쉐도잉 연습: You've (Likely) Been Playing The Game Of Life Wrong - 영상으로 영어 말하기 배우기

연습 모드 선택

각 모드는 전체 화면 연습실로 열립니다.

582 문장

문장이 너무 짧거나 길면 Edit를 눌러 조정하세요.

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 very important to try to understand, you know, which game you're playing and what are the payoffs going to be in the long run.

In the late 1800s, Italian engineer Vilfredo Pareto 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 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 Pareto'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 5 times, 10 times, even 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, Pareto 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 negative 1 .5.

That means each time you double the income, say from 200 pounds to 400 pounds,

the number of people earning at least that amount drops off by a factor of 2 to the power of 1 .5, which is around 2 .8.

And this pattern holds for every doubling of income.

So Pareto 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 over x to the power of 1 .5.

Now that's what Pareto 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 Pareto 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 one half.

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 de Moivre in the early 1700s.

He showed that if you plot the probability of each outcome, you get a bell -shaped curve, curve, which was later coined the normal distribution.

Normal distributions, the traditional explanation is that when there are a lot of effects that 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 if these random effects are additive, that is 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 ahead, you multiply your winnings by 1 .1.

If instead the coin lands on tails, you multiply your winnings by 0 .9.

And after 100 tosses, you take home the total.

That is, the dollar you started with times the string of 1 .1s and 0 .9s.

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 plus 0 .9 divided by 2

which is 1 so

if you start out with one dollar then your expected payout is just one dollar

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 100 heads, you'd win 1 .1 to the power of 100.

That's almost $14 ,000.

Although the chance of that happening is around 1 in 10 to the power 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 $0 .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 $0 .61.

Though either way, if you played the game hundreds of times, your payout would average out to one dollar.

Now watch what happens if we switch the x -axis from a linear scale to a logarithmic scale.

Well then you see the curve transforms into a normal distribution.

That's why this type of distribution is called a log normal 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 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 what was a product of random numbers then gets translated into sums of logs of random numbers.

100

And that's what leads to this so -called log -normal distribution.

101

And log -normal distributions produce big inequalities.

102

You don't just see a mean, you see a mean with a big long tail it's much

103

more likelihood of really big events in this case tremendous wealth being obtained than you would expect from a normal distribution.

104

The reason this curve is so asymmetric is because the downside is capped at zero, so at most you could lose one dollar.

105

But the upside can keep growing up to nearly $14 ,000.

106

Now let's go on to table three.

107

Again you'll be tossing a coin, but this time you start out with a dollar

108

and the payout doubles each time you toss the coin

109

and you keep tossing until you get a heads then the game ends

110

so if you get heads on your first toss you get two dollars

111

if you get a tails first

112

and then hit a heads on your second toss you get four dollars

113

if you flipped two tails

114

and then a head on your third toss you'd get eight dollars

115

and so on

116

if it took you to the nth toss to get a heads you would get two to the n dollars

117

so how much should you pay to play this game well

118

as in our previous example we need to work out the expected value

119

so suppose you throw a head on your first try the payout is two dollars

120

and the probability of that outcome is a half

121

so the expected value of that toss is a dollar

122

if it takes you two tosses to get a heads then the payout is four dollars

123

and the probability of that happening is one over four

124

so again the expected value is one dollar we also need to add in the chance

125

that you flip heads on your third try in

126

that case the payout is eight dollars and the probability of that happening is 1 over 8.

127

So again, the expected value is $1.

128

And we have to keep repeating this calculation over all possible outcomes.

129

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 100 times before you get heads.

130

I know it's extremely unlikely, but the payout is so huge that the expected value of that outcome is still $1.

131

So it still increases the expected value of the whole game this means

132

that theoretically the total expected value of this game is infinite this is known as the saint petersburg paradox

133

if you look at the distribution of payouts you can see it's uncapped.

134

It spans across all orders of magnitude.

135

You could get a payout of $1 ,000, $100 ,000, or even $1 ,000 ,000 or more.

136

And while a million -dollar payout is unlikely, it's not that unlikely.

