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SYSK Selects: Fractals - Whoa · Stuff You Should Know

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Speaker 1: How do folks, Charles W. Chuck Bryant here in the corral,
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Speaker 1: and I'm gonna last so up a Stuff you Should
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Speaker 1: Know select for you from June seventh, two thousand twelve.
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Speaker 1: Fractals Colin Whoa, this is a tough one for me.
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Speaker 1: I'm not gonna lie. Fractals is one of the toughest
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Speaker 1: episodes I've ever had to learn and research. And that's
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Speaker 1: where we're gonna revisit it right here, right now. Welcome
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Speaker 1: to Stuff you Should Know, a production of My Heart
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Speaker 1: Radios How Stuff Works. Hey, and welcome to the podcast.
0:36
Speaker 1: I'm Josh Clark, hanging on by my fingernails with me
0:40
Speaker 1: as always as Charles W. Chuck Bryant, doing much the
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Speaker 1: same as we are about to start speaking on stuff
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Speaker 1: you should know about. Fractals. Yea, more math theoretical, Matt
0:52
Speaker 1: even Yeah, a new branch of geometry. It's non Euclidean
0:58
Speaker 1: since you brought it up, Okay, very new. Euclidean geometry
1:02
Speaker 1: was like three B C and fractals are so there's
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Speaker 1: a little bit of a gap there. There is a
1:11
Speaker 1: little bit of a gap and uh, there's a lot
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Speaker 1: of animosity among the Euclideans towards Fractillians. They need to
1:19
Speaker 1: loosen up and look at some of those far out pictures.
1:22
Speaker 1: I know, you know it's funny. Did you watch um,
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Speaker 1: did you watch that one doc on? Yeah? Okay, did
1:27
Speaker 1: you see the other? The Arthur C. Clark one. It
1:31
Speaker 1: was made in like maybe eight s eighty seven and
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Speaker 1: it had nothing but like um delicate sound of thunder
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Speaker 1: rip off music going on the whole time. It was
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Speaker 1: really really trippy. Well, I posted a picture I don't
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Speaker 1: know if you saw today on the stuff you should
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Speaker 1: know all of the of the Mandel brought set. Its
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Speaker 1: beautiful it is and it's very cool. And I didn't
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Speaker 1: even say what it was. I just posted it, and
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Speaker 1: like I'd say, about half the people were like, very cool, man,
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Speaker 1: this is rad I love the Mantal brought set like
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Speaker 1: fractill talk about fractals. And then the other half were like,
2:03
Speaker 1: well you guys tripping out like what you did a
2:05
Speaker 1: grateful dead day. That's actually math, believe it or not.
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Speaker 1: But it does look very it's very tied eye in
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Speaker 1: nature and that's why the hippies like it. Plus also,
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Speaker 1: I mean, if you've ever seen a fractal play out
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Speaker 1: on a computer screen. Yeah. Um, so we are talking
2:22
Speaker 1: about fractals. I don't I don't necessarily want to give
2:24
Speaker 1: a disclaimer. Chuck and I are not theoretical mathematicians. We're
2:28
Speaker 1: not even like normal mathematicians. I balanced my checkbook my
2:33
Speaker 1: hand just to keep that little part of my brain going.
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Speaker 1: So I don't like forget how to add and subtract
2:39
Speaker 1: later on in life. I make myself do that, and
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Speaker 1: I don't let myself jump ahead. I show my work. Yeah. Um,
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Speaker 1: and that's about the extent of math in my life normally. See,
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Speaker 1: I was the kid in math that when they said
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Speaker 1: you're not allowed to use calculators, I would go, like,
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Speaker 1: there are calculators in life, so why can't we use them. Yeah,
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Speaker 1: Like they made calculators so we didn't have to do maths, right.
3:01
Speaker 1: But at the same time, I find that shoddy because
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Speaker 1: it's like, you're not you're not You're just circumventing learning something,
3:08
Speaker 1: and it's like the calculators there to support you after
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Speaker 1: you know what you're doing. I disagree. Well, I think
3:14
Speaker 1: this is a pretty prime example of like going around
3:19
Speaker 1: to get to the end. So when when I was
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Speaker 1: researching this, I was like, Okay, well, they don't really
3:26
Speaker 1: know what they're doing with this stuff yet, so we
3:27
Speaker 1: can just totally be like, well it's it's there, anything
3:30
Speaker 1: you wanted to be and nothing at all. And then
3:32
Speaker 1: like I started looking a little more deeply into I'm like, oh, no,
3:35
Speaker 1: they do kind of know what they're doing. We really
3:38
Speaker 1: don't know what we're talking about. So I feel like
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Speaker 1: I have, just from researching this, a little bit, um
3:43
Speaker 1: something of a grasp of what fractals are, a little
3:47
Speaker 1: bit For those of you who who don't know what
3:49
Speaker 1: we're talking about, like, take a second to um look
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Speaker 1: up just typing fractal and search images on your favorite
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Speaker 1: search engine and you'll be like, oh, yes, of course
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Speaker 1: it's a fractal um And that's what we're going to
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Speaker 1: talk about, because fractal fractals are a new field, like
4:07
Speaker 1: we said, in geometry, and they do have use and
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Speaker 1: they have usefulness that I think people haven't even considered yet.
