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When Blind People Do Algebra, the Brain's Visual Areas Light Up

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Re: When Blind People Do Algebra, the Brain's Visual Areas Light Up

#52

Post by nkassis »

lawpoop wrote: post #42
cee_el2 wrote: post #10

Would it be fair and/or relevant to say that all areas of math can be represented geometrically

As a layperson, I don't know how you could represent infinite sets, unless you just pick a random, finite symbol.

Check out the Riemann sphere https://en.wikipedia.org/wiki/Riemann_sphere

I thought it was cool when I first saw it. Infinity in the complex plane is one of the poles.

Re: When Blind People Do Algebra, the Brain's Visual Areas Light Up

#53

Post by jakub_h »

omginternets wrote: post #22
neolefty wrote: post #19

Earlier quoted context omitted.

Maybe that explains why I can't see (I bump into things) when I'm doing algebra or other complex logical thinking.

I suspect that's rather a case of inattentional blindness. https://en.wikipedia.org/wiki/Inattentional_blindness

I call it "the reverse case of ZX-80".

Re: When Blind People Do Algebra, the Brain's Visual Areas Light Up

#55

Post by threepipeproblm »

cee_el2 wrote: post #10

Would it be fair and/or relevant to say that all areas of math can be represented geometrically

Evan Miller has a fascinating analysis of this question via a critical analysis of a Bret Victor essay.

http://www.evanmiller.org/dont-kill-math.html

Re: When Blind People Do Algebra, the Brain's Visual Areas Light Up

#56

Post by eric_h »

DavidWanjiru wrote: post #48
rorykoehler wrote: post #25

Earlier quoted context omitted.

I'm pretty sure that I engage the visual part of my brain in those moments when I truly understand algebra. It's very beautifully overwhelming and understanding such complex mathematics through visualisation brings about one of the few moments where I get naturally high through cognitive tasks. I wouldn't consider myself a very visual person otherwise.

This comment reminds me of high school physics, when we were learning about interference and those double slit experiments. The teacher would give different scenarios and ask us to predict what patterns would be observed. In one, the pattern was alternating bands of dark and light. I was the only kid who could figure it out, and the physics teacher was so visibly impressed, he to started calling me the thinker. That…

> That thing, visualizing something given to you in mathematical form, feels very good indeed

I agree completely. I still remember the feeling I got when I was able to visualize differential equations in relation to "normal" calculus. It completely changed the way I thought about math.

Re: When Blind People Do Algebra, the Brain's Visual Areas Light Up

#57

Post by Jcol1 »

rorykoehler wrote: post #25
Practicality wrote: post #24

Earlier quoted context omitted.

Except that the article says sighted people do not have an increase in that area when doing algebra. I tend to agree with the premise of the article, which is brain areas can be reapportioned for different tasks.

I'm pretty sure that I engage the visual part of my brain in those moments when I truly understand algebra. It's very beautifully overwhelming and understanding such complex mathematics through visualisation brings about one of the few moments where I get naturally high through cognitive tasks. I wouldn't consider myself a very visual person otherwise.

Can you describe what exactly happens/feels/what is this visualization of the mathematics?

Re: When Blind People Do Algebra, the Brain's Visual Areas Light Up

#58

Post by bpchaps »

rads wrote: post #43
bpchaps wrote: post #34

Earlier quoted context omitted.

I'm the same way and came to a similar conclusion a while back. For me, understanding math has been an incredibly visual process more than anything. It's a very useful heuristic. Programming is similar, but its discreteness seems to make it significantly less visual.

While I understand that "programming is not visual" is a common point of view, I strongly disagree with it. See here: http://worrydream.com/LearnableProgramming/

I should clarify - it absolutely is visual. Just less so than pure maths.

Re: When Blind People Do Algebra, the Brain's Visual Areas Light Up

#59

Post by lawpoop »

jonsen wrote: post #47
lawpoop wrote: post #42

Earlier quoted context omitted.

As a layperson, I don't know how you could represent infinite sets, unless you just pick a random, finite symbol.

Any line segment, for example, is an infinite set of points.

Yes, as a mathematical object, that is true. But any symbol we render in the physical world is going to be finite.

Drawing a straight mark and calling it an infinite set of points isn't really different from drawing a sideways 8 and calling it an infinite set. It's a symbol that represents something else.

Re: When Blind People Do Algebra, the Brain's Visual Areas Light Up

#60

Post by cee_el2 »

thanatropism wrote: post #41
cee_el2 wrote: post #10

Would it be fair and/or relevant to say that all areas of math can be represented geometrically

I dunno. There's a lot of conceptual metaphors and sometimes even structure from geometry in higher maths, but this is sometimes very abstract and merely makes reference to non-geometric ideas about geometry previously developed. For example, in the kind of stochastic calculus quant finance people learn, there's an isometry (like a transformation that preserves size in some sense) between two very different kinds of…

Thanks for your insightful reply, quant isometry sounds like a great counterexample, will read up on it
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