137

It's around one in a million.

138

Now, if you transform both axes to a log scale, you see a straight line with a gradient of negative one.

139

The payout of the St. Petersburg paradox follows a power law.

140

The specific power law in this case is

141

that the probability of a payout x is equal to x to the power of negative 1, or 1 over x.

142

In the previous games, when you have a normal distribution, or even a log normal distribution, you can measure the width of that distribution, its standard deviation.

143

And in a normal distribution, 95 % of the data fall within two standard deviations from the mean.

144

But with a power law, like in the St. Petersburg paradox, there is no measurable width.

145

The standard deviation is infinite.

146

This makes power laws a fundamentally different beast with some very weird properties.

147

Imagine you take a bunch of random samples and then average them and then take more random samples and average them.

148

You'll find that the average keeps going up.

149

It doesn't converge.

150

The more you measure, the bigger the average is, which is really weird.

151

It sounds impossible but it's

152

because it has such a heavy tail meaning the probability of really whopping big events is

153

so significant that if you keep measuring occasionally you're going to measure one of those extreme outliers

154

and they will totally skew the average it's sort of like saying you know

155

if you're standing in a room with bill gates

156

or elon musk the average wealth in that room is going to be $100 billion or something

157

because the average is dominated by one outlier.

158

And that same idea, one outlier can dominate the average, shows up online too.

159

A handful of companies, servers, and data centers hold the personal information of millions of people.

160

So when one of them gets hacked, it can have ripple effects across the whole network.

161

We've had scammers get a hold of email addresses

162

and phone numbers of writers on our team and then send them messages pretending to be me.

163

That is where today's sponsor, NordVPN, comes in.

164

NordVPN encrypts your internet traffic so your personal data stays private even when the wider system isn't.

165

It protects you from hackers, trackers, and malware with threat protection even when you're not connected to a VPN.

166

Within just 15 minutes of registering a new email, we saw that five leaks had already been detected.

167

NordVPN lets you browse securely from anywhere in the world by routing your connection through encrypted servers in over 60 countries.

168

You can try it completely risk -free with a 30 -day money -back guarantee.

169

Just scan this QR code

170

or go to nordvpn .com slash Veritasium to get a huge discount on a two -year plan plus four extra months free.

171

That's nordvpn .com slash Veritasium for a huge discount.

172

I'll put the link down in the description.

173

I'd like to thank NordVPN for sponsoring this video.

174

And now back to PowerLaws.

175

So why do you get a PowerLaw from the simple St. Petersburg setup?

176

If you look at the payout, x, you can see it grows exponentially with each toss of the coin, x equals 2 to the n.

177

But if you look at the probability of tossing the coin that many times to get a heads, you can see that this probability shrinks exponentially.

178

So the probability of flipping a coin n times is a half to the power of n.

179

But we're not really interested in the number of tosses, we're interested in the payout.

180

Now, we know that x equals 2 to the n, so instead of writing 2 to the n in our probability equation, we can just write x.

181

So we end up with this.

182

The probability of a payout of x dollars is equal to 1 over x, or in other words, x to the power of negative 1.

183

You put them together, the exponentials conspire to make a power law.

184

And that's a very common thing in nature, that a lot of times when we see power laws, there are two underlying exponentials that are dancing together to make a power run.

185

One example of this is earthquakes.

186

If you look at data on earthquakes, you find that small earthquakes are very common.

187

But earthquakes of increasing magnitudes become exponentially rarer.

188

But the destruction that earthquakes cause is not proportional to their magnitude.

189

It's proportional to the energy they release.

190

And as earthquakes grow in magnitude, that energy grows exponentially.

191

So there's this exponential decay in frequency of earthquakes of a given magnitude

192

and an exponential increase in the amount of energy released by earthquakes of a certain magnitude.

193

So when you combine those two exponentials to eliminate the magnitude, what you find is a power law.

194

But power laws also reveal something deeper about the underlying structure of a system.

195

To see this in action, let's go back to the third coin game and the St. Petersburg paradox.