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Speaker 1: But the the stuff that they have figured out how
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Speaker 1: to use it for is pretty amazing stuff. Can I
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Speaker 1: say what a fractal is at least so people know
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Speaker 1: they should clear it all up? It is a geometric
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Speaker 1: shape that is self similar through infinite iterations in a
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Speaker 1: recursive pattern and through infinite detail exactly. So there you
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Speaker 1: have it. Boom, Do we need to even continue? No?
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Speaker 1: But um, and that sounds like really that put me off,
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Speaker 1: Like this article was pretty well done by a guy
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Speaker 1: named Craig Haggett. I don't know who that it is, freelancer.
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Speaker 1: I guess um, it's a pretty well done article. But
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Speaker 1: that a sentence like that can put a person off
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Speaker 1: pretty easy. And he even put it, you know, he
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Speaker 1: made a joke about it, like, oh, you know that,
4:51
Speaker 1: you get it, you know whatever. But um, when you
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Speaker 1: think about it, if you take that apart, one of
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Speaker 1: the hallmarks of fractal fractals, um is that they are
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Speaker 1: a very complex result from a very simple system. And
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Speaker 1: there's like basically three hallmarks two fractals that you just
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Speaker 1: pointed out right. There is um self similarity, which is
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Speaker 1: if you if you cut a chunk, like a microscopic
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Speaker 1: piece of a fractal off and compare it to the
5:23
Speaker 1: whole fractal, it's going to be virtually the same. Yeah,
5:27
Speaker 1: like or a fern. And the cool thing about fractals
5:30
Speaker 1: is is to me the coolest thing is that fractals.
5:35
Speaker 1: The point they made in the Nova documentary is that
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Speaker 1: all of our math up until they discovered fractals and
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Speaker 1: described practicals was based on things that we basically created
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Speaker 1: and built. Like all geometry, right, Euclidean geometry, you have length, width,
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Speaker 1: and height, which should view the three dimensions, right, yes,
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Speaker 1: for like pyramids and buildings and combs and all those things.
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Speaker 1: And you it's extremely useful and we've done quite a
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Speaker 1: bit with this. But what Euclidean geometry, as far as
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Speaker 1: the fractal geometrists or geometers um insist, failed at is
6:13
Speaker 1: when they said, okay, look at that mountain. That's a cone.
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Speaker 1: It's an imperfect cone, it's a rough cone, but it's
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Speaker 1: a cone shape, right, So yeah, Euclidean geometry holds sway.
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Speaker 1: What the fractal geometers say is, yeah, you could say
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Speaker 1: that it's a cone, but if you tried to measure
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Speaker 1: and describe it as such, you're not going to come
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Speaker 1: up with a very descriptive, a very um detailed description
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Speaker 1: of that mountain. So what's the point What fractal geometry
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Speaker 1: does is it says we're going to describe that mountain
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Speaker 1: in every little craig and peak possible. And so what
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Speaker 1: you have is the fractal dimension, which exists in conjunction
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Speaker 1: with length, widthin height. And what the fractal dimension describes
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Speaker 1: is the complex city of the object that exists within
7:03
Speaker 1: those three dimensions as well. That's right. So finishing my point,
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Speaker 1: the cool thing about fractals is that everything that we
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Speaker 1: had done previously in geometry were because of things we've built.
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Speaker 1: Practicals help describe things that were have been here since
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Speaker 1: the beginning of time in nature, and one of the
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Speaker 1: truest examples of that is the fern. Right with self similarity.
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Speaker 1: You take a little snippet off of a fern, although
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Speaker 1: you shouldn't do that. Let's just look at it. Uh,
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Speaker 1: it's gonna look the same as the larger part of
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Speaker 1: the fern, and then the whole fern itself very self
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Speaker 1: similar but not necessarily exact. No, it can be. There
7:39
Speaker 1: is a form of self similarity that is exact and precise,
7:42
Speaker 1: but in nature that's rare, if not just completely not found. Right,
7:47
Speaker 1: that's right. So you've got self similarity, which is the
7:50
Speaker 1: smaller part is virtually the same or looks the same,
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Speaker 1: or structured the same as the whole UM. And this
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Speaker 1: process of self similarity UM going larger smaller in scale
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Speaker 1: is called recursiveness, right, And recursiveness is UM. Like you
8:07
Speaker 1: know those paintings where it's like a guy I think
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Speaker 1: Stephen Colbert, the one that he gave to the Smithsonian
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Speaker 1: has recursiveness in it, where it's a man in a
8:16
Speaker 1: painting standing in front of like a mantle, and above
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Speaker 1: the mantle is the painting that you're looking at, and
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Speaker 1: then it goes on and on and on and on
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Speaker 1: and on anything that's infinitely repeating, right, same with if
8:28
Speaker 1: you're in a dressing room and there's a mirror on
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Speaker 1: either side of the wall, you just keep going on infinitely.
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Speaker 1: It's recursiveness and with fractals the recursiveness of self similarity. Right.
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Speaker 1: So there's two two traits. UM is produced through this
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Speaker 1: thing called iteration, that's right. And that's where you say,
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Speaker 1: here's the whole I'm gonna put it into this formula,
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Speaker 1: and the formula has has the formula. The output of
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Speaker 1: the formula produces the input for the next round of
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Speaker 1: that same formula. It's a loop exactly, so it's self
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Speaker 1: sustaining and it can go on infinitely recursion. Right. That's right.
