Ron Eglash: The fractals at the heart of African designs

134,225 views ใƒป 2007-12-07

TED


์•„๋ž˜ ์˜๋ฌธ์ž๋ง‰์„ ๋”๋ธ”ํด๋ฆญํ•˜์‹œ๋ฉด ์˜์ƒ์ด ์žฌ์ƒ๋ฉ๋‹ˆ๋‹ค.

๋ฒˆ์—ญ: Yong-Geun Song ๊ฒ€ํ† : Jinmyeong Jeong
00:13
I want to start my story in Germany, in 1877,
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์ œ ์ด์•ผ๊ธฐ๋Š” 1877๋…„์˜ ๋…์ผ, ๊ฒŒ์˜ค๋ฅด๊ทธ ์นธํ† ์–ด๋ผ๋Š”
00:16
with a mathematician named Georg Cantor.
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์ˆ˜ํ•™์ž์˜ ์ด์•ผ๊ธฐ์—์„œ ์‹œ์ž‘๋ฉ๋‹ˆ๋‹ค.
00:18
And Cantor decided he was going to take a line and erase the middle third of the line,
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์นธํ† ์–ด๋Š” ํ•œ ์„ ๋ถ„์„ ์‚ผ๋“ฑ๋ถ„ํ•˜์—ฌ ๊ทธ ๊ฐ€์šด๋ฐ๋ฅผ ์ง€์šฐ๊ณ ,
00:23
and then take those two resulting lines and bring them back into the same process, a recursive process.
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๋‚จ์€ ์–‘์ชฝ์˜ ์„ ๋ถ„์„ ๊ฐ™์€ ๋ฐฉ์‹์œผ๋กœ ๊ณ„์†ํ•ด์„œ ์ž˜๋ผ๋‚ด๋Š” ์‹คํ—˜์„ ํ–ˆ์Šต๋‹ˆ๋‹ค.
00:28
So he starts out with one line, and then two,
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ํ•˜๋‚˜์˜ ์„ ๋ถ„์œผ๋กœ ์‹œ์ž‘ํ•˜์—ฌ, ๋‘˜์„ ๋งŒ๋“ค๊ณ ,
00:30
and then four, and then 16, and so on.
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๋‹ค์Œ ๋‹จ๊ณ„์—์„œ๋Š” ๋„ท, ๊ทธ ๋‹ค์Œ ๋‹จ๊ณ„์—์„œ 16๊ฐœ๊ฐ€ ๋˜๋Š” ์‹์œผ๋กœ, ๋ฐ˜๋ณตํ•ฉ๋‹ˆ๋‹ค.
00:33
And if he does this an infinite number of times, which you can do in mathematics,
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์ˆ˜ํ•™์—์„œ ์ž์ฃผ ๊ทธ๋Ÿฌํ•˜๋“ฏ์ด ์ด ๋‹จ๊ณ„๋ฅผ ๋ฌดํ•œํ•˜๊ฒŒ ๋ฐ˜๋ณตํ•˜๋ฉด
00:36
he ends up with an infinite number of lines,
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๋ฌดํ•œํ•œ ์ ๋“ค๋กœ ์ด๋ฃจ์–ด์ง„
00:38
each of which has an infinite number of points in it.
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๋ฌดํ•œํ•œ ๊ฐฏ์ˆ˜์˜ ์„ ๋ถ„๋“ค์ด ๋‚จ๊ฒŒ ๋ฉ๋‹ˆ๋‹ค.
00:41
So he realized he had a set whose number of elements was larger than infinity.
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์นธํ† ์–ด๋Š” ์ด๋ ‡๊ฒŒ ํ•ด์„œ ์–ป์–ด์ง„ ์„ ๋ถ„์˜ ๊ฐฏ์ˆ˜๊ฐ€ ๋ฌดํ•œ๋ณด๋‹ค ๋งŽ๋‹ค๋Š” ๊ฒƒ์„ ๊นจ๋‹ซ๊ณ ,
00:45
And this blew his mind. Literally. He checked into a sanitarium. (Laughter)
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๊ธ€์ž ๊ทธ๋Œ€๋กœ ์ •์‹ ์ด ๋‚˜๊ฐˆ ๋“ฏ์ด ๋†€๋ž์Šต๋‹ˆ๋‹ค. ๊ทธ๋Š” ์š”์–‘์›๊นŒ์ง€ ๊ฐ”์—ˆ์ฃ . (์›ƒ์Œ)
00:48
And when he came out of the sanitarium,
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๊ทธ๋Š” ์š”์–‘์›์—์„œ ๋Œ์•„์™€์„œ๋Š”
00:50
he was convinced that he had been put on earth to found transfinite set theory
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๊ทธ๋™์•ˆ ๊ณ ์•ˆํ•œ ์ดˆํ•œ์ง‘ํ•ฉ(่ถ…้™้›†ๅˆ) ์ด๋ก ์„ ์ˆจ๊ฒจ์™”์Œ์„ ๊ณ ๋ฐฑํ–ˆ์Šต๋‹ˆ๋‹ค.
00:56
because the largest set of infinity would be God Himself.
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์™œ๋ƒํ•˜๋ฉด ๊ฐ€์žฅ ํฐ ์ง‘ํ•ฉ์ธ ๋ฌดํ•œ์€ ์‹  ์ž์ฒด๋ฅผ ์˜๋ฏธํ•˜๋ฉฐ,
00:59
He was a very religious man.
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์นธํ† ์–ด๋Š” ์‹ ์•™์‹ฌ์ด ๊นŠ์€ ์‚ฌ๋žŒ์ด์—ˆ๊ธฐ ๋•Œ๋ฌธ์ž…๋‹ˆ๋‹ค.
01:00
He was a mathematician on a mission.
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๊ทธ๋Š” ์„ ๊ต๋‹จ์˜ ์ˆ˜ํ•™์ž์˜€์Šต๋‹ˆ๋‹ค.
01:02
And other mathematicians did the same sort of thing.
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๋˜ ๋‹ค๋ฅธ ์ˆ˜ํ•™์ž๊ฐ€ ์ด์™€ ๋น„์Šทํ•œ ์‹คํ—˜์„ ํ–ˆ์Šต๋‹ˆ๋‹ค.
01:04
A Swedish mathematician, von Koch,
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์Šค์›จ๋ด์˜ ์ˆ˜ํ•™์ž ํฐ ์ฝ”ํ๋Š” ์„ ์„ ์—†์• ๋Š” ๋Œ€์‹ 
01:06
decided that instead of subtracting lines, he would add them.
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๊ฐ€์šด๋ฐ์— ๋”ํ•˜๋Š” ๋‹จ๊ณ„๋ฅผ ๊ฑฐ์ณค์Šต๋‹ˆ๋‹ค.
01:10
And so he came up with this beautiful curve.
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๊ทธ ๊ณผ์ •์„ ํ†ตํ•ด ๊ทธ๋Š” ์ด๋Ÿฐ ์•„๋ฆ„๋‹ค์šด ๊ณก์„ ์„ ์ฐฝ์•ˆํ–ˆ์Šต๋‹ˆ๋‹ค.
01:12
And there's no particular reason why we have to start with this seed shape;
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์ด ๊ณก์„ ์„ ๋งŒ๋“œ๋Š”๋ฐ ๋ฐ˜๋“œ์‹œ ์ด ์ดˆ๊ธฐ ๋ชจ์–‘์—์„œ ๋ถ€ํ„ฐ ์‹œ์ž‘ํ•ด์•ผ ํ•  ํ•„์š”๋Š” ์—†์Šต๋‹ˆ๋‹ค;
01:15
we can use any seed shape we like.
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์–ด๋–ค ์ดˆ๊ธฐ๋ชจ์–‘์ด๋ผ๋„ ์„ ํƒํ•  ์ˆ˜ ์žˆ์Šต๋‹ˆ๋‹ค.
01:19
And I'll rearrange this and I'll stick this somewhere -- down there, OK --
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์—ฌ๊ธฐ๋ฅผ ์žฌ๋ฐฐ์น˜ํ•ด์„œ ์ด ๋ถ€๊ทผ์— ๋ถ™์—ฌ๋ณด๊ฒ ์Šต๋‹ˆ๋‹ค. -- ๊ทธ ์•„๋ž˜์—, ๋์Šต๋‹ˆ๋‹ค. --
01:23
and now upon iteration, that seed shape sort of unfolds into a very different looking structure.
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์—ฌ๋Ÿฌ๋ฒˆ์˜ ๋ฐ˜๋ณต์„ ํ†ตํ•ด์„œ ์ดˆ๊ธฐ๋ชจ์–‘์€ ๋งค์šฐ ๋‹ค์ฑ„๋กœ์šด ์ ‘ํžŒ ๊ตฌ์กฐ๋ฅผ ๊ฐ–๊ฒŒ ๋ฉ๋‹ˆ๋‹ค.
01:30
So these all have the property of self-similarity:
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์ด๋Ÿฐ ๋ชจ์–‘๋“ค์€ ๋ถ€๋ถ„์ด ์ „์ฒด์˜ ๋ชจ์–‘๊ณผ ๊ฐ™์€
01:32
the part looks like the whole.
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์ž๊ธฐ๋ฐ˜๋ณต์˜ ์„ฑ์งˆ์„ ๊ฐ–๊ณ  ์žˆ์Šต๋‹ˆ๋‹ค.
01:34
It's the same pattern at many different scales.
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์„œ๋กœ ๋‹ค๋ฅธ ์ถ•์ฒ™ํ•˜์—์„œ ๋™์ผํ•œ ํŒจํ„ด์ด ๋ฐ˜๋ณต๋ฉ๋‹ˆ๋‹ค.
01:37
Now, mathematicians thought this was very strange
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์ˆ˜ํ•™์ž๋“ค์€ ์ด๊ฒƒ์ด ๋งค์šฐ ๊ดด์ƒํ•˜๋‹ค๊ณ  ์ƒ๊ฐํ–ˆ์Šต๋‹ˆ๋‹ค.
01:39
because as you shrink a ruler down, you measure a longer and longer length.
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์™œ๋ƒํ•˜๋ฉด ์ธก์ •๋‹จ์œ„๋ฅผ ์ค„์ผ์ˆ˜๋ก ๊ทธ ๊ธธ์ด๊ฐ€ ๊ธธ์–ด์กŒ๊ธฐ ๋•Œ๋ฌธ์ž…๋‹ˆ๋‹ค.
01:44
And since they went through the iterations an infinite number of times,
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์ด๋Ÿฐ ๋‹จ๊ณ„๋ฅผ ๋ฌดํ•œํ•˜๊ฒŒ ๋ฐ˜๋ณตํ•˜์—ฌ ์ธก์ •๋‹จ์œ„๊ฐ€ ๋ฌดํ•œํ•˜๊ฒŒ ์ž‘์•„์ง€๋ฉด,
01:46
as the ruler shrinks down to infinity, the length goes to infinity.
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ํŒจํ„ด์˜ ๊ธธ์ด๋Š” ๋ฌดํ•œ์œผ๋กœ ๋Š˜์–ด๋‚ฉ๋‹ˆ๋‹ค.
01:52
This made no sense at all,
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๊ทธ๋“ค์€ ์ด ํ˜„์ƒ์„ ๋„์ €ํžˆ ์ดํ•ดํ•  ์ˆ˜ ์—†์—ˆ๊ณ ,
01:53
so they consigned these curves to the back of the math books.
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๊ทธ๋“ค์€ ์ˆ˜ํ•™์ฑ…์˜ ๋’ทํ‘œ์ง€์— ์ด ๊ณก์„ ์„ ๊ทธ๋ ค ๋„ฃ์œผ๋ฉฐ
01:56
They said these are pathological curves, and we don't have to discuss them.
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๋ณ‘์ ์ธ ๊ณก์„ ์œผ๋กœ ์น˜๋ถ€ํ•˜๊ณ  ๋…ผ์˜์กฐ์ฐจ ํ•˜์ง€ ์•Š์œผ๋ ค ํ–ˆ์Šต๋‹ˆ๋‹ค.
02:00
(Laughter)
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(์›ƒ์Œ)
02:01
And that worked for a hundred years.
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๊ทธ๋Ÿฐ ๊ฒฝํ–ฅ์ด ๊ธฐ๋ฐฑ๋…„์ด ์ง€๋‚˜์„œ์•ผ
02:04
And then in 1977, Benoit Mandelbrot, a French mathematician,
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1977๋…„ ํ”„๋ž‘์Šค์˜ ์ˆ˜ํ•™์ž ๋ฒ ๋ฅด๋ˆ„์ด ๋งŒ๋ธ๋ธŒ๋กœ๋Š”
02:09
realized that if you do computer graphics and used these shapes he called fractals,
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๊ทธ ์Šค์Šค๋กœ ์นญํ•œ ํ”„๋ž™ํƒˆ์ด๋ผ๋Š” ์ด๋Ÿฌํ•œ ๋ชจ์Šต์„ ์ปดํ“จํ„ฐ ๊ทธ๋ž˜ํ”ฝ์œผ๋กœ ๊ตฌํ˜„ํ•  ๋•Œ
02:14
you get the shapes of nature.
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์ž์—ฐ์˜ ๋ชจ์Šต์„ ์–ป์–ด๋‚ผ ์ˆ˜ ์žˆ๋‹ค๋Š” ๊ฒƒ์„ ๊นจ๋‹ฌ์•˜์Šต๋‹ˆ๋‹ค.
02:16
You get the human lungs, you get acacia trees, you get ferns,
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์ธ๊ฐ„์˜ ํ์กฐ์ง, ์•„์นด์‹œ์•„ ๋‚˜๋ฌด, ๊ณ ์‚ฌ๋ฆฌ๋“ฑ๊ณผ ๊ฐ™์€
02:20
you get these beautiful natural forms.