196

Now, you can draw all the different outcomes as a tree diagram, where the length of each branch is equal to its probability.

197

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.

198

Now, when you zoom in, you keep seeing the same structure repeating at smaller and smaller scales.

199

It's self -similar, like a fractal.

200

And that's no coincidence.

201

We see the same fractal -like pattern in the veins on a leaf, river networks, the blood vessels in our lungs, even lightning.

202

And in all of these cases, we can describe the pattern with a power law.

203

Power laws and fractals are intrinsically linked.

204

That's because power laws reveal something fundamental about a system's structure.

205

So I've got a magnet and I've got a screw.

206

And you'll notice if I bring them close together, then the screw gets attracted to the magnet.

207

And that's because there's a lot of iron in it, which is ferromagnetic.

208

But watch what happens if I start heating this up.

209

Trying to, oh, you see that?

210

Oh, there it went.

211

There it went.

212

You see, you heat it up and and suddenly it becomes non -magnetic.

213

To find out what happened, let's zoom in on this magnet.

214

Inside a magnet, each atom has its own magnetic moment, which means you can think of it like its own little magnet or compass.

215

If one atom's moment points up, its neighbors tend to point that way too, since this lowers the system's overall potential energy.

216

Therefore, at low temperatures, you get large regions called domains where all the moments align.

217

And when many of these domains also align, their individual magnetic fields reinforce to create an overall field around the magnet

218

but if you heat up the magnet each atom starts vibrating vigorously the moments flip up

219

and down and so the alignment can break down and

220

when all the moments cancel out then there's no longer a net magnetic field now

221

if you have the right equipment you can balance any magnetic material right on

222

that transition point right between magnetic and non -magnetic this is called the critical point

223

and it occurs at a specific temperature called the Curie temperature.

224

I asked Casper and the team to build a simulation to show what's going on inside the magnet at this critical point.

225

Each pixel represents the magnetic moment of an individual atom.

226

Let's say red is up and blue is down.

227

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.

228

But if we really crank up the temperature, then all of these moments start flipping up and down and

229

so they cancel out and the magnet loses its magnetism

230

so that's exactly what happened in our demo but

231

if we tune the temperature just right right to

232

that curie temperature then the pattern becomes way more interesting this

233

looks like a map like a map yeah it almost looks like the mediterranean

234

or something it's almost stable like atoms that are pointing one way tend to point that way for a while.

235

But there is clearly fluctuations as well, so domains are constantly coming and going.

236

It's both got some elements of stability and some persistence over time, some features which are consistent,

237

but it's also not locked in place because you notice changes over time.

238

If you zoom in, you find that the same kinds of patterns repeat at all scales.

239

You've got domains of tens of atoms, hundreds, thousands, even millions.

240

There's just no inherent scale to the system.

241

That is, it's scale -free.

242

It's just like a fractal.

243

And if you plot the size distribution of the domains, you get a power law.

244

The underlying geometry suddenly shows a fractal character that it doesn't have on either side of the phase transition.

245

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,

246

that indicates you're dealing with a system that has no intrinsic scale.

247

And that is a signature of a system in a critical state, which it turns out has huge consequences.

248

See, normally in a magnet, below the Curie temperature, each atom influences only its neighbors.

249

If one atom's magnetic moment flips up, then that means that its neighbors are slightly more likely to point up two.

250

But that influence is local.

251

It dies out just a few atoms away.

252

But as the magnet approaches its critical temperature those local influences start to chain together one spin nudges its neighbor

253

and that neighbor nudges the next and

254

so on like a rumor spreading through a crowd

255

and the result is that the effective range of influence keeps expanding

256

and right at the critical point it becomes effectively infinite a flip on one side can cascade throughout the entire material

257

so you get these small causes just a single flip to reverberate throughout the entire system

258

and it gets right into that

259

that point where the system is maximally unstable anything can happen

260

it's also maximally interesting in a way it's it means the system is most unpredictable

261

most uncertain it's really hard to know what's going to happen next

262

and that seems to be a natural procedure that happens in many different systems one such system is forest fires

263

In June 1988, a lightning strike started a small fire near Yellowstone National Park.

