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Russian
00:00:00
- Some things are not normal.00:00:03
By that I mean if you go out in the world00:00:05
and start measuring things
like human height, IQ,00:00:08
or the size of apples on a tree.00:00:10
You will find that for
each of these things,00:00:12
most of the data clusters
around some average value.00:00:16
This is so common that we call
it the normal distribution,00:00:20
but some things in life are not like this.00:00:24
- Nature shows power
laws all over the place.00:00:27
That seems weird.00:00:28
Like, is nature tuning
itself to criticality?00:00:30
- If you make a crude measure
of how big is the world war00:00:33
by how many people it kills,00:00:34
you find that it follows a power law.00:00:37
The outcome will vary in size
over 10 million, 100 million.00:00:42
- It's much more likelihood
of really big events00:00:45
than you would expect from
a normal distribution,00:00:47
and they will totally skew the average.00:00:49
- The system you're
looking at doesn't have00:00:52
any inherent physical scale.00:00:54
It's really hard to know
what's gonna happen next.00:00:56
- The more you measure,
the bigger the average is,00:00:59
which is really weird,
it sounds impossible.00:01:01
- It's very important to try to understand00:01:04
which game you're playing00:01:06
and what are the payoffs
going to be in the long run.00:01:10
- In the late 1800s, Italian
engineer Vilfredo Pareto00:01:13
stumbled upon something
no one had seen before.00:01:17
See, he suspected there
might be a hidden pattern00:01:19
in how much money people make.00:01:21
So he gathered income tax records00:01:23
from Italy, England, France,
and other European countries,00:01:26
and for each country he plotted
the distribution of income.00:01:31
Each country he looked at,
he saw the same pattern,00:01:34
a pattern which still holds
in most countries to this day,00:01:38
and it's not a normal distribution.00:01:41
If you think about a normal
distribution like height,00:01:43
there's a clearly defined average00:01:45
and extreme outliers
basically never happen.00:01:48
I mean, you are never
going to find someone00:01:50
who is, say, five times
the average height,00:01:53
that would be physically impossible,00:01:55
but Pareto's income
distributions were different.00:01:57
Take this curve for England,00:01:59
it shows the number of people00:02:00
who earn more than a certain income.00:02:03
The curve starts off declining steeply,00:02:05
most people earn relatively little,00:02:07
but then it falls away gradually,00:02:09
much more slowly than a
normal distribution would,00:02:12
and it spans several orders of magnitude.00:02:15
There were people who
earned 5 times, 10 times,00:02:18
even 100 times more than others.00:02:21
That kind of spread just wouldn't happen00:02:22
if income were normally distributed.00:02:25
Now to shrink this huge spread of data,00:02:28
Pareto calculated the
logarithms of all the values00:02:30
and plotted those instead.00:02:32
In other words, he used a log-log plot,00:02:35
and when he did that,00:02:36
the broad curve transformed
into a straight line.00:02:39
The gradient was around negative 1.5.00:02:42
That means each time
you double the income,00:02:45
say, from 200 pounds to 400 pounds,00:02:47
the number of people
earning at least that amount00:02:50
drops off by a factor of
two to the power of 1.5,00:02:53
which is around 2.8.00:02:55
And this pattern holds for
every doubling of income.00:02:58
So Pareto could describe
the distribution of incomes00:03:01
with one simple equation.00:03:02
The number of people who
earn an income greater than00:03:05
or equal to X is
proportional to one over X00:03:08
to the power of 1.5.00:03:10
Now, that's what Pareto saw for England,00:03:13
but he performed the same
analysis on data from Italy,00:03:16
France, Prussia, and a
bunch of other countries,00:03:18
and he saw the same thing again and again.00:03:22
Each time the data transformed
into a straight line00:03:26
and the gradients were remarkably similar.00:03:28
That meant Pareto could
describe the income distribution00:03:31
in each country with the same equation,00:03:34
one over the income to some power,00:03:37
where that power is just
the absolute gradient00:03:39
of the logarithmic graph.00:03:42
This type of relationship
is called a power law.00:03:45
When you move from the world
of normal distributions00:03:48
to the world of power laws,00:03:49
things change dramatically.00:03:51
So to illustrate this,00:03:52
let's take a trip to the casino00:03:54
to play three different games.00:03:57
At table number one, you
get 100 tosses of a coin.00:04:01
Each time you flip and it
lands on heads, you win $1.00:04:05
So the question is,00:04:06
how much would you be prepared
to pay to play this game?00:04:09
Well, we need to work out00:04:11
how much you'd expect to win in this game00:04:12
and then pay less than
that expected value.00:04:15
So the probability of
throwing a head is 1/2.00:04:18
Multiply that by $1 and
multiply that by 100 tosses,00:04:22
that gives you an expected payout of $50.00:04:25
So you should be willing to pay00:04:26
anything less than $50 to play this game.00:04:29
Sure, you might not win every time,00:04:31
but if you play the
game hundreds of times,00:04:33
the small variations
either side of the average00:04:35
will cancel out and you can
expect to turn a profit.00:04:39
One of the first people to
study this kind of problem00:04:41
was Abraham de Moivre in the early 1700s.00:04:44
He showed that if you plot the
probability of each outcome,00:04:46
you get a bell-shaped curve,00:04:48
which was later coined
the normal distribution.00:04:51
- Normal distributions,00:04:52
the traditional explanation00:04:54
is that when there are a lot
of effects that are random00:04:56
that are adding up,00:04:58
that's when you expect normals.00:05:00
So like how tall I am depends
on a lot of random things,00:05:03
about my nutrition, about
my parents' genetics,00:05:06
all kinds of things,00:05:07
but if these random effects are additive,00:05:10
that is what tends to lead to normals.00:05:14
- At table number two, there's
a slightly different game.00:05:17
You still get 100 tosses of the coin,00:05:20
but this time,00:05:21
instead of potentially
winning a dollar on each flip,00:05:23
your winnings are
multiplied by some factor.00:05:26
So you start out with $1,00:05:29
and then every time you toss a head,00:05:31
