June 7, 2012 • 34 mins
In the 1980s, IBM mathematician Benoit Mandelbrot gazed for the first time upon his famous fractal. What resulted was a revolution in math and geometry and our understanding of the infinite, not to mention how we see Star Trek II.
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Speaker 1 (00:00):
Brought to you by the reinvented two thousand twelve Camray.
It's ready. Are you welcome to Stuff you Should Know
from House Stuff Works dot Com. Hey, and welcome to
the podcast. I'm Josh Clark, hanging on by my fingernails
(00:20):
with me as always as Charles W. Chuck Bryant, doing
much the same as we were about to start speaking
on stuff you should know about fractals, more math, theoretical
man even, Yeah, a new branch of geometry. It's non
Euclidean since you brought it up, okay, very new Euclidean
(00:42):
geometry was like, and fractals are. So there's a little
bit of a gap there. There is a little bit
of a gap. And uh, there's a lot of animosity
among the Euclideans towards Fractillians. They need to loosen up
and look at some of those far out pictures. I know,
(01:04):
you know it's funny. Did you watch um, did you
watch that one doc on? Yeah? Okay, did you see
the other the Arthur C. Clark one. It was made
in like maybe eighties, six eighty seven, and it had
nothing but like um delicate sound of thunder rip off
music going on the whole time. It was really really trippy. Well,
I posted a picture I don't know if you saw
(01:25):
today on the stuff, you should know all of the
of the Mandel brought set. It's beautiful, it is and
it's very cool. And I didn't even say what it was.
I just posted it, and like I'd say, about half
the people were like, very cool, man, this is rattle
of the Mantal brought set, like fractals, talk about fractals.
And then the other half were like, well, you guys
tripping out like what you did, grateful dead day. That
(01:48):
is actually math, believe or not. But it does look
very it's very tie dye in nature, and that's why
the hippies like it. Plus also, I mean, if you've
ever seen a fractal play out on the computer screen,
like yeah, um, so we are talking about fractals. I
don't necessarily want to give a disclaimer. Chuck and I
are not theoretical mathematicians. We're not even like normal mathematicians.
(02:12):
I balanced my checkbook my hand just to keep that
little part of my brain going. So I don't like
forget how to add and subtract later on in life.
I make myself to that, and I don't let myself
jump ahead. I show my work. Yeah. Um, and that's
about the extent of math and my life normally. See,
I was the kid in math that when they said
(02:33):
you're not allowed to use calculators, I would go like,
there are calculators in life, so why can't we use them. Yeah,
Like they made calculators so we didn't have to do maths, right,
But at the same time, I find that shoddy because
it's like you're not you're not You're just circumventing learning something,
and it's like the calculators there to support you after
you know what you're doing. I disagree. Well, I think
(02:55):
this is a pretty prime example of like going around
to get to the end. So when when I was
researching this, I was like, Okay, well, they don't really
know what they're doing with this stuff yet, so we
can just totally be like, well it's it's there anything
you wanted to be and nothing at all. And then
like I started looking a little more deeply into I'm like, oh, no,
(03:16):
they do kind of know what they're doing. We really
do know what we're talking about. So I feel like
I have, just from researching this a little bit um,
something of a grasp of what fractals are at. For
those of you who who don't know what we're talking about, like,
take a second to um, look up just typing fractal
and search images on your favorite search engine and you'll
(03:39):
be like, oh, yes, of course it's a fractal, um
And that's what we're going to talk about, because fractal
fractals are a new field, like we said, in geometry,
and they do have use and they have usefulness that
I think people haven't even considered yet. But the the
stuff that they have figured out how to use it
for is pretty amazing stuff. Can what if fractal is
(04:01):
at least so people know this should clear it all up.
It is a geometric shape that is self similar through
infinite iterations in a recursive pattern and through infinite detail exactly.
So there you have it. Boom. Do we need to
even continue? No? But um, And that sounds like really
that put me off, Like this article was pretty well
done by a guy named Craig Haggett. I don't know
who that is, freelancer, I guess, um, And it's a
(04:24):
pretty well done article. But that a sentence like that
can put a person off pretty easy, and he even
put it, you know, he made a joke about it like,
oh you know that, you get it, you know whatever.
But um, when you think about it, if you take
that apart, one of the hallmarks of fractal fractals um
is that they are a very complex result from a
(04:45):
very simple system. And there's like basically three hallmarks two
fractals that you just pointed out right. There is um
self similarity, which is if you if you cut a
chunk like a microscopic piece of a fractal off and
compare it to the whole fractal, it's going to be
(05:06):
virtually the same, yeah, like or a fern. And the
cool thing about practicals is is, to me, the coolest
thing is that practicals. The point they made in the
Nova documentary is that all of our math up until
they discovered fractals and described practicals, was based on things
that we've basically created and built. Like all geometry, right
(05:30):
Euclidean geometry. You have length, width, and height, which which
should be the three dimensions, right, yes, for like pyramids
and buildings, cones and all those things. And you it's
extremely useful and we've done quite a bit with this.
But what Euclidean geometry, as far as the fractal geometrists
or geometers um insist fail That is when they said, okay,
(05:56):
look at that mountain, that's a cone. It's an imperfect cone,
it's a rough cone, but it's a cone shape, right,
So yeah, Clidean geometry holds sway. What the fractal geometers
say is, yeah, you could say that it's a cone,
but if you tried to measure and describe it as such,
you're not going to come up with a very descriptive,
(06:16):
a very um detailed description of that mountain. So what's
the point. What fractal geometry does is it says we're
going to describe that mountain in every little craig and
peak possible. And so what you have is the fractal dimension,
which exists in conjunction with length, widthin height. And what
(06:38):
the fractal dimension describes is the complexity of the object
that exists within those three dimensions as well. So, finishing
my point, the cool thing about practicals is that everything
that we had done previously in geometry were because of
things we built. Practicals help describe things that were have
been here since the beginning of time in nature, and
(07:01):
one of the truest examples of that is the fern.
Right with self similarity, you take a little snippet off
of a fern, all that you shouldn't do that, let's
just look at it. Uh, it's gonna look the same
as the larger part of the fern, and then the
whole fern itself very self similar but not necessarily exact. No,
it can be. There is a form of self similarity
(07:22):
that is exact and precise, but in nature that's rare,
if not just completely not found. Right, that's right. So
you've got self similarity, which is the smaller part is
virtually the same or looks the same or structured the
same as the whole um. And this process of self
similarity um going larger smaller in scale, it's called recursiveness, right, yeah,
(07:46):
And recursiveness is um like you know those paintings where
it's like a guy I think Stephen Colbert, the one
that he gave to the Smithsonian has recursiveness in it,
where it's a man in a painting standing in front
of like mantle, and above the mantle is the painting
that you're looking at, and then it goes on and
on and on and on and on anything that's infinitely repeating, right,
(08:08):
same with if you're in a dressing room and there's
a mirror on either side of the wall, you just
keep going on infinitely. It's recursiveness, and with fractals the
recursiveness of self similarity. Right, So there's two two traits.