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Speaker 1: So what we've just come up with is a fractal
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Speaker 1: is anything that has a self similar structure and it's
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Speaker 1: recursive through iteration. That's right. Okay, So um A, really
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Speaker 1: I came upon this kind of easy, one easier explanation
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Speaker 1: of a fractal from Ben wal Mandel brought site. He died,
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Speaker 1: by the way in two. He seemed like a pretty
9:35
Speaker 1: good guy. He was definitely thinking different. Um. And the
9:40
Speaker 1: way that Mandel brought described a really easy way to
9:43
Speaker 1: think of a fractal is um. There's this thing called
9:46
Speaker 1: the Serpinsky gasket, and you take a triangle and you
9:50
Speaker 1: can combine them into a bunch of little triangles and
9:54
Speaker 1: spaces triangular spaces that form a larger triangle. Right, So
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Speaker 1: that that one initial solid triangle is called the initiator,
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Speaker 1: that's the original shape, and then all those other triangles
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Speaker 1: combine that form that larger triangle or a self similar
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Speaker 1: version of that larger triangle to the original triangle. That's
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Speaker 1: called generator. Right. So the formula for creating a fractal
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Speaker 1: would be to go into that generator, the version that
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Speaker 1: has all the little smaller triangles that make up a
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Speaker 1: larger whole triangle. And say, all the ones that look
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Speaker 1: like the initiator, the original just solid black triangle, take
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Speaker 1: that out and swap it with the generator version, and
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Speaker 1: all of a sudden you have one that's exponentially more detailed.
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Speaker 1: There's more to it, And that's a fractal. That's all
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Speaker 1: there is to it. You know what else is a fractal?
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Speaker 1: What the coastline? Yeah, that was a big one. Lewis
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Speaker 1: Fry Richardson was an English mathematician early twenty century, and
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Speaker 1: he very brilliantly said, you know what, if you take
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Speaker 1: a yardstick and you measured the coastline of England, you're
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Speaker 1: gonna get a number. If you take a one ft
11:07
Speaker 1: ruler and measure the coastline, you're gonna get a different number.
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Speaker 1: If you take a one inch ruler and measure the coastline,
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Speaker 1: you're gonna get a different number. And it's basically infinite
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Speaker 1: in that the smaller you go with your your unit
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Speaker 1: of measure or your tool is the larger number you're
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Speaker 1: gonna get. Because the coastline is so infinitely varied in
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Speaker 1: its little nooks and crannies, right exactly It's a very
11:34
Speaker 1: cool way of thinking about it. There's a second part
11:36
Speaker 1: of that to Chuck, is that so depending on the you,
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Speaker 1: what you're using, the measure, the tool you're using, the measure,
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Speaker 1: the number, the perimeter of that coastline could go on infinitely,
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Speaker 1: but it still contains the same finite amount of space
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Speaker 1: within its paradox. That is a big time paradox because
11:52
Speaker 1: things aren't supposed to be infinite and finite at the
11:55
Speaker 1: same time, right right, Um and uh Lewis Fry Richardson
12:00
Speaker 1: he basically established in that coming up with that paradox,
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Speaker 1: this kind of revolution and thought that fractal geometry is
12:09
Speaker 1: based on that. You can have the infinite mixed with
12:12
Speaker 1: the finite. You can get it from pretty simple formulas
12:16
Speaker 1: that create very increasingly complex systems, right Um. And Fry
12:23
Speaker 1: wasn't the He wasn't He was the first guy to
12:25
Speaker 1: really kind of put forth this idea of thought, but
12:28
Speaker 1: he wasn't the first one to notice this paradox. Yeah,
12:30
Speaker 1: and before people even knew they were fractals, there were
12:33
Speaker 1: there were artists like da Vinci that saw this pattern
12:37
Speaker 1: and tree branches that was um I know in the
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Speaker 1: Nova documentary and the article, they point out the uh
12:43
Speaker 1: Katsu Chica Hokusai Japanese artists created the Great Wave off Kanagawa,
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Speaker 1: and uh those are fractals. It's a it's ocean waves
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Speaker 1: breaking and at the top of the crest of the
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Speaker 1: waves are a little self similar or waves breaking off
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Speaker 1: into smaller and smaller self similar versions. And that's a
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Speaker 1: natural fractal, or in this case, it's a depiction of one.
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Speaker 1: So they were you know, early African and Nabajo artists
13:09
Speaker 1: were doing this and they didn't realize that they were
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Speaker 1: fractals and that there were fractals all around us. No,
13:15
Speaker 1: they just saw crystals in a snowflake or another good one, yeah, exactly. Um,
13:19
Speaker 1: they were just they saw that there was what they
13:21
Speaker 1: were looking at was a repeating pattern that was self
13:24
Speaker 1: similar and recursive. Right, yeah, that's it. That's a fractal, right. Yeah.