you multiply your winnings by 1.1.00:05:34
If instead the coin lands on tails,00:05:36
you multiply your winnings by 0.9.00:05:38
And after 100 tosses,00:05:40
you take home the total,00:05:41
that is the dollar you started with00:05:43
times the string of 1.1s and 0.9s.00:05:46
So, how much should you
pay to play this game?00:05:49
Well, on each flip,00:05:51
your payout can either grow or shrink,00:05:53
and each is equally likely
each time you toss the coin,00:05:57
so the expected factor each turn00:05:59
is just 1.1 plus 0.9 divided
by two, which is one.00:06:02
So if you start out with $1,00:06:05
then your expected payout is just $1.00:06:08
That means you should be willing to pay00:06:09
anything less than a dollar
to play this game, right?00:06:13
Well, if you look at the
distribution of payouts,00:06:15
you can see that you could win big.00:06:17
If you tossed 100 heads,00:06:19
you'd win 1.1 to the power of 100.00:06:21
That's almost $14,000,00:06:24
although the chance of that happening00:06:25
is around 1 in 10 to the power of 30.00:06:27
You'd be more likely to win the lottery00:06:29
three times in a row.00:06:30
On the other hand, the median
payout is around 61 cents.00:06:34
So if you're only
playing the game one time00:06:36
and you want even odds
of turning a profit,00:06:39
well, then you should
pay less than 61 cents.00:06:42
Though either way, if you played
the game hundreds of times,00:06:45
your payout would average out to $1.00:06:48
Now, watch what happens
if we switch the x-axis00:06:50
from a linear scale to
a logarithmic scale.00:06:53
Well, then you see the curve transforms00:06:54
into a normal distribution.00:06:56
That's why this type of distribution00:06:58
is called a log normal distribution.00:07:01
- When random effects multiply,00:07:03
if I have a certain wealth00:07:05
and then my wealth goes up by
a certain percentage next year00:07:08
because of my investments,00:07:10
and then the year after that,00:07:11
it changes by another random factor,00:07:14
as opposed to adding, I'm
multiplying year after year.00:07:17
If you have a big product
of random numbers,00:07:19
when you take the log of a product,00:07:21
that's the sum of the logs.00:07:24
So what was a product of random numbers00:07:26
then gets translated into sums
of logs of random numbers,00:07:31
and that's what leads00:07:32
to this so-called log normal distribution.00:07:34
And log normal distributions
produce big inequalities.00:07:38
You don't just see a mean,00:07:40
you see a mean with a big long tail.00:07:42
It's much more likelihood
of really big events,00:07:45
in this case, tremendous
wealth being obtained,00:07:48
than you would expect from
a normal distribution.00:07:51
- The reason this curve is so asymmetric00:07:53
is because the downside is capped at zero,00:07:56
so at most, you could lose $1,00:07:58
but the upside can keep
growing up to nearly $14,000.00:08:03
Now let's go on to table three.00:08:05
Again, you'll be tossing a coin,00:08:07
but this time you start out with a dollar00:08:09
and the payout doubles
each time you toss the coin00:08:12
and you keep tossing
until you get a heads,00:08:15
then the game ends.00:08:17
So if you get heads on your
first toss, you get $2.00:08:20
If you get a tails first00:08:22
and then hit a heads on your
second toss, you get $4.00:08:25
If you flipped two tails and then a head,00:08:27
on your third toss,
you'd get $8, and so on.00:08:30
If it took you to the
nth toss to get a heads,00:08:32
you would get two to the n dollars.00:08:35
So, how much should you
pay to play this game?00:08:38
Well, as in our previous example,00:08:40
we need to work out the expected value.00:08:42
So suppose you throw a
head on your first try,00:08:45
the payout is $200:08:46
and the probability of
that outcome is a half,00:08:49
so the expected value of
that toss is a dollar.00:08:52
If it takes you two tosses to get a heads,00:08:54
then the payout is $400:08:56
and the probability of that
happening is one over four,00:08:59
so again, the expected value is $1.00:09:02
We also need to add in the chance00:09:03
that you flip heads on your third try,00:09:05
in that case, the payout is $800:09:07
and the probability of that
happening is one over eight,00:09:10
so again, the expected value is $1.00:09:13
And we have to keep
repeating this calculation00:09:15
over all possible outcomes.00:09:17
We have to keep adding $1 for
each of the different options00:09:20
for flipping the coin, say, 10
times until it lands on heads00:09:23
or 100 times before you get heads.00:09:26
I know it's extremely unlikely,00:09:28
but the payout is so huge00:09:29
that the expected value of
that outcome is still a dollar,00:09:33
so it still increases the
expected value of the whole game.00:09:37
This means that, theoretically,00:09:39
the total expected value
of this game is infinite.00:09:44
This is known as the
St. Petersburg paradox.00:09:47
If you look at the
distribution of payouts,00:09:49
you can see it's uncapped,00:09:51
it spans across all orders of magnitude.00:09:53
You could get a payout
of $1,000, $100,000,00:09:56
or even a million dollars or more.00:09:59
And while a million
dollar payout is unlikely,00:10:01
it's not that unlikely,00:10:03
it's around one in a million.00:10:06
Now, if you transform
both axes to a log scale,00:10:08
you see a straight line with
a gradient of negative one.00:10:12
The payout of the St. Petersburg paradox00:10:14
follows a power law.00:10:16
The specific power law in this case00:10:18
is that the probability of a payout x00:10:20
is equal to x to the power of
negative one or one over x.00:10:24
In the previous games when
you have a normal distribution00:10:26
or even a log normal distribution,00:10:28
you can measure the width
of that distribution,00:10:31
its standard deviation.00:10:32
And in a normal distribution,00:10:34
95% of the data fall within
two standard deviations00:10:37
from the mean.00:10:38
But with a power law, like in
the St. Petersburg paradox,00:10:41
there is no measurable width,00:10:43
the standard deviation is infinite.00:10:46
This makes power laws a
fundamentally different beast00:10:50
with some very weird properties.00:10:52
- Imagine you take a
bunch of random samples00:10:54
and then average them00:10:55
and then take more random
samples and average them,00:10:58
you'll find that the
average keeps going up,00:11:01
it doesn't converge.00:11:03
And the more you measure,00:11:04
