A beautiful truthful mind
November 23, 2008 3:45 AM Subscribe
Brain reorganizes to make room for math. But does math easily lead to truth? Is it really just beauty?
Brain reorganizes to make room for math.
Yeah, in my brain that would go something like this: "Oh wow, there's all this space I never knew I had! What can I put in it? Math? Nah, I think I'm going to dump a load of feminist theory and surrealist art in there. Yes. That'll be better."
I have a hard time equating beauty with math, though I understand (intellectually) that this is an association that many scientists feel strongly. Like, 'moonMan's into all sorts of math that I can't even understand the titles of his books, let alone what the hell they actually might be talking about (i.e.:"Nonlinear Dynamics") - and he feels *very* strongly that math and beauty go together. Recently, he started re-reading Euclid's Elements and recommended that I try to read it because it's "very beautiful."
Yeah. If you understand that sort of thing. For me, it would only induce headaches. Trying to understand geometry is so far beyond me that it has, on some occasions, reduced me to tears.
I'll just stick to staring at the pretty colors.
posted by grapefruitmoon at 6:19 AM on November 23, 2008
Yeah, in my brain that would go something like this: "Oh wow, there's all this space I never knew I had! What can I put in it? Math? Nah, I think I'm going to dump a load of feminist theory and surrealist art in there. Yes. That'll be better."
I have a hard time equating beauty with math, though I understand (intellectually) that this is an association that many scientists feel strongly. Like, 'moonMan's into all sorts of math that I can't even understand the titles of his books, let alone what the hell they actually might be talking about (i.e.:"Nonlinear Dynamics") - and he feels *very* strongly that math and beauty go together. Recently, he started re-reading Euclid's Elements and recommended that I try to read it because it's "very beautiful."
Yeah. If you understand that sort of thing. For me, it would only induce headaches. Trying to understand geometry is so far beyond me that it has, on some occasions, reduced me to tears.
I'll just stick to staring at the pretty colors.
posted by grapefruitmoon at 6:19 AM on November 23, 2008
One evening Rene Descartes went to relax at a local tavern. The tender approached and said, "Ah, good evening Monsieur Descartes. Shall I serve you the usual drink?" Descartes replied, "I think not," and promptly vanished.
posted by netbros at 6:46 AM on November 23, 2008 [3 favorites]
posted by netbros at 6:46 AM on November 23, 2008 [3 favorites]
I've told my students: I'm not always concerned with getting an answer. it's enough for me that you appreciate (are thinking about) the problem.
In other words, I think "staring at the pretty colors" is an excellent start to understanding math.
posted by jaronson at 6:58 AM on November 23, 2008
In other words, I think "staring at the pretty colors" is an excellent start to understanding math.
posted by jaronson at 6:58 AM on November 23, 2008
From the third ("beauty") link:
This simple setup serves as a model for the more complicated situation where a mathematician has discovered a plausible solution to a problem and now wants a quick assessment of whether this solution “feels” right. These findings suggest a solution to the mystery why beauty serves as a cue for truth in the context of mathematical discovery.
This sort of thing irks me in science redux articles. I really appreciate that someone wrote an article about this really cool study, as I may not have seen it in the Psychonomic Bulletin and Review. I find it unnecessary, though, for the author to make a sweeping universal statement about how a mystery of humanity is now solved. Really, it's not. Knowing something based on empirical findings that humans have intuited for millennia does not solve a mystery; it just helps elucidate the physicality of the mystery.
Really cool FPP, by the way. Sorry to snark. No coffee yet.
posted by nosila at 7:04 AM on November 23, 2008
This simple setup serves as a model for the more complicated situation where a mathematician has discovered a plausible solution to a problem and now wants a quick assessment of whether this solution “feels” right. These findings suggest a solution to the mystery why beauty serves as a cue for truth in the context of mathematical discovery.
This sort of thing irks me in science redux articles. I really appreciate that someone wrote an article about this really cool study, as I may not have seen it in the Psychonomic Bulletin and Review. I find it unnecessary, though, for the author to make a sweeping universal statement about how a mystery of humanity is now solved. Really, it's not. Knowing something based on empirical findings that humans have intuited for millennia does not solve a mystery; it just helps elucidate the physicality of the mystery.
