What the Brain Looks Like When It Solves a Math Problem

A GPU excels at rendering fractals, but would struggle to compile the simple programs that generate them.

>I try to multiply two matrices my head ends up overheating

How do you go about multiplying two matrices? Different people do it differently. It can be easy or hard depending on how you do it..

When you multiply, do you write your matrices in such a way that the bottom left corner of your second matrix sits near the upper right corner of the first matrix? (i.e: b31 is above and slightly to the right of a13)

Here's what I mean:

https://upload.wikimedia.org/wikipedia/commons/e/eb/Matrix_m...

If the resulting matrix is R with elements rij, then r12 (yellow and red) is equal to a11.b12 + a12.b22.

You can multiply matrices really fast just by popping the second one into that position. It avoids clutter and confusion. You'll probably never make mistakes again.

Not a remotely scientific speculation, but as far as the animal world goes you see much more "specialized processing" than "general purpose computing". I think this explains why we suck at general purpose computing but are remarkably good at things that general purpose computers have trouble doing.

For example, your brain (and dog brains!) handle some tasks like catching a ball while running/jumping, perceiving depth, and responding to a name which are very computationally expensive.

If you programmed a robot to do any of those things, you'd be multiplying matrices and doing FFT's everywhere. Somehow our brain does the same thing, but we don't have any means to observe the internal computations required to accomplish the tasks.

I'd also argue that general purpose computing capacity is a very rare thing in the animal kingdom because in most cases only enough capacity is needed to glue the specialized parts together.

Snails don't compute phi.

Of the two, between math and code, code is the more obfuscated form of the pair. Can not most code be expressed as pseudocode? Most pseudocode as an algorithm? And algorithms as math? Math is the purer, more fundamental, less obscured form. What we do with code is adapt and elaborate the unobfuscated essence of the underlying algorithms in order to make them rotely executable by machines, and we further twist and obfuscate the essence in order to optimize the coded algorithn for its bespoke execution environment. The math underlying a given piece of code strips all of this away.

I'd think it's more the 2nd stage: figuring out what to do, i.e. solving the problem. Once you've settled on the solution, typing it out, testing, and refactoring would be 3rd stage.

Of course not. Our brains evolved in a way so that a smiley appears on brain's scans top-rear point-of-view whenever we are in the responding phase of a math problem solving :-)

imho it looks more like a skeleton that didn't manage to solve the math problem