264

This was nothing out of the ordinary.

265

Each year, Yellowstone experiences thousands of lightning strikes.

266

Most don't cause fires, and those that do tend to burn a few trees, maybe even a few acres, before they fizzle out.

267

Three quarters of fires burn less than a quarter of an acre.

268

The largest fire in the park's recent history occurred in 1931.

269

That burned through 18 ,000 acres, an area slightly larger than Manhattan.

270

But the 1988 fire was different.

271

That initial spark spread, slowly at first covering several thousand acres.

272

Then, over the next couple of months, it merged with other small fires to create an enormous complex of megafires that blazed across 1 .4 million acres of land.

273

That's around the size of the entire state of Delaware.

274

That's 70 times bigger than the previous record, and 50 times the area of all the fires over the previous 15 years combined.

275

So what was so special about the 1988 fires?

276

Well, to find out, we made a forest fire simulator.

277

We've got a grid of squares.

278

And on each square, either a tree could be there, it could grow, or it could not be there.

279

There's going to be some probability for lightning strikes.

280

So, you know, the higher the probability, the more fires we're going to have we can run this

281

so trees are growing trees are growing forest is filling in

282

nice getting pretty dense what do you expect is gonna happen

283

I expect to see some fires probably you know now

284

that oh that was good

285

that was a good little fire whoa whoa no way oh

286

that's crazy you haven't adjusted the parameters right it's just like

287

not yet not yet this seems like a very critical situation just by itself i say

288

that because of how big

289

that fire was this sort of system will tune itself to criticality

290

and you can you can see it start to happen

291

so right now i think is a good moment where you have basically domains of a lot of different sizes

292

and then one way to think about it is

293

if some of these domains become too big then you get a single fire like

294

that one perfectly timed burns it's gonna propagate throughout the whole thing

295

and burn it back down a little but then

296

if it goes too hard then now you've got all these domains where there are no trees

297

and so it's gonna you know grow again to bring it back to

298

that critical state i can see how it's the feedback mechanism right

299

that the fire gets rid of all the trees

300

and there's nothing left to burn and then

301

that has to fill in again yeah yeah but

302

if there hasn't been a fire then the forest gets too thick and then it's ripe for this sort of massive

303

fire for a magnet you have to painstakingly tune it to the critical point

304

but the forest naturally drives itself there this phenomenon is called self -organized criticality yeah

305

and if you let it run what you get is again a power law distribution

306

so this is log log so it should be a straight line

307

that kind of stuff seems so totally random and unpredictable

308

and it is in one way

309

and yet it follows a pattern there's a consistent mathematical pattern

310

to all these kind of disasters um it's it's shocking is

311

there something fractal about this mostly in terms of the I guess domains of the trees

312

when you're at that critical state

313

so you get very dense areas you get non -dense areas

314

and as a result

315

when a single lightning bolt strikes you can get fires of

316

all sizes most often you get small fires of 10

317

or fewer trees burning a little less frequently you get fires of less than 100 trees

318

and then every once in a while you get these massive fires

319

that reverberate throughout the entire system now you might expect that

320

because the fire is so large there has to be a significant event causing it.

321

But that's not the case.

322

Because the cause for each fire is the exact same.

323

It's a single lightning strike.

324

The only difference is where it strikes and the exact makeup of the forest at that time.

325

So, in some very real way, the large fires are nothing more than magnified versions of the small ones.

326

And even worse, they're inevitable.

327

So, what we've learned is that for systems in a critical state, there are no special events causing the massive fires.

328

There was nothing special about the Yellowstone fire.

329

In 1935, the U .S.

330

Forest Service established the so -called 10 AM policy.

331

The plan was to suppress every single fire by 10 AM on the day following its initial report.

332

Now, naively, this strategy makes sense.

333

I mean, if you keep all fires under strict control, then none can ever get out of hand.

334

But it turns out this strategy is extremely risky.

335

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.

336

And we're also going to crank up, you know, the tree growth a little bit.

