Kind: captions
Language: en
Some things are not normal. By that I
mean if you go out in the world and
start measuring things like human
height, IQ or the size of apples on a
tree, you will find that for each of
these things, most of the data clusters
around some average value. This is so
common that we call it the normal
distribution. But some things in life
are not like this. Nature shows power
laws all over the place. That seems
weird. Like is nature tuning itself to
criticality?
>> If you make a crude measure of how big
is the world war by how many people it
kills, you find that it follows a power
law. The outcome will vary in size over
10 million, 100 million.
>> It's much more likelihood of really big
events than you would expect from a
normal distribution and they will
totally skew the average.
>> The system you're looking at doesn't
have any inherent physical scale. It's
really hard to know what's going to
happen next. The more you measure, the
bigger the average is, which is really
weird. It sounds impossible.
>> It's it's very important to try to
understand, you know, which game you're
playing. And what are the payoffs going
to be in the in the long run?
>> In the late 1800s, Italian engineer
Vilfredo Paro stumbled upon something no
one had seen before. See, he suspected
there might be a hidden pattern in how
much money people make. So he gathered
income tax records from Italy, England,
France and [music] other European
countries. And for each country, he
plotted the distribution of income. Each
country he looked at, he saw the same
pattern, a pattern which still holds in
most countries to this day. And it's not
a normal distribution. If you think
about a normal distribution like height,
there's a clearly defined average. And
extreme outliers basically never happen.
I mean, you're never going to find
someone who is, say, five times the
average height. That would be physically
impossible. But Paro's income
distributions were different. Take this
curve for England. It shows the number
of people who earn more than a certain
income. The curve starts off declining
steeply. Most people earn relatively
little, but then it falls away
gradually, much more slowly than a
normal distribution would, and it spans
several orders of magnitude. There were
people who earned five times, 10 times,
even a 100 times more than others. That
kind of spread just wouldn't happen if
income were normally distributed.
Now to shrink this huge spread of data,
Paro calculated the logarithms of all
the values and plotted those instead. In
other words, he used a log log plot. And
when he did that, the broad curve
transformed into a straight line. The
gradient was around -1.5.
That means each time you double the
income, say from 200 to 400 lb, the
number of people earning at least that
amount drops off by a factor of 2 to
the^ of 1.5, which is around 2.8. And
this pattern holds for every doubling of
income. So paro could describe the
distribution of incomes with one simple
equation. The number of people who earn
an income greater than or equal to x is
proportional to 1 /x to the power of
1.5.
Now that's what Paro saw for England.
But he performed the same analysis on
data from Italy, France, Prussia and a
bunch of other countries. And he saw the
same thing again and again. Each time
the data transformed into a straight
line and the gradients were remarkably
similar. That meant paro could describe
the income distribution in each country
with the same equation one over the
income to some power where that power is
just the absolute gradient of the
logarithmic graph. This type of
relationship is called a power law. When
you move from the world of normal
distributions to the world of power
laws, things change dramatically. So to
illustrate this, let's take a trip to
the casino to play three different
games. At table number one, you get 100
tosses of a coin. Each time you flip and
it lands on heads, you win $1. So the
question is, how much would you be
prepared to pay to play this game? Well,
we need to work out how much you'd
expect to win in this game and then pay
less than that expected value. So the
probability of throwing a head is 1/2.
Multiply that by $1 and multiply that by
100 tosses. That gives you an expected
payout of $50. So, you should be willing
to pay anything less than $50 to play
this game. Sure, you might not win every
time, but if you play the game hundreds
of times, the small variations either
side of the average will cancel out and
you can expect to turn a profit. One of
the first people to study this kind of
problem was Abraham Demo in the early
1700s. He showed that if you plot the
probability of each outcome, you get a
bell-shaped curve, which was later
coined the normal distribution. Normal
distributions. The traditional
explanation is that when there are a lot
of effects that are random that are
adding up, that's when you expect
normals. So like how tall I am depends
on a lot of random things about my
nutrition, about my parents' genetics,
all kinds of things. But but if they if
these random effects are additive, that
is [music] what tends to lead to
normals.
>> At table number two, there's a slightly
different game. You still get 100 tosses
of the coin, but this time instead of
potentially winning a dollar on each
flip, your winnings are multiplied by
some factor. So, you start out with $1.
And then every time you toss a head, you
multiply your winnings by 1.1. If
instead the coin lands on tails, you
multiply your winnings by.9. And after
100 tosses, you take home the total.
That is the dollar you started with
times the string of 1.1's and.9.