Really cool FPP, by the way. Sorry to snark. No coffee yet.
posted by nosila at 7:04 AM on November 23, 2008
All the first link tells me is that we use one part of our brain to learn, and one part of our brain to store mathematics. I found the second link to be most interesting, especially the bit about only needing 4 colours to colour in any map in a way that a piece of land is never adjacent to another of the same colour. Sweet. I wish I'd known that in grade 4.
posted by sunshinesky at 7:53 AM on November 23, 2008
posted by sunshinesky at 7:53 AM on November 23, 2008
I'm with you nosila -- the studies in the first and third links both seem interesting, but there seems to be a formula for writing the articles -- concoct 3 paragraphs of fluffy hypothesizing that extrapolates way beyond anything that could be reasonably concluded from the actual study, then provide a one-paragraph description of the research that is tantalizing but leaves out key points. Finish with a vague conclusion.
It seems to me that what's most interesting about the first study is the similarity or difference in brain response to quantities presented as numerals and quantities presented as squares or whatever. But I can't tell much about these differences based on the article.
And I've had my coffee.
posted by Killick at 8:10 AM on November 23, 2008
It seems to me that what's most interesting about the first study is the similarity or difference in brain response to quantities presented as numerals and quantities presented as squares or whatever. But I can't tell much about these differences based on the article.
And I've had my coffee.
posted by Killick at 8:10 AM on November 23, 2008
They found that adults and children do (some) math in different parts of the brain.
Their conclusion: The brain "reorganizes".
My conclusion: Brain organization is the same, but kids and adults do math differently. Most kids do math by rote. Even for addition, they rarely understand that they are adding the ones place, carrying a tens, etc. Long division was just an arcane procedure to me until I was probably 25.
The areas of the brain that are lighting up may have to do with this difference.
Or possibly the "reorganization" is what triggers the change from rote to understanding. Or maybe the "reorganization" IS the change from rote to understanding.
posted by DU at 8:25 AM on November 23, 2008 [2 favorites]
Their conclusion: The brain "reorganizes".
My conclusion: Brain organization is the same, but kids and adults do math differently. Most kids do math by rote. Even for addition, they rarely understand that they are adding the ones place, carrying a tens, etc. Long division was just an arcane procedure to me until I was probably 25.
The areas of the brain that are lighting up may have to do with this difference.
Or possibly the "reorganization" is what triggers the change from rote to understanding. Or maybe the "reorganization" IS the change from rote to understanding.
posted by DU at 8:25 AM on November 23, 2008 [2 favorites]
Math is close to sex and gossip. Doubt it if you wanna.
posted by telstar at 8:27 AM on November 23, 2008 [2 favorites]
posted by telstar at 8:27 AM on November 23, 2008 [2 favorites]
My conclusion: Brain organization is the same, but kids and adults do math differently. Most kids do math by rote. Even for addition, they rarely understand that they are adding the ones place, carrying a tens, etc. Long division was just an arcane procedure to me until I was probably 25.
I don't know if that's really true. I distinctly remember figuring out aspects of math out as a little kid (1-3rd grade) and being amazed and excited by the neatness of how it all fit together. And I am pretty average at math.
posted by fshgrl at 8:59 AM on November 23, 2008 [1 favorite]
I don't know if that's really true. I distinctly remember figuring out aspects of math out as a little kid (1-3rd grade) and being amazed and excited by the neatness of how it all fit together. And I am pretty average at math.
posted by fshgrl at 8:59 AM on November 23, 2008 [1 favorite]
The part of my brain that would make room for math is still making room for the delightful G. Sphaerica, that one-celled little track-making protist.
But perhaps in that winsome chamber of my mind, I could take the adorable grape-sized G. Sphaerica aside and introduce it to some simple calculations.
We could chat in a very limited manner (as one must do with the unicellular - no fault of theirs!) about addition.
It is very hard for a unicellular protist to understand addition - they have all they need!
But perhaps, up there in that sunlit attic of my mind, with tiny G. Sphaerica tucked in to the replica 1930's school desk I'd fashioned just for him, a little wooden grape-sized one, I could bring up the ocean floor and how he's adding to it by making his Pre-cambrian motions.
