
What the Brain Looks Like When It Solves a Math Problem - dnetesn
http://www.nytimes.com/2016/07/29/science/brain-scans-math.html?rref=collection%2Fsectioncollection%2Fscience&action=click&contentCollection=science&region=rank&module=package&version=highlights&contentPlacement=1&pgtype=sectionfront
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ivan_ah
For me the most interesting parts are the first (comprehension) and the second
(reasoning). The third part "doing of the math" sounds more of a procedural
thing, which is important for exams but otherwise very meh.

What would be really cool though is if we could see more details about whar
happens in the second phase. When does the correct solutino "click" into
place? What happens before (are many hypotheses begin explored in parallel
(BFS-like), or does the brain follow one track at a time (DFS-like)...

Also interesting would be to quantify the metabolic cost (in watts) for
different types of problems. Does "thinking hard" really require more energy
or is it an illusion?

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Mathnerd314
Paper: [http://act-r.psy.cmu.edu/wordpress/wp-
content/uploads/2016/0...](http://act-r.psy.cmu.edu/wordpress/wp-
content/uploads/2016/05/HiddenStages12.pdf)

The results themselves are not particularly new; he has been working on
similar studies for years:

[http://act-r.psy.cmu.edu/wordpress/wp-
content/uploads/2013/1...](http://act-r.psy.cmu.edu/wordpress/wp-
content/uploads/2013/10/cogs12068.pdf)

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hacker_9
Math being hard has always confused me; spend just one hour learning computer
vision algorithms or neural networks and you'll find them to be very
mathematical. It even explains nature so well, what with fibonnacci and so on.
So why do I struggle? Surely I should be able to tap into the enormous power
that can translate random sound waves into coherent sentences, or a bunch of
pixels into an upside down hippo. Nope. Instead when I try to multiply two
matrices my head ends up overheating...

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munchbunny
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.

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ilaksh
Math is just obfuscated code that doesn't compile or run.

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erdevs
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.

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Jugurtha
I thought they made a mistake in the name of the psychology professor, John R.
Anderson at Carnegie Mellon. There is a John R. Hayes, also at Carnegie
Mellon, author of the "Complete Problem Solver".

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mkagenius
Most of the programming work we do is corresponding to the 3rd stage(solving)
from the article, right? It seems so.

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ivan_ah
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.

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mkagenius
Yeah. I thought typing it out, testing, and refactoring took most of the time
always.

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jimmaswell
It depends on the problem. If you're doing something with the architecture
already planned out for you or a simple script or change, that would be the
case, but if you're figuring out how a whole theoretical system should come
together or what the best way would be to make a certain class of component
interact with others as a whole, the planning stage often takes longer,
although including rearchitecting in "refactoring" can move some of this into
that stage, if that's how you see it.

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lysp
Is it coincidence that the final pic (the "responding" phase) looks like a
Smiley face?

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StreakyCobra
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 :-)