13:29
Speaker 1: And and Ben Wha Mandel brought was the first one
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Speaker 1: to say, you know what, we can we can use
13:35
Speaker 1: math equations to actually apply to this. And he was
13:38
Speaker 1: a big star for a while, and then they sort
13:41
Speaker 1: of turned on him and said, you know what, this
13:44
Speaker 1: is all cool and trippy looking, but it's useless. Right,
13:48
Speaker 1: and he said, oh yeah, screw you guys, watch this
13:52
Speaker 1: and he wrote another book which started to uh give
13:56
Speaker 1: some practical applications which are pretty exciting. UM. So the
14:02
Speaker 1: whole thing, the whole principle that is based on UM
14:05
Speaker 1: is that you can take a formula and plug in
14:09
Speaker 1: a very simple UM, well, a relatively simple formula like
14:13
Speaker 1: mantle Brod's formula. Will take that one. For example, his
14:17
Speaker 1: is um ZED goes to ZED squared plus c. Right,
14:24
Speaker 1: that's what it's called. If you're in England, zed, we
14:27
Speaker 1: say z Z. Well, anyway, Zed goes to which is
14:34
Speaker 1: and the goes to is the key right here. This
14:37
Speaker 1: is what makes it fractal goes to means that um,
14:41
Speaker 1: it's an error. It's an equal sign. It looks like
14:43
Speaker 1: an equal sign with a part of an arrow pointing
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Speaker 1: towards ZED, the other point pointing towards the rest of
14:50
Speaker 1: the formula, which means that the the there's that feedback
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Speaker 1: loop where it's like, okay, once you have the number
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Speaker 1: that this punches out, you have, you feed it back
15:00
Speaker 1: can and you'll get another number and knows, just keep
15:01
Speaker 1: going and going and going, and every time, remember you're
15:04
Speaker 1: swapping out the original the initiator for the the detailed
15:13
Speaker 1: version the generator, and it's just getting exponentially more complex
15:18
Speaker 1: with just that one iteration of that very simple formula.
15:23
Speaker 1: UM and Mandel brought set Uh. This is the one
15:27
Speaker 1: that's like it's probably the most famous one. That's the
15:30
Speaker 1: one that the Deadheads like because it's like this crazy
15:33
Speaker 1: juxtaposition between like black and like different colors and everything.
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Speaker 1: And with his formula, two things happen with the number
15:42
Speaker 1: that you put in. It either goes towards zero or
15:46
Speaker 1: it shoots off to the infinite. And what they did
15:49
Speaker 1: for this for the the Mandel brought set fractals was
15:53
Speaker 1: they assigned a color to a number based on how
15:57
Speaker 1: quickly it goes off to towards infinity. Right, so let's
16:01
Speaker 1: say that you have like four, If you plug four
16:04
Speaker 1: into this and in ten generations, it'll it'll become an
16:07
Speaker 1: infinite number. UM. Then say that that would be grouped
16:12
Speaker 1: into a blue color like ten generations blue, eight generations
16:16
Speaker 1: is red, ninety generations is orange. See what I'm saying. UM.
16:21
Speaker 1: And then the other direction, like say if you put
16:23
Speaker 1: in four point two or something like that, it'll go
16:26
Speaker 1: towards zero and any number that eventually will go towards
16:29
Speaker 1: zero is represented as black. So what you have then,
16:33
Speaker 1: is this really intricate depending on where you're zooming in
16:37
Speaker 1: or out on the fractal, this intricate change of colors,
16:41
Speaker 1: and what you're really just seeing our numbers that are
16:44
Speaker 1: plots on a plane, and that's your fractal, and then
16:47
Speaker 1: the black parts are numbers that will eventually be be zero. Right,
16:51
Speaker 1: And most of the mental mental brought set is black. Yeah,
16:55
Speaker 1: but if you zoom in, like that's the whole point.
16:58
Speaker 1: You zoom in on one of those little uh what
17:01
Speaker 1: do we even call those little spikes? Uh? I guess
17:05
Speaker 1: you could call it a plot. A plot, and it's
17:07
Speaker 1: gonna look like what you just saw. And the Nova
17:10
Speaker 1: documentary is very cool when they zoom in on these,
17:13
Speaker 1: it's sort of mind blowing. Yeah, it is very I
17:16
Speaker 1: strongly recommend watching that because they explain it way better
17:19
Speaker 1: than us. Well, it helps to see it for sure,
17:21
Speaker 1: Oh yeah, big time. So um or draw it as
17:24
Speaker 1: I have done. It's a pretty nice little fract Yeah.
17:53
Speaker 1: So we've talked about fractals, We talked about the Mandel
17:55
Speaker 1: brought set, we talked about where they started to come
17:58
Speaker 1: from um and the the idea. Remember Lewis fried Richardson,
18:05
Speaker 1: he was talking about measuring the coastline and going off
18:09
Speaker 1: into the infinite, but still containing a finite amount um.
18:12
Speaker 1: A guy came after him named Helga von Coke. He
18:15
Speaker 1: came up with a Coke snowflake, which is pretty cool.
18:18
Speaker 1: If you take a straight line, or you take a triangle,
18:21
Speaker 1: and then on each side of the triangle in the
18:23
Speaker 1: middle you bust out the middle into another triangular hump.