Um is produced through this thing called iteration, that's right.
And that's where you say, here's the whole I'm gonna
(08:32):
put it into this formula, and the formula has has
the formula. The output of the formula produces the input
for the next round of that same formula. It's a
loop exactly, so it's self sustaining and it can go
on infinitely recursion. Right. That's right. So what we've just
(08:55):
come up with is the fractal is anything that has
a self similar structure and it recursive through iteration. That's okay.
So um A, really I came upon this kind of
easy one easier explanation of a fractal from Ben wal
Mandel brought site. He died, by the way in two
(09:15):
he seemed like a pretty good guy. He was definitely
thinking different um. And the way that Mandel brought described
A really easy way to think of a fractal is um.
There's this thing called the Serpentsky gasket. And you take
a triangle and you can combine them into a bunch
of little triangles and spaces, triangular spaces that form a
(09:38):
larger triangle. Right, So that that one initial solid triangle
is called the initiator, that's the original shape. And then
all those other triangles combine that form that larger triangle
or a self similar version of that larger triangle, the
original triangle. That's called a generator. Right. So the formula
(10:00):
for creating a fractal would be to go into that generator,
the version that has all the little smaller triangles and
make up a larger whole triangle. And say, all the
ones that look like the initiator, the original just solid
black triangle, take that out and swap it with the
generator version, and all of a sudden you have one
(10:20):
that's exponentially more detailed. There's more to it, And that's
a fractal. That's all there is to it. You know
what else is a fractal? What the coastline? Yeah, that
was a big one. Lewis fried Richardson was an English
mathematician early twenty century, and he very brilliantly said, you
know what, if you take a yardstick and you measured
(10:43):
the coastline of England, you're gonna get a number. If
you take a one ft ruler and measure the coastline,
you're gonna get a different number. If you take a
one inch ruler and measure the coastline, you're gonna get
a different number. And it's basically infinite in that the
smaller you go with your your unit of measure or
(11:04):
your tool is the larger number you're gonna get, because
the coastline is so infinitely varied in its little nooks
and crannies, right exactly. It's a very cool way of
thinking about it. There's a second part of that too, Chuck.
Is that so depending on the you, what you're using,
the measure, the tool you're using the measure, the number
(11:24):
the perimeter of that coastline could go on infinitely, but
it still contains the same finite amount of space within paradox.
That is a big time paradox because things aren't supposed
to be infinite and finite at the same time, right
Um and uh Lewis Fry Richardson. He basically established in
that coming up with that paradox, the this kind of
(11:46):
revolution and thought that fractal geometry is based on that
you can have the infinite mixed with the finite, and
you can get it from pretty simple formulas that create
very increasingly complex systems, right, Um, And Fry wasn't the
He wasn't He was the first guy to really kind
(12:07):
of put forth this idea of thought, but he wasn't
the first one to notice this paradox. Yeah, and before
people even knew there were fractals, there were there were
artists like Da Vinci that saw this pattern and tree branches.
That was um. I know. In the Nova documentary and
the article they point out the uh Catsu Chica Hokusai
(12:29):
Japanese artists created the Great Wave off Kanagawa and uh
those are fractals. It's a it's ocean waves breaking and
at the top of the crest of the waves are
little self similar waves breaking off into smaller and smaller
self similar versions. And that's a natural fractal, or in
this case, it's a depiction of one. So they were
you know, early African and Navajo artists were doing this
(12:50):
and they didn't realize that they were fractals and there
were fractals all around us. No, they just saw crystals
in a snowflake or another good one, Yeah, exactly. Um.
They were just they saw that there was what they
were looking at was a repeating pattern that was self
similar and recursive. Right, yeah, that's it. That's a fractal.
Right yeah. And and Ben Wha mandel Brought was the
(13:13):
first one to say, you know what, we can we
can use math equations to actually apply to this. And
he was a big star for a while. And then
they sort of turned on him and said, you know what,
this is all cool and trippy looking, but it's useless,
right And he said, oh yeah, screw you guys. Watch
this And he wrote another book which started to uh
(13:37):
give some practical applications which are pretty exciting. UM. So
the whole thing, the whole principle that this is based
on UM is that you can take a formula and
plug in a very simple UM, well, a relatively simple
formula like mantel Brought's formula. Will take that one. For example,
(13:57):
his is um Z goes to zed squared plus c. Right,
that's what it's called. If you're in England, z we
say z z Well, anyway zed goes to which is
and the goes to is the key right here, this
(14:18):
is what makes it fractal. Goes to means that um,
it's an error. It's an equal sign. It looks like
an equal sign with an part of an arrow pointing
towards ZED, the other point pointing toward the rest of
the formula, which means that the the there's that feedback
loop where it's like, okay, once you have the number
that this punches out, you have you feed it back
(14:40):
in and you'll get another number and just keep going
and going and going. And every time, remember you're swapping
out the original the initiator for the the detailed version
the generator, and it's just getting exponentially more complex with
just the one iteration of that's very simple formula UM
(15:05):
and Mandel brought set uh. This is the one that's
like it's probably the most famous one. That's the one
that the Deadheads like because it's like this crazy juxtaposition
between like black and like different colors and everything. And
with his formula, two things happen with the number that
you put in. It either goes towards zero, or it
(15:27):
shoots off to the infinite. And what they did for this,
for the the Mandel brought set fractals was they assigned
a color to a number based on how quickly it
goes off to towards infinity. Right, So let's say that
you have like four, If you plug four into this
and in ten generations, it'll it'll become an infinite number. Um.
(15:50):
Then say that that would be grouped into a blue
color like ten generations blue, eight generations is red, ninety
generations is orange. See what I'm saying, um. And then
the other direction, like say if you put in four
point two or something like that, it'll go towards zero.
And any number that eventually will go towards zero is
(16:10):
represented as black. So what you have then is this
really intricate depending on where you're zooming in or out
on the fractal, this intricate change of colors, and what
you're really just seeing our numbers that are plots on
a plane, and that's your fractal, and then the black
parts are numbers that will eventually be be zero. Right,
(16:31):
And most of the mental mental brought set is black. Yeah,
but if you zoom in like that's the whole point
you zoom in on one of those little uh what
do we even call those little spikes? Uh? I guess
you could call it a plot. A plot, and it's
gonna look like what you just saw. And that The
Nova documentary is very cool when they zoom in on
(16:53):
these and it's sort of mind blowing. Yeah, it is
very I strongly recommend watching that because they explain it
way better than us. Well it helps to see it
for sure. So um, it's a pretty nice little friend,
um chuck. So we've talked about fractals, we talked about
(17:13):
the Mandel brought set, we talked about where they started
to come from, UM, and the the idea. Remember Lewis
fried Richardson, he was talking about measuring the coastline and
going off into the infinite but still containing a finite
amount UM. A guy came after him named Helga von Coke.
(17:34):
He came up with a Coke snowflake, which is pretty cool.