But then, little G. might look at me and say, "Where?"
Like the honored chiefs of faraway lands, who, when taken a mile from their homes by caring anthropologists to understand what distance is, get out of the Jeep and say, "Where?"
posted by Lipstick Thespian at 9:07 AM on November 23, 2008 [2 favorites]
But perhaps in that winsome chamber of my mind, I could take the adorable grape-sized G. Sphaerica aside and introduce it to some simple calculations.
We could chat in a very limited manner (as one must do with the unicellular - no fault of theirs!) about addition.
It is very hard for a unicellular protist to understand addition - they have all they need!
But perhaps, up there in that sunlit attic of my mind, with tiny G. Sphaerica tucked in to the replica 1930's school desk I'd fashioned just for him, a little wooden grape-sized one, I could bring up the ocean floor and how he's adding to it by making his Pre-cambrian motions.
But then, little G. might look at me and say, "Where?"
Like the honored chiefs of faraway lands, who, when taken a mile from their homes by caring anthropologists to understand what distance is, get out of the Jeep and say, "Where?"
posted by Lipstick Thespian at 9:07 AM on November 23, 2008 [2 favorites]
It should be noted that the functions most closely associated with the frontal and temporal lobes change over time in general. The frontal lobe does different things for children than it does for adults. This doesn't have anything to do with "making room for math".
posted by a snickering nuthatch at 9:15 AM on November 23, 2008
posted by a snickering nuthatch at 9:15 AM on November 23, 2008
"My brain, unfortunately, doesn't do that."
Ha ha ha! Being bad at math is funny and socially acceptible!
posted by Eideteker at 9:42 AM on November 23, 2008 [2 favorites]
Ha ha ha! Being bad at math is funny and socially acceptible!
posted by Eideteker at 9:42 AM on November 23, 2008 [2 favorites]
Ha ha ha! Being bad at math is funny and socially acceptible!
Uh, not on Metafilter. Though neither is poor spelling.
posted by zoomorphic at 9:52 AM on November 23, 2008 [2 favorites]
Uh, not on Metafilter. Though neither is poor spelling.
posted by zoomorphic at 9:52 AM on November 23, 2008 [2 favorites]
I read that as Brain reorganizes to make room for meth.
posted by C17H19NO3 at 9:58 AM on November 23, 2008
posted by C17H19NO3 at 9:58 AM on November 23, 2008
grapefruitmoon, your comment makes me sad. Aren't you an artist? Just as you can't conceptualize math as beauty, I can't conceptualize beauty without math, at least on some level. Physical beauty is a measure of symmetry. Much of architectural beauty stems from ratios between basic geometric shapes, or more recently, the subversion thereof. Natural beauty, similarly, derives from certain properties of nature.
Yeah, I know. Math education in this country falls terribly short and fails to inspire. We've had this discussion before. Still, it makes me sad.
I can remember the joy I felt when I learned that there were ways to group counting so that you could figure it out faster. That there was a way to figure out how many of something there were just laying them out in a rectrangle, and then by counting two of the sides and "multiplying" them. How elegant! Can you imagine the joy felt by the first person to figure that out, as he was then able to perform his barter transactions much more quickly. He probably felt pretty slick. Or imagine how Mandelbrot felt when he discovered his famous set.
So much of nature and biology is built on fractals and self-similarity. Everything you see around you is built from math, whether natural or man-made. Whenever you're seeing beauty, you're seeing math, whether you know it or not. It's just a shame that are school systems give math such a bad rap from such an early age. I bet you would feel differently, gfm, if you learned geometry as nature, rather than mathematics. Arithmetic is the lowest form of mathematics, and though it has its own beauty, the repetitive and rote method in which it's taught does its best to tarnish that.
Someone should post an askme for resources for teaching kids (or adults) about the beauty of mathematics, and vice-versa.
posted by Eideteker at 10:06 AM on November 23, 2008 [4 favorites]
Yeah, I know. Math education in this country falls terribly short and fails to inspire. We've had this discussion before. Still, it makes me sad.
