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. Get blown away by fractals in this classic episode.
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And IBM problems. Inspire us to push the world forward. That's why so many people work with us on everything from city traffic to ocean plastic. Smart loves problems, IBM, let's put smart to work, visit, IBM dot com, slash Smart, to learn more, I'm Tracy. We will said one of the house
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Toby Chuck Bryant here in the corral and I'm gonna lasso up stuff, you should know select for you from June
with two thousand twelve fractals colon wow. This is a tough one. For me, I'm not gonna lie. Fractals is one of the toughest
since I've ever had to learn and research. That's where we're gonna revisit it right here right now,
Welcome to step you should now production of Iheart Radios Housetop were broken into the pockets of Josh Clark hanging on by my fingernails.
Me, as always, is Charles Doug each upright do in much the same as we are about to start speaking. Instead, we should know about factors
a more math, be ready
old man even a new,
geometry. Its non nuclear
since you brought it up very new UK
and geometry was like three hundred BC and fractals nineteen. Seventy five. Yet this little bit of a gap,
There is a little bit of a gap agenda,
is a lot of animosity among the Ukrainians toward factor millions.
Right now. You may need to loosen up and look at some of those, far out pictures and now
it's funny I did you watch. Did you watch that one dark on yeah? Ok, did you see the other the Arthur? She Clark, one now
it was made in like maybe eighty six,
seven and it had nothing but like a delicate, sound of thunder
off music going on the whole time, it was really really trippy. Well, I put
a picture or if he saw today on the stuff he should know all of the idea of the Mandl brought set it's beautiful,
it is in his very cool, and I didn't say what it was at his posted it. Unlike I'd, say about half the people
very good man. This is rattle of the men brought set like fractals talk about practice,
then the other half or like will you go to bed
I agree that grateful their day,
actually math, we were not buy, it does look there. It's very tight, I in nature, in areas where the hippies, like it puss, also mean if you ve ever seen a fractal play out on
Peter Screen library trivia. So we are talking about fractals
I don't. I don't necessarily want to give a disclaimer chuck and I are not theoretical mathematicians we're not even like normal mathematicians. I balance my checkbook by hand.
Just to keep that little part of my brain going. So I dont like forget how to add an subtract
later on in life. I make myself through the air, and I dont know myself jump ahead. I show my work I really here and that's about the
Stan of Math and my life normally tee. I was
kid in math,
that, when they said you're not allowed to use calculators, I would guy, but there are correct
it is in life. So what can we use? Em like they made calculator, so we didn't have to do math ripe
this entire finance shoddy, because it's like you're, not you're, not you
two circumventing learning something and it's like they calculators there to support you after you know what you're doing discreet well. I think 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. Ok really know what they're deal with this stuff. Yes,
this totally be. Likewise. Is anything you want to be and nothing at all and then like us
looking a little more deeply term like now
You can't know what they're doing their work
do you know atonements? So I feel like I have just from researching this a little bit something
of a grasp of white fractals are any tool.
For those of you who who don't know what we're talking about. Let's take a second to look up just type in fractal and search images on your favorite search engine and
you'll, be like up. Yes, of course, its fractal in that's what we're going to talk about, because fractal fractals are a new.
Feel like we said in geometry, and they do have use and they have usefulness there. I think people haven't even considered yet area, but the they stuff they have figured out how to use a forest. Pretty amazing stuff. Can I say what a reckless yeah it lay Sophie
This clear dollop is the geometric shape that is self similar through infinite adoration and recursive pattern, and through infinite detail exactly so there you have it boom doing
even continue. No, but it in it
sounds like really that put me off like this. Article is pretty well done by a guy named Craig,
hey get. I don't know who that is freelancer, I guess yet it it's a pretty! Well,
article, but that a sentence like that can put a person off pretty easy teacher and even put it, you know him.
The joke about it like I acknowledge you get it in I, whatever threat by when you think about it. If you take that a part, one of the hallmarks of fractal fractals, is that,
you're a very complex result from a very simple system and there's a basically three hallmarks to fractals that you just pointed out,
right, there is 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 gonna be virtually the same
yeah like or a fern and the cool thing about fractals is is to me.
Who are saying is that fractals.