the bigger the average is,00:11:06
which is really weird,
it sounds impossible,00:11:09
but it's because it has such a heavy tail,00:11:12
meaning the probability of
really whopping big events00:11:15
is so significant that
if you keep measuring,00:11:18
occasionally you're gonna measure00:11:19
one of those extreme outliers00:11:21
and they will totally skew the average.00:11:24
It's sort of like saying,00:11:26
if you're standing in a room
with Bill Gates or Elon Musk,00:11:30
the average wealth in that room00:11:32
is gonna be 100 billion
dollars or something (laughs)00:11:36
because the average is
dominated by one outlier.00:11:39
- And that same idea, one
outlier can dominate the average,00:11:43
shows up online too.00:11:45
A handful of companies, servers,00:11:47
and data centers hold
the personal information00:11:49
of millions of people,00:11:50
so when one of them gets hacked,00:11:52
it can have ripple effects
across the whole network.00:11:56
We've had scammers get a
hold of email addresses00:11:58
and phone numbers of writers on our team00:12:01
and then send them messages
pretending to be me.00:12:04
That is where today's
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I'd like to thank NordVPN
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And now, back to power laws.00:12:56
So, why do you get a power law00:12:58
from the simple St. Petersburg setup?00:13:01
If you look at the payout x,00:13:03
you can see it grows exponentially00:13:05
with each toss of the coin,00:13:07
x equals two to the n.00:13:09
But if you look at the
probability of tossing the coin00:13:12
that many times to get a heads,00:13:14
you can see that this probability
shrinks exponentially.00:13:17
So the probability of
flipping a coin n times00:13:20
is 1/2 to the power of n.00:13:22
But we're not really interested
in the number of tosses,00:13:24
we're interested in the payout.00:13:26
Now we know that x equals two to the n,00:13:28
so instead of writing two to the n00:13:29
in our probability equation,00:13:31
we can just write x.00:13:32
So we end up with this,00:13:34
the probability of a payout of x dollars00:13:36
is equal to one over x,00:13:38
or in other words, x to
the power of negative one.00:13:42
- You put them together,00:13:44
the exponentials conspire
to make a power law.00:13:47
And that's a very common thing in nature,00:13:49
that a lot of times
when we see power laws,00:13:51
there are two underlying exponentials00:13:53
that are dancing together
to make a power law.00:13:57
- One example of this is earthquakes.00:13:59
If you look at data on earthquakes,00:14:01
you find that small
earthquakes are very common,00:14:03
but earthquakes of increasing magnitudes00:14:06
become exponentially rarer.00:14:09
But the destruction that earthquakes cause00:14:10
is not proportional to their magnitude,00:14:12
it's proportional to
the energy they release.00:14:15
And as earthquakes grow in magnitude,00:14:17
that energy grows exponentially.00:14:20
- So there's this exponential decay00:14:21
in frequency of earthquakes
of a given magnitude00:14:24
and an exponential increase in
the amount of energy released00:14:29
by earthquakes of a certain magnitude.00:14:31
So when you combine those two exponentials00:14:34
to eliminate the magnitude,00:14:36
what you find is a power law.00:14:38
- But power laws also
reveal something deeper00:14:40
about the underlying
structure of a system.00:14:43
To see this in action,00:14:44
let's go back to the third coin game00:14:46
and the St. Petersburg paradox.00:14:48
Now, you can draw all
the different outcomes00:14:50
as a tree diagram00:14:51
where the length of each branch
is equal to its probability.00:14:54
So starting with a
single line of length one00:14:56
and then 1/2 for the first two branches,00:14:59
1/4 for the next four, and so on.00:15:01
Now, when you zoom in,00:15:03
you keep seeing the
same structure repeating00:15:05
at smaller and smaller scales.00:15:07
It's self-similar like a fractal,00:15:10
and that's no coincidence.00:15:12
We see the same fractal-like
pattern in the veins on a leaf,00:15:15
river networks, the blood
vessels in our lungs,00:15:18
even lightning,00:15:19
and in all of these cases,00:15:20
we can describe the
pattern with a power law.00:15:23
Power laws and fractals
are intrinsically linked.00:15:26
That's because power laws
reveal something fundamental00:15:29
about a system's structure.00:15:31
- So I've got a magnet
and I've got a screw,00:15:34
and you'll notice if I
bring them close together,00:15:36
then the screw gets
attracted to the magnet,00:15:39
and that's because
there's a lot of iron it,00:15:40
which is ferromagnetic.00:15:42
But watch what happens if
I start heating this up.00:15:46
Trying to...00:15:47
Oh!00:15:48
You see that?00:15:49
Ah, there it went!00:15:50
There it went! You see, you heat it up and
suddenly it becomes nonmagnetic.00:15:54
To find out what happened,00:15:55
let's zoom in on this magnet.00:15:58
- Inside a magnet,00:15:59
each atom has its own magnetic moment,00:16:01
which means you can think of it00:16:02
like its own little magnet or compass.00:16:04
If one atom's moment points up,00:16:06
its neighbors tend to point that way too00:16:08
since this lowers the system's
overall potential energy.00:16:11
Therefore at low temperatures,00:16:12
you get large regions called domains00:16:15
where all the moments align.00:16:17
And when many of these domains also align,00:16:19
their individual magnetic fields reinforce00:16:21
to create an overall
field around the magnet.00:16:24
But if you heat up the magnet,00:16:26
each atom starts vibrating vigorously.00:16:29
The moments flip up and down00:16:31
and so the alignment can break down.00:16:33
And when all the moments cancel out,00:16:35
then there's no longer
a net magnetic field.00:16:38
Now, if you have the right equipment,00:16:40
you can balance any magnetic material00:16:42
right on that transition point,00:16:44
right between magnetic and nonmagnetic.00:16:47
This is called the critical point00:16:48
and it occurs at a specific temperature00:16:51
called the Curie temperature.00:16:53
I asked Casper and the
team to build a simulation00:16:55
to show what's going on inside the magnet00:16:58
at this critical point.00:17:00
- Each pixel represents
the magnetic moment00:17:02
of an individual atom.00:17:04
Let's say red is up and blue is down.00:17:07
Now, when the temperature is low,00:17:08
we get these big domains00:17:10