I can remember the joy I felt when I learned that there were ways to group counting so that you could figure it out faster. That there was a way to figure out how many of something there were just laying them out in a rectrangle, and then by counting two of the sides and "multiplying" them. How elegant! Can you imagine the joy felt by the first person to figure that out, as he was then able to perform his barter transactions much more quickly. He probably felt pretty slick. Or imagine how Mandelbrot felt when he discovered his famous set.
So much of nature and biology is built on fractals and self-similarity. Everything you see around you is built from math, whether natural or man-made. Whenever you're seeing beauty, you're seeing math, whether you know it or not. It's just a shame that are school systems give math such a bad rap from such an early age. I bet you would feel differently, gfm, if you learned geometry as nature, rather than mathematics. Arithmetic is the lowest form of mathematics, and though it has its own beauty, the repetitive and rote method in which it's taught does its best to tarnish that.
Someone should post an askme for resources for teaching kids (or adults) about the beauty of mathematics, and vice-versa.
posted by Eideteker at 10:06 AM on November 23, 2008 [4 favorites]
This is very interesting on a personal level. I was never bad at math but it seemed more mechanical to me when I was an adolescent. Having recently (re)started by undergraduate in an engineering specialty I see the math very differently. It has function and purposes far beyond what I had ever considered and learning new functions seems to come much easier now. I had figured it was just that I was more disciplined and focused but maybe my brain is handling it differently now.
posted by Octoparrot at 12:24 PM on November 23, 2008
posted by Octoparrot at 12:24 PM on November 23, 2008
This webcomic sums up exactly how I feel about math. To me, it is the ultimate parable of logic vs. love. As a lifelong hopeless-at-math individual I can completely understand how the authour feels, and how he expresses his frustration and hopelessness at ultimately failing to parse love via a method that he understands. It works for me on so many levels, including the mouseover text, which reads: "even the identity matrix doesn't work normally".
I may never be able to grok matrices or comprehend how to use integrals but this pretty much sums it up for me.
posted by lonefrontranger at 1:29 PM on November 23, 2008
I may never be able to grok matrices or comprehend how to use integrals but this pretty much sums it up for me.
posted by lonefrontranger at 1:29 PM on November 23, 2008
I can't conceptualize beauty without math...
I am not surprised.
Physical beauty is a measure of symmetry.
Except when physical beauty is asymmetrical.
posted by flapjax at midnite at 3:10 PM on November 23, 2008
I am not surprised.
Physical beauty is a measure of symmetry.
Except when physical beauty is asymmetrical.
posted by flapjax at midnite at 3:10 PM on November 23, 2008
Are you talking about wabi-sabi? Things being beautiful because they're imperfect? I would argue that something that's beautiful because it's asymmetric is a subversion (as discussed in my earlier comment), and therefore still requires at least some concept of symmetry. It's dashing your expectation of symmetry that you're reacting to.
But that's beside the point. Physical beauty correlates with facial symmetry in humans. It's not a perfect 1:1 relation; it's a correlation.
Either way, even if you can find exceptions, most of the things people think of as beautiful have some underlying math to their beauty.
posted by Eideteker at 3:29 PM on November 23, 2008
But that's beside the point. Physical beauty correlates with facial symmetry in humans. It's not a perfect 1:1 relation; it's a correlation.
Either way, even if you can find exceptions, most of the things people think of as beautiful have some underlying math to their beauty.
posted by Eideteker at 3:29 PM on November 23, 2008
grapefruitmoon, your comment makes me sad. Aren't you an artist? Just as you can't conceptualize math as beauty, I can't conceptualize beauty without math, at least on some level. Physical beauty is a measure of symmetry. Much of architectural beauty stems from ratios between basic geometric shapes, or more recently, the subversion thereof. Natural beauty, similarly, derives from certain properties of nature.
From an intellectual level, I totally get this. On a personal, emotional, gut level - it doesn't really interest me what mathematical properties something has if I find it beautiful.
F'rinstance. This is a pretty good example of what I mean. I have a tattoo. Of a nautilus (photo taken immediately post-tattooing, it is not that puffy). I got the tattoo because I have a really great emotional attachment to the ocean, it was also inspired by a Georgia O'Keefe drawing (in the middle of the page here) which resonates with me for artsy-feminist reasons.