If you take a straight line, or you take a triangle,
and then on each side of the triangle in the
middle you bust out the middle into another triangular hump.
You do that over and over and over again. It
goes off into infinity. Although it contains a finite amount
of space, the perimeter goes off to the infinite. A
(17:55):
guy named Georg Cantor came up with the Cancer set,
which is just take a straight line and you take
the middle out of it, and then for each of
those two lines that produces, you do the same thing
and it just keeps going on and on and rather
than going to nothingness like you're like, well, if you
take a six inch line, eventually you're gonna bust it
down and nothingness again, that doesn't happen. They found that
(18:15):
it goes off to the infinite. So they realized ben
Wa Mantel brought was plugging all these into computers. Because
that's what it took. People realize it's like George Cantor
um Man, I hope that's how you say his first name.
He was he was working in the eighteen eighties. Um
Gaston Julio came up with the Julius sets for producing
(18:35):
a repeating pattern using feedback loop. All these guys were
like nineteenth century early twentieth century mathematicians, and it was
strictly theoretical until the late seventies, when guys like Mantel
brought who worked at IBM started feeding these things into
these new fangled computers and seeing the results like this,
fractals like the mantel brought set that he saw right,
(18:58):
so um, almost immediately there was a practical use for
fractals that came in the form of c g I. Yeah,
they interviewed that one guy and the documentary um who
worked on the first c g I shot in motion
picture history, which was Star Trek to the Wrath of
(19:20):
con and uh. He was tasked with making a c
g I uh land surface like mountain range and pretty
mind blowing with it. Yeah, and he did. I mean,
now you look back and it kind of looks silly,
but at the time it was completely revolutionary. And once
he learned about fractals in the geometry and the math
of practicals, it was pretty easy for him. And he
(19:42):
made it seem like he's like, oh, well, this is
the key, this is how you do it right. So well,
and it is kind of easy, especially if you know
what you're doing with computer programming and math, because what
you're basically doing to create a fractal generator is teaching
your computer to to do something within a certain formula
that's a fractal formula, right, and so what Lauren Carpenter,
(20:04):
the guy who created them the star Trek to landscape
for the first c G all c g I shot. Ever,
what he basically did was created a computer program that said, hey, computer,
I'm gonna give you a bunch of triangles. Because I
think that was the earliest stuff he was working with. Um,
I'm gonna give you a bunch of triangles, and I
want you to take those triangles and generate a new
(20:26):
fractal set from it, right, And then I want you
to do it again and again and again, and then
every third time I want you to start turning them
forty degrees. So that's going to change the pattern slightly,
and then all of a sudden you have these infinite variations.
The reason why when you go back and look at
that shot that it still looks kind of you know today,
(20:48):
is because the computer he was working at didn't have
the computing power to do that many times. Now we
have higher computer computing power, and so what we're doing
is telling our computers to keep going and going and going,
swapping out the initiator that one single black triangle everywhere
it can find it in this pattern. This pattern of
triangles in the fractal with a brand new fractal. So
(21:11):
it's just creating more and more and more and more fractals,
which creates a finer and finer and finer resolution, which
makes something look all the more realistic. Yeah, like the
part in the doc about the Star Wars's making the
lava splashing, it's amazing. Yes, it was because they showed
the first one that he did. It looks kind of plain,
and then once you fed it through this infinite feedback loop,
(21:32):
it just like shattered and and and uh, fractured, not fractal,
although I want to say fractal off and just look
more detailed, more detailed, more detailed, until it looked like
lava splashing, right, it's pretty amazing. Well, that's where the
word fractal comes from. Is um Mandel brought coined in
to say, to indicate how the things fracture off and
(21:56):
they form irregular patterns. Um, you can create to fractal
that that is regularly repeating, but it doesn't look as natural.
And with like say, if you're creating lava, right, you've
got to have that one rule that like every third
generation kicks forty degrees or whatever. The rule is that
(22:17):
just kind of throws a little bit of dissimilarity into it,
because if something's too self similar, it's not going to
look right. It's not gonna look natural, it's not gonna
look real, which kind of leads you to think, chuck,
then that there is a an application for studying natural
phenomenon using fractals, right, while there are I guess all
kinds um, well, this isn't so much natural. But the
(22:42):
documentary interviewed Nathan Cohen who was a ham radio operator,
and his landlord said, dude, you can't have that huge
antenna hanging out of your apartment. So he started bending
wires a straight wire into essentially a fractal and found
that on the very first go it got better reception
um merely by the fact that it was bent in
(23:04):
that way and it was self similar. So he eventually
used that two I hope make a lot of money.
I got the imperson that he did, okay, um by
applying that technology to cell phones um, and the way
that they describe it as all the different things a
cell phone can do, if you were to have a
different antenna for each one of those functions, it would
(23:25):
be like carrying around a little porcupine. So what cell
phones now are based on is a fractal design called
Manger sponge Minger sponge and uh, it's basically a box fractal.
And if you crack up in your little cell phone,
you're gonna see it wired that way. Yeah, You're going
to be looking at a fractal it's a square, right,
(23:46):
and then within it or a bunch of little squares
in a recursive, self similar pattern. And you friend, are
looking at a fractal. It's all around us. Yeah, Um,
it's also all around us in nature. There's uh in
that same UH documentary, that Nova program, there was a
team from i think University of Arizona. There's a team
(24:09):
of academics. That was pretty cool. Who Um, we're trying
to figure out if you predict the amount of carbon
capturing capacity an entire rainforest has just by measuring UM
and figuring out this self similar system that a single
tree in that rainforest UM has. That makes sense, Well,
(24:30):
it does, but it's kind of a leap. It's like, okay,
so it's one tree, does it follow the same system
that the whole rainforest does? And they apparently found that yes,
in fact it does right. The same branching uh system
found in that tree is similar to the the growth
of the trees in the rainforest as a whole. Pretty cool, yes,
(24:54):
um in the human body, uh, one of the keys
to getting rid of cancer is or any kind of
tumors spotting these tumors early on. But with our ultrasound
technology you can only get so small and so detailed
that you can't see some of these natural fractals that
you know, your blood vessels are fractals essentially, just like
(25:15):
the branches of a tree are um So they are
now using geometry two. Now if I'm not sure if
I got this right, but I think it shows up.
It shows the flow of the blood because ultrasound can
pick that up through these fractals when they can't even
pick up the vessels themselves. Is that right? Early earlier
(25:37):
tumor spotting right. Well, for all intents of purposes, they're
looking at the vessels by finding the blood because they
see where it's flowing. But yeah, depending on the pattern
that it follows. If it follows like a like a
tree branching shape, it's healthy, right, Yeah, And then the
tumors all the veins are all bent and crooking, going
in all crazy directions. The readoubt of a heartbeat, it's
(25:58):
not consistent. It's a fractal Yeah, So the use fractal
analysis now to study your heart rate and use that
to better understand how arrhythmia happens through math. So there's
the especially with natural systems. That's kind of like the
biggest contribution that um fractal geometry is produced so far,
(26:20):
I think, aside from c g I is what medical
uh well, just that that whole understanding that was first
really kind of um voiced by Lewis Fry Richardson with
the coastline that there's, um, there are natural systems out
there that we can't really that we're not quite paying
attention to, we don't really know how to deal with that.