So, how much should you pay to play this
game? Well, on each flip, your payout
can either grow or shrink. And each is
equally likely each time you toss the
coin. So, the expected factor each turn
is just 1.1 +.9 / two, which is one. So,
[music] if you start out with $1, then
your expected payout is just $1. That
means you should be willing to pay
anything less than a dollar to play this
game, right? Well, if you look at the
distribution of payouts, you can see
that you could win big. If you tossed a
100 heads, you'd win 1.1 to the^ of 100.
That's almost $14,000.
Although, the chance of that happening
is around 1 in 10 the^ of 30. You'd be
more likely to win the lottery three
times in a row. On the other hand, the
median payout is around 61. So, if
you're only playing the game one time
and you want even odds of turning a
profit, well, then you should pay less
than 61. though. Either way, if you
played the game hundreds of times, your
payout would average out to $1. Now,
watch what happens if we switch the
x-axis [music] from a linear scale to a
logarithmic scale. Well, then you see
the curve transforms [music] into a
normal distribution. That's why this
type of distribution is called a
lognormal distribution. when random
effects multiply. If I have a certain
wealth and then my wealth goes up by a
certain percentage next year because of
my investments and then the year after
that it it changes by another random
factor as opposed to adding I'm
multiplying year after year. If you have
a big product of random numbers when you
take the log of a product that's the sum
of the logs. So if so what was a product
of random numbers then gets translated
into sums of logs of random numbers and
that's [music] what leads to this
so-called lognormal distribution and
lognormal distributions produce big
inequalities. You don't just see a mean
you see a mean with a big long tail.
It's much more likelihood of really big
events in this case tremendous wealth
being obtained than you would expect
from a normal distribution.
The reason this curve is so asymmetric
is because the downside is capped at
zero. So at most you could lose $1, but
the upside can keep growing up to nearly
$14,000.
Now let's go on to table three. Again,
you'll be tossing a coin, but this time
you start out with a dollar and the
payout doubles each time you toss the
coin. And you keep tossing until you get
a heads. Then the game ends. So if you
get heads on your first toss, you get
$2. If you get a tails first and then
hit a heads on your second toss, you'd
get $4. If you flipped two tails and
then a head on your third toss, you'd
get $8 and so on. If it took you to the
nth toss to get aheads, you would get $2
to the n. So, how much should you pay to
play this game? Well, as in our previous
example, we need to work out the
expected value. So, suppose you throw a
head on your first try. The payout is $2
and the probability of that outcome is a
half. So the expected value of that toss
is a dollar. If it takes you two tosses
to get a heads, then the [music] payout
is $4 and the probability of that
happening is one over4. So again, the
expected value is $1. We also need to
add in the chance that you flip heads on
your third try. In that case, the payout
is $8 and the probability of that
happening is 1 over8. So again, the
expected value is $1.
And we have to keep repeating this
calculation over all possible outcomes.
[music] we have to keep adding $1 for
each of the different options for
flipping the coin, say 10 times until it
lands on heads or a 100 times before you
get heads. I know it's extremely
unlikely, but the payout is so huge that
the expected value of that outcome is
still a dollar. So, it still [music]
increases the expected value of the
whole game. This means that
theoretically the total [music] expected
value of this game is infinite.
This is known as the St. Petersburg
paradox. If you look at the distribution
of payouts, you can see it's uncapped.
It spans across all orders of magnitude.
You could get a payout of $1,000,
$100,000, or even a million or more. And
while a million dollar payout is
unlikely, it's not that unlikely. It's
around 1 in a million. Now, if you
transform both axes to a log scale, you
see a straight line with a gradient of
-1. The payout of the St. Petersburg
paradox follows a power law. The
specific power law in this case is that
the probability of a payout X is equal
to X ^ of - 1 or 1 /X. In the previous
games when you have a normal
distribution or even a log normal
distribution you can measure the width
of that distribution. It's standard
deviation. And in a normal distribution
95% of the data fall within two standard
deviations from the mean. But with a
power law like in the St. Petersburg
paradox there is no measurable width.
the standard deviation is infinite. This
makes power laws a fundamentally
different beast with some very weird
properties. [music] Imagine you take a
bunch of random samples and then average
them and then take more random samples
and average them. You'll find that the
average keeps going up. It doesn't
converge. And the more you measure, the
bigger the average is, [music] which is
really weird. It sounds impossible, but
it's because it has such a heavy tail,
meaning the probability of really
whopping big events is so significant
that if you keep measuring, occasionally
you're going to measure one of those
extreme outliers and they will totally
skew the average. It's sort of like
saying, you know, if [music] you're
standing in a room with Bill Gates or
Elon Musk, the average wealth in that
room, you know, is going to be hundred
billion dollars or something [laughter]
because the average is dominated by one
outlier. [music] And that same idea, one
outlier can dominate the average, shows
up online, too. A handful of companies,
servers, and data centers hold the
personal information of millions of
people. So when one of them gets hacked,
it can have ripple effects across the
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We've had scammers get a hold of email
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on our team and then send them messages
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this video. And now back to power laws.