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์•„๋ฆ„๋‹ค์šด ์ž์—ฐ์˜ ๋ชจ์–‘๋“ค์„ ๋ง์ด์ฃ .
02:22
If you take your thumb and your index finger and look right where they meet --
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์—ฌ๋Ÿฌ๋ถ„์˜ ์†์—์„œ ์—„์ง€์™€ ๊ฒ€์ง€์˜ ์‚ฌ์ด๋ฅผ ์ž˜ ๊ด€์ฐฐํ•˜๋ฉด --
02:26
go ahead and do that now --
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์ง€๊ธˆ ํ•œ ๋ฒˆ ํ•ด ๋ณด์„ธ์š” --
02:28
-- and relax your hand, you'll see a crinkle,
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์†์„ ํ’€๊ณ  ๋ณด๋ฉด, ์ฃผ๋ฆ„๋“ค์ด ์žˆ๊ณ ,
02:31
and then a wrinkle within the crinkle, and a crinkle within the wrinkle. Right?
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์ฃผ๋ฆ„๋“ค ์•ˆ์— ๋‹ค์‹œ ์ฃผ๋ฆ„์ด ์žˆ๊ณ , ๊ทธ ์ฃผ๋ฆ„ ์•ˆ์— ๋‹ค์‹œ ์ฃผ๋ฆ„์ด ์žˆ๋Š” ๊ฒƒ์„ ๋ณผ ์ˆ˜ ์žˆ์Šต๋‹ˆ๋‹ค. ๋งž์ฃ ?
02:34
Your body is covered with fractals.
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์—ฌ๋Ÿฌ๋ถ„์˜ ์‹ ์ฒด๋„ ํ”„๋ž™ํƒˆ๋กœ ์ด๋ฃจ์–ด์ ธ ์žˆ์Šต๋‹ˆ๋‹ค.
02:36
The mathematicians who were saying these were pathologically useless shapes?
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์˜› ์ˆ˜ํ•™์ž๋“ค์ด ์ด ๋ชจ์–‘์„ ์“ธ๋ชจ์—†๋Š” ๋ณ‘์ ์ธ ๋ชจ์–‘์ด๋ผ๊ณ  ํ–ˆ์—ˆ์ฃ ?
02:39
They were breathing those words with fractal lungs.
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์—ญ์„ค์ ์ด๊ฒŒ๋„ ๊ทธ๋“ค์€ ์ž์‹ ์˜ ํ”„๋ž™ํƒˆ ํ๋ฅผ ํ†ตํ•ด ๊ทธ ๋ง์„ ํ•œ ๊ฒƒ์ž…๋‹ˆ๋‹ค.
02:41
It's very ironic. And I'll show you a little natural recursion here.
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์žฌ๋ฏธ์žˆ์ฃ , ์—ฌ๊ธฐ ์ž์—ฐ์˜ ์žฌ๊ท€์ ์ธ ๋ชจ์–‘๋“ค์„ ์ข€๋” ๋ณด์—ฌ๋“œ๋ฆฌ๊ฒ ์Šต๋‹ˆ๋‹ค.
02:45
Again, we just take these lines and recursively replace them with the whole shape.
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๋‹ค์‹œ, ๋ช‡ ๊ฐœ์˜ ์„ ๋ถ„์„ ๊ฐ–๊ณ  ๋ฐ˜๋ณต์ ์œผ๋กœ ์ „์ฒด ๋ชจ์–‘์„ ์น˜ํ™˜ํ•ด ๋‚˜๊ฐ€๋ฉด,
02:50
So here's the second iteration, and the third, fourth and so on.
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๋‘๋ฒˆ์งธ ๋ฐ˜๋ณต, ์„ธ๋ฒˆ์งธ, ๋„ค๋ฒˆ์งธ, ์ด๋ ‡๊ฒŒ ์ด์–ด์ง‘๋‹ˆ๋‹ค.
02:55
So nature has this self-similar structure.
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์ด๋ ‡๊ฒŒ ์ž์—ฐ์€ ์ž๊ธฐ๋ฐ˜๋ณต์ ์ธ ๊ตฌ์กฐ๋ฅผ ๊ฐ–๊ณ  ์žˆ๋Š” ๊ฒƒ์ž…๋‹ˆ๋‹ค.
02:57
Nature uses self-organizing systems.
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์ž์—ฐ์€ ์ž๊ธฐ๋ฐ˜๋ณต์ ์ธ ์‹œ์Šคํ…œ์œผ๋กœ ๊ตฌ์„ฑ๋˜์–ด ์žˆ์œผ๋‹ˆ๊นŒ์š”.
02:59
Now in the 1980s, I happened to notice
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๊ทธ๋ฆฌ๊ณ  1980๋…„๋Œ€์—, ์ €๋Š” ์•„ํ”„๋ฆฌ์นด ๋งˆ์„์˜ ํ•ญ๊ณต์‚ฌ์ง„์„ ๋ณด๋ฉด์„œ
03:02
that if you look at an aerial photograph of an African village, you see fractals.
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๊ทธ ๋ชจ์–‘์ด ํ”„๋ž™ํƒˆ์ด๋ผ๋Š” ๊ฒƒ์„ ๊นจ๋‹ฌ์•˜์Šต๋‹ˆ๋‹ค.
03:06
And I thought, "This is fabulous! I wonder why?"
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"ํ™˜์ƒ์ ์ธ๋ฐ! ์™œ ๊ทธ๋Ÿด๊นŒ?" ๋ผ๊ณ  ์ƒ๊ฐํ–ˆ์Šต๋‹ˆ๋‹ค.
03:10
And of course I had to go to Africa and ask folks why.
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๊ทธ๊ฑด ์•„ํ”„๋ฆฌ์นด๋ฅผ ๋ฐฉ๋ฌธํ•ด ์‚ฌ๋žŒ๋“ค์—๊ฒŒ ๋ฌผ์–ด์•ผ ํ–ˆ์Šต๋‹ˆ๋‹ค.
03:12
So I got a Fulbright scholarship to just travel around Africa for a year
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ํ•ด์„œ, ์ €๋Š” ํ’€๋ธŒ๋ผ์ดํŠธ ์žฅํ•™๊ธˆ์„ ๋ฐ›์•„ ํ•œ ํ•ด๋™์•ˆ ์•„ํ”„๋ฆฌ์นด๋ฅผ ์—ฌํ–‰ํ•˜๋ฉด์„œ
03:18
asking people why they were building fractals,
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์‚ฌ๋žŒ๋“ค์—๊ฒŒ ์–ด๋–ป๊ฒŒ ์ด ํ”„๋ž™ํƒˆ๋“ค์„ ๊ตฌ์„ฑํ•œ ๊ฒƒ์ธ์ง€,
03:20
which is a great job if you can get it.
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์ดํ•ดํ•  ์ˆ˜ ์žˆ๋‹ค๋ฉด ๋Œ€๋‹จํ•  ๊ฒƒ์ด๋ผ๊ณ  ์งˆ๋ฌธํ•ด ์™”์Šต๋‹ˆ๋‹ค.
03:22
(Laughter)
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(์›ƒ์Œ)
03:23
And so I finally got to this city, and I'd done a little fractal model for the city
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๊ทธ๋ ‡๊ฒŒํ•ด์„œ ์ €๋Š” ์ด ๋„์‹œ์— ๋„์ฐฉํ•˜์—ฌ, ์ด ๋„์‹œ์˜ ๋ชจ์–‘์ด ์–ด๋–ป๊ฒŒ ํŽผ์นœ ๋ชจ์–‘์ด ๋ ์ง€
03:30
just to see how it would sort of unfold --
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์ž‘์€ ํ”„๋ž™ํƒˆ ๋ชจ๋ธ์„ ์‹คํ—˜ ํ•ด ๋ณด์•˜์Šต๋‹ˆ๋‹ค.
03:33
but when I got there, I got to the palace of the chief,
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ํ•˜์ง€๋งŒ ์ œ๊ฐ€ ๊ฑฐ๊ธฐ ๋„์ฐฉํ–ˆ์„ ๋•Œ, ์ €๋Š” ์ถ”์žฅ์˜ ๊ถ์— ๋“ค์–ด๊ฐ€
03:36
and my French is not very good; I said something like,
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๋ชจ์ž๋ž€ ํ”„๋ž‘์Šค์–ด๋กœ, ์ด๋Ÿฐ ์‹์œผ๋กœ ๋งํ–ˆ์„๊ฒ๋‹ˆ๋‹ค.
03:39
"I am a mathematician and I would like to stand on your roof."
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"๋‚˜๋Š” ์ˆ˜ํ•™์ž์ด๊ณ  ๋‹น์‹ ์˜ ์ง€๋ถ• ์œ„์— ์˜ฌ๋ผ๊ฐ€๊ณ  ์‹ถ์Šต๋‹ˆ๋‹ค."
03:42
But he was really cool about it, and he took me up there,
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๊ทธ๋Š” ๋งค์šฐ ํ”์พŒํžˆ ์Šน๋ฝํ•˜๊ณ  ๋‚˜๋ฅผ ์œ„๋กœ ๋ฐ๋ ค๋‹ค ์ฃผ์—ˆ์Šต๋‹ˆ๋‹ค.
03:45
and we talked about fractals.
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๊ทธ๋ฆฌ๊ณ  ์šฐ๋ฆฌ๋Š” ํ”„๋ž™ํƒˆ์— ๋Œ€ํ•ด ์–˜๊ธฐํ–ˆ์Šต๋‹ˆ๋‹ค.
03:46
And he said, "Oh yeah, yeah! We knew about a rectangle within a rectangle,
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๊ทธ๋Š”, "์•„, ๋งž์•„์š”. ๋„ค๋ชจ ์•ˆ์— ๋„ค๋ชจ๊ฐ€ ๋ฐ˜๋ณต๋˜๋Š” ๋ชจ์–‘์— ๋Œ€ํ•ด์„  ์•Œ๊ณ  ์žˆ์Šต๋‹ˆ๋‹ค."
03:49
we know all about that."
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๋ผ๊ณ  ๋ง ํ–ˆ์Šต๋‹ˆ๋‹ค.
03:51
And it turns out the royal insignia has a rectangle within a rectangle within a rectangle,
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์‹ค์ œ๋กœ ์ง€๋ฐฐ์ธต์˜ ๋ฌธ์žฅ์€ ์‚ฌ๊ฐํ˜• ์•ˆ์— ์‚ฌ๊ฐํ˜•์ด ๋ฐ˜๋ณต๋˜๋Š” ๋ชจ์–‘์ด์—ˆ๊ณ ,
03:55
and the path through that palace is actually this spiral here.
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๊ถ์œผ๋กœ ๊ฐ€๋Š” ๊ธธ์€ ์ด์ฒ˜๋Ÿผ ๋‚˜์„ ์ด ๋ฐ˜๋ณต๋˜๋Š” ๋ชจ์–‘์ด์—ˆ์Šต๋‹ˆ๋‹ค.
03:59
And as you go through the path, you have to get more and more polite.
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์ด ๊ธธ ์•ˆ์ชฝ์œผ๋กœ ๋“ค์–ด๊ฐˆ ์ˆ˜๋ก ๋” ์ •์ค‘ํ•ด์ ธ์•ผ ํ•ฉ๋‹ˆ๋‹ค.
04:03
So they're mapping the social scaling onto the geometric scaling;
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๊ทธ๋“ค์€ ์‚ฌํšŒ์ ์ธ ๋‹จ์œ„๋ฅผ ์ง€๋ฆฌ์ ์ธ ๋‹จ์œ„์— ๋Œ€์‘์‹œํ‚จ ๊ฒƒ์ž…๋‹ˆ๋‹ค.
04:06
it's a conscious pattern. It is not unconscious like a termite mound fractal.
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์ด๊ฒƒ์€ ํฐ๊ฐœ๋ฏธ ๊ตด๊ณผ ๊ฐ™์€ ๋ฌด์˜์‹์ ์ธ ํŒจํ„ด๊ณผ๋Š” ๋‹ฌ๋ฆฌ ์˜์‹์ ์œผ๋กœ ๋งŒ๋“ค์–ด์ง„ ํ”„๋ž™ํƒˆํŒจํ„ด์ž…๋‹ˆ๋‹ค.
04:11
This is a village in southern Zambia.
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์ด ์‚ฌ์ง„์€ ์ž ๋น„์•„ ๋‚จ๋ถ€์˜ ๋งˆ์„์ž…๋‹ˆ๋‹ค.
04:13
The Ba-ila built this village about 400 meters in diameter.
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๋ฐ”-๋ผ์กฑ์ด ์ง€๋ฆ„ 400m ์ •๋„์˜ ๊ณต๊ฐ„์— ์ด ๋งˆ์„์„ ๊ฑด์„คํ–ˆ์Šต๋‹ˆ๋‹ค.
04:17
You have a huge ring.
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๊ฑฐ๋Œ€ํ•œ ๊ณ ๋ฆฌํ˜• ๊ตฌ์กฐ๊ฐ€ ์žˆ๊ณ ,
04:19
The rings that represent the family enclosures get larger and larger as you go towards the back,
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๋’ค์ชฝ์œผ๋กœ ๊ฐˆ์ˆ˜๋ก ์ปค์ง€๋Š” ํ™˜ํ˜• ๊ตฌ์กฐ๋Š” ํ˜ˆ์—ฐ์˜ ์ธ์ ‘์„ฑ์„ ๋‚˜ํƒ€๋ƒ…๋‹ˆ๋‹ค.