(26:43):
We're trying to apply something like Euclidean geometry to something
that you can't really use that for um. That that's
what fractal geometry is really contributed so far, is to
basically say, hey, there's a lot of natural systems out
here that are self similar and recursive and now that
we kind of see in the fractal world, we see
(27:03):
them everywhere, and we have a better understanding of them.
And one of the best examples of that, I thought
was figuring out how larger animals use less energy and
smaller animals they use energy more efficiently. And um, this
is a kind of a biological paradox for a really
long time, and these guys figured it out using I guess,
(27:24):
kind of the um same kind of insight that fractal
geometry has. That if you take genes and genes are
the mathematical formula or the equivalent of a mathematical formula,
and you UH feed in uh these genetic processes, what
it's going to put out is this self similar recursive
(27:49):
pattern to where the bigger the organism is, the more
this thing goes and goes and goes, the less energy
it's going to use because there's more of it and
it doesn't require very much energy to produce past a
certain point. So if you have a very small animal,
it's using a lot of energy to do these things
to carry this out. But there's that economy of scale
(28:09):
because you're still using a relatively simple formula, your genetic code,
right UM, to carry out a very complex, seemingly complex
um system, which is your organs or you as an organism.
So in the end, an elephant uses less energy than
a mouse, Yes, because they're both using the same formula,
(28:30):
the same input. And then eventually you reach a point
where it just gets easier and easier and easier to
to use something simple to create a complex system. I
love it too. Uh. I got one more thing. You
heard this guy Jason Paget, Huh, this is pretty crazy. UM.
This guy, like nine years ago, I think UM, was
(28:52):
mugged in Tacoma, Washington, got hit in the back of
the head really hard, knocked him out, and he acquired UM,
a form of synesthesia in which he sees fractals from
being hit in the head and UM basically it's an
acquired savant savantasm, which is pretty rare to acquire this.
(29:13):
Later on, UM, and this guy hated math, and his
family used to make fun of him, he said, because
he was the worst at pictionary. Uh. I couldn't draw
a thing, couldn't draw a lick. Now this guy can
draw reportedly mathematically correct fractals by hand, and he's the
(29:33):
only person on earth that can do this. And you
should see these things. They're like, you know, a huge
you know, two by two fractal that looks like it
was plotted by like a supercomputer. And this guy does
these by hand now out of nowhere because he got
hit on the head. That's pretty amazing. Yeah, it's crazy.
He got him in the fractal center. Huh. Did that's
(29:54):
strange that we would have like that ability latent in
us you know. Yeah, Well they studied his brain of course, um,
and they found that the two areas that lit up
in the left hemisphere were the areas that control exact
math and mental imagery. So they dont have it. And he's,
you know, he's fine with it, although he says that
(30:14):
he's a bit obsessive about it because he's it's one
of those deals where everywhere he looks now he sees fractals.
Oh yeah, well I got the impression that people who
are who are fractal geometers have the same thing. Yeah,
you know, they're like, look at that cloud. I I
can figure out how to describe it completely. Yeah with math, Yeah,
it's crazy. Um. And then it's everywhere canopies of the trees. Like.
(30:36):
I got that impression as well that once you start
seeing fractals in natural systems, like then everything becomes um,
fractals and a lot simpler to understand. I realized today
that I have always doodled in fractals. Yeah yeah, because
I can't really draw, so whenever I doodle, it's like
it's always been um little fractal shapes, Like I would
(30:57):
draw some kind of geometric shape, then split off from
that and make it smaller, and in the end they're
sort of like fractals. Oh, your fractal tree that you
showed me, it's pretty awesome. So you got anything else?
Uh No, I would strongly urge you to read this
article a few more times and then maybe go off
and read some more about fractals, because we definitely have
(31:18):
not covered all of it. I'll watch that Nova documentary. Yeah,
good stuff. What is it chasing the hidden? To mention?
Is that what it's called? Diould call it chasing the dragon? Well,
there's the dragon curve fractal. It's pretty boss, that's right,
it is. UM. So you want to type fractals in
the search bar how stuff works dot com to start,
and that will bring up this very very good article.
(31:41):
And I said search bar, which means it's time for
listening to ma'am Josh. I'm gonna call this, uh, don't
eat your peanuts around me, jerk. Yeah. Remember when the
Air Traffic Control remarked that I never heard the announcement that, uh,
no one can eat peanuts on the plane. Yeah. I've
flown a lot in my life and I've never heard
that before. So Ian Hammer writes in on the Air
(32:04):
Traffic Control episode, you were talking about peanuts being completely
absent on some flights, And as a person that is
really allergic to peanuts, I can shed some light. My
allergy is bad enough to wear. The smell of peanuts,
which is really just the presence of peanut molecules in
the air, will cause me to get itchy and swollen. Uh.
In the case that I am in contact with a peanut,
(32:25):
have the superpower of becoming a balloon, and I'll swell
up to the point where I will be dead in
a matter of minutes. I can delay the anaphylactic shock
for ten minutes, give or take with an injection of epinephrin,
and this will only work twice, I think. So um,
if I do have reaction, I have twenty minutes plus
the fifteen minutes I have before normal anaphylactic shock would
(32:48):
kill me. There really is in a way to save
me in that instance, unless I can be administered the
proper treatment that you can get only at a hospital,
because you can imagine when a plane is at thirty
feet there's not much can be done and to get
me to a hospital within that thirty five minute time frame.
So flying can be a pretty scary thing when someone
near you. Besides that they really want a peanut buttercup.
(33:09):
People do this sometimes and it's a real pain to
have to deal with. I just wanted to give you
guys an overview of peanut allergy sufferers when it comes
to flying. Keep up the incredible work. Look forward to
seeing a TV pilot Ian Hammer. So incredible, is right.
If we were insensitive to that, then all apologies. He
didn't indicate that, but I think we weren't. I just
(33:30):
remember being surprised. Yeah, I was surprised, but and I
knew allergies could get bad, but man, that I think
on the plane, I was like, what I've known about
this since I saw an episode of Freaks and Geeks
wherein one of the characters almost died because like some
bully at school, like you gave him some peanuts. Oh yeah,
was that it was the Martin Star character, the analog
(33:51):
to Paul from Wonder Years, Okay, which was I can't
remember something, illok freaks some Yeah, it's good good. Um,
well let's see allergen. How about a practice story if
you know something about fractals that we don't, or can
correct us or explain it better than we did, which
(34:12):
I'm not sure that that's much of a long shot. Um,
we want to hear about it. You can tweet to
us at s Y s K podcast. You can visit
us on Facebook at Facebook dot com slash stuff you
Should Know, or send us an email at Stuff Podcast
at Discovery dot com. For more on this and thousands
(34:35):
of other topics, visit how Stuff works dot com. Brought
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are you
Brought to you by the reinvented two thousand twelve Camray.