18:28
Speaker 1: You do that over and over and over again. It
18:30
Speaker 1: goes off into infinity. Although it contains a finite amount
18:33
Speaker 1: of space. The perimeter goes off to the infinite. A
18:36
Speaker 1: guy named Georg Cantor came up with the cancer set,
18:40
Speaker 1: which is you just take a straight line and you
18:42
Speaker 1: take the middle out of it, and then for each
18:44
Speaker 1: of those two lines that produces, you do the same
18:46
Speaker 1: thing and it just keeps going on and on and
18:48
Speaker 1: rather than going to nothingness like you're like, well, if
18:51
Speaker 1: you take a six inch line, eventually you're gonna bust
18:53
Speaker 1: it down and nothingness again. That doesn't happen. They found
18:56
Speaker 1: that it goes off to the infinite. So they realized
18:59
Speaker 1: Ben Wall mantel Brought was plugging all these into computers,
19:03
Speaker 1: because that's what it took people realize this, Like George
19:06
Speaker 1: Cantor um Man I hope that's how you say his
19:09
Speaker 1: first name. He was he was working in the eighteen eighties,
19:13
Speaker 1: Um Gaston Julio came up with the Julia sets for
19:16
Speaker 1: producing a repeating pattern using feedback loop. All these guys
19:19
Speaker 1: were like nineteenth century early twentieth century mathematicians and it
19:23
Speaker 1: was strictly theoretical until the late seventies when guys like
19:27
Speaker 1: Mantel Brought who worked at IBM, started feeding these things
19:31
Speaker 1: into these new fangled computers and seeing the results like
19:35
Speaker 1: this fractals like the mantel Brought set that he saw right,
19:39
Speaker 1: So Um, almost immediately there was a practical use for
19:45
Speaker 1: fractals that came in the form of c g I. Yeah.
19:51
Speaker 1: They interviewed that one guy in the documentary um who
19:54
Speaker 1: worked on the first c g I shot in motion
19:58
Speaker 1: picture history, which was Star Trek to the Wrath of
20:01
Speaker 1: con and Uh. He was tasked with making a c
20:05
Speaker 1: g I uh land surface like mountain range and pretty
20:10
Speaker 1: mind blowing with it. Yeah, and he did. I mean,
20:12
Speaker 1: now you look back and it kind of looks silly,
20:14
Speaker 1: but at the time it was completely revolutionary. And once
20:18
Speaker 1: he learned about fractals in the geometry and the math
20:21
Speaker 1: of fractals, it was pretty easy for him, and he
20:23
Speaker 1: made it seem like he was like, oh, well, this
20:25
Speaker 1: is the key, this is how you do it right.
20:27
Speaker 1: So well, and it is kind of easy, especially if
20:29
Speaker 1: you know what you're doing with computer programming and math,
20:32
Speaker 1: because what you're basically doing to create a fractal generator
20:36
Speaker 1: is teaching your computer to to do something within a
20:40
Speaker 1: certain formula. That's your fractal formula, right, And so what
20:44
Speaker 1: Lauren Carpenter, the guy who created the the Star Trek
20:47
Speaker 1: to landscape for the first c G all c g
20:50
Speaker 1: I shot ever, what he basically did was created a
20:53
Speaker 1: computer program that said, hey, computer, I'm gonna give you
20:56
Speaker 1: a bunch of triangles. Because I think that was the
20:58
Speaker 1: earliest stuff he was working with. Um, I'm gonna give
21:01
Speaker 1: you a bunch of triangles, and I want you to
21:04
Speaker 1: take those triangles and generate a new fractal set from it, right,
21:09
Speaker 1: And then I want you to do it again and
21:10
Speaker 1: again and again, and then every third time I want
21:13
Speaker 1: you to start turning them forty degrees, so it's going
21:18
Speaker 1: to change the pattern slightly, and then all of a
21:21
Speaker 1: sudden you have these infinite variations. The reason why when
21:24
Speaker 1: you go back and look at that shot that it
21:26
Speaker 1: still looks kind of you know today, is because the
21:30
Speaker 1: computer he was working at didn't have the computing power
21:33
Speaker 1: to do that many times. Now we have higher computer
21:37
Speaker 1: computing power, and so what we're doing is telling our
21:40
Speaker 1: computers to keep going and going and going, swapping out
21:43
Speaker 1: that initiator, that one single black triangle everywhere it can
21:47
Speaker 1: find it in this pattern, this pattern of triangles in
21:50
Speaker 1: the fractal with a brand new fractal. So it's just
21:53
Speaker 1: creating more and more and more and more fractals, which
21:55
Speaker 1: creates a finer and finer and finer resolution, which makes
21:58
Speaker 1: something look all the more real. Yeah, like the part
22:01
Speaker 1: in the doc about the Star Wars, I was making
22:04
Speaker 1: the lava splashing. It's amazing, Yes, it was because they
22:08
Speaker 1: showed the first one they did it looks kind of plain,
22:10
Speaker 1: and then once you fed it through this infinite feedback loop,
22:14
Speaker 1: it just like shattered and and and uh, fractured, not fractaled,
22:20
Speaker 1: although I want to say fractaled off and just look
22:23
Speaker 1: more detailed, more detailed, more detailed, until it looked like
22:26
Speaker 1: lava splashing. Right, it's pretty amazing. Well, that's where the
22:28
Speaker 1: word fractal comes from. Is um Mandel brought coined in
22:32
Speaker 1: to say, to indicate how the things fracture off and
22:37
Speaker 1: they form irregular patterns. Um, you can create a fractal
22:41
Speaker 1: that that is regularly repeating, but it doesn't look as natural.
