Trying to explain the beauty of math

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Twelfthroot
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Trying to explain the beauty of math

Postby Twelfthroot » Mon Jun 11, 2012 1:43 am UTC

I want to make something to convey how I see mathematics, particularly in an attempt to reach people who generally enjoy or at least respect learning and curiosity but see math as the hollow, boring, meaningless number-crunching that the American public school curriculum presents it as. As such, I figured my best chance or reaching a high school / college audience that might not particularly care about math was with something audiovisual and not too serious. Unfortunately, my drawing / graphical skills are not good and I don't enjoy drawing / video editing enough to improve. Case in point:

I wrote this script for a video introducing complex numbers. It's kind of silly at parts but it gets across some of the themes I want to touch on, particularly on the importance of meaning and motivation in math -- what do they symbols actually say, why do we define this and that, why do we have this rule and not that rule? And then I tried to make a video out of it. Here is the first minute, which is as far as I got before my sense of accomplishing anything wilted.

Even if the animation might have a sort of so-bad-it's-good charm to it, I worry it's not going to work for trying to show that math can be wonderful or awe-inspiring. I suppose that showing it's fun and interesting would be a good accomplishment in itself, but I guess my concern is more that my artistic abilities are forced and won't complement the audio, but I feel obligated to make a video if I want anybody to actually hear the ideas. So I thought I should back up a bit and ask: is there some way I can get my writing to reach an audience wider than "people who already care about math enough to read an essay that's clearly about math"? What other modes of presentation should I consider?

And beyond that -- what do you think can be done to show people what math is really like? I cringe every time I hear "when are we going to use this?" and much more so when teachers try to respond with contrived job examples. I wish more people could see math as a means of playing with abstractions, being creative with patterns and discussing them, and as a means to improve rational thought. How can this be communicated?

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Qaanol
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Re: Trying to explain the beauty of math

Postby Qaanol » Mon Jun 11, 2012 2:14 am UTC

First of all, who is your target audience? The students who would be excited about math if they knew what it was (a lot of *NTP types most likely), and you want to show them? The students who look at thing from a pragmatic standpoint, are never going to get excited about math, and most likely will never use advanced topics in real life, but could still understand them if they had to (*STJ for example), and you want them to at least respect what math entails for those who do it? Someone else?
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jestingrabbit
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Re: Trying to explain the beauty of math

Postby jestingrabbit » Mon Jun 11, 2012 2:37 am UTC

I think that some of the best attempts at really convincing people about the underlying beauty of maths is this thing

http://www.youtube.com/watch?v=JX3VmDgiFnY

and also this

http://www.youtube.com/watch?v=R_w4HYXuo9M

They use stuff that is actually good, not so bad that its good. I think that's worth thinking about, the fact that to engage people now, today, you need to make something that looks good.
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Twelfthroot
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Re: Trying to explain the beauty of math

Postby Twelfthroot » Mon Jun 11, 2012 3:20 am UTC

In general, my target audience would be more a "target misconception": people who think math is arbitrarily made up for no reason, that "doing math" is churning through unmotivated computations, that what happens in math class is at all what mathematicians do, that math is all numbers and shapes... I feel like education largely fails to even teach what math is. I've talked to too many people who can solve equations or even find derivatives without being able to, say, coherently explain what pi is or prove there is no largest integer. Mainly, I'd like to reach the people who already appreciate creativity, beauty, and learning but understandably think that math is devoid of creativity and beauty. If somebody thinks learning is stupid or only cares about practicality, I don't think I could possibly convince them that math is great because of all the things you could learn with/about it. But I want to appeal to people who, say, love the liberal arts but don't see why math could ever be considered an art, because to them it's rules made up hundreds of years ago for no reason that leads to arbitrary busywork and answers they'd never actually want to find.

Jestingrabbit: I think those visualizations are terrific, but what worries me are the comments like these: "Then whats the fucking point if you cant do it with an ordinary ball?" "scientists always do that. They make up random rules whenever it suits them." Yes, most people think the videos look pretty neat, but they might not see the point, or know why or how one would go about exploring these concepts. I'd like to address the mathematical process -- identifying, describing, and abstracting patterns or relations, playing with them, observing their properties, modifying them, relating them to other abstractions -- of which computation is such a small aspect but the cornerstone of the math curriculum.

jestingrabbit wrote:They use stuff that is actually good, not so bad that its good. I think that's worth thinking about, the fact that to engage people now, today, you need to make something that looks good.

Yeah, great, I realize that. I can't make something that looks good. I can write music, code, and I think I can explain things pretty well. I'm asking what my options are to engage people non-visually.

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PM 2Ring
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Re: Trying to explain the beauty of math

Postby PM 2Ring » Mon Jun 11, 2012 5:14 am UTC

Twelfthroot wrote:I want to make something to convey how I see mathematics, particularly in an attempt to reach people who generally enjoy or at least respect learning and curiosity but see math as the hollow, boring, meaningless number-crunching that the American public school curriculum presents it as.

[...]

I wrote this script for a video introducing complex numbers. It's kind of silly at parts but it gets across some of the themes I want to touch on, particularly on the importance of meaning and motivation in math

[...]