It's ready. Are you welcome to Stuff you Should Know
from House Stuff Works dot Com. Hey, and welcome to
the podcast. I'm Josh Clark, hanging on by my fingernails
(00:20):
with me as always as Charles W. Chuck Bryant, doing
much the same as we were about to start speaking
on stuff you should know about fractals, more math, theoretical
man even, Yeah, a new branch of geometry. It's non
Euclidean since you brought it up, okay, very new Euclidean
(00:42):
geometry was like, and fractals are. So there's a little
bit of a gap there. There is a little bit
of a gap. And uh, there's a lot of animosity
among the Euclideans towards Fractillians. They need to loosen up
and look at some of those far out pictures. I know,
(01:04):
you know it's funny. Did you watch um, did you
watch that one doc on? Yeah? Okay, did you see
the other the Arthur C. Clark one. It was made
in like maybe eighties, six eighty seven, and it had
nothing but like um delicate sound of thunder rip off
music going on the whole time. It was really really trippy. Well,
I posted a picture I don't know if you saw
(01:25):
today on the stuff, you should know all of the
of the Mandel brought set. It's beautiful, it is and
it's very cool. And I didn't even say what it was.
I just posted it, and like I'd say, about half
the people were like, very cool, man, this is rattle
of the Mantal brought set, like fractals, talk about fractals.
And then the other half were like, well, you guys
tripping out like what you did, grateful dead day. That
(01:48):
is actually math, believe or not. But it does look
very it's very tie dye in nature, and that's why
the hippies like it. Plus also, I mean, if you've
ever seen a fractal play out on the computer screen,
like yeah, um, so we are talking about fractals. I
don't necessarily want to give a disclaimer. Chuck and I
are not theoretical mathematicians. We're not even like normal mathematicians.
(02:12):
I balanced my checkbook my hand just to keep that
little part of my brain going. So I don't like
forget how to add and subtract later on in life.
I make myself to that, and I don't let myself
jump ahead. I show my work. Yeah. Um, and that's
about the extent of math and my life normally. See,
I was the kid in math that when they said
(02:33):
you're not allowed to use calculators, I would go like,
there are calculators in life, so why can't we use them. Yeah,
Like they made calculators so we didn't have to do maths, right,
But at the same time, I find that shoddy because
it's like you're not you're not You're just circumventing learning something,
and it's like the calculators there to support you after
you know what you're doing. I disagree. Well, I think
(02:55):
this is a pretty prime example of like going around
to get to the end. So when when I was
researching this, I was like, Okay, well, they don't really
know what they're doing with this stuff yet, so we
can just totally be like, well it's it's there anything
you wanted to be and nothing at all. And then
like I started looking a little more deeply into I'm like, oh, no,
(03:16):
they do kind of know what they're doing. We really
do know what we're talking about. So I feel like
I have, just from researching this a little bit um,
something of a grasp of what fractals are at. For
those of you who who don't know what we're talking about, like,
take a second to um, look up just typing fractal
and search images on your favorite search engine and you'll
(03:39):
be like, oh, yes, of course it's a fractal, um
And that's what we're going to talk about, because fractal
fractals are a new field, like we said, in geometry,
and they do have use and they have usefulness that
I think people haven't even considered yet. But the the
stuff that they have figured out how to use it
for is pretty amazing stuff. Can what if fractal is
(04:01):
at least so people know this should clear it all up.
It is a geometric shape that is self similar through
infinite iterations in a recursive pattern and through infinite detail exactly.
So there you have it. Boom. Do we need to
even continue? No? But um, And that sounds like really
that put me off, Like this article was pretty well
done by a guy named Craig Haggett. I don't know
who that is, freelancer, I guess, um, And it's a
(04:24):
pretty well done article. But that a sentence like that
can put a person off pretty easy, and he even
put it, you know, he made a joke about it like,
oh you know that, you get it, you know whatever.
But um, when you think about it, if you take
that apart, one of the hallmarks of fractal fractals um
is that they are a very complex result from a
(04:45):
very simple system. And there's like basically three hallmarks two
fractals that you just pointed out right. There is um
self similarity, which is if you if you cut a
chunk like a microscopic piece of a fractal off and
compare it to the whole fractal, it's going to be
(05:06):
virtually the same, yeah, like or a fern. And the
cool thing about practicals is is, to me, the coolest
thing is that practicals. The point they made in the
Nova documentary is that all of our math up until
they discovered fractals and described practicals, was based on things
that we've basically created and built. Like all geometry, right
(05:30):
Euclidean geometry. You have length, width, and height, which which
should be the three dimensions, right, yes, for like pyramids
and buildings, cones and all those things. And you it's
extremely useful and we've done quite a bit with this.
But what Euclidean geometry, as far as the fractal geometrists
or geometers um insist fail That is when they said, okay,
(05:56):
look at that mountain, that's a cone. It's an imperfect cone,
it's a rough cone, but it's a cone shape, right,
So yeah, Clidean geometry holds sway. What the fractal geometers
say is, yeah, you could say that it's a cone,
but if you tried to measure and describe it as such,
you're not going to come up with a very descriptive,
(06:16):
a very um detailed description of that mountain. So what's
the point. What fractal geometry does is it says we're
going to describe that mountain in every little craig and
peak possible. And so what you have is the fractal dimension,
which exists in conjunction with length, widthin height. And what
(06:38):
the fractal dimension describes is the complexity of the object
that exists within those three dimensions as well. So, finishing
my point, the cool thing about practicals is that everything
that we had done previously in geometry were because of
things we built. Practicals help describe things that were have
been here since the beginning of time in nature, and
(07:01):
one of the truest examples of that is the fern.
Right with self similarity, you take a little snippet off
of a fern, all that you shouldn't do that, let's
just look at it. Uh, it's gonna look the same
as the larger part of the fern, and then the
whole fern itself very self similar but not necessarily exact. No,
it can be. There is a form of self similarity
(07:22):
that is exact and precise, but in nature that's rare,
if not just completely not found. Right, that's right. So
you've got self similarity, which is the smaller part is
virtually the same or looks the same or structured the
same as the whole um. And this process of self
similarity um going larger smaller in scale, it's called recursiveness, right, yeah,
(07:46):
And recursiveness is um like you know those paintings where
it's like a guy I think Stephen Colbert, the one
that he gave to the Smithsonian has recursiveness in it,
where it's a man in a painting standing in front
of like mantle, and above the mantle is the painting
that you're looking at, and then it goes on and
on and on and on and on anything that's infinitely repeating, right,
(08:08):
same with if you're in a dressing room and there's
a mirror on either side of the wall, you just
keep going on infinitely. It's recursiveness, and with fractals the
recursiveness of self similarity. Right, So there's two two traits.
Um is produced through this thing called iteration, that's right.