22:48
Speaker 1: And with like say, if you're creating lava, you've got
22:52
Speaker 1: to have that one rule that like every third generation
22:55
Speaker 1: kicks forty degrees or whatever the rule is. That just
22:59
Speaker 1: kind of throws a little bit of dissimilarity and too
23:01
Speaker 1: because if something is too self similar, it's not going
23:04
Speaker 1: to look right. It's not gonna look natural, it's not
23:06
Speaker 1: gonna look real, which kind of leads you to think, chuck.
23:09
Speaker 1: Then that there is a an application for studying natural
23:13
Speaker 1: phenomenon using fractals, right, while there are I guess all kinds, Um,
23:20
Speaker 1: well this isn't so much natural. But the documentary interviewed
23:24
Speaker 1: Nathan Cohen who was a ham radio operator and his
23:28
Speaker 1: landlord said, dude, you can't have that huge antenna hanging
23:31
Speaker 1: out of your apartment so he started bending wires a
23:35
Speaker 1: straight wire into essentially a fractal and found that on
23:39
Speaker 1: the very first go it got better reception, um, merely
23:43
Speaker 1: by the fact that it was bent in that way
23:46
Speaker 1: and it was self similar. So he eventually used that
23:51
Speaker 1: two I hope make a lot of money. I got
23:54
Speaker 1: the impressing that he did, okay, um by applying that
23:57
Speaker 1: technology to cell phones. Um, and the way they describe
24:00
Speaker 1: it as all the different things a cellphone can do,
24:03
Speaker 1: if you were to have a different antenna for each
24:05
Speaker 1: one of those functions, it would be like carrying around
24:07
Speaker 1: a little porcupine. So what cell phones now are based
24:10
Speaker 1: on is a fractal design called Manger sponge. Minger sponge, Yeah,
24:17
Speaker 1: I think, man, and uh it's basically a box fractal.
24:20
Speaker 1: And if you crack up in your little cell phone,
24:23
Speaker 1: you're gonna see it wired that way. Yeah, You're going
24:25
Speaker 1: to be looking at a fractal. It's a square, right,
24:28
Speaker 1: and then within it are a bunch of little squares
24:31
Speaker 1: in a recursive, self similar pattern. And you, friend, are
24:35
Speaker 1: looking at a fractal. It's all around us. Yeah, Um,
24:39
Speaker 1: it's also all around us in nature. There's uh in
24:42
Speaker 1: that same uh documentary that NOVA program. There was a
24:47
Speaker 1: team from I think University of Arizona. There's a team
24:50
Speaker 1: of academics. Yeah, that was pretty cool. Who um, we're
24:53
Speaker 1: trying to figure out if you predict the amount of
24:56
Speaker 1: carbon capturing capacity an entire rainforest has just by measuring
25:01
Speaker 1: UM and figuring out the self similar system that a
25:05
Speaker 1: single tree in that rainforest UM has. That makes sense? Well,
25:11
Speaker 1: it does, but it's kind of a leap. It's like, okay,
25:13
Speaker 1: so as one tree does it follow the same system
25:17
Speaker 1: that the whole rainforest does? And they apparently found that yes,
25:21
Speaker 1: in fact it does, right, The same branching UH system
25:25
Speaker 1: found in that tree is similar to the the growth
25:30
Speaker 1: of the trees in the rainforest as a whole. Pretty cool. Yes, UM.
26:01
Speaker 1: Tumors in the human body. UH. One of the keys
26:05
Speaker 1: to getting rid of of cancer is or any kind
26:08
Speaker 1: of tumors. Spotting these tumors early on. But with our
26:11
Speaker 1: ultrasound technology you can only get so small and so
26:14
Speaker 1: detailed that you can't see some of these natural fractals
26:18
Speaker 1: that you know, your blood vessels are fractals essentially, just
26:21
Speaker 1: like the branches of a tree are UM. So they
26:25
Speaker 1: are now using geometry too. Now if I'm not sure
26:30
Speaker 1: if I got this right, but I think it shows up.
26:33
Speaker 1: It shows the flow of the blood because ultrasound can
26:36
Speaker 1: pick that up through these fractals when they can't even
26:38
Speaker 1: pick up the vessels themselves. Is that right, early earlier
26:43
Speaker 1: tumor spotting, which right, well, for all intents of purposes,
26:46
Speaker 1: they're looking at the vessels by finding the blood because
26:48
Speaker 1: they see where it's flowing. But yeah, depending on the
26:51
Speaker 1: pattern that it follows. If it follows like a like
26:55
Speaker 1: a tree branching shape, it's healthy, right, yeah. And then
26:58
Speaker 1: the tumors, all the veins are all bent and crooking,
27:01
Speaker 1: going in all crazy directions. The read out of a heartbeat, yeah,
27:04
Speaker 1: it's not consistent. It's a fractical yeah. So they use
27:07
Speaker 1: fractal analysis now to study your heart rate and use
27:11
Speaker 1: that to better understand how arrhythmia happens through math. So
27:18
Speaker 1: there's the especially with natural systems. That's kind of like
27:22
Speaker 1: the biggest contribution that UM Fractal geometry is produced so far,
27:27
Speaker 1: I think, aside from c G I is what medical
27:31
Speaker 1: uh well, just the that whole understanding that was first
27:35
Speaker 1: really kind of um voiced by Lewis Fry Richardson with
27:38
Speaker 1: the coastline that there's, um, there are natural systems out
27:43
Speaker 1: there that we can't really that we're not quite paying
27:46
Speaker 1: attention to, we don't really know how to deal with that.