The point I made the Novo documentary is that all of our math, up until they discovered fractals and describe fractals, was based on things that we basically created and built like it
I'll geometry, right, euclidean geometry. You have linked yet width and height. We would surely the three dimensions right. Yes,
like pyramids and building the cube, sidewalks and homes and other things, and you it's extremely useful. We done quite a bit with this, but
euclidean geometry. As far as the fractal geometry, wrists or geometers insist, failed,
is when they said. Ok, look at that mountain, that's a cone! It's an imperfect cone is a rough cone yeah, but it's a cone shape Bryant so
Euclidean geometry hold sway what the fractal geometers
say is yet it. You could say that it's a com,
but if you tried to measure and describe it as such you're not going to come up with a very descriptive, a very detailed description of that mountain. So what's the point, what fractal geometry does is
says we're going to describe that mountain in every little kragan peak possible right
and so what you have is the fractal dimension, which exists in conjunction with length within height and what the fractal dimension describes as the complexity of the object that exist within those three dimensions as well. The track soap finishing my point
cool thing about fractals. Is that everything that we had done previously and geometry? Where, because of things we built practice, help described things that were have been here since the beginning of time, yeah in nature
one of the tourists examples of that is. The fern right was
similarity you take a little snippet off of a fern.
Although you shouldn't do that was just look at it. It's gonna! Look!
same as the larger part of the fern and then the whole fern itself very self, similar right, but not necessarily exact, no again
Maybe there is a form of self similarity that is exact and precise, but in nature that's rare, if not just completely, not found right
So you got self similarity which is the smaller part is virtually the same, looks the same restructured the same as the whole and this process of self similarity
going larger. Smaller scale is covered, curse Agnes I yeah recursive. This is like you know those paintings where it's like a guy. I think Stephen Colbert, the one that he gave to the Smithsonian, has recursive innocent, where it's a man in a painting standing in front of like a man,
above the mantle is the painting yeah you're looking at, and then it goes on and on and on and on and on yet anything this infinitely repeating right same with, if you're in a dressing room and there's a mere on either side of the wall, you just keep going on infinitely its recursive ness and with fractals the recursive nests of self similarity right. So there's two two traits is produced through this thing called adoration and that's where you say: here's the whole. I wouldn't put it into this formula, and the formula has: has the formulate the output of the formula produces the input for the next round of that same formula to loop, exactly
So it's self sustaining and it can go on infinitely recursion right, that's right! So what we just cover this fractals anything that has a self similar structure and its recursive through iteration that right, ok, so a really,
I came upon this kind of easy one easier explanation of fractal.
The more Mendel broadside. He died by the way into doesn't in Yahoo said he seemed like a pretty good guy. He was deafening, think indifferent,
in the way that men are brought described
the easy way to think of a fractal is there's. This thing called the serpents key gasket and you take a triangle:
You can combine them into a bunch of little triangles and spaces triangular spaces, yeah that form a larger triangle right, so that that one initial solid triangle-
called the initiator. That's the original shape right and then all those other triangles combine that form that larger triangle,
self, similar version of that larger triangle. The original triangle- that's called generator right, so the formula for creating a frank.
So 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
like the initiators of the original just solid black triangle, take that out and swap it with the generator version right,
and all of a sudden. You have one that exponentially more detailed. There is more to it and that's a fractal. That's all there is to it. You know what else is a fragile, because
as a big one. Louis right, Richardson was an english mathematician early Twentyth century and
very brilliantly said in a lot. If you take a yardstick,
any measure the coastline of England, you're gonna get a number he take a one foot ruler
and measure the coastline. You're gonna get a different number. If you take a one inch ruler,
The coastline you're gonna get a different number and its basically infinite. In there.
The smaller you go with your ear.
Of measure or your tool is
larger number, you're gonna get because
the coastline is so infinitely very
in its little nooks and crannies right, exactly does very cool way of thinking about it. There is a second part of that to chuck is that so
depending on the youth and what the what you're, using the measure to using the measure. Yet the number, the perimeter of that coastline
one infinitely, but it still contains the same finite amount of space within the paradox. That is a big time paradox, because things aren't supposed to be infinite and finite at the same time
right right and Louis FRY Richardson. He basically established in that coming up with that paradox
the this kind of revolution in thought that fractal geometry is based on that you can have the infinite mixed with the finite ray. You can get it from pretty simple formulas that create very increasingly complex systems right yet and fry. Wasn't he wasn't that he was the first got a really.