337

Now, what do you think is going to happen?

338

We're going to get some big fires, I would imagine.

339

Like a lot of not fire and then some huge fires.

340

Yeah.

341

Yep.

342

Oh, boy.

343

So nowadays the fire service has a very different approach.

344

They acknowledge that some fires are essential to make the megafires less likely.

345

So, they let most small fires burn and only intervene when necessary.

346

In some cases, they even intentionally create small fires to burn through some of the buildup.

347

Though it could take years to return the forest to its natural state after a century of fire suppression.

348

But it's more than just the Earth's forests that are balanced in this critical state.

349

Every day, the Earth's crust is moving and rearranging itself.

350

Stresses build up slowly as tectonic plates rub against each other.

351

Most of the time, you get a few rocks crumbling.

352

The ground might move just a fraction of a millimeter.

353

But the stresses dissipate in many earthquakes that you wouldn't even feel.

354

There are really tiny earthquakes that are happening right now beneath your feet.

355

You just can't feel them because they're very small.

356

But they are earthquakes.

357

They're driven by small, slipping movements in the Earth's crust.

358

But sometimes those random movements can trigger a powerful chain reaction.

359

In Kobe, Japan, the morning of January 17th, 1995 seemed just like any other.

360

This was a peaceful city, and although Japan as a country is no stranger to earthquakes, Kobe hadn't suffered a major quake for centuries.

361

Generations grew up believing the ground beneath them was stable.

362

But that morning, deep underground, a stress released nearby the Nojima fault line.

363

The stress propagated to the next section of the fault and the next.

364

Within seconds, the rupture cascaded along 40 kilometers of crust, shifting the ground by up to two meters and releasing the energy equivalent of numerous atomic bombs.

365

The resulting quake destroyed thousands of homes, along with most major roads and railways leading into the city.

366

It killed over 6 ,000 people and forced 300 ,000 from their homes.

367

How far it goes depends a lot on chance and the organization of all that stress field in the Earth's crust.

368

And it just seems to be organized in such a way

369

that it is possible oftentimes for the earthquake to trickle along an avalanche along a long way

370

and produce a very large unusual earthquake.

371

But if you look at the process behind that earthquake, it is exactly the same physical process.

372

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.

373

We have this ingrained assumption that we can use the past to predict the future.

374

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.

375

So how can you even begin to model something like the behavior of earthquakes?

376

In 1987, Danish physicist Per Back and his colleagues considered a simple thought experiment.

377

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

378

so steep that the grains tumble down onto different squares.

379

What they looked at was the size of these, what they were calling avalanches, these reorganizations of numbers of grains of sand.

380

They asked for how often do you see avalanches of a certain size?

381

This is the most simple version of a sand pile simulator

382

that you could almost imagine we're gonna drop a little grain of sand at first always in the center

383

and then it's just gonna keep going up for one grain

384

it'll be fine for two grains it'll be fine three grains it'll be fine

385

but it's on the edge of toppling and then when it reaches four or more it's gonna basically go

386

feels a bit like a i don't know pulsing thing like something's trying to escape

387

or something very video game like that seemed pretty crazy and it is symmetrical yeah nice geometric features

388

So this might be interesting, because right now we've passed it at a point where this middle one is going to go.

389

And then you look around it and you see,

390

essentially you can think of these brown or these three tall grain stacks as being maximally unstable.

391

They're about to go.

392

And so you can think of them as these fingers of instability.

393

If anything touches them, the whole system, like they're just going to go.

394

I see it propagating out.

395

It's cool seeing it slower.

396

I feel like you can see several waves propagating at the same time.

397

Some people have reasoned that the Earth's crust becomes riddled with similar fingers of instability, where you get stresses building up.

398

And then when one rock crumbles, it can propagate along these fingers, potentially triggering massive earthquakes.

399

If you look at the data, there's some.. even more compelling evidence that links the sand pile simulation to earthquakes.

400

Let's say instead of dropping it at the center, pretty unrealistic to have it drop in the center,

401

I'm going to drop at random. That is crazy.