where the magnetic moments are all aligned00:17:12
and you get an overall magnetic field.00:17:15
But if we really crank up the temperature,00:17:17
then all of these moments
start flipping up and down00:17:20
and so they cancel out and the
magnet loses its magnetism,00:17:23
so that's exactly what
happened in our demo.00:17:26
But if we tune the temperature just right,00:17:29
right to that Curie temperature,00:17:31
then the pattern becomes
way more interesting.00:17:34
- This looks like a map.00:17:36
- Like a map?00:17:38
- Yeah, it almost looks like
the Mediterranean or something.00:17:40
It's almost stable,00:17:43
like atoms that are pointing one way00:17:45
tend to point that way for a while,00:17:49
but there is clearly fluctuations as well,00:17:53
so domains are constantly
coming and going.00:17:56
It's both got some elements of stability00:18:00
and some persistence over time,00:18:02
some features which are consistent,00:18:04
but it's also not locked in place00:18:08
because you notice changes over time.00:18:12
- [Casper] If you zoom in, you find that the same kinds of patterns00:18:14
repeat at all scales.00:18:16
You've got domains of tens of atoms,00:18:17
hundreds, thousands, even millions.00:18:20
There's just no inherent
scale to the system,00:18:22
that is, it's scale-free,00:18:24
it's just like a fractal.00:18:26
And if you plot the size
distribution of the domains,00:18:28
you get a power law.00:18:31
- The underlying geometry
suddenly shows a fractal character00:18:34
that it doesn't have on either
side of the phase transition.00:18:38
Right at the phase transition,00:18:39
you get fractal behavior00:18:41
and that pops out as a power law.00:18:43
- In fact, whenever you find a power law,00:18:45
that indicates you're
dealing with a system00:18:47
that has no intrinsic scale,00:18:49
and that is a signature of a
system in a critical state,00:18:53
which turns out has huge consequences.00:18:56
- See, normally in a magnet
below the Curie temperature,00:18:59
each atom influences only its neighbors.00:19:01
If one atom's magnetic moment flips up,00:19:04
then that means that its
neighbors are slightly more likely00:19:06
to point up too.00:19:07
But that influence is local,00:19:09
it dies out just a few atoms away.00:19:11
But as the magnet approaches
its critical temperature,00:19:13
those local influences
start to chain together.00:19:16
One spin nudges its neighbor00:19:17
and that neighbor nudges
the next and so on,00:19:20
like a rumor spreading through a crowd.00:19:22
And the result is that the
effective range of influence00:19:25
keeps expanding,00:19:26
and right at the critical point,00:19:28
it becomes effectively infinite.00:19:30
A flip on one side can cascade00:19:32
throughout the entire material.00:19:35
So you get these small
causes, just a single flip,00:19:38
to reverberate throughout
the entire system.00:19:41
- And it gets right into that point00:19:44
where the system is maximally unstable,00:19:47
anything can happen.00:19:48
It's also maximally interesting in a way.00:19:51
It means the system is most unpredictable,00:19:55
most uncertain,00:19:56
it's really hard to know
what's gonna happen next,00:19:58
and that seems to be a natural procedure00:20:00
that happens in many different
systems in the world.00:20:03
- One such system is forest fires.00:20:06
In June, 1988,00:20:08
a lightning strike started a small fire00:20:10
near Yellowstone National Park.00:20:12
This was nothing out of the ordinary.00:20:14
Each year, Yellowstone
experiences thousands00:20:16
of lightning strikes.00:20:17
Most don't cause fires00:20:19
and those that do tend
to burn a few trees,00:20:21
maybe even a few acres
before they fizzle out.00:20:24
3/4 of fires burn less
than 1/4 of an acre.00:20:28
The largest fire in the
park's recent history00:20:30
occurred in 1931.00:20:32
That burned through 18,000 acres,00:20:34
an area slightly larger than Manhattan.00:20:37
But the 1988 fire was different,00:20:39
that initial spark spread slowly at first00:20:42
covering several thousand acres.00:20:44
Then over the next couple of months,00:20:46
it merged with other small fires00:20:47
to create an enormous complex of megafires00:20:50
that blazed across 1.4
million acres of land.00:20:54
That's around the size of
the entire state of Delaware.00:20:58
That's 70 times bigger
than the previous record,00:21:01
and 50 times the area of all the fires00:21:03
over the previous 15 years combined.00:21:07
So, what was so special
about the 1988 fires?00:21:10
Well, to find out, we made
a forest fire simulator.00:21:13
- We've got a grid of squares,00:21:16
and on each square,00:21:17
either a tree could be
there, it could grow,00:21:20
or it could not be there.00:21:21
There's gonna be some probability
for lightning strikes.00:21:24
So the higher that probability,00:21:26
the more fires we're gonna have.00:21:27
We can run this.00:21:29
- So trees are growing.00:21:30
- [Casper] Trees are growing,00:21:32
- Forest is filling in.00:21:35
Nice.00:21:36
Getting pretty dense.00:21:38
- What do you expect is gonna happen?00:21:39
- I expect to see some fires.00:21:43
Probably, you know, now that...00:21:45
Oh!00:21:46
That was good,00:21:47
that was a good little fire.00:21:49
Whoa!00:21:52
Whoa!00:21:54
No way!00:21:57
Well, that's crazy.00:21:59
You haven't adjusted
the parameters, right?00:22:00
It's just like-
- Not yet, not yet.00:22:02
- This seems like a very critical
situation just by itself.00:22:07
I say that because of
how big that fire was.00:22:09
- This sort of system will
tune itself to criticality,00:22:14
and you can see it start to happen.00:22:16
So right now, I think it's a good moment
where you have basically domains00:22:19
of a lot of different sizes.00:22:21
And then one way to think about it00:22:23
is if some of these
domains become too big,00:22:26
then you get a single fire
like that one, perfectly timed.00:22:30
- Burns them all out.
- It's just gonna propagate00:22:31
throughout the whole thing and
burn it back down a little.00:22:34
But then if it goes too hard,00:22:36
then now you've got all these domains00:22:37
where there are no trees00:22:38
and so it's gonna grow again00:22:40
to bring it back to that critical state.00:22:42
- I can see how it's the
feedback mechanism, right,00:22:45
that the fire gets rid of all the trees00:22:47
and there's nothing left to burn,00:22:49
and then that has to fill in again.00:22:51
- [Casper] Yeah.