So, why do you get a power law from the
simple St. Petersburg setup?
If you look at the payout X, you can see
it grows exponentially with each toss of
the coin. X= 2 the N. But if you look at
the probability of tossing the coin that
many times to get aheads, you can see
that this probability shrinks
exponentially. So the probability of
flipping a coin n times is a half to the
power of n. But we're not really
interested in the number of tosses,
we're interested in the payout. Now we
know that x= 2 the n. So instead of
writing 2 the n in our probability
equation, we can just write x. So we end
up with this. The probability of a
payout of x is equal to 1 /x. or in
other words x to the power of -1.
>> You put them together, the exponentials
[music] conspire to make a power law.
And that's a very common thing in nature
that a lot of times when we see power
laws, there are two [music] underlying
exponentials that are dancing together
to make a power law.
>> One example of this is earthquakes. If
you look at data on earthquakes, you
find that small earthquakes are very
common. [music] But earthquakes of
increasing magnitudes become
exponentially rarer. But the destruction
that earthquakes cause is not
proportional to their magnitude. It's
proportional to the energy they release.
And as earthquakes grow in magnitude,
that energy grows exponentially. So
there's this exponential decay in
frequency of earthquakes of [music] a
given magnitude and an exponential
increase in the amount of energy
released by earthquakes of a certain
magnitude. So when you combine those two
exponentials
to eliminate the magnitude, what you
find is a power law.
>> But power laws also reveal something
deeper about the underlying structure of
a system. To see this in action, let's
go back to the third coin game and the
St. Petersburg paradox. Now you can draw
all the different outcomes as a tree
diagram where the length of each branch
is equal to its probability. So starting
with a single line of length one and
then a half for the first two branches,
a quarter for the next four and so on.
Now when you zoom in, you keep seeing
the same structure repeating at smaller
and smaller scales. It's self- similar
like a fractal. And that's no
coincidence. We see the same
fractal-like pattern in the veins on a
leaf, river networks, the blood vessels
in our lungs, even lightning. And in all
of these cases, we can describe the
pattern with a power law. Power laws and
fractals are intrinsically linked.
That's because power laws reveal
something fundamental about a systems
structure. So, I've got a magnet and
I've got a screw. And you'll notice if I
bring them close together, then the
screw gets attracted to the magnet. And
that's because there's a lot of iron in
it, which is ferroagnetic.
But watch what happens if I start
heating this up.
Trying to Oh, you see that? Ah, there it
went. There it went. You see, you heat
it up and suddenly it becomes
non-magnetic. [music] To find out what
happened, let's zoom in on this magnet.
Inside a magnet, each atom has its own
magnetic moment, which means you can
think of it like its own little magnet
or compass. If one atom's moment points
up, its neighbors tend to point that
way, too, since this lowers the system's
overall potential energy. Therefore, at
low temperatures, you get large regions
called domains where all the moments
align. And when many of these domains
also align, their individual magnetic
fields reinforce to create an overall
field around the magnet. But if you heat
up the magnet, each atom starts
vibrating vigorously. The moments flip
up and down, and so the alignment can
break down. And when all the moments
cancel out, then there's no longer a net
magnetic field. Now if you have the
right equipment you can balance any
magnetic material right on that
transition point right between magnetic
and non-magnetic. [music] This is called
the critical point and it occurs at a
specific temperature called the cury
temperature. I asked Casper and the team
to build a simulation to show what's
going on inside the magnet at this
critical point. Each pixel represents
the magnetic moment of an individual
atom. Let's say red is up and blue is
down. Now when the temperature is low,
we get these big domains where the
magnetic moments are all aligned and you
get an overall magnetic field. But if we
really crank up the temperature, then
all of these moments start flipping up
and down and so they cancel out and the
magnet loses its magnetism. So that's
exactly what happened in our demo. But
if we tune the temperature just right,
right to that cury temperature, then the
pattern becomes way more interesting.