402

You can actually see it tune itself to the critical state.

403

Like at the start, you only see these super tiny avalanches.

404

And then now it's everything.

405

There are events of all sizes.

406

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.

407

And if you look at the power law you get from the sandpal simulation, it closely resembles the power law of the energy released by real earthquakes earthquakes.

408

But if you look at the sandpile experiment more closely, it doesn't just resemble earthquakes.

409

What does it remind you of?

410

Forest fires.

411

Right?

412

Feels like it's the exact same behavior.

413

That's the really surprising thing.

414

And that's why this little paper with a sandpile was published in the world's top journal.

415

Because it did something that people just didn't really think was possible.

416

Now what's ironic is, if you look at real sandpiles, they don't behave like this.

417

okay you said sand i'm gonna do an experiment on a real sand pile

418

and of course it doesn't follow a power law distribution of avalanches at all it's totally wrong

419

pair buck naturally gets a chance to reply to the criticism

420

and he says i'm pretty close to quoting he says self -organized criticality only applies to the systems it applies to

421

so he doesn't care the fact

422

that his theory is not relevant to real sand piles

423

so what get out of my face he's interested in bigger

424

fish to fry than than you know sand piles it's like

425

you're taking me too literally i'm talking about a universal mechanism for generating power laws

426

and the fact

427

that it doesn't depend it doesn't work in real sand is uninteresting to him I thought that took some real nerve.

428

You could think about the Earth and the Earth going around the Sun.

429

That's a very complex system.

430

You've got the molten core, everything slashing around, then you've got oceans, and you've even got the Moon going around the Earth, which in theory, you know,

431

all should affect the exact motion of the Earth around the Sun.

432

But Newton ignored all of

433

that all he looked at was just a single parameter essentially the mass of the earth and with

434

that he could correctly for the most part predict how the

435

earth was going to go around the sun similarly here there are people

436

that have looked at these phenomena

437

that go to the critical state in this in this case it's self -organized criticality is it brings itself there

438

and what they find is

439

that there's this universal behavior where it doesn't even really matter

440

what the sub parts are you You just get the behavior that's the exact same.

441

At that critical point, when all the forces are poised and the system is right on that delicate balance between being organized,

442

highly organized, or being totally disorganized, it turns out that almost none of the physical details about that system matter to how it behaves.

443

There's just a universal behavior that is irrespective of what physical system you're talking about.

444

The term that was used is called universality.

445

And it's kind of a miracle.

446

It means you can make extremely powerful theories without involving any technical details, any real details of the material.

447

What this means is that you could have these systems that on the surface seem totally different.

448

But when you get to the critical point, they all behave in the exact same way.

449

The other thing you could do is instead of this being trees, you could imagine it being people.

450

And the thing that's spreading is disease.

451

Is disease, yeah.

452

You almost get something for nothing at these critical points.

453

See, many of these systems fall into what's known as universality classes.

454

Some of them you need to tune to get there, like magnets at their curie temperature, or fluids like water or carbon dioxide at their critical point.

455

But some other systems seem to organize themselves to criticality, like the forest fires or sand piles or earthquakes.

456

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.

457

And that includes even the crudest, simplest toy models, like the simulations we've looked at.

458

So you can model incredibly complex systems with the most basic of models.

459

And some people think this critical thinking applies even further.

460

When we look around the world, there are lots of systems that show the same power law behavior that we see in this.

461

Thank you critical systems.

462

It's in everything from DNA sequencing to the distribution of species in an ecosystem to the size of mass extinctions throughout history.

463

We even see the same behavior in human systems, like the populations of cities, fluctuations in stock prices, citations of scientific papers,

464

and even the number of deaths in wars.

465

So some people argue that these systems, and perhaps many parts of our world, also organize themselves to this critical point.

466

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

467

are much more common than you would think based on normal distribution thinking.

468

If you find yourself in a situation or an environment that is sort of governed by a power law, how should you change your behavior?