Put forth this idea of thought, but he wasn't the first one to notice paradox yeah and am before
believing you there were fractals there were. There were artists, like divinity that's all this pattern
tree branches was on and on
the documentary and the article they point out, the cat sues Shaker Hokosa. I
eighteen, twenty japanese artist created the great wave off canna
and those are fractals. It's a bit ocean waves breaking and at the top of the crest of the waves
our little self similar waves breaking off in a smaller and smaller self, similar versions and its nature
frank to earn the alleys, it's a depiction of one. So they were. You know early african and never hoarders for doing this, and they didn't realize that they were fractals in their fractals,
all around us. Now they just saw crystals in it.
Flickr another good one yeah exactly they were just stayed saw that there was what they were look
That was a repeating pattern that was self similar am recursive right. That's it! That's a fractal,
yeah and in
then, why Mandl brought was the first one to
say, you know what we can. We can use math equations
to actually apply to this, and he was a big
for a while and then they
they turned on him and said you know what this is.
Cool and trippy lookin, but it's useless
right and he said oh yeah screw.
You guys watch
and he wrote another book which
to give some practical applications ratchet pretty exciting year, so that the whole thing the whole principle it is based on is that you can take a formula.
And plug in a very simple, was a relatively
before me like mantle brought formula the I'll. Take that one, for example, his is Zed, goes to Zed, squared plus see right, say said: that's what it's called if you're in England there
we say see then put Edward Rabies it's dead anyway. That goes to witches, and the goes to is the key right here, the yet what makes it fractal goes to means that
it's an air is an equal. Silent, looks like an equal sign within it,
part of a narrow pointing towards Zed, yet the other point pointing towards the rest of the formula, which means that the the it there's that feedback loop words like ok, once you have the number that this plan.
His out, you have you feed it back in and you'll get another number noses keep going and going in going right in every time. Remember your swapping out the original, the initiator for thee, the detailed version, the generator yet, and it it's just getting exponentially more complex with just that one adoration of that very simple formula. The train in man brought said this is the one that's like it's probably the most famous one, that's one of the dead heads like cause. It's like this crazy juxtaposition between like black and like different colors. You everything
and with his formula to things happen with a number that you put in it either goes towards zero or shoot off to the infinite and what they did
this further. The mental brought set fractals was they assigned a color to a number based on how quickly it goes off to return
infinity right. So let's say that you have like for, if you plug for into this
ten generations it'll if it'll becoming
infinite number right then say that that would be
grouped into a blue color like ten generations, blue agent.
Nations is red Knight.
Generations is orange, it's sort, I'm saying, and then the other direction like say. If you put him four point two,
like that, it'll go towards zero,
and any number that eventually will go towards? Zero is represented as black
so what you have, then, is this really intricate, depending on where you resuming?
out on the fractal. This intricate change of
colours and what you're really to seeing our numbers that are plots on a plane near and
That's your fractal, then the black parts or numbers that will eventually be be zero bright,
most of the men Dollah Mental brought said his black yeah. But if you zoom in
That's the whole point you zoom in on one of those little. What do we call those full spikes? I guess you could call a plot a plot, and it's going to look like what you just saw.
And then the Nova document is very cool when they zoom in on these ants sort of my blowing yeah. It is very, I strongly recommend watching that cause. They explain it way better than us. Well, it helps to see it pressure area big time,
so or draw. As I have done. My pay. I says it's a pretty nice little frankly there. My name is RON variety and that's a very big deal. Nbc comedy is a big deal, do not as big as my deal but pretty be ignored. Last, just there's a notice will drop off from my big deal to their big deal, but they are still technically a big deal. Nbc comedy
HU the things I know about this part gas, and you don't have to give you some straight job here. The podcast world is assessed and you could close sorted world strange, drifters drifters, which, what's the difference between a drifter Griffith anyway, were a bit like pirates, rob from rich give to the boy.