27:50
Speaker 1: We're trying to apply something like Euclidean geometry to something
27:53
Speaker 1: that you can't really use that for um. That that's
27:57
Speaker 1: what fractal geometry is really contributed so far as basically say, hey,
28:01
Speaker 1: there's a lot of natural systems out here that are
28:03
Speaker 1: self similar and recursive, and now that we kind of
28:07
Speaker 1: see in the fractal world, we see them everywhere and
28:11
Speaker 1: we have a better understanding of them. And one of
28:13
Speaker 1: the best examples of that, I thought was figuring out
28:17
Speaker 1: how larger animals use less energy than smaller animals. They
28:22
Speaker 1: use energy more efficiently, and um, this is a kind
28:25
Speaker 1: of a biological paradox for a really long time, and
28:28
Speaker 1: these guys figured it out using I guess kind of
28:31
Speaker 1: the um same kind of insight that fractal geometry has.
28:35
Speaker 1: That if you take genes and genes are the mathematical
28:40
Speaker 1: formula or the equivalent of a mathematical formula, and you
28:46
Speaker 1: uh feed in uh, these genetic processes, what it's going
28:50
Speaker 1: to put out. Is this self similar recursive pattern to
28:56
Speaker 1: where the bigger the organism is, the more this thing
29:01
Speaker 1: goes and goes and goes, the less energy it's going
29:03
Speaker 1: to use because there's more of it and it doesn't
29:06
Speaker 1: require very much energy to produce past a certain point.
29:09
Speaker 1: So if you have a very small animal, it's using
29:11
Speaker 1: a lot of energy to do these things to carry
29:13
Speaker 1: this out. But there's that economy of scale because you're
29:16
Speaker 1: still using a relatively simple formula your genetic code, right UM,
29:22
Speaker 1: to carry out a very complex, seemingly complex UM system,
29:27
Speaker 1: which is your organs or you as an organism. So
29:31
Speaker 1: in the end, an elephant uses less energy than a mouse, yes,
29:34
Speaker 1: because they're both using the same formula, the same input.
29:38
Speaker 1: And then eventually you reach a point where it just
29:41
Speaker 1: gets easier and easier and easier to to use something
29:44
Speaker 1: simple to create a complex system. I love it. I
29:47
Speaker 1: do too. Uh. I got one more thing. You heard
29:50
Speaker 1: this guy, Jason Paget, Huh, this is pretty crazy. UM.
29:54
Speaker 1: This guy like nine years ago, I think UM was
29:58
Speaker 1: mugged and to come Washington got hit in the back
30:02
Speaker 1: of the head really hard, knocked him out, and he
30:05
Speaker 1: acquired UM a form of synesthesia in which he sees
30:10
Speaker 1: fractals from being hit in the head. And um, basically
30:14
Speaker 1: it's an acquired savant savantism, which is pretty rare to
30:19
Speaker 1: acquire this later on. Um, and this guy hated math,
30:24
Speaker 1: and his family used to make fun of him, he said,
30:26
Speaker 1: because he was the worst at pictionary. Uh, I couldn't
30:30
Speaker 1: draw a thing, couldn't draw a lick. Now, this guy
30:33
Speaker 1: can draw reportedly mathematically correct fractals by hand, and he's
30:40
Speaker 1: the only person on earth that can do this. And
30:42
Speaker 1: you should see these things. They're like, you know, a
30:45
Speaker 1: huge you know, two by two fractal that looks like
30:50
Speaker 1: it was plotted by like a supercomputer. And this guy
30:53
Speaker 1: does these by hand now out of nowhere because he
30:55
Speaker 1: got hit on the head. That's pretty amazing. Yeah, it's crazy.
30:58
Speaker 1: He got him in the fractal center. Huh he did.
31:01
Speaker 1: That's strange that we would have like that ability latent
31:04
Speaker 1: in us, you know. Yeah. Well, they studied his brain,
31:07
Speaker 1: of course, UM, and they found that the two areas
31:10
Speaker 1: that lit up in the left hemisphere were the areas
31:13
Speaker 1: that control exact math and mental imagery. So they have
31:16
Speaker 1: it well, and he's you know, he's fine with it,
31:20
Speaker 1: although he says that he's a bit obsessive about it
31:22
Speaker 1: because he's it's one of those deals where everywhere he
31:25
Speaker 1: looks now he sees fractals. Oh yeah, Well, I got
31:28
Speaker 1: the impression that people who are who are fractal geometers
31:32
Speaker 1: have the same thing. Yeah, you know, they're like, click
31:34
Speaker 1: at that cloud. I I can figure out how to
31:36
Speaker 1: describe it completely. Yeah with math. Yeah, it's crazy, um.
31:40
Speaker 1: And then it's everywhere canopies of the trees. Like. I
31:43
Speaker 1: got that impression as well that once you start seeing
31:45
Speaker 1: fractals in natural systems, like then everything becomes um fractals
31:50
Speaker 1: and a lot simpler to understand. I realized today that
31:53
Speaker 1: I have always doodled in fractals. Oh yeah, yeah, because
31:56
Speaker 1: I can't really draw, so whenever I doodle, it's like
31:59
Speaker 1: it's all aways been um little fractal shapes. Like I
32:03
Speaker 1: would draw some kind of geometric shape, then split off
32:06
Speaker 1: from that and make it smaller, and in the end
32:09
Speaker 1: they're sort of like fractals. Oh your fractal tree that
32:11
Speaker 1: you showed me, it's pretty awesome. So you got anything else?