04:26
and then you have the chief's ring here towards the back
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๋งจ ๋’ค๋กœ ๊ฐ€๋ฉด ์ถ”์žฅ์˜ ๊ณ ๋ฆฌ๊ฐ€ ์žˆ๊ณ 
04:30
and then the chief's immediate family in that ring.
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์ด ๊ณ ๋ฆฌ ์ฃผ๋ณ€์— ์ถ”์žฅ์˜ ์ง๊ณ„์กด์†๋“ค์ด ์žˆ์Šต๋‹ˆ๋‹ค.
04:33
So here's a little fractal model for it.
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์ด๊ฒƒ์ด ๊ทธ ํ”„๋ž™ํƒˆ ๋ชจํ˜•์ž…๋‹ˆ๋‹ค.
04:34
Here's one house with the sacred altar,
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์—ฌ๊ธฐ๋Š” ์‹ ์„ฑํ•œ ์ œ๋‹จ์ด ์žˆ๋Š” ์ง‘์ด๊ณ ,
04:37
here's the house of houses, the family enclosure,
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์—ฌ๊ธฐ๋Š” ๊ฐ€์กฑ๋“ค์ด ์‚ด๊ฒŒ ๋˜๋Š” ๊ฐ€์˜ฅ๊ณผ ๊ทธ ๋‚ด๋ถ€์˜ ๊ฐ€์˜ฅ๋“ค์ž…๋‹ˆ๋‹ค.
04:40
with the humans here where the sacred altar would be,
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์—ฌ๊ธฐ๋Š” ์ œ๋‹จ๊ณผ ๊ด€๋ จ๋œ ์‚ฌ๋žŒ๋“ค์ด ๊ฑฐ์ฃผํ•˜๊ณ ,
04:43
and then here's the village as a whole --
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์ด์ชฝ์— ๋งˆ์„ ์ „์ฒด์˜ ์‚ฌ๋žŒ๋“ค์ด ๊ฑฐ์ฃผํ•˜๋ฉด์„œ --
04:45
a ring of ring of rings with the chief's extended family here, the chief's immediate family here,
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๊ณ ๋ฆฌ์˜ ๊ณ ๋ฆฌ์˜ ๊ณ ๋ฆฌ์ธ ์ด ๊ณณ์— ์ถ”์žฅ์˜ ๋ฐฉ๊ณ„ ๊ฐ€์กฑ์ด, ๊ทธ๋ฆฌ๊ณ  ์ด ์•ˆ์ชฝ์— ์ง๊ณ„ ๊ฐ€์กฑ์ด ๊ฑฐ์ฃผํ•˜๊ณ 
04:50
and here there's a tiny village only this big.
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์ด ์•ˆ์ชฝ์—” ์ด ์ •๋„์˜ ์ž‘์€ ๋งˆ์„์ด ์žˆ๊ฒŒ ๋ฉ๋‹ˆ๋‹ค.
04:53
Now you might wonder, how can people fit in a tiny village only this big?
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์ด์ฏค์—์„œ ์–ด๋–ป๊ฒŒ ์‚ฌ๋žŒ๋“ค์ด ์ด ์ž‘์€ ๋งˆ์„์— ์‚ด ์ˆ˜ ์žˆ์„์ง€ ์˜๋ฌธ์ด ๋“ค ๊ฒƒ์ž…๋‹ˆ๋‹ค.
04:57
That's because they're spirit people. It's the ancestors.
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์ด ๋งˆ์„์€ ๊ทธ๋“ค์˜ ์กฐ์ƒ์‹ ์„ ์œ„ํ•œ ๊ฒƒ์ž…๋‹ˆ๋‹ค.
05:00
And of course the spirit people have a little miniature village in their village, right?
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๊ทธ๋Ÿผ, ๋‹น์—ฐํžˆ ์ด ์กฐ์ƒ์‹ ๋“ค์€ ์ž์‹ ๋“ค์˜ ์กฐ์ƒ์‹ ์„ ์œ„ํ•œ ์ž‘์€ ๋งˆ์„์„ ๊ฐ–๊ณ  ์žˆ๊ฒ ์ฃ ?
05:05
So it's just like Georg Cantor said, the recursion continues forever.
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๊ฒŒ์˜ค๋ฅด๊ทธ ์นธํ† ์–ด๊ฐ€ ๋งํ•œ ๊ฒƒ ๊ฐ™์€, ๋ฌดํ•œํžˆ ์žฌ๊ท€์ ์œผ๋กœ ๋ฐ˜๋ณต๋˜๋Š” ํŒจํ„ด์ž…๋‹ˆ๋‹ค.
05:08
This is in the Mandara mountains, near the Nigerian border in Cameroon, Mokoulek.
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์ด๊ณณ์€ ๋‚˜์ด์ง€๋ฆฌ์•„์˜ ์นด๋ฉ”๋ฃฌ๊ณผ์˜ ๊ตญ๊ฒฝ์ง€๋Œ€์— ์œ„์น˜ํ•œ ๋งŒ๋‹ค๋ผ ์‚ฐ๋งฅ์˜ ๋ชจ์ฝ”์šฐ๋ ‰์ž…๋‹ˆ๋‹ค.
05:12
I saw this diagram drawn by a French architect,
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์ €๋Š” ๊ทธ๊ณณ์—์„œ ํ•œ ํ”„๋ž‘์Šค ๊ฑด์ถ•๊ฐ€๊ฐ€ ๊ทธ๋ฆฐ ๋„์•ˆ์„ ๋ฐœ๊ฒฌํ–ˆ๊ณ ,
05:15
and I thought, "Wow! What a beautiful fractal!"
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"๋Œ€๋‹จํžˆ ์•„๋ฆ„๋‹ค์šด ํ”„๋ž™ํƒˆ์ด๋‹ค!" ๋ผ๊ณ  ๊ฐํƒ„ํ–ˆ์Šต๋‹ˆ๋‹ค.
05:17
So I tried to come up with a seed shape, which, upon iteration, would unfold into this thing.
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๊ทธ๋ž˜์„œ ์ด ๋„์•ˆ์„ ํŽผ์น˜๊ธฐ ์ด์ „์˜ ์ดˆ๊ธฐ ๋ชจ์–‘์„ ๋ฐ˜๋ณต ๊ณผ์ •์„ ํ†ตํ•ด์„œ ์ฐพ์•„๋‚ด๋ ค ํ–ˆ์Šต๋‹ˆ๋‹ค.
05:23
I came up with this structure here.
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๊ทธ๋ ‡๊ฒŒ ํ•ด์„œ ์ฐพ์•„๋‚ธ ๊ตฌ์กฐ์ž…๋‹ˆ๋‹ค.
05:25
Let's see, first iteration, second, third, fourth.
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๋ณด์‹œ์ฃ , ์ฒซ ๋‹จ๊ณ„, ๋‘ ๋ฒˆ์งธ, ์„ธ ๋ฒˆ์งธ, ๋„ค ๋ฒˆ์งธ๋กœ ๋ฐ˜๋ณตํ•ฉ๋‹ˆ๋‹ค.
05:29
Now, after I did the simulation,
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์ด์ œ ์ด๋Ÿฐ ์‹œ๋ฎฌ๋ ˆ์ด์…˜์„ ํ†ตํ•ด์„œ
05:31
I realized the whole village kind of spirals around, just like this,
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์ „์ฒด ๋งˆ์„์˜ ๋ชจ์–‘์ด ์ด์™€ ๊ฐ™์€ ๋‚˜์„ ๋“ค๋กœ ์ด๋ฃจ์–ด์ ธ ์žˆ๋‹ค๋Š” ๊ฒƒ์„ ๊นจ๋‹ฌ์•˜์Šต๋‹ˆ๋‹ค.
05:34
and here's that replicating line -- a self-replicating line that unfolds into the fractal.
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์ด์ชฝ์ด ๊ทธ ๋‹ฎ์€ ๋ชจ์–‘์ด๊ตฌ์š” -- ์ด๋ ‡๊ฒŒ ์ž๊ธฐ๋ฐ˜๋ณต์ ์œผ๋กœ ํŽผ์นœ ํ”„๋ž™ํƒˆ ๋ชจ์–‘์ด ๋ฉ๋‹ˆ๋‹ค.
05:40
Well, I noticed that line is about where the only square building in the village is at.
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๊ทธ๋ฆฌ๊ณ  ์ด ์„ ๋“ค์ด ์ด ๋งˆ์„์˜ ์œ ์ผํ•œ ์‚ฌ๊ฐ ๊ฑด๋ฌผ์—์„œ ์ด์–ด์ง€๋Š” ๊ฒƒ์„ ์•Œ์•„๋ƒˆ์Šต๋‹ˆ๋‹ค.
05:45
So, when I got to the village,
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๊ทธ๋ž˜์„œ ์ด ๋งˆ์„์— ๋„์ฐฉํ–ˆ์„ ๋•Œ,
05:47
I said, "Can you take me to the square building?
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"๋„ค๋ชจ๋‚œ ๊ฑด๋ฌผ๋กœ ๊ฐˆ ์ˆ˜ ์žˆ์„๊นŒ์š”? ๊ฑฐ๊ธฐ์— ๋ญ”๊ฐ€๊ฐ€ ์žˆ์„ ๊ฒƒ ๊ฐ™์Šต๋‹ˆ๋‹ค."
05:49
I think something's going on there."
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๋ผ๊ณ  ํ–ˆ์Šต๋‹ˆ๋‹ค.
05:51
And they said, "Well, we can take you there, but you can't go inside
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๊ทธ๋“ค์ด ๋งํ•˜๊ธฐ๋ฅผ, "๊ทธ์ชฝ์œผ๋กœ ๋‹น์‹ ์„ ๋ฐ๋ ค๊ฐˆ ์ˆ˜๋Š” ์žˆ์ง€๋งŒ,
05:54
because that's the sacred altar, where we do sacrifices every year
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๊ทธ ์•ˆ์€ ์šฐ๋ฆฌ๊ฐ€ ๋งค๋…„ ํ’์š”๋ฅผ ๊ธฐ์›ํ•˜๋ฉฐ ํฌ์ƒ์ œ๋ฅผ ์ง€๋‚ด๋Š” ์‹ ์„ฑํ•œ ์ œ๋‹จ์ด๊ธฐ ๋•Œ๋ฌธ์—
05:57
to keep up those annual cycles of fertility for the fields."
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์•ˆ์œผ๋กœ ๋“ค์—ฌ๋ณด๋‚ผ ์ˆ˜๋Š” ์—†์Šต๋‹ˆ๋‹ค." ๋ผ๊ณ  ํ–ˆ์Šต๋‹ˆ๋‹ค.
06:00
And I started to realize that the cycles of fertility
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๊ทธ์ œ์„œ์•ผ ์ €๋Š” ๊ทธ ํ’์š”์˜ ์›๋“ค์ด
06:02
were just like the recursive cycles in the geometric algorithm that builds this.
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์ด ๊ฑด๋ฌผ๋“ค์˜ ๋ชจ์–‘์ฒ˜๋Ÿผ ์ž๊ธฐ๋ฐ˜๋ณต์ ์ธ ์›๋“ค๋กœ ์ด๋ฃจ์–ด ์ง„ ๊ฒƒ์„ ์•Œ์•„์ฑ˜์Šต๋‹ˆ๋‹ค.
06:06
And the recursion in some of these villages continues down into very tiny scales.
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์ด๋Ÿฐ ๋งˆ์„๋“ค์ด ์ž๊ธฐ๋ฐ˜๋ณต์ ์œผ๋กœ ๋งค์šฐ ์ž‘์€ ํฌ๊ธฐ๊นŒ์ง€ ๋ฐ˜๋ณต๋˜๋Š” ๊ฒƒ์ฒ˜๋Ÿผ์š”.
06:10
So here's a Nankani village in Mali.
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์ด๊ณณ์€ ๋ง๋ฆฌ์˜ ๋‚œ์นด๋‹ˆ ๋งˆ์„์ž…๋‹ˆ๋‹ค.
06:12
And you can see, you go inside the family enclosure --
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์—ฌ๊ธฐ ๊ฐ€์กฑ ๊ตฌ์„ฑ์˜ ์•ˆ์œผ๋กœ ๊ฐ€๋ฉด --
06:15
you go inside and here's pots in the fireplace, stacked recursively.
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๋ถˆ ํ”ผ์šฐ๋Š” ๊ณณ ์ฃผ๋ณ€์œผ๋กœ ๋ƒ„๋น„๋“ค์ด ์žฌ๊ท€์ ์œผ๋กœ ์Œ“์—ฌ ์žˆ๋Š” ๊ฒƒ์„ ๋ณผ ์ˆ˜ ์žˆ์Šต๋‹ˆ๋‹ค.
06:19
Here's calabashes that Issa was just showing us,
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์ด๊ฒƒ์€ ์ด์‚ฌ๊ฐ€ ์šฐ๋ฆฌ์—๊ฒŒ ๋ณด์—ฌ์ค€ ํ˜ธ๋ฆฌ๋ณ‘๋ฐ•๋“ค์ž…๋‹ˆ๋‹ค.
06:23
and they're stacked recursively.
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์ด๊ฒƒ๋“ค ๋˜ํ•œ ์žฌ๊ท€์ ์œผ๋กœ ์Œ“์—ฌ ์žˆ์Šต๋‹ˆ๋‹ค.
06:25
Now, the tiniest calabash in here keeps the woman's soul.