Sometimes we don't give to the poor. Sometimes we keep it ourselves. We keep the booty for ourselves. So keep your eye on the prize. Look for the second season of my podcast in stores
So we talked about fractals. We talked about the Mandl brought set, we talked about where they certainly come from, and
That's the idea. Remember Louis fry Richardson. He was talking about measuring the coast
going off into the infinite, but still retaining a finite about the guy,
him after him new Hell given Coke there, he came over the coke snowflake, which is pretty call if you take a straight line,
Are you take a triangle and then on
say the triangle: in the middle you bust out the middle into another triangular huh.
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 guy named York, Canter came over the cancer set, which is you just take a straight line and you take the middle out of it and then free to this
lines that produces. You do the same thing in 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 right, eventually, you're gonna bust done nothingness again that doesn't happen. They found that it goes out to the infinite, so they
it been warm and brought. It was plugging all these into computers because that's what it took Yasser people realise this. Like George Canter man, I gotta tell you say: firstly,
he was dead. He was working in the eighteen eighties.
Guest on Julio came with the Julia sets for producing repeating pattern, using feedback loop
there's really nineteenth century early twentieth century mathematicians. It was strictly theoretical until the late seventies
guys, like men brought, who worked IBM started feeding these things into these new fangled computers,
right and seeing the results like this fractals, like the man, oh brought said that he saw right. So
almost immediately, there is a practical use for fractals that came in the form of sea gee. I
yeah. They interview that one guy in the documentary who worked on the first.
See gee I shot in motion picture history Mitch was STAR Trek to the wrath of cod
and he was tasked with making a cd land surface,
and when he mine blowing was in the end he did I mean now you look back and I can look silly, but at the time it was
completely revolutionary in
once he learned about fractals in the geometry in the math fractals, it was pretty easy form of Amy made. It seem like he's like. Oh, this is the key the site you do it right so well,
It is kind of easy, especially if you know what you're doing with computer programming and math, because what you are basically doing to create a fractal generator is teaching your computer two eggs to do something with
certain formula that fractal formula right and so what Lauren
but you're the guy who created the and the STAR Trek to landscape for the first see g
I'll, see. Gee I shot ever knew what he basically did was created computer program. That said: hey, computer,
I'm to give you a bunch of triangles, because I think that was the early stuff is working with you. I'm gonna give you a bunch of triangles and I want you did-
those triangles and generate a new fractal set from right
to do it again and again and again and then every third time. I want you to start turning item. Forty two,
is so that's gonna change the pattern slightly and then all of a sudden yellow is infinite. Variations
The reason why, when you go back and look at that shot that it still looks kind of today is because the computer he was working at didn't have the computing power to do that many times. Yes, sir. Now we have higher com
computing power, and so what we are doing is telling our computers to keep going and going in going swapping
that initiated that one single black trying
everywhere it can find it in this pattern. This pattern of triangles in the fractal with a brand new fractal,
just creating more and more and more more fractals, which creates a finer and finer finer resolution, which makes something
all the more realistic yet like the part in the dock,
the star wars, wafts, making the lava splashing yeah the maid
yes, it was because they show the first one. They did is looks gonna plain and then once you felt it through this infinite feedback loop. It just like shit,
n n N, fractured, not rattled, although I want to say fractal off
and just look more detailed, more detailed, more detailed until it looked like lava, splashing right, pretty amazing. Well, that's where the word fractal comes from
Mental brought coined? Nineteen, seventy five to say to indicate how things fracture off
and they form a regular patterns. You can create a fractal that that
is regularly repeating, but it doesn't look is natural in with like
save your creating lava
you gotta have that one rule that, like every third generation yeah kicks forty degrees
whatever the rule is that just Kenneth rose.
Little bit of dissimilarity into because of some things to self similar. It's not going to look right as that can elect naturalist. I can look real right, which kind of lead.
Think Chuck, then that there is a an application for studying natural phenomenon using fractals right while there are, I guess I'll
and while this isn't so much natural, but the
documentary interviewed Nathan, Cohen, who was a ham radio operator and his landlord said
you can't have that huge antenna hang out of your apartment so
He started bending wires straight wire
into essentially a fractal and
on the very first ago it got better reception.