>> This looks like a map.
like a map.
>> Yeah, it almost looks like the
Mediterranean or something. [music] It's
almost stable.
Like atoms that are pointing one way
tend to point that way for a while,
[music] but there is clearly
fluctuations as well. So [music] domains
are constantly coming and going. It's
both got some elements of stability and
some persistence over time, some
features which are consistent, [music]
but it's also not locked in place
>> because [music] you notice changes over
time.
>> If you zoom in, you find that the same
kinds of patterns [music] repeat at all
scales. You've got domains of tens of
atoms, hundreds, thousands, even
millions. There's just no inherent skill
to the system. [music] That is, it's
skillfree. It's just like a fractal. And
if you plot the size distribution of the
domains, you get a [music] power law.
>> The underlying geometry suddenly shows a
fractal character that it doesn't have
on either side of the phase [music]
transition. Right at the phase
transition, you get fractal behavior and
that pops out as a power law.
>> In fact, whenever you find a power law,
that indicates you're dealing with a
system that has no intrinsic scale. And
that is a signature of a system in a
critical state which it turns out has
huge consequences. See normally in a
magnet below the cury temperature each
atom influences only its neighbors. If
one atom's magnetic moment flips up then
that means that its neighbors are
slightly more likely to point up too.
But that influence is local. It dies out
just a few atoms away. But as the magnet
approaches its critical temperature,
those local influences [music] start to
chain together. One spin nudges its
neighbor and that neighbor nudges the
next. and [music] so on like a rumor
spreading through a crowd and the result
is that the effective range of influence
[music] keeps expanding and right at the
critical point it becomes effectively
infinite. A flip on one side can cascade
throughout the entire material. So you
get these small causes just a single
flip to reverberate throughout the
entire system and it gets right into
that that point where the system is
maximally unstable. Anything can happen.
It's also maximally interesting in a
way. It's it means the system is most
unpredictable,
most uncertain. It's really hard to know
what's going to happen next. And that
seems to be a natural procedure that
happens in many different systems in the
world.
>> One such system is forest fires.
In June 1988, a lightning strike started
a small fire near Yellowstone National
Park. This was nothing out of the
ordinary. Each year, Yellowstone
experiences thousands of lightning
strikes. Most don't cause fires, and
those that do tend to burn a few trees,
maybe even a few acres before they
fizzle out. 3/4 of fires burn less than
a quarter of an acre. The largest fire
in the park's recent history occurred in
1931. That burned through 18,000 acres,
an area slightly larger than Manhattan.
But the 1988 fire was different. That
initial spark spread slowly at first,
covering several thousand acres. Then
over the next couple of months, it
merged with other small fires to create
an enormous complex of mega fires that
blazed across 1.4 million acres of land.
That's around the size of the entire
state of Delaware. That's 70 times
bigger than the previous record and 50
times the area of all the fires over the
previous 15 years combined. So, what was
so special about the 1988 fires? Well,
to find out, we made a forest fire
simulator. We've got a grid of squares
and on each square either a tree could
be there, it could grow, or it could not
be there. There's going to be some
probability for lightning strikes. So,
you know, the higher the probability,
the more fires we're going to have. We
can run this.
>> So, trees are growing.
>> Trees are growing.
>> Forest is filling in.
Nice. Getting pretty dense.
>> What do you expect is going to happen?
>> I expect to see some fires.
probably, you know, now that Oh, that
was good. That was a good little fire.
Whoa.
No way.
Oh, that's crazy. You haven't adjusted
the parameters, right? It's just like
>> not yet. Not yet.
>> This seems like a very critical
situation just by itself. I say that
because of how big that fire was. this
sort of system will tune itself to
criticality and you can you can see it
start to happen. So right now I think is
a good moment where you have [music]
basically domains of a lot of different
sizes. And then one way to think about
it is if some of these domains become
too big then you get a single fire like
that one perfectly timed
propagate throughout the whole thing and
burn it back down a little. But then if
it goes too hard then now you've got all
these domains where there are no trees
and so it's going to you know grow again
to bring it back to that critical
[music] state. I can see how it's the
feedback mechanism, right, that the fire
gets rid of all the trees and there's
nothing left to burn and then that has
to fill in again.
>> Yeah.
>> Yeah. But if there hasn't been a fire,
then the forest gets too [music] thick
and then it's ripe for this sort of
massive fire. For a magnet, you have to
painstakingly tune it to the critical
point. But the forest naturally drives
itself there. This phenomenon is called
self-organized criticality.