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์ด ์ค‘์˜ ๊ฐ€์žฅ ์ž‘์€ ํ˜ธ๋ฆฌ๋ณ‘๋ฐ• ์•ˆ์—๋Š” ์—ฌ์„ฑ์˜ ์˜ํ˜ผ์ด ๋‹ด๊ฒจ ์žˆ๋‹ค๊ณ  ํ•˜๊ณ ,
06:27
And when she dies, they have a ceremony
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๊ทธ๋…€๊ฐ€ ์‚ฌ๋งํ•˜๋ฉด ์ด ๋ฌด๋”๊ธฐ๋ฅผ ๋ฌด๋„ˆ๋œจ๋ฆฌ๋Š” ์ž˜๋ž€๊ฐ€๋ผ๋Š” ์˜์‹์„ ํ†ตํ•ด
06:29
where they break this stack called the zalanga and her soul goes off to eternity.
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์˜ํ˜ผ์„ ์˜์›์œผ๋กœ ์ „์†กํ•˜๋Š” ์˜์‹์„ ์น˜๋ฃน๋‹ˆ๋‹ค.
06:34
Once again, infinity is important.
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๋‹ค์‹œ ํ•œ ๋ฒˆ, ๋ฌดํ•œ์ด ๋ถ€๊ฐ๋ฉ๋‹ˆ๋‹ค.
06:38
Now, you might ask yourself three questions at this point.
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์ด์ฏค์—์„œ ์—ฌ๋Ÿฌ๋ถ„์€ ์ด๋Ÿฐ ์งˆ๋ฌธ์„ ๋˜์ง€๊ฒŒ ๋  ๊ฒƒ์ž…๋‹ˆ๋‹ค.
06:42
Aren't these scaling patterns just universal to all indigenous architecture?
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์ด๋Ÿฐ ์ž๊ธฐ๋ฐ˜๋ณต์ ์ธ ํŒจํ„ด์€ ๋ชจ๋“  ํ† ์ฐฉ ๊ฑด์ถ•์—์„œ ๋ณดํŽธ์ ์œผ๋กœ ๋ฐœ๊ฒฌ๋˜๋Š” ๊ฒƒ์ผ๊นŒ?
06:46
And that was actually my original hypothesis.
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์‚ฌ์‹ค ์ด๊ฒƒ์ด ์ €์˜ ๋ณธ๋ž˜ ๊ฐ€์„ค์ด์—ˆ์Šต๋‹ˆ๋‹ค.
06:48
When I first saw those African fractals,
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์ œ๊ฐ€ ์•„ํ”„๋ฆฌ์นด์˜ ํ”„๋ž™ํƒˆ ๋ชจ์–‘๋“ค์„ ์ฒ˜์Œ ๋ดค์„ ๋•Œ,
06:50
I thought, "Wow, so any indigenous group that doesn't have a state society,
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"ํ˜น์‹œ, ๊ตญ๊ฐ€ ์‚ฌํšŒ ๊ฐ™์€ ๊ตฌ์กฐ๋ฅผ ์ง€๋‹ˆ์ง€ ์•Š๋Š” ๋ชจ๋“  ํ† ์ฐฉ ์ง‘๋‹จ๋“ค์ด
06:54
that sort of hierarchy, must have a kind of bottom-up architecture."
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์ด๋Ÿฐ ์‹์˜ ์ƒํ–ฅ์‹ ๊ตฌ์กฐ๋ฅผ ๊ฐ–์ง€ ์•Š์„๊นŒ?" ๋ผ๊ณ  ์ƒ๊ฐํ–ˆ๊ณ ,
06:57
But that turns out not to be true.
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๊ทธ๊ฒƒ์€ ์˜ณ์ง€ ์•Š๋‹ค๊ณ  ๋“œ๋Ÿฌ๋‚ฌ์Šต๋‹ˆ๋‹ค.
06:59
I started collecting aerial photographs of Native American and South Pacific architecture;
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์ €๋Š” ์•„๋ฉ”๋ฆฌ์นด ์ธ๋””์•ˆ๊ณผ ๋‚จํƒœํ‰์–‘ ๋ถ€์กฑ๋“ค์˜ ํ•ญ๊ณต ์‚ฌ์ง„๋“ค๋กœ๋ถ€ํ„ฐ ์‹œ์ž‘ํ–ˆ๊ณ ,
07:03
only the African ones were fractal.
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์˜ค์ง ์•„ํ”„๋ฆฌ์นด์—์„œ๋งŒ ํ”„๋ž™ํƒˆ ๋ชจ์–‘์„ ๊ฐ–๋Š” ๊ฒƒ์„ ๋ฐœ๊ฒฌํ–ˆ์Šต๋‹ˆ๋‹ค.
07:05
And if you think about it, all these different societies have different geometric design themes that they use.
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์ƒ๊ฐํ•ด ๋ณด์ž๋ฉด, ๊ทธ๋“ค์˜ ๋‹ค๋ฅธ ์‚ฌํšŒ ๊ตฌ์„ฑ์€ ๊ทธ๋“ค์ด ์‚ฌ์šฉํ•˜๋Š” ์ง€๋ฆฌ์  ๋„ํ˜•์— ์˜ํ–ฅ์„ ์ฃผ๋Š” ๊ฒƒ์ž…๋‹ˆ๋‹ค.
07:11
So Native Americans use a combination of circular symmetry and fourfold symmetry.
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์•„๋ฉ”๋ฆฌ์นด ์ธ๋””์•ˆ๋“ค์€ ๊ทธ๋“ค์˜ ๋„์ž๊ธฐ๋‚˜ ๋ฐ”๊ตฌ๋‹ˆ์—์„œ ๋ณผ ์ˆ˜ ์žˆ๋Š” ๊ฒƒ์ฒ˜๋Ÿผ
07:17
You can see on the pottery and the baskets.
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์›๋Œ€์นญ๊ณผ ์‚ฌ๋ฐฉ๋Œ€์นญํ˜• ์กฐํ•ฉ์˜ ๋ฌธ์–‘์„ ์‚ฌ์šฉํ•ฉ๋‹ˆ๋‹ค.
07:19
Here's an aerial photograph of one of the Anasazi ruins;
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์ด๊ฒƒ์€ ์•„๋‚˜์‚ฌ์น˜ ์œ ์ ์˜ ํ•ญ๊ณต ์‚ฌ์ง„์ž…๋‹ˆ๋‹ค.
07:22
you can see it's circular at the largest scale, but it's rectangular at the smaller scale, right?
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๋ณด์‹œ๋Š” ๊ฒƒ์ฒ˜๋Ÿผ ํฌ๊ฒŒ๋Š” ์›ํ˜•์ด๊ณ , ์ž‘์€ ๋‹จ์œ„์—์„œ ์‚ฌ๊ฐํ˜•์„ ์ด๋ฃจ๊ณ  ์žˆ์Œ์„ ์•Œ ์ˆ˜ ์žˆ์Šต๋‹ˆ๋‹ค.
07:27
It is not the same pattern at two different scales.
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๋‹ค๋ฅธ ๋‹จ์œ„์—์„œ ๊ฐ™์€ ํŒจํ„ด์„ ์ด๋ฃจ๊ณ  ์žˆ์ง€ ์•Š์ฃ .
07:31
Second, you might ask,
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๋‘ ๋ฒˆ์งธ๋กœ, "๊ธ€์Ž„์š”,
07:32
"Well, Dr. Eglash, aren't you ignoring the diversity of African cultures?"
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Eglash ๋ฐ•์‚ฌ, ํ˜น ์•„ํ”„๋ฆฌ์นด ๋ฌธํ™”์˜ ๋‹ค์–‘์„ฑ์„ ๋ฌด์‹œํ•˜๊ณ  ์žˆ๋Š” ๊ฒƒ์€ ์•„๋‹™๋‹ˆ๊นŒ?" ๋ผ๊ณ  ๋ฌผ์œผ์‹ค ์ˆ˜ ์žˆ์Šต๋‹ˆ๋‹ค.
07:36
And three times, the answer is no.
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์„ธ ๊ฐ€์ง€ ์ด์œ ๋กœ, ๋‹ต์€ "์•„๋‹™๋‹ˆ๋‹ค."
07:38
First of all, I agree with Mudimbe's wonderful book, "The Invention of Africa,"
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์ฒซ์งธ๋กœ, ์ €๋Š” ๋ฌด๋”ค๋ฒ ์˜ ํ›Œ๋ฅญํ•œ ์ฑ…, [์•„ํ”„๋ฆฌ์นด์˜ ๋ฐœ๋ช…] ์— ์ฃผ์žฅํ•˜๋Š” ๋ฐ”์™€ ๊ฐ™์ด
07:42
that Africa is an artificial invention of first colonialism,
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์•„ํ”„๋ฆฌ์นด๊ฐ€ ์‚ฌ์‹ค ์˜› ์‹๋ฏผ์‹œ๋Œ€์™€ ๊ทธ ๋ฐ˜ํ–ฅ ์šด๋™๋“ค๋กœ ์ธํ•œ
07:45
and then oppositional movements.
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์ธ๊ณต์ ์œผ๋กœ ๋ฐœ๋ช…๋œ ๊ฐœ๋…์ด๋ผ๋Š” ๋ฐ ๋™์˜ํ•ฉ๋‹ˆ๋‹ค.
07:47
No, because a widely shared design practice doesn't necessarily give you a unity of culture --
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๋„๋ฆฌ ํผ์ ธ์žˆ๋Š” ์‹ค์ œ์ ์ธ ๋””์ž์ธ ํŒจํ„ด์ด ๋ฌธํ™”์˜ ํ•„์—ฐ์ ์œผ๋กœ ๋ฌธํ™”์˜ ๋™์งˆ์„ฑ์œผ๋กœ ์ด์–ด์ง€๋Š” ๊ฒƒ์€ ์•„๋‹ˆ๋ฉฐ--
07:52
and it definitely is not "in the DNA."
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DNA ์— ๋Œ€ํ•ด์„œ๋„ ๋™์ผํ•ฉ๋‹ˆ๋‹ค.
07:55
And finally, the fractals have self-similarity --
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๋‘ ๋ฒˆ์งธ๋กœ, ํ”„๋ž™ํƒˆ์€ ์ž๊ธฐ๋ฐ˜๋ณต์ ์ธ ์„ฑ์งˆ์„ ๊ฐ–๊ณ  ์žˆ์–ด์„œ
07:57
so they're similar to themselves, but they're not necessarily similar to each other --
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๊ทธ ์ž์‹ ์˜ ๋ชจ์–‘๊ณผ ๋‹ฎ์•„ ์žˆ๋Š” ๊ฒƒ์€ ์‚ฌ์‹ค์ด์ง€๋งŒ, ๊ทธ๋“ค ๊ฐ„์˜ ๋ชจ์–‘์ด ๋‹ฎ์„ ํ•„์š”๋Š” ์—†์Šต๋‹ˆ๋‹ค.
08:01
you see very different uses for fractals.
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์ด๋ฅผ ํ†ตํ•ด ๋‹ค์–‘ํ•œ ๋ชจ์–‘์˜ ํ”„๋ž™ํƒˆ ๋„ํ˜•๋“ค์„ ๋ณผ ์ˆ˜ ์žˆ์Šต๋‹ˆ๋‹ค.
08:03
It's a shared technology in Africa.
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ํ”„๋ž™ํƒˆ ๋„ํ˜•์€ ์•„ํ”„๋ฆฌ์นด์— ํผ์ ธ ์žˆ๋Š” ๊ธฐ์ˆ  ํ˜„์ƒ์ธ ๊ฒƒ์ด์ฃ .
08:06
And finally, well, isn't this just intuition?
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๋งˆ์ง€๋ง‰์œผ๋กœ, ๊ธ€์Ž„์š”, ๊ทธ์ € ์šฐ์—ฐ์ด ์•„๋‹ˆ๋ƒ๊ณ  ๋ฌผ์„ ์ˆ˜๋„ ์žˆ์Šต๋‹ˆ๋‹ค.
08:09
It's not really mathematical knowledge.
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์‹ค์ œ๋กœ ์ˆ˜ํ•™์ ์ธ ์ง€์‹์ด ์ „์Šน๋˜์–ด ์˜จ ๊ฒƒ์€ ์•„๋‹ˆ๋ผ๊ณ  ๋ง์ด์ฃ .
08:11
Africans can't possibly really be using fractal geometry, right?
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์•„ํ”„๋ฆฌ์นด์ธ๋“ค์ด ํ”„๋ž™ํƒˆ ๋„ํ˜•์„ ์•Œ๊ณ  ์ด์šฉํ•  ์ˆ˜๋Š” ์—†์—ˆ๊ฒ ์ง€์š”,
08:14
It wasn't invented until the 1970s.
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๊ทธ๊ฒƒ์€ 1970๋…„๋Œ€์— ์ฒ˜์Œ ์•Œ๋ ค์กŒ์œผ๋‹ˆ๊นŒ์š”.
08:17
Well, it's true that some African fractals are, as far as I'm concerned, just pure intuition.
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๋ญ, ๋ช‡๋ช‡ ์•„ํ”„๋ฆฌ์นด์˜ ํ”„๋ž™ํƒˆ๋“ค์ด ์ˆœ์ˆ˜ํ•˜๊ฒŒ ์ง๊ด€์ ์œผ๋กœ ์ด๋ฃจ์–ด ์ง„ ๊ฑด ์‚ฌ์‹ค์ž…๋‹ˆ๋‹ค.
08:22
So some of these things, I'd wander around the streets of Dakar
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๊ทธ๋ž˜์„œ ์ด๋ ‡๊ฒŒ, ๋‹ค์นด๋ฅด์˜ ๊ฑฐ๋ฆฌ๋ฅผ ๋Œ์•„๋‹ค๋‹ˆ๋ฉด์„œ ์‚ฌ๋žŒ๋“ค์—๊ฒŒ ๋ฌผ์—ˆ์„ ๋•Œ,
08:25
asking people, "What's the algorithm? What's the rule for making this?"