Merely by the fact that it was bent in that way, but in itself similar so
He eventually use that too. I hope make a lot of money. I get the impression it. Ok,
by applying that technology, does cell phones and waited
describe it as all the different things a cellphone can do if you were to have a different
and every one of those functions. It would be like carrying around little porcupine. So what
cellphones now are based on. Is
fractal design called major sponge mingle sponge I have mentioned
and it's basically a box fractal and if you crack open, your,
cell phone you're gonna see it wire that way, yeah you're going to be looking at a fractal, it's a square right and then within it are a bunch of little squares in a recurrence of self similar pattern, and
you friend or looking at a fractal tal around,
it's also all around us and nature theirs. In that same
documentary that Nova programme. There is a team from the University of Arizona there's a team of academics, yells critical, who were trying to figure out if you could predict the amount of carbon capture and command
city and entire rain. Forests has just by
measuring and figuring out the self similar system that a single tree in that rain forest here has makes it well. It does, but it's kind of a leap. It's like okay, so is one tree. Does it follow the same system that the whole rainforest does and they apparently found that? Yes, in fact, it does right through the same branching system founded that tree is similar to the they grow
of the trees in the rain forests as a whole. People, yes, pay everybody its Josh and check your pals and get this for the new episodes of stuff. You should know we're going to have a little help from Alexa, hello
me Alexa. I know a lot about what you're looking for low, not yet elixir not yet now for new episodes, she'll be charming in with stuff. You should know like this. The pitch of some crickets is so closely related to the temperature that you can use them as a thermometer, or this more than twenty universities, including Oxford in Cambridge, were founded before the Astor Empire and are still in operation today so tune into the latest episodes of stuff. You should know for stuff: Alexa thinks you should know, hey you, wanna do or more sure Alexa the king COBRA is not strictly speaking a cobra. It also makes a noise like a growl or a bark instead of hissing barking cobras, who knew just the king cobra is not strictly speaking. A code
an elixir thanks for telling us some stuff. We should know any time. I love to talk about stuff
tumors in the human body
One of the keys to getting rid of of cancer is our or any kind of tumor spotting these tumors early on, but with our altered
Technology can only get so small and so detailed that you can't see
some of these natural fractals that you know your blood vessels or fractals, essentially disliked the branches of a tree are
so they are now using geometry. To now,
A much regret this right, but I think it shows up. It shows the flow
of the blood because alteration,
and pick that up to these fractals when they can even pick up the vessel.
Themselves Zara, yeah early earlier tumor
spotting when I worked, for all intents and purposes there looking at the vessels by finding the blood, because they ve words flowing, but yet, depending on the the pattern that it follows. If it follows lichen and like a tree, branching shape right, it's healthy right now and then the tomb resolve the veins or albanian crooking, going all crazy directions. The redoubt of a heartbeat
consistency fractal yeah. So these fractal analysis now to study your heart rate and
I use that to better understand how arrhythmia happens through math, so there's
especially with natural systems, that's kind of like the biggest contribution that fractal geometries produced so far, I think aside
from Cgi is what medical le well just that that huh
understanding that was first really kind of voiced by Louis FRY Richardson, with the coastline that there's there are natural systems out there that we can really. There were not.
Quite paying attention to right. We don't really know how to deal with them
trying to apply something like euclidean geometry, to something that you can't really you.
Therefore right that that's what fractal, geometries really contributed so far is basically say
hey there's a lot of natural systems out here that are self similar and recursive and
now that we kind of sea in the fractal world, we see
everywhere and we have a better understanding of one of the best examples of
and I thought was figuring out how
larger animals used lesson
yeah smaller animals, they use energy more efficiently, and this is kind of a biological paradox for a really long time and
guys figured it out using, I guess kind of the same kind of insight that fractal geometry has that if you too,
genes and genes, are the mathematical formula.
Equivalent of a mathematical formula, and you feed in these genetic processes waits gonna put out. Is this self similar recursive pattern near to where the bigger the organism is the more? This thing goes and goes and goes.