>> Yeah. And if you let it run, what you
get is again a power law distribution.
So this is block log. So it should be a
straight line. That kind of stuff seems
so totally random and unpredictable and
it is in one way and yet it follows a
pattern. There's a consistent
mathematical pattern to all these kind
of disasters. Um it's it's shocking.
>> Is there something fractal about this?
mostly in terms of the I guess domains
of the trees when you're [music] at that
critical state. So you get very dense
areas, you get non-dense areas, and as a
result, when a single lightning bolt
strikes, you can get fires of all sizes.
Most often, you get small fires of 10 or
fewer trees burning. A little less
frequently, you get fires of less than
100 [music] trees. And then every once
in a while, you get these massive fires
that reverberate throughout the entire
system. Now, you might expect that
because the fire is so large, there has
to be a significant event causing it.
But that's not the case because the
cause for each fire is the exact same.
It's a single lightning strike. The only
difference is where it strikes and the
exact makeup of the forest at that time.
So, in some very real way, the large
fires are nothing more than magnified
versions of the small ones. [music] And
even worse, they're inevitable. So, what
we've learned is that for systems in a
critical state, there are no special
events causing the massive fires. There
was nothing special about the
Yellowstone fire. In 1935, the US Forest
Service established the so-called 10:00
a.m. policy. The plan was to suppress
every single fire by 10:00 a.m. on the
day following its initial report. Now,
naively, this strategy makes sense. I
mean, if you keep all fires [music]
under strict control, then none can ever
get out of hand. But it turns out this
strategy is extremely risky.
>> So let's say we're going to bring down
the lightning probability. So it's very
small, only one in a million right now.
And we're also going to crank up, you
know, the tree growth a little bit. Now,
what do you think's going to happen?
>> We're going to get some big fires, I
would imagine. Like a lot of not fire
and then some huge fires. Yeah.
[laughter]
>> Yep. Oh boy. So nowadays, the fire
service has a very different approach.
They acknowledge that some fires are
essential to make the mega fires less
likely. So they let most small fires
burn and only intervene when necessary.
In some cases, they even intentionally
create small fires to burn through some
of the buildup. Though it could take
years to return the forest to its
natural state after a century of fire
suppression. But it's more than just the
Earth's forests that are balanced in
this critical state.
Every day, the Earth's crust is moving
and rearranging itself. Stresses build
up slowly as tectonic plates rupt
against each other. Most of the time,
you get a few rocks crumbling. The
ground might move just a fraction of a
millimeter. But the stresses dissipate
in many earthquakes that you wouldn't
even feel. There are [music] really tiny
earthquakes that are happening right now
between beneath your feet. You just
can't feel them because they're very
small. But they are earthquakes. They're
driven by small slipping movements
[music] in the Earth's crust.
>> But sometimes those random movements can
trigger [music] a powerful chain
reaction. In Coobe, Japan, the morning
of January 17th, 1995 seemed just like
any other. This was a peaceful city. And
although Japan as a country is no
stranger to earthquakes, Coobe hadn't
suffered a major quake for centuries.
Generations grew up believing the ground
beneath them was stable. But that
morning, deep underground, a stress
released nearby the Nojima fault line.
The stress propagated to the next
section of the fault. And the next,
within seconds, the rupture cascaded
along 40 km of crust, shifting the
ground by up to 2 m and releasing the
energy equivalent of numerous atomic
bombs. The resulting quake destroyed
thousands of homes along with most major
roads and railways leading into the
city. It killed over 6,000 people and
forced 300,000 from their homes.
How far it goes depends a lot on chance
and the organization of all that stress
field in the earth's crust. And it just
seems to be organized in such a way that
it is possible often times for the
earthquake to trickle along and
avalanche along a long way and produce a
very large unusual earthquake. But if
you look at the process behind that
earthquake, it is exactly the same
physical process. It's just that the
earthquake generating process naturally
produces events that range over an
enormous range of scale. And we're not
really used to thinking about that. We
have this ingrained assumption that we
can use the past to predict the future.
But when it comes to earthquakes or any
system that's in a critical state, that
assumption can be catastrophic because
they're famously unpredictable. So how
can you even begin to model something
like the behavior of earthquakes? In
1987, Danish physicist Perback and his
colleagues considered a simple thought
experiment. Take a grain of sand and
drop it on a grid. Then keep dropping
grains on top until at some point the
sand pile gets so steep that the grains
tumble down onto different squares. What
they looked at was the size of these
what they were calling avalanches. These
reorganizations of numbers of grains of
sand. They asked for how often do you
see avalanches of a certain size? This
is the most simple version of a sand pal
simulator that you could almost imagine.