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"์–ด๋–ค ์•Œ๊ณ ๋ฆฌ์ฆ˜์ž…๋‹ˆ๊นŒ? ๊ทธ๋Ÿฌ๋‹ˆ๊นŒ, ์ด๊ฑธ ๋งŒ๋“œ๋Š” ๊ทœ์น™์ด ๋ญ์ฃ ?" ๋ผ๊ณ  ํ–ˆ์„ ๋•Œ,
08:28
and they'd say,
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๊ทธ๋“ค์€ ์ด๋ ‡๊ฒŒ ๋‹ตํ–ˆ์Šต๋‹ˆ๋‹ค.
08:29
"Well, we just make it that way because it looks pretty, stupid." (Laughter)
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"๊ทธ๋ƒฅ ๊ทธ ๋ชจ์–‘์ด ์˜ˆ์˜๋‹ˆ๊นŒ์š”. ๋ฉ์ฒญํ•œ ์–‘๋ฐ˜์•„." (์›ƒ์Œ)
08:32
But sometimes, that's not the case.
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ํ•˜์ง€๋งŒ ๊ฐ„ํ˜น๊ฐ€๋‹ค๊ฐ€ ์•„๋‹Œ ๊ฒฝ์šฐ๋„ ์žˆ์Šต๋‹ˆ๋‹ค.
08:35
In some cases, there would actually be algorithms, and very sophisticated algorithms.
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๊ฐ„ํ˜น, ๊ทธ ์•ˆ์—๋Š” ์‹ค์ œ๋กœ ๋ณต์žกํ•œ ์•Œ๊ณ ๋ฆฌ์ฆ˜์ด ์ ์šฉ๋˜๋Š” ๊ฒฝ์šฐ๊ฐ€ ์žˆ์Šต๋‹ˆ๋‹ค.
08:40
So in Manghetu sculpture, you'd see this recursive geometry.
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์ด ๋งŒ๊ฒŒํˆฌ ์กฐ๊ฐ์„ ๋ณด๋ฉด ์—ํ‹ฐ์˜คํ”ผ์•„ ์‹ญ์ž๊ฐ€์˜
08:43
In Ethiopian crosses, you see this wonderful unfolding of the shape.
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์žฌ๊ท€์ ์ธ ํŽผ์นจ ๋ฌธ์–‘์„ ๋ณผ ์ˆ˜ ์žˆ์Šต๋‹ˆ๋‹ค.
08:48
In Angola, the Chokwe people draw lines in the sand,
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์•™๊ณจ๋ผ์—์„ , ์ดˆ์ผ€์กฑ ์‚ฌ๋žŒ๋“ค์€ ๋ชจ๋ž˜์— ๊ทธ๋ฆผ์„ ๊ทธ๋ฆฌ๋Š”๋ฐ
08:52
and it's what the German mathematician Euler called a graph;
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์ด๊ฒƒ์€ ๋…์ผ์˜ ์ˆ˜ํ•™์ž ์˜ค์ผ๋Ÿฌ๊ฐ€ ์–˜๊ธฐํ•œ ๊ทธ๋ž˜ํ”„ ์ด๋ก ์˜
08:55
we now call it an Eulerian path --
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์˜ค์ผ๋Ÿฌ ๊ฒฝ๋กœ๋ฅผ ํ†ตํ•ด์„œ ๊ทธ๋ ค์ง‘๋‹ˆ๋‹ค.
08:57
you can never lift your stylus from the surface
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ํŽœ์„ ํ‘œ๋ฉด์—์„œ ๋–ผ์ง€ ์•Š๊ณ , ๊ฐ™์€ ์„ ์„ ๋‘ ๋ฒˆ ์ด์ƒ ๊ฒน์ณ ๊ทธ๋ฆฌ์ง€ ์•Š์œผ๋ฉฐ
08:59
and you can never go over the same line twice.
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๋ฌธ์–‘์„ ๊ทธ๋ฆฌ๊ฒŒ ๋ฉ๋‹ˆ๋‹ค.
09:02
But they do it recursively, and they do it with an age-grade system,
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๋ฌธ์–‘์€ ์žฌ๊ท€์ ์œผ๋กœ ๋ฐ˜๋ณต๋˜๊ณ , ์ด ๋ฌธ์–‘์€ ์—ฐ๋ น๋Œ€์— ๋”ฐ๋ผ ๋‹ฌ๋ผ์ง€๋Š”๋ฐ,
09:05
so the little kids learn this one, and then the older kids learn this one,
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๊ผฌ๋งˆ๋“ค์€ ์ด ๋ฌธ์–‘์„ ๊ทธ๋ฆฌ๊ณ , ๋” ๋‚˜์ด ๋“  ์•„์ด๋“ค์€ ์ด ๋ฌธ์–‘์„ ๋ฐฐ์›๋‹ˆ๋‹ค.
09:08
then the next age-grade initiation, you learn this one.
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๋” ์ž๋ผ์„œ๋Š” ์ด ๋ฌธ์–‘์„ ๋ฐฐ์šฐ๊ฒŒ ๋ฉ๋‹ˆ๋‹ค.
09:11
And with each iteration of that algorithm,
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์ด ๋ฒ•์น™์˜ ๊ฐ ๋ฐ˜๋ณต ๋‹จ๊ณ„๋“ค์„ ํ†ตํ•ด์„œ
09:14
you learn the iterations of the myth.
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๊ทธ ๋ฐ˜๋ณต์— ์–ฝํžŒ ์‹ ํ™”๋ฅผ ๊ฐ™์ด ๋ฐฐ์šฐ๊ฒŒ ๋ฉ๋‹ˆ๋‹ค.
09:16
You learn the next level of knowledge.
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๊ทธ๋ฆฌ๊ณ  ๋‹ค์Œ ๋‹จ๊ณ„์˜ ์ง€์‹์„ ์Šต๋“ํ•˜๊ฒŒ ๋˜๋Š” ๊ฒƒ์ด์ฃ .
09:19
And finally, all over Africa, you see this board game.
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๋งˆ์ง€๋ง‰์œผ๋กœ, ์•„ํ”„๋ฆฌ์นด ์ „์—ญ์—์„œ ์ด๋Ÿฐ ๋ณด๋“œ๊ฒŒ์ž„์„ ๋ณผ ์ˆ˜ ์žˆ์Šต๋‹ˆ๋‹ค.
09:21
It's called Owari in Ghana, where I studied it;
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์ œ๊ฐ€ ์ด ๊ฒŒ์ž„์„ ๋ฐฐ์šด ๊ฐ€๋‚˜์—์„œ๋Š” ์˜ค์™€๋ฆฌ๋ผ๊ณ  ๋ถˆ๋ฆฝ๋‹ˆ๋‹ค.
09:24
it's called Mancala here on the East Coast, Bao in Kenya, Sogo elsewhere.
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๋™๋ถ€ ํ•ด์•ˆ์ง€๋Œ€์—์„  ๋งŒ์นผ๋ผ, ์ผ€๋ƒ์—์„œ๋Š” ๋ฐ”์˜ค, ๋‹ค๋ฅธ ๊ณณ์—์„œ๋Š” ์†Œ๊ณ  ๋กœ ๋ถˆ๋ฆฝ๋‹ˆ๋‹ค.
09:29
Well, you see self-organizing patterns that spontaneously occur in this board game.
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์ด ๊ฒŒ์ž„ ์•ˆ์—์„œ ์—„์ฒญ๋‚œ ์ž๊ธฐ๋ฐ˜๋ณต์ ์ธ ํŒจํ„ด์ด ๋ฐœ์ƒํ•˜๋Š” ๊ฒƒ์„ ๋ณผ ์ˆ˜ ์žˆ์Šต๋‹ˆ๋‹ค.
09:34
And the folks in Ghana knew about these self-organizing patterns
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๊ฐ€๋‚˜ ์‚ฌ๋žŒ๋“ค์€ ์ด๋Ÿฐ ์ž๊ธฐ๋ฐ˜๋ณต์ ์ธ ํŒจํ„ด์„ ์ดํ•ดํ•˜์—ฌ
09:37
and would use them strategically.
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์ „๋žต์ ์œผ๋กœ ์ด์šฉํ•ฉ๋‹ˆ๋‹ค.
09:39
So this is very conscious knowledge.
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์ด๋ ‡๊ฒŒ ๋ณด๋ฉด ๋งค์šฐ ์˜์‹์ ์œผ๋กœ ์ „์Šน๋˜๋Š” ์ง€์‹์ด์ฃ .
09:41
Here's a wonderful fractal.
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์—ฌ๊ธฐ ์žˆ๋Š” ๋ฉ‹์ง„ ํ”„๋ž™ํƒˆ์ฒ˜๋Ÿผ
09:43
Anywhere you go in the Sahel, you'll see this windscreen.
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์‚ฌํ—ฌ์ง€๋Œ€ ์•ˆ ์–ด๋””์„œ๋‚˜ ์ด ๋ฐ”๋žŒ๋ง‰์ด ๋„ํ˜•์„ ๋ณผ ์ˆ˜ ์žˆ์Šต๋‹ˆ๋‹ค.
09:47
And of course fences around the world are all Cartesian, all strictly linear.
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์„ธ๊ณ„ ์–ด๋Š ๊ณณ์„ ๊ฐ€๋˜ ํŽœ์Šค๋Š” ์ง๊ต ์ขŒํ‘œ๋กœ, ๊ณง์€ ์ง์„ ์œผ๋กœ ์ด๋ฃจ์–ด์ง‘๋‹ˆ๋‹ค.
09:51
But here in Africa, you've got these nonlinear scaling fences.
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ํ•˜์ง€๋งŒ ์ด๊ณณ, ์•„ํ”„๋ฆฌ์นด์—์„œ ํŽœ์Šค๋Š” ๋น„์„ ํ˜•์œผ๋กœ ์ด๋ฃจ์–ด์ ธ ์žˆ์Šต๋‹ˆ๋‹ค.
09:55
So I tracked down one of the folks who makes these things,
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๊ทธ๋ž˜์„œ ์ €๋Š” ์ด ํŽœ์Šค๋ฅผ ๋งŒ๋“  ์‚ฌ๋žŒ์„ ์ถ”์ ํ•ด,
09:57
this guy in Mali just outside of Bamako, and I asked him,
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๋ฐ”๋งˆ์ฝ” ์™ธ๊ณฝ์— ์‚ฌ๋Š” ๋ง๋ฆฌ์กฑ ์‚ฌ๋žŒ์—๊ฒŒ ๋ฌผ์—ˆ์Šต๋‹ˆ๋‹ค.
10:01
"How come you're making fractal fences? Because nobody else is."
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"์–ด๋–ป๊ฒŒ ์ด๋Ÿฐ ํ”„๋ž™ํƒˆ ํŽœ์Šค๋ฅผ ๋งŒ๋“ค๊ฒŒ ๋˜์—ˆ์Šต๋‹ˆ๊นŒ? ๋‹ค๋ฅธ ์‚ฌ๋žŒ๋“ค์€ ๊ทธ๋ ‡์ง€ ์•Š์Šต๋‹ˆ๋‹ค."
10:03
And his answer was very interesting.
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๊ทธ์˜ ๋‹ต๋ณ€์€ ์•„์ฃผ ํฅ๋ฏธ๋กœ์› ์Šต๋‹ˆ๋‹ค.
10:05
He said, "Well, if I lived in the jungle, I would only use the long rows of straw
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"๋งŒ์•ฝ ๋‚ด๊ฐ€ ์ •๊ธ€์— ์‚ด์•„์„œ, ๊ธด ์งšํ’€์„ ๋นจ๋ฆฌ, ์‹ธ๊ฒŒ ๊ตฌํ•  ์ˆ˜ ์žˆ๋‹ค๋ฉด
10:10
because they're very quick and they're very cheap.
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๋‚˜๋„ ์„ ํ˜• ํŽœ์Šค๋ฅผ ๋งŒ๋“ค์—ˆ์„ ๊ฒƒ์ž…๋‹ˆ๋‹ค.
10:12
It doesn't take much time, doesn't take much straw."
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์‹œ๊ฐ„๋„ ์–ผ๋งˆ ์•ˆ ๊ฑธ๋ฆฌ๊ณ  ์งšํ’€๋„ ์ ๊ฒŒ ๋“œ๋‹ˆ๊นŒ์š”.
10:15
He said, "but wind and dust goes through pretty easily.
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ํ•˜์ง€๋งŒ ๊ทธ๋ ‡๊ฒŒ ํ•˜๋ฉด ๋ฐ”๋žŒ๊ณผ ๋จผ์ง€๊ฐ€ ์‰ฝ๊ฒŒ ํ†ต๊ณผํ•ฉ๋‹ˆ๋‹ค.
10:17
Now, the tight rows up at the very top, they really hold out the wind and dust.
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์ด๋ ‡๊ฒŒ ๋งจ ๊ผญ๋Œ€๊ธฐ๊นŒ์ง€ ๋‹จ๋‹จํ•˜๊ฒŒ ์—ฐ๊ฒฐํ•ด์•ผ ๋ฐ”๋žŒ๊ณผ ๋จผ์ง€๋ฅผ ๋ง‰์•„์ค๋‹ˆ๋‹ค.
10:21
But it takes a lot of time, and it takes a lot of straw because they're really tight."
