form that such a solution must take.

~dlgn

Right. I know that bit. It's the fact that we can't have a formula using radicals that bugs me. For some real solutions, we can only find an approximate value. There's also the n-body problem in physics. We can know the exact path, path-time derivative, etc. for two bodies in any arrangement, but when you widen your view to a greater n, some arrangements are simple enough that we can predict the future, while others are not. Many people find these exact solutions elegant. To connect back to your essay, I think Conway argues in favor of human thought proofs for the same reason - they're elegant.

I can bring up another analogy here which reflects my viewpoint: When you widen your view to more complicated things in math, it's like zooming out of a fractal, but instead of seeing the same pattern, you see something completely different. It's chaotic.

I'm not saying we shouldn't use math. I'm just sharing my philosophical view on it.

[eah]

So... apparently some stars actually become diamonds in the sky - planet sized.

http://www.cfa.harvard.edu/news/archive/pr0407.html

Kinda freaky to know there's a lot of something so expensive in one place. It's only 50 light years away. Unfortunately, it's 11730 Kelvin. There goes the chance to fund our space programs for the next million years.

[dlgn]

[krinbros]

It's Legit in 80 years :0

[Meowrocket]

I just had to.
It was just too unrealistic, I had to fix it.