- Yeah.00:22:52
But if there hasn't been a fire,00:22:54
then the forest gets too thick00:22:55
and then it's ripe for
this sort of massive fire.00:23:00
- For a magnet,00:23:01
you have to painstakingly
tune it to the critical point,00:23:03
but the forest naturally
drives itself there.00:23:06
This phenomenon is called
self-organized criticality.00:23:10
Yeah, and if you let it run,00:23:11
what you get is, again,
a power law distribution.00:23:15
So this is log-log,00:23:16
so it should be a straight line.00:23:18
- That kind of stuff
seems so totally random00:23:22
and unpredictable,00:23:23
and it is in one way,00:23:25
and yet it follows a pattern.00:23:26
There's a consistent mathematical pattern00:23:28
to all these kind of disasters.00:23:31
It's shocking.00:23:33
- Is there something fractal about this?00:23:36
- Mostly in terms of the, I
guess, domains of the trees00:23:39
when you're at that critical state.00:23:42
So you get very dense areas,
you get non-dense areas.00:23:45
And as a result, when a
single lightning bolt strikes,00:23:48
you can get fires of all sizes.00:23:50
Most often you get small fires
of 10 or fewer trees burning.00:23:54
A little less frequently,00:23:55
you get fires of less than 100 trees.00:23:57
And then every once in a while,00:23:59
you get these massive fires00:24:01
that reverberate throughout
the entire system.00:24:04
Now, you might expect that
because the fire is so large,00:24:06
there has to be a
significant event causing it,00:24:09
but that's not the case00:24:11
because the cause for each
fire is the exact same,00:24:13
it's a single lightning strike.00:24:16
The only difference is where it strikes00:24:18
and the exact makeup of
the forest at that time.00:24:21
So in some very real way,00:24:23
the large fires are nothing more00:24:24
than magnified versions of the small ones,00:24:27
and even worse, they're inevitable.00:24:29
So what we've learned00:24:30
is that for systems in a critical state,00:24:32
there are no special events
causing the massive fires.00:24:35
There was nothing special
about the Yellowstone fire.00:24:39
- In 1935, the US Forest
Service established00:24:41
the so-called 10:00 AM policy.00:24:44
The plan was to suppress every single fire00:24:46
by 10:00 AM on the day
following its initial report.00:24:49
Now, naively, this strategy makes sense.00:24:52
I mean, if you keep all
fires under strict control,00:24:54
then none can ever get out of hand.00:24:57
But it turns out this
strategy is extremely risky.00:25:01
- So let's say we're gonna bring down00:25:04
the lightning probability,00:25:05
so it's very small,00:25:06
only one in a million right now,00:25:08
and we're also gonna crank up
the tree growth a little bit.00:25:12
Now what do you think is gonna happen?00:25:14
- We're gonna get some big
fires, I would imagine,00:25:17
like a lot of not fire
and then some huge fires.00:25:21
Yeah.00:25:22
(Derek laughs)00:25:25
- [Casper] Yep.00:25:26
- Oh boy.00:25:27
- [Casper] So nowadays,00:25:28
the fire service has a
very different approach.00:25:30
They acknowledge that
some fires are essential00:25:32
to make the megafires less likely.00:25:34
So they let most small fires burn00:25:36
and only intervene when necessary.00:25:39
In some cases, they even
intentionally create small fires00:25:42
to burn through some of the buildup,00:25:44
though it could take years00:25:45
to return the forest to its natural state00:25:47
after a century of fire suppression.00:25:49
But it's more than just
the Earth's forests00:25:51
that are balanced in this critical state.00:25:54
Every day, the Earth's crust is moving00:25:56
and rearranging itself.00:25:58
Stresses build up slowly00:25:59
as tectonic plates rub against each other.00:26:02
Most of the time, you get
a few rocks crumbling,00:26:04
the ground might move just
a fraction of a millimeter,00:26:07
but the stresses dissipate
in many earthquakes00:26:09
that you wouldn't even feel.00:26:11
- There are really tiny earthquakes00:26:13
that are happening right
now beneath your feet,00:26:16
you just can't feel 'em
because they're very small.00:26:19
But they are earthquakes,00:26:20
they're driven by small slipping movements00:26:23
in the Earth's crust.00:26:25
- [Casper] But sometimes
those random movements00:26:27
can trigger a powerful chain reaction.00:26:30
- [Derek] In Kobe, Japan,00:26:31
the morning of January 17, 1995
seemed just like any other.00:26:35
This was a peaceful city,00:26:36
and although Japan as a country00:26:38
is no stranger to earthquakes,00:26:39
Kobe hadn't suffered a
major quake for centuries.00:26:42
Generations grew up00:26:43
believing the ground
beneath them was stable,00:26:46
but that morning, deep underground,00:26:48
a stress released nearby
the Nojima fault line.00:26:51
The stress propagated to the
next section of the fault00:26:54
and the next.00:26:55
Within seconds,00:26:56
the ruptured cascaded along
40 kilometers of crust,00:26:59
shifting the ground by up to two meters00:27:01
and releasing the energy equivalent00:27:03
of numerous atomic bombs.00:27:05
The resulting quake
destroyed thousands of homes00:27:07
along with most major roads00:27:09
and railways leading into the city.00:27:10
It killed over 6,000 people00:27:12
and forced 300,000 from their homes.00:27:16
- How far it goes depends a lot on chance00:27:19
and the organization of
all that stress field00:27:22
in the Earth's crust.00:27:23
And it just seems to be
organized in such a way00:27:26
that it is possible oftentimes00:27:28
for the earthquake to
trickle along an avalanche00:27:31
along a long way00:27:32
and produce a very large
unusual earthquake.00:27:35
But if you look at the process
behind that earthquake,00:27:37
it is exactly the same physical process.00:27:40
It's just that the
earthquake-generating process00:27:43
naturally produces events00:27:45
that range over an
enormous range of scale,00:27:47
and we're not really used
to thinking about that.00:27:50
- We have this ingrained assumption00:27:51
that we can use the past
to predict the future,00:27:54
but when it comes to earthquakes00:27:56
or any system that's in a critical state,00:27:58
that assumption can be catastrophic00:28:00
because they're famously unpredictable.00:28:02
So, how can you even
begin to model something00:28:05
like the behavior of earthquakes?00:28:07
- [Derek] In 1987,
Danish physicist Per Bak00:28:09
and his colleagues considered
a simple thought experiment.00:28:12
Take a grain of sand
and drop it on a grid,00:28:15
then keep dropping grains on top00:28:17
until at some point the
sandpile gets so steep00:28:20
that the grains tumble down
onto different squares.00:28:23
- What they looked at
was the size of these,00:28:27
what they were calling avalanches,00:28:28
these reorganizations of
numbers of grains of sand.00:28:32
They asked for how often
do you see avalanches00:28:34
of a certain size.00:28:36
- This is the most simple
version of a sandpile simulator00:28:40
that you could almost imagine.00:28:41
We're gonna drop a little grain of sand00:28:43
at first always in the center,00:28:45
and then it's just gonna keep going up.00:28:47
For one grain, it'll be fine.00:28:49
For two grains, it'll be fine.00:28:50
Three grains, it'll be fine,00:28:51
but it's on the edge of toppling.00:28:53
And then when it reaches four or more,00:28:55
it's gonna basically go.00:28:58
It feels a bit like a, I
don't know, pulsing thing,00:29:01
like something's trying
to escape or something,00:29:03
very video game-like.00:29:05
That seemed pretty crazy.00:29:06
And it is symmetrical.00:29:08
- Yeah, nice geometric features.00:29:11
- So this might be interesting00:29:12
because right now we passed it at a point00:29:14
where this middle one is gonna go,00:29:17
and then you look around it and you see,00:29:19
essentially you can think of these brown00:29:25
or these three tall grain stacks00:29:29
as being maximally unstable.00:29:30
They're about to go,00:29:31
and so you could think of them00:29:33
as these fingers of instability.00:29:35
If anything touches them,00:29:37
like, they're just gonna go.00:29:40
(lively music)00:29:42
- I see it propagating out.00:29:45
- It's cool seeing it slower.00:29:46
I feel like you can see several waves00:29:50
propagating at the same time.00:29:52
- Some people have reasoned
that the Earth's crust00:29:54
becomes riddled with similar
fingers of instability00:29:57
where you get stresses building up,00:29:59
and then when one rock crumbles,00:30:01
it can propagate along these fingers,00:30:03
potentially triggering
massive earthquakes.00:30:06
If you look at the data,00:30:07
there's some even more compelling evidence00:30:09
that links the sandpile
simulation to earthquakes.00:30:13
- Let's say instead of
dropping it at the center,00:30:15
pretty unrealistic to have
it drop in the center,00:30:18
I'm gonna drop at random.00:30:23
- Hah!00:30:25
That's crazy.00:30:26
- You can actually see it tune itself00:30:28
to the critical state.00:30:30
Like at the start,00:30:31
you only see these super tiny avalanches00:30:35
and then now it's everything.00:30:36
- It has to build up.00:30:38
- We can slow down a little.00:30:42
Oh, and that's a super clean power law.00:30:45
There are events of all sizes.00:30:47
One grain of sand might
knock over just a few others00:30:50
or it could trigger an
avalanche of millions of grains00:30:53
that cascade throughout the entire system.00:30:56
And if you look at the power law00:30:58
you get from the sandpile simulation,00:31:00
it closely resembles the power law00:31:02
of the energy released
by real earthquakes.00:31:05
But if you look at the sandpile
experiment more closely,00:31:08
it doesn't just resemble earthquakes.00:31:10
What does it remind you of?00:31:12
- Forest fires.