What's 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 lane,
its using a lot of energy to do these things to carry this out, but there's that economy of scale, because you're still using a relatively simple formula, your genetic code right to carry out a very complex, seemingly complex system, which is you
organs. Are you, as an organism bright, send the end? An elephant uses less energy than a mouse. Yes, because they're both using the same formula, the same input
and then eventually reach a point where it just gets easier and easier and easier crazy to tell you something simple: they create a complex system. I love it. I do too
I got one more thing: you heard this guy Jason Padgett. This is pretty
easy on the sky like nine years ago. I think was mugged into come a Washington
that hit in the back of the head really hard not to mount an. He acquired a form of sinister Asia in which he said.
Fractals well being hidden ahead. Teeth and
Basically, it's an acquired, savant, savant ISM, which is pretty rare
to acquire this later on and
sky hated, math and
his family's to make fun of them. He said because he was the worst pensionary can draw thing, could draw lots
now. This guy can draw reportedly mathematically correct, fractals by hand well and he's only personal on earth. It can do
holy cow, and you should see these things there, like you know a huge. You know two by two fractal that looks like it was
I did by like a supercomputer in the sky, does he's by hand now out of nowhere because he got hit on the head. That's pretty amazing! Yet crazy. He get him the Fractal Centre, her intended that's strange
We would have liked that ability, lateness, Una yeah,
they studied his brain of course, and they found that the two areas that lit up in the left hemisphere were the
Is it control, exact, math and mental imagery climate and he's gonna he's fine or that, although he says it is a bit obsessive about it, because he is
was deals where everywhere he looks now. He sees fractals area. While I get the impression that people who are who are fractal geometers have the same thing here. In other likely that cloud I can figure out how to describe it completely.
With math yeah grazing and then it's everywhere. Canopies of the trees like I got the impression as well that when neither seeing fractals in natural systems like then everything becomes fractals, alot, simpler,
don't understand. I realized today that I have always doodle than fractals, oh yeah, yeah,
because I accurately draw so whenever I doodle it's like it's all,
It's been a little fractal shapes like I would draw
I'm gonna geometric shape than split off from that make it smaller and, in the end, the sort of like fractals. Oh your fractal tree. That issue is pretty answer
so you anything else.
I would strongly urge you to read this article a few more times and then
if you go off and read some more about fractals, because we definitely not covered all the watch that nobody documentary good stuff, what is it chasing? The hidden dimension is always come intricate chasing the dragon.
Others dragging her Franco's pre boss is boss,
you, wanna type fractals in the search bar. How supports that com to start? And that will bring up this very, very good article and I said, search bar, which we stand for this momentum
We call this, don't eat you
not around me
number. When the air traffic control, I remarked that never heard the announcement that no one can be financed from the plane
a flown a lot in my life. I have never heard them
so in human rights and on the air traffic Control episode, you're 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 algae is bad enough to wear the smell of peanuts, which is really just the presence of peanut molecules and air will cause me to get itchy and swollen
In the case that I am in contact with a peanut at the superpower of becoming a balloon and our swell up to the point where I will
Dead in a matter of minutes
in the way that in a black shock for ten minutes give or take with an injection
Evan Efron, and this will only work twice
That is why I think she's. If you every action, have twenty minutes plus the fifteen minutes. I have
before normal and reflected shock, would kill me other really is in a way to save me in that instance,
I can be administered the proper treatment that you can get only a hostile,
you can imagine when the plane is at thirty thousand feet. There's not much can be done to get me to a hospital within that thirty five minute timeframe.
Supplying, can be pretty scary thing when someone near you say
They really want a peanut butter cup. People do this
and it's a real pain to have to deal with
I just want to give you guys an overview of peanut allergy sufferers. I, when it comes to flying and keep up the incredible work, look forward to seeing the tv pilot Ian Hammer so
incredible, is right. If we are in
sensitive to that. Then all apology, seated
that but- and I we were in addition, memories, surprise yeah, surprise, but in a new allergies could get bad men that I think on the plane. I like what
What about this? Since I saw an episode of freaks and geeks, were in one of the characters, almost died because, like some bully at school like gave him some
Oh yeah was that it was born star
here, the analogue Nepal, from wonder years, ok, which was on the policy challenges
the story, if you know of their prices, that we don't or can correct this or explain it better than we did, which I am not sure that this much of a long shot.
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Transcript generated on 2019-12-24.