And that's where you say, here's the whole I'm gonna
(08:32):
put it into this formula, and the formula has has
the formula. The output of the formula produces the input
for the next round of that same formula. It's a
loop exactly, so it's self sustaining and it can go
on infinitely recursion. Right. That's right. So what we've just
(08:55):
come up with is the fractal is anything that has
a self similar structure and it recursive through iteration. That's okay.
So um A, really I came upon this kind of
easy one easier explanation of a fractal from Ben wal
Mandel brought site. He died, by the way in two
(09:15):
he seemed like a pretty good guy. He was definitely
thinking different um. And the way that Mandel brought described
A really easy way to think of a fractal is um.
There's this thing called the Serpentsky gasket. And you take
a triangle and you can combine them into a bunch
of little triangles and spaces, triangular spaces that form a
(09:38):
larger triangle. Right, So that that one initial solid triangle
is called the initiator, that's the original shape. And then
all those other triangles combine that form that larger triangle
or a self similar version of that larger triangle, the
original triangle. That's called a generator. Right. So the formula
(10:00):
for creating a fractal would be to go into that generator,
the version that has all the little smaller triangles and
make up a larger whole triangle. And say, all the
ones that look like the initiator, the original just solid
black triangle, take that out and swap it with the
generator version, and all of a sudden you have one
(10:20):
that's exponentially more detailed. There's more to it, And that's
a fractal. That's all there is to it. You know
what else is a fractal? What the coastline? Yeah, that
was a big one. Lewis fried Richardson was an English
mathematician early twenty century, and he very brilliantly said, you
know what, if you take a yardstick and you measured
(10:43):
the coastline of England, you're gonna get a number. If
you take a one ft ruler and measure the coastline,
you're gonna get a different number. If you take a
one inch ruler and measure the coastline, you're gonna get
a different number. And it's basically infinite in that the
smaller you go with your your unit of measure or
(11:04):
your tool is the larger number you're gonna get, because
the coastline is so infinitely varied in its little nooks
and crannies, right exactly. It's a very cool way of
thinking about it. There's a second part of that too, Chuck.
Is that so depending on the you, what you're using,
the measure, the tool you're using the measure, the number
(11:24):
the perimeter of that coastline could go on infinitely, but
it still contains the same finite amount of space within paradox.
That is a big time paradox because things aren't supposed
to be infinite and finite at the same time, right
Um and uh Lewis Fry Richardson. He basically established in
that coming up with that paradox, the this kind of
(11:46):
revolution and thought that fractal geometry is based on that
you can have the infinite mixed with the finite, and
you can get it from pretty simple formulas that create
very increasingly complex systems, right, Um, And Fry wasn't the
He wasn't He was the first guy to really kind
(12:07):
of put forth this idea of thought, but he wasn't
the first one to notice this paradox. Yeah, and before
people even knew there were fractals, there were there were
artists like Da Vinci that saw this pattern and tree branches.
That was um. I know. In the Nova documentary and
the article they point out the uh Catsu Chica Hokusai
(12:29):
Japanese artists created the Great Wave off Kanagawa and uh
those are fractals. It's a it's ocean waves breaking and
at the top of the crest of the waves are
little self similar waves breaking off into smaller and smaller
self similar versions. And that's a natural fractal, or in
this case, it's a depiction of one. So they were
you know, early African and Navajo artists were doing this
(12:50):
and they didn't realize that they were fractals and there
were fractals all around us. No, they just saw crystals
in a snowflake or another good one, Yeah, exactly. Um.
They were just they saw that there was what they
were looking at was a repeating pattern that was self
similar and recursive. Right, yeah, that's it. That's a fractal.
Right yeah. And and Ben Wha mandel Brought was the
(13:13):
first one to say, you know what, we can we
can use math equations to actually apply to this. And
he was a big star for a while. And then
they sort of turned on him and said, you know what,
this is all cool and trippy looking, but it's useless,
right And he said, oh yeah, screw you guys. Watch
this And he wrote another book which started to uh
(13:37):
give some practical applications which are pretty exciting. UM. So
the whole thing, the whole principle that this is based
on UM is that you can take a formula and
plug in a very simple UM, well, a relatively simple
formula like mantel Brought's formula. Will take that one. For example,
(13:57):
his is um Z goes to zed squared plus c. Right,
that's what it's called. If you're in England, z we
say z z Well, anyway zed goes to which is
and the goes to is the key right here, this
(14:18):
is what makes it fractal. Goes to means that um,
it's an error. It's an equal sign. It looks like
an equal sign with an part of an arrow pointing
towards ZED, the other point pointing toward the rest of
the formula, which means that the the there's that feedback
loop where it's like, okay, once you have the number
that this punches out, you have you feed it back
(14:40):
in and you'll get another number and just keep going
and going and going. And every time, remember you're swapping
out the original the initiator for the the detailed version
the generator, and it's just getting exponentially more complex with
just the one iteration of that's very simple formula UM
(15:05):
and Mandel brought set uh. This is the one that's
like it's probably the most famous one. That's the one
that the Deadheads like because it's like this crazy juxtaposition
between like black and like different colors and everything. And
with his formula, two things happen with the number that
you put in. It either goes towards zero, or it
(15:27):
shoots off to the infinite. And what they did for this,
for the the Mandel brought set fractals was they assigned
a color to a number based on how quickly it
goes off to towards infinity. Right, So let's say that
you have like four, If you plug four into this
and in ten generations, it'll it'll become an infinite number. Um.
(15:50):
Then say that that would be grouped into a blue
color like ten generations blue, eight generations is red, ninety
generations is orange. See what I'm saying, um. And then
the other direction, like say if you put in four
point two or something like that, it'll go towards zero.
And any number that eventually will go towards zero is
(16:10):
represented as black. So what you have then is this
really intricate depending on where you're zooming in or out
on the fractal, this intricate change of colors, and what
you're really just seeing our numbers that are plots on
a plane, and that's your fractal, and then the black
parts are numbers that will eventually be be zero. Right,
(16:31):
And most of the mental mental brought set is black. Yeah,
but if you zoom in like that's the whole point
you zoom in on one of those little uh what
do we even call those little spikes? Uh? I guess
you could call it a plot. A plot, and it's
gonna look like what you just saw. And that The
Nova documentary is very cool when they zoom in on
(16:53):
these and it's sort of mind blowing. Yeah, it is
very I strongly recommend watching that because they explain it
way better than us. Well it helps to see it
for sure. So um, it's a pretty nice little friend,
um chuck. So we've talked about fractals, we talked about
(17:13):
the Mandel brought set, we talked about where they started
to come from, UM, and the the idea. Remember Lewis
fried Richardson, he was talking about measuring the coastline and
going off into the infinite but still containing a finite
amount UM. A guy came after him named Helga von Coke.
(17:34):
He came up with a Coke snowflake, which is pretty cool.
If you take a straight line, or you take a triangle,
and then on each side of the triangle in the
middle you bust out the middle into another triangular hump.