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๋‹จ๋‹จํ•˜๊ฒŒ ์—ฐ๊ฒฐํ•˜๊ธฐ ์œ„ํ•ด ์ œ์ž‘์‹œ๊ฐ„๋„ ์˜ค๋ž˜ ๊ฑธ๋ฆฌ๊ณ , ์งšํ’€๋„ ๋งŽ์ด ์‚ฌ์šฉ๋˜์ง€๋งŒ์š”.
10:26
"Now," he said, "we know from experience
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์šฐ๋ฆฌ๋Š” ๊ฒฝํ—˜์ ์œผ๋กœ,
10:28
that the farther up from the ground you go, the stronger the wind blows."
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์ง€๋ฉด์—์„œ ๋†’์ด ์˜ฌ๋ผ๊ฐˆ์ˆ˜๋ก ๋ฐ”๋žŒ์ด ๊ฐ•ํ•˜๊ฒŒ ๋ถ„๋‹ค๋Š” ๊ฒƒ์„ ์•Œ๊ณ  ์žˆ์Šต๋‹ˆ๋‹ค."
10:33
Right? It's just like a cost-benefit analysis.
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์–ด๋–ป์Šต๋‹ˆ๊นŒ? ์ •ํ™•ํžˆ ๋น„์šฉ-ํšจ์ต ๋ถ„์„์˜ ๋‚ด์šฉ์ž…๋‹ˆ๋‹ค.
10:36
And I measured out the lengths of straw,
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์ €๋Š” ์งšํ’€์˜ ๊ฐ•๋„๋ฅผ ์ธก์ •ํ•˜๊ณ ,
10:38
put it on a log-log plot, got the scaling exponent,
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๊ทธ๊ฒƒ์„ ๋กœ๊ทธ-๋กœ๊ทธ ๊ทธ๋ž˜ํ”„๋กœ ๊ทธ๋ ธ์„ ๋•Œ,
10:40
and it almost exactly matches the scaling exponent for the relationship between wind speed and height
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๋†’์ด์™€ ๋ฐ”๋žŒ์˜ ์„ธ๊ธฐ๊ฐ€ ๊ธฐํ•˜๊ธ‰์ˆ˜์ ์ธ ๋น„๋ก€์— ๋งž์•„ ๋–จ์–ด์ง„๋‹ค๋Š” ๊ฒƒ์„
10:45
in the wind engineering handbook.
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ํ’๋™์—ญํ•™ ์ฑ…์—์„œ ์ฐพ์•„๋ƒˆ์Šต๋‹ˆ๋‹ค.
10:46
So these guys are right on target for a practical use of scaling technology.
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์ด ์‚ฌ๋žŒ๋“ค์€ ์ •ํ™•ํ•œ ์ธก์ • ๊ธฐ์ˆ ์„ ์‹ค์ „์—์„œ ํ™œ์šฉํ•˜๊ณ  ์žˆ๋Š” ๊ฒƒ์ด์ฃ .
10:51
The most complex example of an algorithmic approach to fractals that I found
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์ œ๊ฐ€ ๋ฐœ๊ฒฌํ•œ ๊ฒƒ ์ค‘ ๊ฐ€์žฅ ๋ณต์žกํ•œ ๊ทœ์น™์˜ ํ”„๋ž™ํƒˆ์€
10:56
was actually not in geometry, it was in a symbolic code,
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์ง€๋ฆฌ์ ์ธ ๊ฒƒ์ด ์•„๋‹Œ, ์‹ฌ๋ณผ๋ฌธ์ž์—์„œ ๋‚˜ํƒ€๋‚ฌ์Šต๋‹ˆ๋‹ค.
10:58
and this was Bamana sand divination.
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์ด๊ฒƒ์€ ๋ฐ”๋งˆ๋‚˜์กฑ์˜ ๋ชจ๋ž˜ ์‹ ์„ฑ๋ฌธ์ž์ž…๋‹ˆ๋‹ค.
11:01
And the same divination system is found all over Africa.
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์ด์™€ ๊ฐ™์€ ์‹ ์„ฑ๋ฌธ ์‹œ์Šคํ…œ์„ ์•„ํ”„๋ฆฌ์นด ์ „์—ญ์—์„œ ์ฐพ์•„ ๋ณผ ์ˆ˜ ์žˆ์Šต๋‹ˆ๋‹ค.
11:04
You can find it on the East Coast as well as the West Coast,
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๋Œ€๋ฅ™ ์„œ์•ˆ์—์„œ ๋™์•ˆ๊นŒ์ง€ ๊ฑฐ์˜ ์œ ์‚ฌํ•ฉ๋‹ˆ๋‹ค.
11:09
and often the symbols are very well preserved,
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๊ฐ„ํ˜น ์ด ์‹ฌ๋ณผ์ด ์•„์ฃผ ์ž˜ ๋ณด์กด ๋œ ๊ฒƒ์„ ๋ณผ ์ˆ˜ ์žˆ๋Š”๋ฐ,
11:11
so each of these symbols has four bits -- it's a four-bit binary word --
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๊ฐ ์‹ฌ๋ณผ์€ ๋„ค๊ฐœ์˜ ๋น„ํŠธ๋กœ ์ด๋ฃจ์–ด์ ธ ์žˆ์Šต๋‹ˆ๋‹ค. -- 4๋น„ํŠธ์˜ ์ด์ง„ ๋‹จ์–ด์ฃ  --
11:17
you draw these lines in the sand randomly, and then you count off,
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์ž„์˜๋กœ ๋ชจ๋ž˜ ์œ„์— ์ด ์„ ๋“ค์„ ๊ทธ๋ฆฌ๋‹ค๊ฐ€, ์„ ์˜ ์ˆซ์ž๋ฅผ ์„ธ์–ด
11:22
and if it's an odd number, you put down one stroke,
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๊ทธ ์ˆซ์ž๊ฐ€ ํ™€์ˆ˜์ด๋ฉด ํ•˜๋‚˜์˜ ์„ ์„ ๋‚ด๋ ค ๊ทธ๋ฆฌ๊ณ ,
11:24
and if it's an even number, you put down two strokes.
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์ง์ˆ˜์ด๋ฉด ๋‘ ์„ ์„ ๋‚ด๋ ค ๊ทธ๋ฆฝ๋‹ˆ๋‹ค.
11:26
And they did this very rapidly,
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์ด ์ž‘์—…์€ ๊ต‰์žฅํžˆ ๋น ๋ฅด๊ฒŒ ์ง„ํ–‰๋˜๋ฉฐ,
11:29
and I couldn't understand where they were getting --
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์ €๋Š” ๊ทธ๋“ค์ด ์ด๊ฒƒ์œผ๋กœ ๋ญ˜ ํ•˜๋ ค๋Š”์ง€ --
11:31
they only did the randomness four times --
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๊ทธ๋“ค์€ ๋‹จ์ˆœํžˆ ์ž„์˜์ ์ธ ๋„ค ๋ฒˆ์˜ ํ–‰๋™์„ ํ•œ ๊ฒƒ์œผ๋กœ ๋ณด์ด์ง€๋งŒ --
11:33
I couldn't understand where they were getting the other 12 symbols.
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์–ด๋–ป๊ฒŒ ๋‚˜๋จธ์ง€ 12๊ฐœ์˜ ์‹ฌ๋ณผ์„ ์“ฐ๊ฒŒ ๋˜๋Š”์ง€ ์ดํ•ดํ•  ์ˆ˜ ์—†์—ˆ์Šต๋‹ˆ๋‹ค.
11:35
And they wouldn't tell me.
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๊ทธ๋“ค๋„ ์ด์•ผ๊ธฐ ํ•ด ์ฃผ์ง€ ์•Š์•˜๊ตฌ์š”.
11:37
They said, "No, no, I can't tell you about this."
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๊ทธ๋“ค์€, "์•„๋‹ˆ, ์•ˆ๋ฉ๋‹ˆ๋‹ค. ์ด๊ฒƒ์„ ์•Œ๋ ค ๋“œ๋ฆด ์ˆ˜๋Š” ์—†์Šต๋‹ˆ๋‹ค." ๋ผ๊ณ  ํ–ˆ๊ณ ,
11:39
And I said, "Well look, I'll pay you, you can be my teacher,
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์ œ๊ฐ€ "์ œ๊ฐ€ ๋ˆ์„ ์ง€๋ถˆํ•˜๊ฒ ์Šต๋‹ˆ๋‹ค. ๋‹น์‹ ์ด ๋‚ด ์Šค์Šน์ด ๋˜์–ด์ฃผ๋ฉด,
11:41
and I'll come each day and pay you."
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๋งค์ผ ์™€์„œ ๋ฐฐ์šฐ๊ณ  ๋Œ“๊ฐ€๋ฅผ ์ง€๋ถˆํ•˜๊ฒ ์Šต๋‹ˆ๋‹ค" ๋ผ๊ณ  ํ•ด๋„
11:43
They said, "It's not a matter of money. This is a religious matter."
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"๋ˆ์˜ ๋ฌธ์ œ๊ฐ€ ์•„๋‹™๋‹ˆ๋‹ค. ์ข…๊ต์ ์ธ ๋ฌธ์ œ์ž…๋‹ˆ๋‹ค." ๋ผ๋ฉฐ ๊ฑฐ์ ˆํ–ˆ์Šต๋‹ˆ๋‹ค.
11:46
And finally, out of desperation, I said,
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๊ฒฐ๊ตญ์—” ์ ˆ๋ฐ•ํ•œ ์‹ฌ์ •์œผ๋กœ,
11:47
"Well, let me explain Georg Cantor in 1877."
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"1877๋…„์˜ ๊ฒŒ์˜ค๋ฅด๊ทธ ์นธํ† ์–ด์— ๋Œ€ํ•ด์„œ ์„ค๋ช…์„ ํ•ด ๋“œ๋ ค๋„ ๋˜๊ฒ ์Šต๋‹ˆ๊นŒ"
11:50
And I started explaining why I was there in Africa,
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๋ผ๋Š” ๋ง๋กœ ์‹œ์ž‘ํ•˜์—ฌ ์ œ๊ฐ€ ์™œ ์•„ํ”„๋ฆฌ์นด์— ๊ฐ”๋Š”์ง€ ์„ค๋ช…์„ ํ–ˆ๊ณ ,
11:54
and they got very excited when they saw the Cantor set.
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๊ทธ๋“ค์€ ์นธํ† ์–ด ์ง‘ํ•ฉ์— ํฅ๋ฏธ๋ฅผ ๋ณด์˜€์Šต๋‹ˆ๋‹ค.
11:56
And one of them said, "Come here. I think I can help you out here."
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๊ฒฐ๊ตญ ๊ทธ ์ค‘ ํ•œ ๋ช…์ด "์˜ค์‹œ์ฃ , ์ œ๊ฐ€ ๋„์›€์„ ๋“œ๋ฆด ์ˆ˜ ์žˆ์„ ๋“ฏ ํ•ฉ๋‹ˆ๋‹ค." ๋ผ๊ณ  ํ•˜๋ฉฐ
12:00
And so he took me through the initiation ritual for a Bamana priest.
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์ œ๊ฐ€ ๋ฐ”๋งˆ๋‚˜ ์‚ฌ์ œ์˜ ์ž…๋ฌธ์˜ˆ๋ฅผ ํ†ต๊ณผํ•˜๋„๋ก ํ•˜์˜€์Šต๋‹ˆ๋‹ค.
12:05
And of course, I was only interested in the math,
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๋ฌผ๋ก  ์ €๋Š” ์˜ค์ง ์ˆ˜ํ•™์—๋งŒ ๊ด€์‹ฌ์ด ์žˆ์—ˆ๊ณ ,
12:07
so the whole time, he kept shaking his head going,
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๊ณ„์†ํ•ด์„œ ๊ทธ๋ฅผ ๋ฌผ์–ด ๋ณด๋ฉด ๊ทธ๋Š” ๊ณ„์† ๋จธ๋ฆฌ๋ฅผ ๋‚ด์ €์œผ๋ฉฐ,
12:09
"You know, I didn't learn it this way."
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"๊ธ€์Ž„, ์ €๋Š” ๊ทธ๋ ‡๊ฒŒ ๋ฐฐ์šฐ์ง€ ์•Š์•˜์Šต๋‹ˆ๋‹ค." ๋ผ๊ณ  ํ•˜๋ฉฐ
12:10
But I had to sleep with a kola nut next to my bed, buried in sand,
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๋‚˜๋ฅผ ๋ชจ๋ž˜ ์†์— ๋ฌป์€ ์ฝœ๋ผ์—ด๋งค ๊ณ์˜ ์นจ์ƒ์—์„œ ์žฌ์šฐ๊ณ 
12:14
and give seven coins to seven lepers and so on.
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์ผ๊ณฑ๊ฐœ์˜ ๋™์ „์„ ์ผ๊ณฑ๋ช…์˜ ๋‚˜ํ™˜์ž๋“ค์—๊ฒŒ ๋‚˜๋ˆ„์–ด์ฃผ๊ณ ... ๊ทธ๋Ÿฐ ์ผ๋“ค์„ ํ–ˆ์Šต๋‹ˆ๋‹ค.
12:17
And finally, he revealed the truth of the matter.
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๊ฒฐ๊ตญ ๊ทธ๋Š” ๋ฌธ์ œ์˜ ์ง„์‹ค์„ ์•Œ๋ ค์ฃผ์—ˆ์Šต๋‹ˆ๋‹ค.
12:22
And it turns out it's a pseudo-random number generator using deterministic chaos.
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๊ทธ ์‹ฌ๋ณผ์€ ์œ ํ•œ ์นด์˜ค์Šค๋ฅผ ์ด์šฉํ•œ ์œ ์‚ฌ๋‚œ์ˆ˜ ๋ฐœ์ƒ๊ธฐ๋กœ ์ž‘์šฉํ•ฉ๋‹ˆ๋‹ค.