469

If you have events with one of these power distributions what you're seeing most of the time is small events

470

and this can lull you into a full sense of security

471

you think you understand how things are going you know floods for example there are a lot of small floods

472

and then every once in a

473

while there's a huge one response to this is insurance

474

that insurance is designed precisely to protect you against the large rare events

475

that would otherwise be very bad but then there's the other side of that picture which is

476

You're the insurance company that needs to insure people

477

and they have a particularly difficult job

478

because they have to be able to say how much to charge

479

so that they have enough money to pay out when the big bad thing comes along.

480

In 2018, a forest fire tore through Paradise, California.

481

It became the deadliest and most destructive fire in the state's history.

482

But the insurance company, Merced Property and Casualty, hadn't planned for something that huge.

483

And when the claims came in, they just didn't have the reserves to pay out.

484

So just like that, the company went bust.

485

But while extreme events can cripple some companies, there are entire industries that are built on parallel distributions.

486

Between 1985 and 2014, private equity firm Horsley Bridge invested in 7 ,000 different startups,

487

and over half of their investments actually lost money.

488

But the top 6 % more than 10x in value and generated 60 % of the firm's overall profit.

489

In fact, the best venture capital firms often have more investments that lose money.

490

They just have a few crazy outliers that show extraordinary growth, a few outliers that carry the entire performance. In 2012,

491

Y Combinator calculated that 75 % of their returns came from just two out of the 280 startups they invested in.

492

So, venture capital is a world that depends on taking risks in the hope

493

that you'll get a few of these extreme outliers which outperform all of the rest of the investments combined.

494

Book publishers operate in a similar fashion.

495

Most titles flop, but in 1997, a small independent UK publisher called Bloomsbury took a chance on a story about a boy wizard.

496

The boy's name, of course, was Harry Potter.

497

And now Bloomsbury is a globally recognized brand.

498

We see a similar pattern play out on streaming platforms.

499

On Netflix, the top 6 % of shows account for over half of all viewing hours on the platform.

500

On YouTube, less than 4 % of videos ever reach 10 ,000 views, but those videos account for over 93 % of all views.

501

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.

502

The entire game is defined by the rare runaway hits.

503

But not every industry can play this game.

504

Like if you're running a restaurant, you need to fill tables night after night.

505

You can't have one particularly busy summer evening

506

that brings in millions of customers to make up for a bunch of quiet nights.

507

Over a year, the busy nights and quiet ones balance out, and you're left with the average.

508

Airlines are similar.

509

An airline needs to fill seats on each flight.

510

You can't squeeze a million passengers onto one plane.

511

So it's the average number of passengers over the year that defines an airline's success.

512

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,

513

you need to start acting vastly different.

514

It really pays to know what kind of world you're, or what kind of game you're playing.

515

That is good, that's good, yes.

516

You should come on camera and just say that, just like that.

517

If you're in a world where random additive variations cancel out over time, then you get a normal distribution.

518

And in this case, it's the average performance, so consistency, which is important.

519

But if you're in a world that's governed by a power law where your returns can multiply

520

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.

521

In other words, it becomes more important to be persistent than consistent.

522

Though, as we saw in the second coin game, totally random multiplicative returns give you a log normal distribution, not a power law.

523

To get a power law, there must be some other mechanism at play.

524

In the early 2000s, Albert Laszlo Barbasci was studying the internet.

525

And to his surprise, he found that there was no normal web page with some average number of links.

526

Instead, the distribution followed a power law.

527

A few sites, like Yahoo, had thousands of times more connections than most of the others.

528

Birabashi wondered what could be causing this power law of the internet, so he made a simple prediction.

529

As new sites were added to the internet, they were more likely to link to well -known pages.

530

To test this prediction, he and his colleague, Reika Albert, ran a simulation.

531

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.

532

As the network grew, a power law emerged.

533

The power was around negative two, which almost exactly matched the real data of the internet.

534

Look at that.

535

That's fun.

536

It's still so satisfying.

537

This will basically also distribute a power law.

538

One of the ideas here is that, you know, this could be individuals or even companies.