Yet, seeing or hearing about my tattoo *one* person has correctly exclaimed "Wow, you must love the ocean." Surprisingly (to me), most people assume it has to do with the Golden Ratio or Fibonacci sequences. Since getting the tattoo, I read a book on the Golden Ratio and found it pretty interesting, but it didn't make anything that I already considered beautiful to come any *more* alive for me. It was interesting to me in the same way that mysteries are interesting - like, it connected plot points. It connected art to science and that's pretty cool, but it didn't *enhance* any sense I had of the beauty of the art pieces and natural phenomena discussed.
I'm a fairly intelligent person, but I totally fail to grasp even basic mathematical concepts. I don't doubt that my life is lacking for it, but an appreciation for beauty isn't something that I feel is part of that lack.
posted by grapefruitmoon at 3:35 PM on November 23, 2008
From an intellectual level, I totally get this. On a personal, emotional, gut level - it doesn't really interest me what mathematical properties something has if I find it beautiful.
F'rinstance. This is a pretty good example of what I mean. I have a tattoo. Of a nautilus (photo taken immediately post-tattooing, it is not that puffy). I got the tattoo because I have a really great emotional attachment to the ocean, it was also inspired by a Georgia O'Keefe drawing (in the middle of the page here) which resonates with me for artsy-feminist reasons.
Yet, seeing or hearing about my tattoo *one* person has correctly exclaimed "Wow, you must love the ocean." Surprisingly (to me), most people assume it has to do with the Golden Ratio or Fibonacci sequences. Since getting the tattoo, I read a book on the Golden Ratio and found it pretty interesting, but it didn't make anything that I already considered beautiful to come any *more* alive for me. It was interesting to me in the same way that mysteries are interesting - like, it connected plot points. It connected art to science and that's pretty cool, but it didn't *enhance* any sense I had of the beauty of the art pieces and natural phenomena discussed.
I'm a fairly intelligent person, but I totally fail to grasp even basic mathematical concepts. I don't doubt that my life is lacking for it, but an appreciation for beauty isn't something that I feel is part of that lack.
posted by grapefruitmoon at 3:35 PM on November 23, 2008
Right. My comment wasn't meant to open your eyes, or proselytize. I just wanted to sort of express the opposite perspective from yours. Beauty, for me, is irrevocably braided with mathematics. You know, intellectually, that math and beauty are linked for some folks. I know, intellectually, that it's not for some folks. And ne'er the twain shall meet.
Want to go to an art museum some time? You're still in Boston, right? We should do that some time. Not for the purposes of converting each other, or any great revelation. I just think it would be fun.
posted by Eideteker at 4:04 PM on November 23, 2008
Want to go to an art museum some time? You're still in Boston, right? We should do that some time. Not for the purposes of converting each other, or any great revelation. I just think it would be fun.
posted by Eideteker at 4:04 PM on November 23, 2008
Are you talking about wabi-sabi? Things being beautiful because they're imperfect?
Not really, no. I was more thinking of how, for me, "symmetricality" is simply not (necessarily) a crucial element of "beauty". For example, overtly symmetrical creations like this monstrosity (essentially a monument to symmetricality and the perceived "order" therein) hold no beauty for me. They don't move me. On the other hand, a celebration of asymmetry like this or this, well, those speak to me.
Now that you mention it, though, the wabi-sabi, beauty-in-imperfection thing is, of course, very strong, and has great resonance for me. Like Leonard Cohen said:
there is a crack, a crack in everything
that's how the light gets in
But I think that's another point, really, and doesn't necessarily relate to this symmetrical/assymmetrical discussion.
On preview, why, Eideteker, I do believe you're asking grapefruitmoon for a date! You devil, you! :)
posted by flapjax at midnite at 4:14 PM on November 23, 2008
Not really, no. I was more thinking of how, for me, "symmetricality" is simply not (necessarily) a crucial element of "beauty". For example, overtly symmetrical creations like this monstrosity (essentially a monument to symmetricality and the perceived "order" therein) hold no beauty for me. They don't move me. On the other hand, a celebration of asymmetry like this or this, well, those speak to me.
Now that you mention it, though, the wabi-sabi, beauty-in-imperfection thing is, of course, very strong, and has great resonance for me. Like Leonard Cohen said:
there is a crack, a crack in everything
that's how the light gets in
But I think that's another point, really, and doesn't necessarily relate to this symmetrical/assymmetrical discussion.