32:16
Speaker 1: Uh No, I would strongly urge you to read this
32:20
Speaker 1: article a few more times. And then maybe go off
32:23
Speaker 1: and read some more about fractals, because we definitely have
32:25
Speaker 1: not covered all of it. I watched that Nova documentary. Yeah,
32:28
Speaker 1: that's good stuff. What is it? Chasing the hidden dimentioned?
32:31
Speaker 1: Is that what it's called? And you call it chasing
32:33
Speaker 1: the dragon? Well, there's the dragon curve fractal. It's pretty boss,
32:37
Speaker 1: That's right, it is boss. Um. So you want to
32:40
Speaker 1: type fractals in the search bar how stuff works dot
32:44
Speaker 1: com to start, and that will bring up this very
32:46
Speaker 1: very good article. And I said search bar, which means
32:49
Speaker 1: it's time for a listener mail. Josh, I'm gonna call this, uh,
32:55
Speaker 1: don't eat your peanuts around me, jerk. Yeah. Remember when
32:58
Speaker 1: the Air Traffic Control remark that never heard the announcement that, uh,
33:03
Speaker 1: no one can eat peanuts on the plane. I've flown
33:05
Speaker 1: a lot in my life and I've never heard that before.
33:08
Speaker 1: So Ian Hammer writes in on the Air Traffic Control episode,
33:12
Speaker 1: you were talking about peanuts being completely absent on some flights,
33:16
Speaker 1: And as a person that is really allergic to peanuts,
33:18
Speaker 1: I can shed some light. My allergy is bad enough
33:21
Speaker 1: to wear the smell of peanuts, which is really just
33:24
Speaker 1: the presence of peanut molecules in the air will cause
33:27
Speaker 1: me to get itchy and swollen. Uh. In the case
33:29
Speaker 1: that I am in contact with a peanut have the
33:32
Speaker 1: superpower of becoming a balloon, and I'll swell up to
33:35
Speaker 1: the point where I will be dead in a matter
33:36
Speaker 1: of minutes. I can delay the anaphylactic shock for ten minutes,
33:40
Speaker 1: give or take with an injection of epinephrin, and this
33:43
Speaker 1: will only work twice twice in his life. I think, so, um,
33:48
Speaker 1: if I do have a reaction, I have twenty minutes
33:50
Speaker 1: plus the fifteen minutes I have before normal anaphylactic shock
33:54
Speaker 1: would kill me. There really is in a way to
33:56
Speaker 1: save me in that instance, unless I can be administered
33:59
Speaker 1: the proper treatment that you can get only at a hospital.
34:02
Speaker 1: Because you can imagine when a plane is at thirty
34:04
Speaker 1: feet there's not much can be done to get me
34:07
Speaker 1: to a hospital within that thirty five minute time frame.
34:10
Speaker 1: So flying can be a pretty scary thing when someone
34:12
Speaker 1: near you. Besides that they really want a peanut buttercup.
34:16
Speaker 1: People do this sometimes and it's a real pain to
34:18
Speaker 1: have to deal with. I just wanted to give you
34:19
Speaker 1: guys an overview of peanut allergy sufferers when it comes
34:22
Speaker 1: to flying. Keep up the incredible work. Look forward to
34:26
Speaker 1: seeing a TV pilot Ian Hammer. So incredible, is right?
34:30
Speaker 1: If we were insensitive to that, then all apologies. He
34:34
Speaker 1: didn't indicate that, but I know we weren't. I just
34:37
Speaker 1: remember being surprised. Yeah, I was surprised, but I knew
34:39
Speaker 1: allergies could get bad. But man, that I think on
34:43
Speaker 1: the plane, I was like, what I've known about this
34:45
Speaker 1: since I saw an episode of Freaks and Geeks wherein
34:47
Speaker 1: one of the characters almost died because like some bully
34:50
Speaker 1: at school like gave him some peanuts. Oh yeah, was
34:54
Speaker 1: that it was the Martin Star character, the analog to
34:58
Speaker 1: Paul from Wonder Years, Okay, which was, Um, I can't
35:05
Speaker 1: remember his name. I book for some weeks. Yeah, it's good,
35:07
Speaker 1: good show. Um, well, let's see allergies. How about a
35:12
Speaker 1: practice story if you know something about fractals that we don't,
35:15
Speaker 1: or can correct us or explain it better than we did,
35:18
Speaker 1: which I'm not sure that that's much of a long shot. Um,
35:22
Speaker 1: we want to hear about it. You can tweet to
35:24
Speaker 1: us at s Y s K Podcast. You can visit
35:27
Speaker 1: us on Facebook at facebook dot com. Slash Stuff you
35:30
Speaker 1: Should Know, or you can send us an email to
35:32
Speaker 1: Stuff podcast at how stuff works dot com. Stuff you
35:38
Speaker 1: Should Know is a production of iHeart Radio's How Stuff Works.
35:41
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35:43
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35:46
Speaker 1: your favorite shows.