12:26
When you have a four-bit symbol, you then put it together with another one sideways.
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4๋น„ํŠธ ์‹ฌ๋ณผ ์‹œ์Šคํ…œ์œผ๋กœ ์ด๊ฒƒ๋“ค์„ ์˜†์œผ๋กœ ์ด์–ด๋ถ™์ผ ์ˆ˜ ์žˆ๊ฒŒ ๋ฉ๋‹ˆ๋‹ค.
12:32
So even plus odd gives you odd.
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์ง์ˆ˜์™€ ํ™€์ˆ˜๋ฅผ ๋”ํ•˜๋ฉด ํ™€์ˆ˜๊ฐ€ ๋‚˜์˜ค๊ณ 
12:34
Odd plus even gives you odd.
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ํ™€์ˆ˜์™€ ์ง์ˆ˜๋ฅผ ๋”ํ•˜๋ฉด ํ™€์ˆ˜๊ฐ€ ๋‚˜์˜ค๊ฒŒ ๋ฉ๋‹ˆ๋‹ค.
12:36
Even plus even gives you even. Odd plus odd gives you even.
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์ง์ˆ˜์™€ ์ง์ˆ˜๋ฅผ ๋”ํ•˜๋ฉด ์ง์ˆ˜๊ฐ€, ํ™€์ˆ˜์™€ ํ™€์ˆ˜๋ฅผ ๋”ํ•ด๋„ ์ง์ˆ˜๊ฐ€ ๋‚˜์˜ต๋‹ˆ๋‹ค.
12:39
It's addition modulo 2, just like in the parity bit check on your computer.
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2์˜ ๋‚˜๋จธ์ง€๋ฅผ ๋”ํ•˜๋Š” ๊ฒƒ์œผ๋กœ, ์—ฌ๋Ÿฌ๋ถ„์˜ ์ปดํ“จํ„ฐ ์•ˆ์—์„œ ์‚ฌ์šฉ๋˜๋Š” ํŒจ๋ฆฌํ‹ฐ ๋น„ํŠธ ๊ฒ€์ฆ ๊ณผ์ •๊ณผ ๊ฐ™์Šต๋‹ˆ๋‹ค.
12:43
And then you take this symbol, and you put it back in
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๊ทธ๋ฆฌ๊ณ  ์ด ์‹ฌ๋ณผ๋“ค์„ ๋‹ค์‹œ ๊ณ„์‚ฐ์— ์ฐธ์—ฌ์‹œ์ผœ์„œ
12:47
so it's a self-generating diversity of symbols.
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์ž๊ธฐ๋ฐ˜๋ณต์ ์ธ ์‹ฌ๋ณผ์˜ ๋‹ค์–‘์„ฑ์„ ๊ฐ–๊ฒŒ ํ•ฉ๋‹ˆ๋‹ค.
12:49
They're truly using a kind of deterministic chaos in doing this.
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๊ทธ๋“ค์€ ์‹ค์ œ๋กœ ์ด ์ž‘์—…์— ๊ฒฐ์ •๋ก ์  ํ˜ผ๋ˆ ์ด๋ก ์„ ์‚ฌ์šฉํ•ฉ๋‹ˆ๋‹ค.
12:53
Now, because it's a binary code,
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์ด์ œ, ์ด๊ฒƒ์€ ์ด์ง„์ฝ”๋“œ๋กœ ์ด๋ฃจ์–ด์ง€๋ฏ€๋กœ
12:55
you can actually implement this in hardware --
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์ด๊ฒƒ์„ ์ „์žํšŒ๋กœ๋กœ ๊ตฌํ˜„ํ•  ์ˆ˜ ์žˆ์Šต๋‹ˆ๋‹ค.
12:57
what a fantastic teaching tool that should be in African engineering schools.
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์•„ํ”„๋ฆฌ์นด์˜ ๊ณตํ•™๊ต์‹ค์— ์ด๋Ÿฐ ๊ฒƒ์„ ๊ฐ€๋ฅด์น˜๋Š” ๊ฒƒ์ด ์–ผ๋งˆ๋‚˜ ํ™˜์ƒ์ ์ด๊ฒ ์Šต๋‹ˆ๊นŒ?
13:02
And the most interesting thing I found out about it was historical.
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์ œ๊ฐ€ ์•Œ์•„๋‚ธ ์•„์ฃผ ํฅ๋ฏธ๋กœ์šด ์‚ฌ์‹ค์€ ์ด ์‹ฌ๋ณผ์˜ ์—ญ์‚ฌ๊ฐ€
13:05
In the 12th century, Hugo of Santalla brought it from Islamic mystics into Spain.
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12์„ธ๊ธฐ์— ํœด๊ณ  ์‚ฐํƒˆ๋ฆฌ์•„๊ฐ€ ์ด ์‹ฌ๋ณผ์‹œ์Šคํ…œ์„ ์ด์Šฌ๋žŒ์œผ๋กœ ๋ถ€ํ„ฐ ์ŠคํŽ˜์ธ์œผ๋กœ ์ „ํ•ด
13:11
And there it entered into the alchemy community as geomancy:
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์—ฐ๊ธˆ์ˆ ์‚ฌ ์ง‘๋‹จ์— ๋Œ€์ง€๋ฅผ ํ†ตํ•ด ์ด๋ฃจ์–ด์ง€๋Š” ์‹ ์„ฑํ•œ
13:17
divination through the earth.
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ํ™์ ์œผ๋กœ ์ด์–ด์กŒ๋‹ค๋Š” ์‚ฌ์‹ค์ž…๋‹ˆ๋‹ค.
13:19
This is a geomantic chart drawn for King Richard II in 1390.
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์ด ๊ฒƒ์€ 1390๋…„์— ๋ฆฌ์ฒ˜๋“œ 2์„ธ ์™•์„ ์œ„ํ•ด ๊ทธ๋ ค์ง„ ํ™์  ๋„์•ˆ์ž…๋‹ˆ๋‹ค.
13:24
Leibniz, the German mathematician,
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๋…์ผ์˜ ์ˆ˜ํ•™์ž ๋ผ์ดํ”„๋‹ˆ์ธ ๋Š”, ๊ทธ์˜ ๋…ผ๋ฌธ์—์„œ
13:27
talked about geomancy in his dissertation called "De Combinatoria."
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์ด ํ™์ ์„ "De Combinatoria" ๋ผ๊ณ  ์นญํ•˜๋ฉฐ
13:31
And he said, "Well, instead of using one stroke and two strokes,
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"ํ•˜๋‚˜, ํ˜น์€ ๋‘ ๊ฐœ์˜ ์„ ์„ ์‚ฌ์šฉํ•˜๋Š” ๋Œ€์‹ ,
13:35
let's use a one and a zero, and we can count by powers of two."
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1 ๋˜๋Š” 0์„ ์‚ฌ์šฉํ•จ์œผ๋กœ์จ 2์˜ ์Šน์ˆ˜๋กœ ์ˆซ์ž๋ฅผ ์…€ ์ˆ˜ ์žˆ๋‹ค" ๊ณ  ํ–ˆ์Šต๋‹ˆ๋‹ค.
13:39
Right? Ones and zeros, the binary code.
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๊ทธ๋ ‡์ฃ ? 1๊ณผ 0์„ ์ด์šฉํ•œ ์ด์ง„ ์ฝ”๋“œ์ž…๋‹ˆ๋‹ค.
13:41
George Boole took Leibniz's binary code and created Boolean algebra,
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์กฐ์ง€ ๋ถ€์šธ์ด ๋ผ์ดํ”„๋‹ˆ์ธ ์˜ ์ด์ง„ ์ฝ”๋“œ๋กœ ๋ถˆ๋ฆฌ์–ธ ๋Œ€์ˆ˜ํ•™์„ ๋งŒ๋“ค๊ณ ,
13:44
and John von Neumann took Boolean algebra and created the digital computer.
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์š”ํ•œ ํฐ ๋…ธ์ด๋งŒ์ด ๋ถˆ๋ฆฌ์–ธ ๋Œ€์ˆ˜๋ฅผ ํ†ตํ•ด ๋””์ง€ํ„ธ ์ปดํ“จํ„ฐ๋ฅผ ๋งŒ๋“ค์—ˆ์Šต๋‹ˆ๋‹ค.
13:47
So all these little PDAs and laptops --
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๊ทธ๋Ÿฌ๋ฏ€๋กœ ์ด ์ž‘์€ PDA ๋˜๋Š” ๋žฉํƒ‘๊ฐ™์€ ๊ฒƒ๋“ค์€ --
13:50
every digital circuit in the world -- started in Africa.
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๊ทธ๋ฆฌ๊ณ  ์„ธ์ƒ์˜ ๋ชจ๋“  ๋””์ง€ํ„ธ ํšŒ๋กœ๋“ค์€ -- ์•„ํ”„๋ฆฌ์นด์—์„œ ์‹œ์ž‘๋œ ๊ฒƒ์ž…๋‹ˆ๋‹ค.
13:53
And I know Brian Eno says there's not enough Africa in computers,
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์ €๋Š” ๋ธŒ๋ผ์ด์–ธ ์—๋…ธ๊ฐ€ ์•„ํ”„๋ฆฌ์นด์— ์ปดํ“จํ„ฐ๊ฐ€ ๋ถ€์กฑํ•˜๋‹ค๊ณ  ํ–ˆ๋‹ค ๋“ค์—ˆ๋Š”๋ฐ,
13:58
but you know, I don't think there's enough African history in Brian Eno.
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๋ธŒ๋ผ์ด์–ธ ์—๋…ธ์—๊ฒŒ๋Š” ์•„ํ”„๋ฆฌ์นด์˜ ์—ญ์‚ฌ ๊ณต๋ถ€๊ฐ€ ๋ชจ์ž๋ž๋˜ ๋ชจ์–‘์ž…๋‹ˆ๋‹ค.
14:03
(Laughter) (Applause)
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(๋ฐ•์ˆ˜)
14:06
So let me end with just a few words about applications that we've found for this.
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์ด์ œ ์—ฌ๊ธฐ์„œ ์ฐพ์•„๋‚ธ ๋ช‡ ๊ฐ€์ง€ ์‘์šฉ๋“ค์„ ์ธ์šฉํ•œ ์–˜๊ธฐ๋กœ ๋งˆ์น˜๊ฒ ์Šต๋‹ˆ๋‹ค.
14:10
And you can go to our website,
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์—ฌ๋Ÿฌ๋ถ„์€ ์šฐ๋ฆฌ ์›น์‚ฌ์ดํŠธ์—์„œ
14:12
the applets are all free; they just run in the browser.
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์›น๋ธŒ๋ผ์šฐ์ €์—์„œ ๊ตฌ๋™๋˜๋Š”, ์„ธ์ƒ ๋ˆ„๊ตฌ๋ผ๋„ ๋ฌด๋ฃŒ๋กœ ์‚ฌ์šฉํ•  ์ˆ˜ ์žˆ๋Š”
14:14
Anybody in the world can use them.
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ํ”„๋กœ๊ทธ๋žจ์„ ์‚ฌ์šฉํ•ด ๋ณด์‹ค ์ˆ˜ ์žˆ์Šต๋‹ˆ๋‹ค.
14:16
The National Science Foundation's Broadening Participation in Computing program
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์ตœ๊ทผ ๊ตญ๊ฐ€ ๊ณผํ•™ ์žฌ๋‹จ์ด ์šฐ๋ฆฌ ์—ฐ๊ตฌ์— ์ปดํ“จํ„ฐ ํ”„๋กœ๊ทธ๋ž˜๋ฐ์„ ์ง€์›ํ•˜์—ฌ
14:21
recently awarded us a grant to make a programmable version of these design tools,
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์ด๋Ÿฌํ•œ ๋””์ž์ธ ๋„๊ตฌ๋ฅผ ์‚ฌ์šฉํ•  ์ˆ˜ ์žˆ๋„๋ก ๋„์™€ ์ฃผ์—ˆ์Šต๋‹ˆ๋‹ค.
14:28
so hopefully in three years, anybody'll be able to go on the Web
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๋ฐ”๋ผ๊ฑด๋Œ€ ์•ฝ 3๋…„ ์•ˆ์—, ์›น์„ ์‚ฌ์šฉํ•˜๋Š” ๋ˆ„๊ตฌ๋ผ๋„
14:30
and create their own simulations and their own artifacts.
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์ž์‹ ์˜ ์‹œ๋ฎฌ๋ ˆ์ด์…˜์„ ํ†ตํ•ด ์ž์‹ ๋งŒ์˜ ๋„ํ˜•์„ ๋งŒ๋“ค ์ˆ˜ ์žˆ์„ ๊ฒƒ์ž…๋‹ˆ๋‹ค.
14:33
We've focused in the U.S. on African-American students as well as Native American and Latino.
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์šฐ๋ฆฌ๋Š” ๋ฏธ๊ตญ์˜ ํ‘์ธ ํ•™์ƒ๋“ค, ๋ฏธ๊ตญ ์ธ๋””์•ˆ ํ•™์ƒ๋“ค๊ณผ ๋ผํ‹ด๊ณ„์—ด ํ•™์ƒ๋“ค์— ์ง‘์ค‘ํ•˜์—ฌ
14:38
We've found statistically significant improvement with children using this software in a mathematics class
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๊ทธ๋“ค์ด ์ˆ˜ํ•™ ์ˆ˜์—…์— ์ด ํ”„๋กœ๊ทธ๋žจ์„ ์ด์šฉํ•˜์˜€์„ ๋•Œ, ์‚ฌ์šฉํ•˜์ง€ ์•Š์€ ํ†ต์ œ์ง‘๋‹จ์— ๋น„ํ•ด
14:44
in comparison with a control group that did not have the software.