We're going to drop a little grain of
sand. At first, always in the center,
[music] and then it's just going to keep
going up. For one grain, it'll be fine.
For two grains, it'll be fine. Three
grains, it'll be fine, but it's on the
edge of toppling. And then when it
[music] reaches four or more, it's going
to basically go.
Feels a bit like a I don't know, pulsing
thing like something's trying to escape
or something. very video game like that
seemed pretty crazy. And it is
symmetrical.
>> Yeah, nice geometric features. [music]
>> So, this might be interesting because
right now we paused it at a point where
this middle one is going to go and then
you look around it and you see
essentially you can think of these
brown [music] or you know these three
tall grain stacks as being maximally
unstable. They're about to go. [music]
And so you could think of them as these
fingers of instability. If anything
touches them, the whole system like
they're they're just going to go.
>> I see it propagating out.
>> It's cool seeing it slower. I feel like
you can see several waves propagating at
the same time. Some people have reasoned
that the Earth's crust becomes riddled
with similar fingers of instability
where you get stresses building up and
then when one rock crumbles, it can
propagate along these fingers,
potentially [music] triggering massive
earthquakes. If you look at the data,
there's some even more compelling
evidence that links the sand pile
simulation to earthquakes. Let's say
instead of dropping it at the center,
pretty unrealistic to have it drop at
the center. I'm going to drop at random.
>> That is crazy.
>> You can actually see it tune itself to
the critical state. [bell]
>> Like at the start, you only see these
super tiny avalanches.
>> Yeah.
>> And then now it's everything.
>> It has to build up.
>> We can slow down a little.
>> Oh, that's a super clean power law.
There are events of all sizes. One grain
of sand might knock over just a few
others or it could trigger an avalanche
of millions of grains that cascade
throughout the entire system. And if you
look at the power law you get from the
senpow simulation, it closely resembles
the power law of the energy released by
real earthquakes.
But if you look at the senpai experiment
more closely, it doesn't just resemble
earthquakes. What does it remind you of?
>> Forest fires,
>> right? Feels like it's the exact same
behavior. That's the really surprising
thing and that's why this little paper
with a sand pile was published [music]
in the world's top journal because it
did something that people just didn't
really think was was possible.
>> Now, what's ironic is if you look at
real sand piles, they don't behave like
this.
>> Okay, you [music] said sand. I'm going
to do an experiment on a real sand pile.
And of course, it doesn't follow a power
law distribution of avalanches at all.
It's totally wrong.
[laughter]
Perbach naturally gets a chance to reply
to the criticism and he says I'm pretty
close to quoting. He says self-organized
criticality only applies to the systems
it applies to.
[laughter]
So he doesn't care the fact that his
theory is not relevant to real sand
piles. So what? Get out of my face. He's
interested in bigger fish to fry than
than you know sand piles. It's like
you're taking me too literally. I'm
talking about a universal mechanism for
generating power laws and the fact that
it doesn't depend it doesn't work in
real sand is uninteresting to him. I
thought that took some real nerve.
>> You could think about the earth and the
earth going around the sun. That's a
very complex system. You've got all the
you've got the molten core, everything
slushing around and you've got oceans
and you've even got the moon going
around the earth which in theory, you
know, all should affect the exact motion
of the earth around the sun. But Newton
ignored all of that. All he looked at
was just a single uh parameter
essentially the mass of the earth. And
with that he could correctly for the
most part predict how the earth was
going to go around the sun. Similarly
here there are people that have looked
at these phenomena that go to the
critical state. In this in this case
it's self-organized criticality is it
brings itself there. And what they find
is that there's this universal behavior
where it doesn't even really matter what
the subp parts are. You just get the
behavior that's the exact same
>> at that critical point when when all the
forces are pulleys and the system is
right on that delicate balance between
being organized, highly organized or
being totally disorganized. It turns out
that almost none of the physical details
about that system matter to how it
behaves. There's just a universal
behavior that is irrespective of what
physical system you're talking about.
The term that was used is called
universality. And it's kind of a
miracle. It means you can make extremely
powerful theories without involving any
technical details, any real details of
the material.
>> What this means is that you could have
these systems that on the surface seem
totally different, but when you get to
the critical point, they all behave in
the exact same way. The other thing you
could do is instead of this being trees,
you could imagine it being people. And
the thing that's spreading is disease.
>> Is disease. Yeah.