- [Casper] Right?00:31:14
It feels like it's the
exact same behavior.00:31:16
- That's the really surprising thing,00:31:18
and that's why this little
paper with a sandpile00:31:20
was published in the world's top journal00:31:23
because it did something00:31:24
that people just didn't
really think was possible.00:31:27
- Now, what's ironic is if
you look at real sandpiles,00:31:31
they don't behave like this.00:31:33
- Okay, you said sand,00:31:35
I'm gonna do an experiment
on a real sandpile.00:31:37
And of course, it doesn't
follow a power law distribution00:31:39
of avalanches at all.00:31:41
It's totally wrong.00:31:43
(Steven and Derek laugh)00:31:44
Per Bak, naturally, gets a
chance to reply to the criticism,00:31:49
and he says, I'm pretty close to quoting,00:31:52
he says, "Self-organized criticality00:31:54
only applies to the
systems it applies to."00:31:57
(Steven laughs)00:31:58
So he doesn't care,00:32:00
the fact that his theory is
not relevant to real sandpiles.00:32:03
So what?00:32:04
Get out of my face.00:32:05
He's interested in bigger
fish to fry than sandpiles.00:32:10
It's like, you're taking me too literally.00:32:12
I'm talking about a universal mechanism00:32:14
for generating power laws.00:32:15
And the fact that it
doesn't work in real sand00:32:18
is uninteresting to him.00:32:20
I thought that took some real nerve.00:32:22
- You could think about the Earth00:32:26
and the Earth going around the Sun.00:32:28
That's a very complex system.00:32:31
You've got the molten core,00:32:32
everything sloshing around,00:32:33
and you've got oceans,00:32:34
and you've even got the
moon going around the Earth,00:32:36
which in theory, you know,00:32:38
all should affect the exact motion00:32:40
of the Earth around the Sun.00:32:42
But Newton ignored all of that,00:32:44
all he looked at was just a
single parameter, essentially,00:32:48
the mass of the Earth.00:32:50
And with that, he could
correctly, for the most part,00:32:52
predict how the Earth was
gonna go around the Sun.00:32:54
Similarly here,00:32:56
there are people that have
looked at these phenomena00:32:58
that go to the critical state,00:33:00
in this case it's
self-organized criticality,00:33:03
is it brings itself there,00:33:05
and what they find is that
there's this universal behavior00:33:07
where it doesn't even really
matter what the subparts are,00:33:11
you just get the behavior
that's the exact same.00:33:14
- At that critical point00:33:16
when all the forces are poised00:33:18
and the system is right
on that delicate balance00:33:21
between being organized, highly organized,00:33:24
or being totally disorganized,00:33:26
it turns out that almost
none of the physical details00:33:29
about that system matter
to how it behaves.00:33:33
There's just a universal
behavior that is irrespective00:33:37
of what physical system
you're talking about.00:33:39
The term that was used
is called universality,00:33:42
and it's kind of a miracle,00:33:44
it means you can make
extremely powerful theories00:33:47
without involving any technical details,00:33:49
any real details of the material.00:33:52
- What this means is that
you could have these systems00:33:54
that on the surface
seem totally different,00:33:57
but when you get to the critical point,00:33:58
they all behave in the exact same way.00:34:01
The other thing you could do
is instead of this being trees,00:34:05
you could imagine it being people00:34:07
and the thing that's spreading-00:34:08
- Is disease.00:34:09
- Is disease, yeah.00:34:12
- You almost get something for nothing00:34:15
at these critical points.00:34:16
- See, many of these systems
fall into what's known00:34:18
as universality classes.00:34:20
Some of them you need
to tune to get there,00:34:22
like magnets at their Curie temperature00:34:24
or fluids like water or carbon dioxide00:34:27
at their critical point,00:34:28
but some other systems00:34:29
seem to organize
themselves to criticality,00:34:32
like the forest fires or
sandpiles or earthquakes.00:34:36
But what's crazy is that if you succeed00:34:38
in understanding just
one system from a class,00:34:41
then you know how all the
systems in that class behave,00:34:44
and that includes even the
crudest simplest toy models,00:34:48
like the simulations we've looked at.00:34:50
So you can model
incredibly complex systems00:34:53
with the most basic of models.00:34:55
And some people think
this critical thinking00:34:57
applies even further.00:34:59
When we look around the world,00:35:00
there are lots of systems00:35:01
that show the same power law behavior00:35:03
that we see in this critical systems.00:35:05
It's in everything from DNA sequencing00:35:08
to the distribution of
species in an ecosystem00:35:10
to the size of mass
extinctions throughout history.00:35:13
We even see the same
behavior in human systems,00:35:16
like the populations of cities,00:35:18
fluctuations in stock prices,00:35:20
citations of scientific papers,00:35:22
and even the number of deaths in wars.00:35:25
So some people argue that these systems00:35:27
and perhaps many parts of our
world also organize themselves00:35:31
to this critical point.00:35:33
- So the fact that all
these natural hazards,00:35:35
as they call them,00:35:36
floods, wildfires, and earthquakes,00:35:38
they all follow power law distributions00:35:40
means that these extreme
events are much more common00:35:45
than you would think based on
normal distribution thinking.00:35:48
- If you find yourself in a situation00:35:50
or an environment that is sort
of governed by a power law,00:35:54
how should you change your behavior?00:35:56
- If you have events with one
of these power distributions,00:36:01
what you're seeing most of
the time is small events.00:36:04
And this can lull you into
a false sense of security,00:36:08
you think you understand
how things are going.00:36:10
You know, floods for example,00:36:11
there are a lot of small floods,00:36:12
and then every once in a