You do that over and over and over again. It
goes off into infinity. Although it contains a finite amount
of space, the perimeter goes off to the infinite. A
(17:55):
guy named Georg Cantor came up with the Cancer set,
which is just take a straight line and you take
the middle out of it, and then for each of
those two lines that produces, you do the same thing
and it just keeps going on and on and rather
than going to nothingness like you're like, well, if you
take a six inch line, eventually you're gonna bust it
down and nothingness again, that doesn't happen. They found that
(18:15):
it goes off to the infinite. So they realized ben
Wa Mantel brought was plugging all these into computers. Because
that's what it took. People realize it's like George Cantor
um Man, I hope that's how you say his first name.
He was he was working in the eighteen eighties. Um
Gaston Julio came up with the Julius sets for producing
(18:35):
a repeating pattern using feedback loop. All these guys were
like nineteenth century early twentieth century mathematicians, and it was
strictly theoretical until the late seventies, when guys like Mantel
brought who worked at IBM started feeding these things into
these new fangled computers and seeing the results like this,
fractals like the mantel brought set that he saw right,
(18:58):
so um, almost immediately there was a practical use for
fractals that came in the form of c g I. Yeah,
they interviewed that one guy and the documentary um who
worked on the first c g I shot in motion
picture history, which was Star Trek to the Wrath of
(19:20):
con and uh. He was tasked with making a c
g I uh land surface like mountain range and pretty
mind blowing with it. Yeah, and he did. I mean,
now you look back and it kind of looks silly,
but at the time it was completely revolutionary. And once
he learned about fractals in the geometry and the math
of practicals, it was pretty easy for him. And he
(19:42):
made it seem like he's like, oh, well, this is
the key, this is how you do it right. So well,
and it is kind of easy, especially if you know
what you're doing with computer programming and math, because what
you're basically doing to create a fractal generator is teaching
your computer to to do something within a certain formula
that's a fractal formula, right, and so what Lauren Carpenter,
(20:04):
the guy who created them the star Trek to landscape
for the first c G all c g I shot. Ever,
what he basically did was created a computer program that said, hey, computer,
I'm gonna give you a bunch of triangles. Because I
think that was the earliest stuff he was working with. Um,
I'm gonna give you a bunch of triangles, and I
want you to take those triangles and generate a new
(20:26):
fractal set from it, right, And then I want you
to do it again and again and again, and then
every third time I want you to start turning them
forty degrees. So that's going to change the pattern slightly,
and then all of a sudden you have these infinite variations.
The reason why when you go back and look at
that shot that it still looks kind of you know today,
(20:48):
is because the computer he was working at didn't have
the computing power to do that many times. Now we
have higher computer computing power, and so what we're doing
is telling our computers to keep going and going and going,
swapping out the initiator that one single black triangle everywhere
it can find it in this pattern. This pattern of
triangles in the fractal with a brand new fractal. So
(21:11):
it's just creating more and more and more and more fractals,
which creates a finer and finer and finer resolution, which
makes something look all the more realistic. Yeah, like the
part in the doc about the Star Wars's making the
lava splashing, it's amazing. Yes, it was because they showed
the first one that he did. It looks kind of plain,
and then once you fed it through this infinite feedback loop,
(21:32):
it just like shattered and and and uh, fractured, not fractal,
although I want to say fractal off and just look
more detailed, more detailed, more detailed, until it looked like
lava splashing, right, it's pretty amazing. Well, that's where the
word fractal comes from. Is um Mandel brought coined in
to say, to indicate how the things fracture off and
(21:56):
they form irregular patterns. Um, you can create to fractal
that that is regularly repeating, but it doesn't look as natural.
And with like say, if you're creating lava, right, you've
got to have that one rule that like every third
generation kicks forty degrees or whatever. The rule is that
(22:17):
just kind of throws a little bit of dissimilarity into it,
because if something's too self similar, it's not going to
look right. It's not gonna look natural, it's not gonna
look real, which kind of leads you to think, chuck,
then that there is a an application for studying natural
phenomenon using fractals, right, while there are I guess all
kinds um, well, this isn't so much natural. But the
(22:42):
documentary interviewed Nathan Cohen who was a ham radio operator,
and his landlord said, dude, you can't have that huge
antenna hanging out of your apartment. So he started bending
wires a straight wire into essentially a fractal and found
that on the very first go it got better reception
um merely by the fact that it was bent in
(23:04):
that way and it was self similar. So he eventually
used that two I hope make a lot of money.
I got the imperson that he did, okay, um by
applying that technology to cell phones um, and the way
that they describe it as all the different things a
cell phone can do, if you were to have a
different antenna for each one of those functions, it would
(23:25):
be like carrying around a little porcupine. So what cell
phones now are based on is a fractal design called
Manger sponge Minger sponge and uh, it's basically a box fractal.
And if you crack up in your little cell phone,
you're gonna see it wired that way. Yeah, You're going
to be looking at a fractal it's a square, right,
(23:46):
and then within it or a bunch of little squares
in a recursive, self similar pattern. And you friend, are
looking at a fractal. It's all around us. Yeah, Um,
it's also all around us in nature. There's uh in
that same UH documentary, that Nova program, there was a
team from i think University of Arizona. There's a team
(24:09):
of academics. That was pretty cool. Who Um, we're trying
to figure out if you predict the amount of carbon
capturing capacity an entire rainforest has just by measuring UM
and figuring out this self similar system that a single
tree in that rainforest UM has. That makes sense, Well,
(24:30):
it does, but it's kind of a leap. It's like, okay,
so it's one tree, does it follow the same system
that the whole rainforest does? And they apparently found that yes,
in fact it does right. The same branching uh system
found in that tree is similar to the the growth
of the trees in the rainforest as a whole. Pretty cool, yes,
(24:54):
um in the human body, uh, one of the keys
to getting rid of cancer is or any kind of
tumors spotting these tumors early on. But with our ultrasound
technology you can only get so small and so detailed
that you can't see some of these natural fractals that
you know, your blood vessels are fractals essentially, just like
(25:15):
the branches of a tree are um So they are
now using geometry two. Now if I'm not sure if
I got this right, but I think it shows up.
It shows the flow of the blood because ultrasound can
pick that up through these fractals when they can't even
pick up the vessels themselves. Is that right? Early earlier
(25:37):
tumor spotting right. Well, for all intents of purposes, they're
looking at the vessels by finding the blood because they
see where it's flowing. But yeah, depending on the pattern
that it follows. If it follows like a like a
tree branching shape, it's healthy, right, Yeah, And then the
tumors all the veins are all bent and crooking, going
in all crazy directions. The readoubt of a heartbeat, it's
(25:58):
not consistent. It's a fractal Yeah, So the use fractal
analysis now to study your heart rate and use that
to better understand how arrhythmia happens through math. So there's
the especially with natural systems. That's kind of like the
biggest contribution that um fractal geometry is produced so far,
(26:20):
I think, aside from c g I is what medical
uh well, just that that whole understanding that was first
really kind of um voiced by Lewis Fry Richardson with
the coastline that there's, um, there are natural systems out
there that we can't really that we're not quite paying
attention to, we don't really know how to deal with that.