And beyond that -- what do you think can be done to show people what math is really like? I cringe every time I hear "when are we going to use this?" and much more so when teachers try to respond with contrived job examples. I wish more people could see math as a means of playing with abstractions, being creative with patterns and discussing them, and as a means to improve rational thought. How can this be communicated?


I wish you luck, but I don't expect that you'll have a lot of success. It's not easy to open people's eyes to the beauty of mathematics, especially when they've come through a school system that
tends to teach maths as a bunch of stuff that you need to pass exams. It's not completely the fault of the teachers or the syllabus - it's not easy to teach all the required information without making maths look like a bunch of arbitrary rules that were concocted centuries ago.

Some people can appreciate that mathematics is important because of its practical applications, but relatively few people get to the point where they have enough mathematical skill to appreciate the beauty of mathematics itself - by the time they've acquired sufficient knowledge most students have developed various negative associations with the subject and only a small minority get how awesome maths really is. Luckily, some of us realize when we're still quite young that mathematical truths are the Secrets Of The Universe, and manage to retain that perspective despite our schooling. :)

So if you want to spread the joy of maths, I suggest that you choose a more receptive audience: people who already agree that maths is neat but who want to know more. Trying to convert people who are already convinced that maths is boring and arbitrary is really hard - you'd have more luck teaching appreciation of classical music harmony to the tone deaf. :)

FWIW, I thought your crude video was cute, although the voice-over was too fast in many parts. As XKCD and many other web comics show, your cartoon characters don't need to be fancy to communicate effectively.

If you want some inspiration, I recommend taking a tour through the works of Jos Leys, a world leader in creating beautiful mathematical imagery. Jos did the graphics for Dimensions, a 2 hour film that discusses geometry in 2, 3 and 4 dimensions, projection, and complex numbers.

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Re: Trying to explain the beauty of math

Postby mfb » Mon Jun 11, 2012 3:29 pm UTC

PM 2Ring wrote:Some people can appreciate that mathematics is important because of its practical applications, but relatively few people get to the point where they have enough mathematical skill to appreciate the beauty of mathematics itself

I still think that the beauty of applied mathematics can be used.

Probably not suitable for your audience, but here are two things I always find amazing:
"A rotation of a (2-)sphere has at least one fixed point" is related to "every real polynomial of 3rd order has at least one zero"
In physics, there are 8 different gluons as the group SU(3) has 8 degrees of freedom (the same is true for other groups and interactions).

dshizzle
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Re: Trying to explain the beauty of math

Postby dshizzle » Tue Jun 12, 2012 1:12 pm UTC

Most of the time when people talk about math being beautiful it seems like their just being pompous, but the other day I think I finally got a feeling of what they mean. I was thinking about a progression of cardinals and I had this vision of pillars rising one after another with each Aleph sitting on one, and the ordinals rising up between them. I know it sounds stupid, but in that moment it was both beautiful and terrifying. I'm not a religious person, but it gave me a sense of grandeur that I think most people would describe as a spiritual experience. That being said, anyone that can show the beauty of math to another person is doing them a great service, but I think even better than showing them, is motivating them to find it for themselves.
Reality must take precedence over public relations, for nature cannot be fooled. - Feynman

erik542
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Re: Trying to explain the beauty of math

Postby erik542 » Thu Jun 14, 2012 7:49 am UTC

I have found that physics is a great lead in. If you can explain the math behind commonplace things without throwing a lot of vocabulary at them that'll get interested.

dshizzle
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Re: Trying to explain the beauty of math

Postby dshizzle » Thu Jun 14, 2012 2:12 pm UTC

erik542 wrote:I have found that physics is a great lead in. If you can explain the math behind commonplace things without throwing a lot of vocabulary at them that'll get interested.


This is very true.
Reality must take precedence over public relations, for nature cannot be fooled. - Feynman

lorb
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Re: Trying to explain the beauty of math

Postby lorb » Thu Jun 14, 2012 8:08 pm UTC

Khanacadamy has a video titled the beauty of algebra. I think it does a good job at showing some of the beauty of math while still being comprehensible even to an audience with next to 0 math-literacy.
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madd0ct0r
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Re: Trying to explain the beauty of math

Postby madd0ct0r » Fri Jun 15, 2012 3:41 am UTC

the OP's video s more the history of imaginary numbers rather then why they are so awesome.

I'd like to see it finished all the same.

polymer
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Re: Trying to explain the beauty of math

Postby polymer » Sun Jun 17, 2012 6:24 pm UTC

I'm surprised this hasn't been mentioned. An individual won't understand why math is beautiful unless they do math themselves. Math is argument, not rhetoric. At least this seems to be the rule in my experience.
Last edited by polymer on Sun Jun 24, 2012 9:31 pm UTC, edited 1 time in total.

chuchundra2
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Re: Trying to explain the beauty of math

Postby chuchundra2 » Sat Jun 23, 2012 5:04 pm UTC

One of my favorite - MinutePhysics - (http://www.youtube.com/user/minutephysics), mostly about the beauty of physics, obviously :). But - "How to Count Infinity" (http://www.youtube.com/watch?v=A-QoutHCu4o) - simply awesome (this one involves a quite abstract mathematical concepts, in a very spectacular way). One more - http://www.youtube.com/watch?v=bWzdjehfpIY - a little bit boring and less emotional :(


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