>> You almost get something for nothing at
these at these critical points.
>> See, many of these systems fall into
what's known as universality classes.
Some of them you need to tune to get
there, like magnets at their cury
temperature or fluids like water or
carbon dioxide at their critical point.
But some other systems seem to organize
themselves to criticality like the
forest fires or sand pals or
earthquakes. But what's crazy is that if
you succeed in understanding just one
system from a class, then you know how
all the systems in that class behave.
[music] And that includes even the
crudest, simplest toy models, like the
simulations we've looked at. So you can
model incredibly complex systems with
the most basic of models. And some
people think this critical thinking
applies even further. When we look
around the world, there are lots of
systems that show the same power law
behavior that we see in these critical
systems. It's in everything from DNA
sequencing to the distribution of
species in an ecosystem to the size of
mass extinctions throughout history. We
even see the same behavior in human
systems like the populations of cities,
fluctuations in stock prices, citations
of scientific papers, and even the
number of deaths in wars. So some people
argue that these systems and perhaps
many parts of our world also organize
themselves to this critical point. So
the fact that all these natural hazards,
as they call them, floods, wildfires,
and earthquakes, they all follow power
law distributions, means that these
extreme events are um much more common
than you would think based on normal
distribution thinking.
>> If you find yourself in a situation or
an environment that is sort of governed
by a power [music] law, how how should
you change your behavior? If you have
events [music] with one of these
parallel distributions, what you're
seeing most of the time is small events
[music] and uh this can lull you into a
false sense of security. You think you
understand how things are going. You
know, floods for example, there are a
lot of small floods and then every once
in a while there's [music] a huge one.
One response to this is insurance.
That insurance is designed precisely
[music] to protect you against the large
rare events that would otherwise be very
bad. But then there's the other side of
that picture which is you're the
insurance company that needs to insure
people and [music] they have a
particularly difficult job because they
have to be able to say how much to
[music] charge so that they have enough
money to pay out when the big bad thing
comes along.
>> In 2018, a forest fire tore through
Paradise, California. It became the
deadliest and most destructive fire in
the state's history. But the insurance
company, Mercer Property and Casualty,
hadn't planned for something that huge.
And when the claims came in, they just
didn't have the reserves to pay out. So,
just like that, the company went bust.
But while extreme events can
some companies, there are entire
industries that are built on power law
distributions. Between 1985 and 2014,
private equity firm Horsesley Bridge
invested in 7,000 different startups.
and over half of their investments
actually lost money. But the top 6% more
than 10xed in value [music] and
generated 60% of the firm's overall
profit. In fact, the best venture
capital firms often have more
investments that lose money. They just
have a few crazy outliers that show
extraordinary growth, a few outliers
that carry the entire performance. In
2012, Y Combinator calculated that 75%
of their returns came from just two out
of the 280 startups they invested in. So
venture capital is a world that depends
on taking risks in the hope that you'll
get a few of these extreme outliers
which outperform all of the rest of the
investments combined. Book publishers
operate in a similar fashion. Most
titles flop, but in 1997, a small
independent UK publisher called
Bloomsbury took a chance on a story
about a boy wizard. [music] The boy's
name, of course, was Harry Potter, and
now Bloomsbury is a globally recognized
brand. We see a similar pattern play out
on streaming platforms. On Netflix, the
top 6% of shows account [music] for over
half of all viewing hours on the
platform. On YouTube, less than 4% of
videos ever reach 10,000 views, but
those videos account for over 93% of all
views. All these domains follow the same
principle that Pareto identified over
100 years ago, where the majority of the
wealth goes to the richest few. The
entire game is defined by the rare
runaway hits. But not every industry can
play this game. Like if you're running a
restaurant, you need to fill tables
night after night. You can't have one
particularly busy summer evening that
brings in millions of customers to make
up for a bunch of quiet nights. Over a
year, the busy nights and quiet ones
balance out, and you're left with the
average. Airlines are similar. An
airline needs to fill seats on each
flight. You can't squeeze a million
passengers onto one plane. So, it's the
average number of passengers over the
year that defines an airline success.
We're used to living in this world of
normal distributions and you act a
certain way,
>> but as soon as you switch to this realm
that is governed by a power law, you
need to start acting vastly different.
It really pays to know what kind of
world you're or what kind of game you're
playing.
>> That is good. That's good. Yes, you
should come on camera and just say that
just like that. You were [laughter] on
camera. You just did do it.