while, there's a huge one.00:36:15
One response to this is insurance,00:36:18
that insurance is designed precisely00:36:21
to protect you against
the large rare events00:36:24
that would otherwise be very bad.00:36:25
But then there's the other
side of that picture,00:36:29
which is you are the insurance company00:36:31
that needs to insure people00:36:33
and they have a particularly difficult job00:36:35
because they have to be able
to say how much to charge00:36:39
so that they have enough money to pay out00:36:41
when the big bad thing comes along.00:36:44
- [Derek] In 2018, a forest fire tore through
Paradise, California,00:36:47
it became the deadliest00:36:48
and most destructive fire
in the state's history,00:36:51
but the insurance company,
Merced Property & Casualty,00:36:54
hadn't planned for something that huge,00:36:57
and when the claims came in,00:36:58
they just didn't have
the reserves to pay out.00:37:01
So just like that, the company went bust.00:37:04
- But while extreme events
can cripple some companies,00:37:07
there are entire industries00:37:09
that are built on power law distributions.00:37:12
Between 1985 and 2014,00:37:15
private equity firm Horsley Bridge00:37:17
invested in 7,000 different startups00:37:20
and over half of their
investments actually lost money,00:37:23
but the top 6% more than 10xed in value00:37:26
and generated 60% of the
firm's overall profit.00:37:29
In fact, the best venture capital firms00:37:31
often have more investments
that lose money,00:37:34
they just have a few crazy outliers00:37:36
that show extraordinary growth,00:37:38
a few outliers that carry
the entire performance.00:37:41
In 2012, Y Combinator calculated
that 75% of their returns00:37:46
came from just two out of the
280 startups they invested in.00:37:50
So venture capital is a world
that depends on taking risks00:37:53
in the hope that you'll get a
few of these extreme outliers00:37:57
which outperform all of the rest00:37:58
of the investments combined.00:38:00
- [Derek] Book publishers
operate in a similar fashion,00:38:03
most titles flop,00:38:05
but in 1997,00:38:06
a small independent UK
publisher called Bloomsbury00:38:09
took a chance on a story
about a boy wizard.00:38:12
The boy's name, of
course, was Harry Potter,00:38:14
and now Bloomsbury is a
globally recognized brand.00:38:18
We see a similar pattern play
out on streaming platforms.00:38:21
On Netflix, the top 6% of
shows account for over half00:38:24
of all viewing hours on the platform.00:38:26
On YouTube,00:38:27
less than 4% of videos
ever reach 10,000 views,00:38:30
but those videos account
for over 93% of all views.00:38:35
- All these domains
follow the same principle00:38:37
that Pareto identified over 100 years ago00:38:39
where the majority of the
wealth goes to the richest few.00:38:43
The entire game is defined
by the rare runaway hits.00:38:47
- But not every industry
can play this game.00:38:50
Like if you're running a restaurant,00:38:51
you need to fill tables night after night.00:38:54
You can't have one particularly
busy summer evening00:38:56
that brings in millions of customers00:38:57
to make up for a bunch of quiet nights.00:39:00
Over a year, the busy nights
and quiet ones balance out00:39:02
and you're left with the average.00:39:04
Airlines are similar,00:39:05
an airline needs to fill
seats on each flight.00:39:08
You can't squeeze a million
passengers onto one plane,00:39:11
so it's the average number
of passengers over the year00:39:13
that defines an airline's success.00:39:16
- We're used to living in this world00:39:17
of normal distributions
and you act a certain way,00:39:20
but as soon as you switch to this realm00:39:22
that is governed by a power law,00:39:24
you need to start acting vastly different.00:39:26
It really pays to know what kind of world00:39:28
or what kind of game you're playing.00:39:30
- That is good.00:39:31
That's good, yes.00:39:32
You should come on camera and
just say that just like that.00:39:35
You were on camera, you just did do it.00:39:37
(Steven laughs)
- If you are in a world00:39:40
where random additive
variations cancel out over time,00:39:42
then you get a normal distribution.00:39:44
And in this case, it's
the average performance,00:39:47
so consistency, which is important.00:39:50
But if you are in a world
that's governed by a power law00:39:52
where your returns can multiply00:39:54
and they can grow over
many orders of magnitude,00:39:57
then it might make sense
to take some riskier bets00:39:59
in the hope that one
of them pays off huge.00:40:02
In other words,00:40:03
it becomes more important to
be persistent than consistent.00:40:07
- [Derek] Though as we saw
in the second coin game,00:40:08
totally random multiplicative returns00:40:10
give you a log normal
distribution, not a power law.00:40:14
To get a power law,00:40:15
there must be some
other mechanism at play.00:40:18
In the early 2000s,00:40:19
Albert-László Barabási
was studying the internet,00:40:22
and to his surprise,00:40:23
he found that there was no normal webpage00:40:26
with some average number of links.00:40:28
Instead, the distribution
followed a power law.00:40:30
A few sites like Yahoo00:40:32
had thousands of times more connections00:40:34
than most of the others.00:40:36
Barabasi wondered what could be causing00:40:38
this power law of the internet,00:40:39
so he made a simple prediction.00:40:41
As new sites were added to the internet,00:40:43
they were more likely to
link to well-known pages.00:40:46
To test this prediction,00:40:48
he and his colleague Réka Albert
ran a simulation.00:40:51
They started with a
network of just a few nodes00:40:53
and gradually they added
new nodes to the network00:40:56
with each new node more
likely to connect to those00:40:59
with the most links.00:41:00
As the network grew, a power law emerged.00:41:03
The power was around negative two,00:41:05
which almost exactly matched
the real data of the internet.00:41:08
- [Casper] Look at that.