On preview, why, Eideteker, I do believe you're asking grapefruitmoon for a date! You devil, you! :)
posted by flapjax at midnite at 4:14 PM on November 23, 2008
To me, it is the ultimate parable of logic vs. love.
Ugh. "Those stupid scientists in their ivory towers. They don't have any FEEEEEELINGS!"
posted by DU at 4:40 PM on November 23, 2008
Ugh. "Those stupid scientists in their ivory towers. They don't have any FEEEEEELINGS!"
posted by DU at 4:40 PM on November 23, 2008
DU that wasn't where I was even going with that. geezus why does everything have to be so polarised?
posted by lonefrontranger at 6:08 PM on November 23, 2008
posted by lonefrontranger at 6:08 PM on November 23, 2008
Want to go to an art museum some time? You're still in Boston, right? We should do that some time. Not for the purposes of converting each other, or any great revelation. I just think it would be fun.
That'd be awesome. I am still in Boston and I have an unlimited supply of free tickets to the MFA. Email me (in profile) and we'll set up a date :)
(And I wasn't trying to be defensive, merely stating my own POV on the beauty/truth/math dichotomy. And I know you can't have a dichotomy in three parts, but trichotomy just sounds weird.)
posted by grapefruitmoon at 6:13 PM on November 23, 2008
That'd be awesome. I am still in Boston and I have an unlimited supply of free tickets to the MFA. Email me (in profile) and we'll set up a date :)
(And I wasn't trying to be defensive, merely stating my own POV on the beauty/truth/math dichotomy. And I know you can't have a dichotomy in three parts, but trichotomy just sounds weird.)
posted by grapefruitmoon at 6:13 PM on November 23, 2008
f-jax, thanks for the links. I, of course, gravitate to the geometrical elements of both pictures. So I think I'll stick with my original original point that I basically made here. That is to say, as mind-boggling as it is to me that there are people who have trouble not merely finding but feeling the beauty in mathematics, it's an ugly fact of life. And I blame our educational system (more than just "schools"; it's also cultural, and the love of math needs to start at home).
There are different values of date. I believe we're both taken, so the date would likely be of the "double" variety. ;)
posted by Eideteker at 6:27 PM on November 23, 2008
There are different values of date. I believe we're both taken, so the date would likely be of the "double" variety. ;)
posted by Eideteker at 6:27 PM on November 23, 2008
There are different values of date. I believe we're both taken, so the date would likely be of the "double" variety. ;)
OBVS. Though 'moonMan is notoriously overworked, so it would probably either be a platonic date or a platonic threesome.
posted by grapefruitmoon at 6:43 PM on November 23, 2008
OBVS. Though 'moonMan is notoriously overworked, so it would probably either be a platonic date or a platonic threesome.
posted by grapefruitmoon at 6:43 PM on November 23, 2008
"The mathematical sciences particularly exhibit order, symmetry, and limitation; and these are the greatest forms of the beautiful." - Aristotle
"Mathematics, rightly viewed, possesses not only truth, but supreme beauty." - Bertrand Russell
"The mathematician's patterns, like the painter's or the poet's must be beautiful; the ideas, like the colours or the words must fit together in a harmonious way. Beauty is the first test: there is no permanent place in this world for ugly mathematics." - G. H. Hardy
"No matter how correct a mathematical theorem may appear to be, one ought never to be satisfied that there was not something imperfect about it until it also gives the impression of being beautiful." - George Boole
"The mathematician does not study pure mathematics because it is useful; he studies it because he delights in it and he delights in it because it is beautiful." - Henri Poincare
"The mathematician is only complete in so far as he feels within himself the beauty of the true." - Goetheposted by twoleftfeet at 10:24 PM on November 23, 2008
Um, excuse me, but beauty is truth, and truth beauty.
That's ALL.
posted by shakespeherian at 11:13 AM on November 24, 2008
That's ALL.
posted by shakespeherian at 11:13 AM on November 24, 2008
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My brain, unfortunately, doesn't do that.
posted by flapjax at midnite at 4:53 AM on November 23, 2008