>> If you're in a world where random
additive variations cancel out over
time, then you get a normal
distribution. And in this case, it's the
average performance, so consistency,
which is important. But if you're in a
world that's governed by a power law
where your returns can multiply and they
can grow over many orders of magnitude,
then it might make sense to take some
riskier bets in the hope that one of
them pays off huge. In other words, it
becomes more important to be persistent
than consistent. Though, as we saw in
the second coin game, totally random
multiplicative returns give you a loged
normal distribution, not a power law. To
get a power law, there must be some
other mechanism at play. In the early
2000s, Albert Llo Barabashi was studying
the internet [music] and to his
surprise, he found that there was no
normal web page with some average number
of links. Instead, the distribution
followed a power law. A few sites like
Yahoo had thousands of times more
connections than most the others.
Barabashi wondered what could be causing
this power law of the internet. So, he
made a simple prediction. [music] As new
sites were added to the internet, they
were more likely to link to well-known
pages. To test this prediction, he and
his colleague Reika Albert ran a
simulation. They started with a network
of just a few nodes, and gradually they
added new nodes to the network. With
each new node more likely to connect to
those with the most links. As the
network grew, a power law emerged. The
power was around -2, which almost
exactly matched the real data of the
internet.
>> Look at that.
>> That's fun. It's still so satisfying.
This will basically also distribute a
power law. One of the ideas here is
that, you know, this could be
individuals or even companies. And so if
you're more likely to become more
successful or more wellknown, the well
more known or successful you already
are, you're going to get this sort of
runaway effect where you you get a few
that sort of dominate, you know, the
distributions.
I wonder if part of the takeaway is like
if you're playing some sort of game that
is dominated by power law then you
better do the work as much of it as
early as possible so you get to benefit
from the [music] snowball effect
essentially.
>> Yeah, I guess I guess that's that's a
good idea. I'm not sure whether you can
control it though. human beings [music]
like to think of ourselves as being a
bit special and that maybe somehow
because we're intelligent [music] and
have free will um we will escape the
provenence of the laws of of physics and
order and organization but I think
that's probably not not the case. So if
you look at at the number of world
[music] wars and if you make a crude
measure of how big is a world war by how
many people it kills which is a bit
macob but still you find that again it
follows a power law virtually identical
to the power law you find in stock
market crashes. So if the world is
shaped by power laws, then it feels like
we're poised in this kind of critical
state where [music] two identical grains
of sand, two identical actions can have
wildly different effects. Most things
barely move the needle, but a few rare
events totally dwarf the [music] rest.
And that, I think, is the most important
lesson. If you choose to pursue areas
governed by the normal distribution, you
can pretty much guarantee average
results. But if you select pursuits
ruled by power laws, the goal isn't to
avoid risk. It's to make repeated
intelligent bets. Most of them will
fail, but you only need one wild success
to pay for all the rest. And the thing
is that beforehand, you cannot know
which bet it's going to be because the
system is maximally unpredictable. It
could be that your next bet does
nothing, it could do a little bit, or it
could change your entire life. In fact,
around 3 years ago, I was reading this
little book. And in the book, there was
this little line saying something like,
"One idea could transform your entire
life." So, right underneath that, I
wrote, "Send an email to Veritassium." A
couple days later, I wrote an email to
Derek saying, "Hey, Derek, I'm Casper. I
study physics and I can help you
research videos." I didn't hear back for
4 [music] weeks, so I was getting pretty
sad and just wanted to forget about it
and move on. But then a couple days
later, I got an email back saying, "Hey,
Casper, we can't do an internship right
[music] now, but how would you like to
research, write, and produce a video as
a freelancer?" So, I did. And [music]
that's how I got started at Veritasium.
Hey, just a few quick final things. All
the simulations that we used in this
video, we'll make available for free for
you to use in the link in the
description. And the other thing is that
we just launched the official Veritasium
game. It's called Elements of Truth and
it's a tabletop game with over 800
questions. It's the perfect way to
challenge your friends and see who comes
out on top. Now, at Veritasium, we're
all quite competitive. So, every time we
play, things get a little bit heated,
but that's honestly a big part of the
fun. Now, when we launched on
Kickstarter, we got a lot of questions
asking if we could ship to specific
countries. [music] And originally we
didn't enable this and this is our
mistake. This is on us and we totally
hear you. But I'm glad to say that right
now we have enabled worldwide shipping.
So no matter where you are in the world,
you can get your very own copy. To
reserve your copy and get involved, scan
this QR code or click the link in the
description. I want to thank you for all
your support and most of all, thank you
for watching.