- [Derek] That's fun.00:41:11
- It's still so satisfying.00:41:12
This will basically also
distribute a power law.00:41:15
One of the ideas here is that
this could be individuals00:41:18
or even companies,00:41:19
and so if you're more likely00:41:21
to become more successful
or more well known00:41:25
or successful you already are,00:41:26
you're gonna get this
sort of runaway effect00:41:28
where you get a few that sort
of dominate the distributions.00:41:33
I wonder if part of the takeaway00:41:34
is like if you're
playing some sort of game00:41:37
that is dominated by a power law,00:41:39
then you better do the work as much of it00:41:41
as early as possible00:41:42
so you get to benefit from the
snowball effect, essentially.00:41:46
- Yeah, I guess that's a good idea.00:41:48
I'm not sure whether you
can control it, though.00:41:50
Human beings like to think of ourselves00:41:52
as being a bit special,00:41:54
and that maybe somehow
because we're intelligent00:41:56
and have free will.00:41:59
We will escape the provenance
of the laws of physics00:42:05
in order and organization,00:42:06
but I think that's probably not the case.00:42:09
So if you look at the
number of world wars,00:42:12
and if you make a crude measure
of how big is the world war00:42:15
by how many people it kills,00:42:18
which is a bit macabre, but still,00:42:21
you find that, again,
it follows a power law00:42:23
virtually identical to
the power law you find00:42:25
in stock market crashes.00:42:27
- So if the world is shaped by power laws,00:42:30
then it feels like we're poised00:42:32
in this kind of critical state00:42:33
where two identical grains of sand,00:42:36
two identical actions can
have wildly different effects.00:42:40
Most things barely move the needle,00:42:42
but a few rare events
totally dwarf the rest,00:42:44
and that, I think, is the
most important lesson.00:42:47
If you choose to pursue areas00:42:49
governed by the normal distribution,00:42:51
you can pretty much
guarantee average results.00:42:54
But if you select pursuits
ruled by power laws,00:42:56
the goal isn't to avoid risk,00:42:58
it's to make repeated intelligent bets.00:43:00
Most of them will fail,00:43:02
but you only need one wild
success to pay for all the rest.00:43:06
- And the thing is that
beforehand you cannot know00:43:08
which bet is going to be00:43:10
because the system is
maximally unpredictable.00:43:12
It could be that your
next bet does nothing,00:43:14
it could do a little bit,00:43:15
or it could change your entire life.00:43:18
In fact, around three years ago,00:43:19
I was reading this little book,00:43:21
and in the book there was this little line00:43:23
saying something like,00:43:24
"One idea could transform
your entire life."00:43:27
So right underneath that, I wrote,00:43:29
"Send an email to Veritasium."00:43:32
A couple days later, I wrote
an email to Derek, saying,00:43:34
"Hey, Derek, I'm Casper.00:43:36
I study physics and I can
help you research videos."00:43:39
I didn't hear back for four weeks,00:43:41
so I was getting pretty sad00:43:42
and just wanted to forget
about it and move on,00:43:46
but then a couple days later
I got an email back saying,00:43:49
"Hey, Casper, we can't do
an internship right now,00:43:52
but how would you like to research, write,00:43:54
and produce a video as a freelancer?"00:43:57
So I did,00:43:58
and that's how I get
started at Veritasium.00:44:04
Hey, just a few quick final things.00:44:06
All the simulations that
we used in this video00:44:09
we'll make available
for free for you to use00:44:11
in the link in the description.00:44:14
And the other thing is
that we just launched00:44:16
the official Veritasium game.00:44:18
It's called Elements of Truth00:44:19
and it's a tabletop game
with over 800 questions.00:44:22
It's the perfect way to
challenge your friends00:44:25
and see who comes out on top.00:44:27
Now, at Veritasium, we're
all quite competitive,00:44:30
so every time we play, things
get a little bit heated,00:44:32
but that's honestly a big part of the fun.00:44:35
Now, when we launched on Kickstarter,00:44:37
we got a lot of questions asking00:44:39
if we could ship to specific countries.00:44:42
And originally we didn't enable this,00:44:44
and this is our mistake,00:44:45
this is on us and we totally hear you,00:44:48
but I'm glad to say00:44:49
that right now we have
enabled worldwide shipping.00:44:52
So no matter where you are in the world,00:44:54
you can get your very own copy.00:44:55
To reserve your copy and get involved,00:44:58
scan this QR code or click
the link in the description.00:45:02
I wanna thank you for all your support,00:45:03
and most of all, thank you for watching.Description:
The world is not Normal. Sponsored by NordVPN. 🌏 Get exclusive NordVPN deal here ➵ https://nordvpn.com/veritasium It’s risk free with Nord’s 30 day money-back guarantee!✌ Get your exclusive edition of Veritasium’s first tabletop game - join 6,000+ backers - https://www.kickstarter.com/projects/elements-of-truth/elements-of-truth-by-veritasium?ref=2hi2cc To play around with the simulations in the video, you can follow these links: Sandpiles - https://www.veritasium.com/simulation3 Ising model (magnetism) - https://www.veritasium.com/simulation4 Forest fires - https://www.veritasium.com/simulation5 ▀▀▀ A huge thanks to Steven Strogatz, Mark Buchanan and Mark Newman for their time and expertise. ▀▀▀ CHAPTERS: 0:00 What is a power law? 4:31 Expected Values 8:49 The St. Petersburg Paradox 11:37 Outliers Dominate Averages 15:23 Fractals and Power Laws 19:28 Self-Organized Criticality 24:08 Why do we light controlled forest fires? 26:40 How We Can Predict Earthquakes 32:11 Critical Systems and Universality 36:31 How Some Businesses Are Built On Power Laws 39:30 What game are you playing? Normal or power? ▀▀▀ References: https://docs.google.com/document/d/182bjrapzAIbnrBu0BaBgfO2oEnef4KAfuIOTOZ9d58I/edit?tab=t.0 ▀▀▀ Special thanks to our Patreon supporters: Adam Foreman, Albert Wenger, Alex Porter, Alexander Tamas, Anton Ragin, Anupam Banerjee, armedtoe, Bertrand Serlet, Blake Byers, Bruce, Dave Kircher, David Johnston, David Tseng, Evgeny Skvortsov, Garrett Mueller, Gnare, gpoly, Hayden Christensen, Ibby Hadeed, Jeromy Johnson, Jon Jamison, Juan Benet, KeyWestr, Kyi, Lee Redden, Marinus Kuivenhoven, Matthias Wrobel, Meekay, meg noah, Michael Bush, Michael Krugman, Orlando Bassotto, Paul Peijzel, Richard Sundvall, Robert Oliveira, Sam Lutfi, Tj Steyn, Ubiquity Ventures & wolfee ▀▀▀ Writers - James Moore, Casper Mebius & Derek Muller Producer & Director - James Moore Presenters - Derek Muller & Casper Mebius Editors - Jack Saxon & Peter Nelson Animators - Fabio Albertelli, Emma Wright, Saif Javed & Andrew Neet Additional Editor - James Stuart Researchers - Aakash Singh Bagga & Callum Cuttle Simulations - Aakash Singh Bagga Thumbnail Designers - Abdallah Rabah, Ren Hurley & Ben Powell Production Team - Josh Pitt, Matthew Cavanagh, Anna Milkovic & Katy Southwood Executive Producers - Derek Muller & Casper Mebius Additional video/photos supplied by Getty Images, Storyblocks Music from Epidemic Sound
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