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ํ†ต๊ณ„์ ์œผ๋กœ ๋ช…๋ฐฑํ•˜๊ฒŒ ์šฐ์ˆ˜ํ•œ ์„ฑ์ ์„ ๊ฑฐ๋‘ ์„ ๋ฐœ๊ฒฌํ–ˆ์Šต๋‹ˆ๋‹ค.
14:47
So it's really very successful teaching children that they have a heritage that's about mathematics,
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์ด๋Š” ๊ทธ๋“ค์ด ๊ฐ–๊ณ  ์žˆ๋Š” ์ˆ˜ํ•™์ ์ธ ์œ ์‚ฐ์— ๋Œ€ํ•œ ์„ฑ๊ณต์ ์ธ ๊ต์œก ์‚ฌ๋ก€์ž…๋‹ˆ๋‹ค.
14:53
that it's not just about singing and dancing.
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์ถค๊ณผ ๋…ธ๋ž˜์™€ ๊ฐ™์€ ์œ ์‚ฐ๊ณผ ๋”๋ถˆ์–ด ๋ง์ž…๋‹ˆ๋‹ค.
14:57
We've started a pilot program in Ghana.
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์šฐ๋ฆฌ๋Š” ๊ฐ€๋‚˜์—์„œ ํŒŒ์ผ๋Ÿฟ ํ”„๋กœ๊ทธ๋žจ์„ ์‹œ์ž‘ํ–ˆ๊ณ ,
15:00
We got a small seed grant, just to see if folks would be willing to work with us on this;
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์šฐ๋ฆฌ์—๊ฒŒ ํ˜‘์กฐ์˜์‚ฌ๋ฅผ ๊ฐ–๋Š” ์‚ฌ๋žŒ๋“ค์„ ๋Œ€์ƒ์œผ๋กœ ์ด ๊ต์œก์„ ์ˆ˜ํ–‰ํ•˜๋ฉฐ,
15:05
we're very excited about the future possibilities for that.
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๋ฏธ๋ž˜์— ๋‹ค๊ฐ€์˜ฌ ๊ฐ€๋Šฅ์„ฑ์— ๋งค์šฐ ๊ณ ๋ฌด๋˜์–ด ์žˆ์Šต๋‹ˆ๋‹ค.
15:08
We've also been working in design.
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์šฐ๋ฆฌ๋Š” ์ด๊ฒƒ์„ ๋˜ํ•œ ๋””์ž์ธ์— ์ ‘๋ชฉ์‹œ์ผœ
15:10
I didn't put his name up here -- my colleague, Kerry, in Kenya, has come up with this great idea
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์—ฌ๊ธฐ ์ด๋ฆ„์„ ๋น ํŠธ๋ ธ๋„ค์š” -- ์ œ ๋™๋ฃŒ, ์ผ€๋ƒ์— ์žˆ๋Š” ์ผ€๋ฆฌ๋Š” ํ”„๋ž™ํƒˆ ๊ตฌ์กฐ์˜ ๋งˆ์„์—
15:15
for using fractal structure for postal address in villages that have fractal structure,
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์šฐํŽธ ์ฃผ์†Œ๋ฅผ ๋งค๊ธฐ๋Š” ๊ธฐ๊ฐ€ ๋ง‰ํžŒ ํ”„๋ž™ํƒˆ ๊ตฌ์กฐ์˜ ๋ฐฉ๋ฒ•๋ก ์„ ๊ณ ์•ˆํ•ด๋ƒˆ์Šต๋‹ˆ๋‹ค.
15:20
because if you try to impose a grid structure postal system on a fractal village,
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ํ”„๋ž™ํƒˆ ๊ตฌ์กฐ์˜ ๋งˆ์„์— ๊ฒฉ์ž๊ตฌ์กฐ์˜ ์šฐํŽธ ์‹œ์Šคํ…œ์„ ์‚ฌ์šฉํ•˜๋ฉด
15:24
it doesn't quite fit.
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์ž˜ ๋งž์•„๋–จ์–ด์ง€์ง€ ์•Š๊ธฐ ๋งˆ๋ จ์ž…๋‹ˆ๋‹ค.
15:26
Bernard Tschumi at Columbia University has finished using this in a design for a museum of African art.
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์ฝœ๋กฌ๋น„์•„ ๋Œ€ํ•™์˜ ๋ฒ ๋ฅด๋‚˜๋“œ ์ธ„๋ฏธ๋Š” ์•„ํ”„๋ฆฌ์นด ์˜ˆ์ˆ  ๋ฐ•๋ฌผ๊ด€์„ ์ด ํ”„๋ž™ํƒˆ ๋„์•ˆ์„ ํ†ตํ•ด ์„ค๊ณ„ํ–ˆ๊ณ ,
15:31
David Hughes at Ohio State University has written a primer on Afrocentric architecture
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์˜คํ•˜์ด์˜ค ์ฃผ๋ฆฝ๋Œ€์˜ ๋ฐ์ด๋น„๋“œ ํœด์ฆˆ๋Š” ํ”„๋ž™ํƒˆ ๊ตฌ์กฐ์— ๊ธฐ๋ฐ˜ํ•œ
15:39
in which he's used some of these fractal structures.
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์•„ํ”„๋ฆฌ์นด ๊ฑด์ถ•์ˆ ์˜ ์ž…๋ฌธ์„œ๋ฅผ ์ €์ˆ ํ–ˆ์Šต๋‹ˆ๋‹ค.
15:41
And finally, I just wanted to point out that this idea of self-organization,
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๋งˆ์ง€๋ง‰์œผ๋กœ, ์ €๋Š” ์ด๋Ÿฌํ•œ, ์ „์— ์–˜๊ธฐ ํ•œ ๊ฒƒ ์ฒ˜๋Ÿผ ์šฐ๋ฆฌ ๋‡Œ ์†์—๋„ ์žˆ๋Š”
15:46
as we heard earlier, it's in the brain.
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์ž๊ธฐ๋ฐ˜๋ณต์ ์ธ ์•„์ด๋””์–ด๊ฐ€ --
15:48
It's in the -- it's in Google's search engine.
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๊ตฌ๊ธ€์˜ ๊ฒ€์ƒ‰ ์—”์ง„์—๋„ ์žˆ์Œ์„ ์งš๊ณ  ์‹ถ์Šต๋‹ˆ๋‹ค.
15:53
Actually, the reason that Google was such a success
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์‚ฌ์‹ค, ๊ตฌ๊ธ€์ด ๊ทธ๋ ‡๊ฒŒ ์„ฑ๊ณตํ•  ์ˆ˜ ์žˆ๋˜ ์ด์œ ๋Š”
15:55
is because they were the first ones to take advantage of the self-organizing properties of the web.
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๊ทธ๋“ค์ด ์›น์˜ ์ž๊ธฐ๋ฐ˜๋ณต์ ์ธ ์„ฑ์งˆ์„ ์ตœ์ดˆ๋กœ ์ด์šฉํ–ˆ๊ธฐ ๋•Œ๋ฌธ์ž…๋‹ˆ๋‹ค.
15:59
It's in ecological sustainability.
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์ƒํƒœ์ ์ธ ์œ ์ง€์„ฑ์— ์žˆ์ฃ .
16:01
It's in the developmental power of entrepreneurship,
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๋ชจํ—˜์ ์œผ๋กœ ์ƒˆ๋กœ์šด ๊ฒƒ์„ ์ฐฝ์กฐํ•˜๋Š” ๊ธฐ์—…๊ฐ€์ •์‹ ์—๋„ ์žˆ๊ณ ,
16:03
the ethical power of democracy.
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๋ฏผ์ฃผ์ฃผ์˜์˜ ์œค๋ฆฌ์„ฑ์—๋„ ์žˆ์Šต๋‹ˆ๋‹ค.
16:06
It's also in some bad things.
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๋ฌผ๋ก  ๋‚˜์œ ๊ณณ์—์„œ๋„ ๋ฐœ๊ฒฌ๋ฉ๋‹ˆ๋‹ค.
16:08
Self-organization is why the AIDS virus is spreading so fast.
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์ž๊ธฐ๋ฐ˜๋ณต์„ฑ์€ AIDS ๋ฐ”์ด๋Ÿฌ์Šค๊ฐ€ ๊ธ‰๊ฒฉํžˆ ํ™•์‚ฐ๋˜๋Š” ์›์ธ์ด๊ณ ,
16:11
And if you don't think that capitalism, which is self-organizing, can have destructive effects,
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์ž๊ธฐ๋ฐ˜๋ณต์ฒด์ธ ์ž๋ณธ์ฃผ์˜๋ฅผ ์ƒ๊ฐํ•ด๋ณด๋ฉด, ๊ทธ๊ฒƒ์ด ์–ด๋–ป๊ฒŒ ํŒŒ๊ดด์ ์ธ ํšจ๊ณผ๋ฅผ ๊ฐ–๋Š”์ง€ ๋ณผ ์ˆ˜ ์žˆ์Šต๋‹ˆ๋‹ค.
16:15
you haven't opened your eyes enough.
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๊ทธ ์™ธ์—๋„ ์•„์ฃผ ๋งŽ์€ ๊ฒƒ๋“ค์ด ์žˆ์Šต๋‹ˆ๋‹ค.
16:17
So we need to think about, as was spoken earlier,
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์ผ์ „์— ๋งํ•ด์ง€๋˜ ๊ฒƒ๊ณผ ๊ฐ™์ด, ์šฐ๋ฆฌ๋Š” ์ข€ ๋”
16:21
the traditional African methods for doing self-organization.
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์•„ํ”„๋ฆฌ์นด์˜ ์ž๊ธฐ๋ฐ˜๋ณต์ ์ธ ์ „ํ†ต์„ ์ข€ ๋” ์ƒ๊ฐํ•˜์—ฌ์•ผ ํ•ฉ๋‹ˆ๋‹ค.
16:23
These are robust algorithms.
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์—ฌ๊ธฐ์—” ๋ช…๋ฐฑํ•œ ๊ทœ์น™์„ฑ์ด ์žˆ์Šต๋‹ˆ๋‹ค.
16:26
These are ways of doing self-organization -- of doing entrepreneurship --
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์ž๊ธฐ์กฐ์ง์ ์ธ ๋ฐฉ๋ฒ•๋“ค - ๊ธฐ์—…๊ฐ€์ ์ธ ์ผ์„ ํ•˜๋Š” - ๋ฐฉ๋ฒ•๋“ค์ด ์กด์žฌํ•˜๋ฉฐ
16:29
that are gentle, that are egalitarian.
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๊ทธ๊ฒƒ๋“ค์€ ๋ถ€๋“œ๋Ÿฝ๊ณ , ํ‰๋“ฑํ•ฉ๋‹ˆ๋‹ค.
16:31
So if we want to find a better way of doing that kind of work,
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์ด๋Ÿฐ ์ผ์— ๋Œ€ํ•ด์„œ ๋” ์ข‹์€ ๋ฐฉ๋ฒ•์„ ์ฐพ๊ณ ์ž ํ•œ๋‹ค๋ฉด,
16:35
we need look only no farther than Africa to find these robust self-organizing algorithms.
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๋‹ค๋งŒ ์•„ํ”„๋ฆฌ์นด์˜ ์ด๋Ÿฐ ๋ช…๋ฐฑํ•œ ์ž๊ธฐ๋ฐ˜๋ณต์ ์ธ ์•Œ๊ณ ๋ฆฌ์ฆ˜๋“ค์„ ์—ฐ๊ตฌํ•ด์•ผ ํ•  ๊ฒƒ์ž…๋‹ˆ๋‹ค.
16:40
Thank you.
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๊ฐ์‚ฌํ•ฉ๋‹ˆ๋‹ค.
์ด ์›น์‚ฌ์ดํŠธ ์ •๋ณด

์ด ์‚ฌ์ดํŠธ๋Š” ์˜์–ด ํ•™์Šต์— ์œ ์šฉํ•œ YouTube ๋™์˜์ƒ์„ ์†Œ๊ฐœํ•ฉ๋‹ˆ๋‹ค. ์ „ ์„ธ๊ณ„ ์ตœ๊ณ ์˜ ์„ ์ƒ๋‹˜๋“ค์ด ๊ฐ€๋ฅด์น˜๋Š” ์˜์–ด ์ˆ˜์—…์„ ๋ณด๊ฒŒ ๋  ๊ฒƒ์ž…๋‹ˆ๋‹ค. ๊ฐ ๋™์˜์ƒ ํŽ˜์ด์ง€์— ํ‘œ์‹œ๋˜๋Š” ์˜์–ด ์ž๋ง‰์„ ๋”๋ธ” ํด๋ฆญํ•˜๋ฉด ๊ทธ๊ณณ์—์„œ ๋™์˜์ƒ์ด ์žฌ์ƒ๋ฉ๋‹ˆ๋‹ค. ๋น„๋””์˜ค ์žฌ์ƒ์— ๋งž์ถฐ ์ž๋ง‰์ด ์Šคํฌ๋กค๋ฉ๋‹ˆ๋‹ค. ์˜๊ฒฌ์ด๋‚˜ ์š”์ฒญ์ด ์žˆ๋Š” ๊ฒฝ์šฐ ์ด ๋ฌธ์˜ ์–‘์‹์„ ์‚ฌ์šฉํ•˜์—ฌ ๋ฌธ์˜ํ•˜์‹ญ์‹œ์˜ค.

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