(26:43):
We're trying to apply something like Euclidean geometry to something
that you can't really use that for um. That that's
what fractal geometry is really contributed so far, is to
basically say, hey, there's a lot of natural systems out
here that are self similar and recursive and now that
we kind of see in the fractal world, we see
(27:03):
them everywhere, and we have a better understanding of them.
And one of the best examples of that, I thought
was figuring out how larger animals use less energy and
smaller animals they use energy more efficiently. And um, this
is a kind of a biological paradox for a really
long time, and these guys figured it out using I guess,
(27:24):
kind of the um same kind of insight that fractal
geometry has. That if you take genes and genes are
the mathematical formula or the equivalent of a mathematical formula,
and you UH feed in uh these genetic processes, what
it's going to put out is this self similar recursive
(27:49):
pattern to where the bigger the organism is, the more
this thing goes and goes and goes, the less energy
it's going to use because there's more of it and
it doesn't require very much energy to produce past a
certain point. So if you have a very small animal,
it's using a lot of energy to do these things
to carry this out. But there's that economy of scale
(28:09):
because you're still using a relatively simple formula, your genetic code,
right UM, to carry out a very complex, seemingly complex
um system, which is your organs or you as an organism.
So in the end, an elephant uses less energy than
a mouse, Yes, because they're both using the same formula,
(28:30):
the same input. And then eventually you reach a point
where it just gets easier and easier and easier to
to use something simple to create a complex system. I
love it too. Uh. I got one more thing. You
heard this guy Jason Paget, Huh, this is pretty crazy. UM.
This guy, like nine years ago, I think UM, was
(28:52):
mugged in Tacoma, Washington, got hit in the back of
the head really hard, knocked him out, and he acquired UM,
a form of synesthesia in which he sees fractals from
being hit in the head and UM basically it's an
acquired savant savantasm, which is pretty rare to acquire this.
(29:13):
Later on, UM, and this guy hated math, and his
family used to make fun of him, he said, because
he was the worst at pictionary. Uh. I couldn't draw
a thing, couldn't draw a lick. Now this guy can
draw reportedly mathematically correct fractals by hand, and he's the
(29:33):
only person on earth that can do this. And you
should see these things. They're like, you know, a huge
you know, two by two fractal that looks like it
was plotted by like a supercomputer. And this guy does
these by hand now out of nowhere because he got
hit on the head. That's pretty amazing. Yeah, it's crazy.
He got him in the fractal center. Huh. Did that's
(29:54):
strange that we would have like that ability latent in
us you know. Yeah, Well they studied his brain of course, um,
and they found that the two areas that lit up
in the left hemisphere were the areas that control exact
math and mental imagery. So they dont have it. And he's,
you know, he's fine with it, although he says that
(30:14):
he's a bit obsessive about it because he's it's one
of those deals where everywhere he looks now he sees fractals.
Oh yeah, well I got the impression that people who
are who are fractal geometers have the same thing. Yeah,
you know, they're like, look at that cloud. I I
can figure out how to describe it completely. Yeah with math, Yeah,
it's crazy. Um. And then it's everywhere canopies of the trees. Like.
(30:36):
I got that impression as well that once you start
seeing fractals in natural systems, like then everything becomes um,
fractals and a lot simpler to understand. I realized today
that I have always doodled in fractals. Yeah yeah, because
I can't really draw, so whenever I doodle, it's like
it's always been um little fractal shapes, Like I would
(30:57):
draw some kind of geometric shape, then split off from
that and make it smaller, and in the end they're
sort of like fractals. Oh, your fractal tree that you
showed me, it's pretty awesome. So you got anything else?
Uh No, I would strongly urge you to read this
article a few more times and then maybe go off
and read some more about fractals, because we definitely have
(31:18):
not covered all of it. I'll watch that Nova documentary. Yeah,
good stuff. What is it chasing the hidden? To mention?
Is that what it's called? Diould call it chasing the dragon? Well,
there's the dragon curve fractal. It's pretty boss, that's right,
it is. UM. So you want to type fractals in
the search bar how stuff works dot com to start,
and that will bring up this very very good article.
(31:41):
And I said search bar, which means it's time for
listening to ma'am Josh. I'm gonna call this, uh, don't
eat your peanuts around me, jerk. Yeah. Remember when the
Air Traffic Control remarked that I never heard the announcement that, uh,
no one can eat peanuts on the plane. Yeah. I've
flown a lot in my life and I've never heard
that before. So Ian Hammer writes in on the Air
(32:04):
Traffic Control episode, you were talking about peanuts being completely
absent on some flights, And as a person that is
really allergic to peanuts, I can shed some light. My
allergy is bad enough to wear. The smell of peanuts,
which is really just the presence of peanut molecules in
the air, will cause me to get itchy and swollen. Uh.
In the case that I am in contact with a peanut,
(32:25):
have the superpower of becoming a balloon, and I'll swell
up to the point where I will be dead in
a matter of minutes. I can delay the anaphylactic shock
for ten minutes, give or take with an injection of epinephrin,
and this will only work twice, I think. So um,
if I do have reaction, I have twenty minutes plus
the fifteen minutes I have before normal anaphylactic shock would
(32:48):
kill me. There really is in a way to save
me in that instance, unless I can be administered the
proper treatment that you can get only at a hospital,
because you can imagine when a plane is at thirty
feet there's not much can be done and to get
me to a hospital within that thirty five minute time frame.
So flying can be a pretty scary thing when someone
near you. Besides that they really want a peanut buttercup.
(33:09):
People do this sometimes and it's a real pain to
have to deal with. I just wanted to give you
guys an overview of peanut allergy sufferers when it comes
to flying. Keep up the incredible work. Look forward to
seeing a TV pilot Ian Hammer. So incredible, is right.
If we were insensitive to that, then all apologies. He
didn't indicate that, but I think we weren't. I just
(33:30):
remember being surprised. Yeah, I was surprised, but and I
knew allergies could get bad, but man, that I think
on the plane, I was like, what I've known about
this since I saw an episode of Freaks and Geeks
wherein one of the characters almost died because like some
bully at school, like you gave him some peanuts. Oh yeah,
was that it was the Martin Star character, the analog
(33:51):
to Paul from Wonder Years, Okay, which was I can't
remember something, illok freaks some Yeah, it's good good. Um,
well let's see allergen. How about a practice story if
you know something about fractals that we don't, or can
correct us or explain it better than we did, which
(34:12):
I'm not sure that that's much of a long shot. Um,
we want to hear about it. You can tweet to
us at s Y s K podcast. You can visit
us on Facebook at Facebook dot com slash stuff you
Should Know, or send us an email at Stuff Podcast
at Discovery dot com. For more on this and thousands
(34:35):
of other topics, visit how Stuff works dot com. Brought
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