539

And so if you're more likely to become more successful or more well -known, the more known or successful you already are,

540

you're going to get this sort of runaway effect where you you get a few

541

that sort of dominate you know the distributions i wonder

542

if part of the takeaway is like if you're playing some sort of game

543

that is dominated by power law then you better do the work as much of it as early as possible

544

so you get to benefit from the snowball effect essentially yeah

545

i guess i guess that's that's a good idea i'm not

546

sure whether you can control it though human beings like to think of ourselves as being a bit special

547

and that maybe somehow because we're intelligent and have free will we will escape the

548

provenance of the laws of physics in order in organization

549

but I think that's probably not not the case so

550

if you look at at the number of world wars and

551

if you make a crude measure of how big is the world war by how many people it kills

552

which is a bit macabre but still you find that again it follows a power law.

553

Virtually identical to the power law you find in stock market crashes." So if the world is shaped by power laws,

554

then it feels like we're poised in this kind of critical state, where two identical grains of sand, two identical actions can have wildly different effects.

555

Most things barely move the needle, but a few rare events totally dwarf the rest, and that I think is the most important lesson.

556

If you choose to pursue areas governed by the normal distribution, you can pretty much guarantee average results.

557

But if you select pursuits ruled by power laws, the goal isn't to avoid risk, it's to make repeated intelligent bets.

558

Most of them will fail, but you only need one wild success to pay for all the rest.

559

And the thing is that beforehand, you cannot know which bet it's going to be, because the system is maximally unpredictable.

560

It could be that your next bet does nothing, it could do a little bit, or it could change your entire life.

561

In fact, around three years ago, I was reading this little book.

562

And in the book, there was this little line saying something like, one idea could transform your entire life.

563

So right underneath that, I wrote, send an email to Veritasio.

564

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.

565

I didn't hear back for four weeks, so I was getting pretty sad and just wanted to forget about it

566

and move on

567

but then a couple days later i got an email back

568

saying hey casper we can't do an internship right now

569

but how would you like to research write

570

and produce a video as a freelancer so i did and that's how i got started at paratassia

571

hey just a few quick final things all the simulations

572

that we used in this video So we'll make available for free for you to use in the link in the description.

573

And the other thing is that we just launched the official Veritasium game.

574

It's called Elements of Truth, and it's a tabletop game with over 800 questions.

575

It's the perfect way to challenge your friends and see who comes out on top.

576

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.

577

Now, when we launched on Kickstarter, we got a lot of questions asking if we could ship to specific countries.

578

And originally we didn't enable this, and this is our mistake, this is on us, and we totally hear you.

579

But I'm glad to say that right now we have enabled worldwide shipping.

580

So no matter where you are in the world, you can get your very own copy.

581

To reserve your copy and get involved, scan this QR code or click the link in the description.

582

I want to thank you for all your support, and most of all, thank you for watching.

앱 다운로드

유창하게 말하는 데 필요한 모든 것

AI 발음 평가문장마다 점수 확인

IPA 발음 연습모든 소리 마스터

단어 학습나만의 단어장 만들기

단어 게임놀면서 외우기

QR 스캔

Download on theApp Store Get it onGoogle Play

같은 채널

FOR YOU

이 영상으로 배울 영어 말하기 실력

이 영상은 영상 영어 공부에 최적화된 내용으로, 복잡한 주제를 명료하게 전달하는 스피킹 기술을 연마할 수 있습니다. 특히 IELTS 스피킹처럼 논리적 설명이 중요한 시험 준비에 도움이 되는, "현상-원인-예시" 구조의 이야기 전개법을 배울 수 있습니다. 또한, 통계 용어나 전문 용어를 일상적인 말로 풀어내는 능력도 기를 수 있어, 실생활에서의 영어 의사소통 능력이 향상됩니다.

듣고 주목해야 할 발음 패턴

영어 발음 교정에 도움이 되는 연결음과 축약형이 많이 등장합니다. 예를 들어 "You've (Likely) Been"에서 "You've"와 "Been" 사이의 연결음이 두드러지며, "Likely"는 빠르게 발음되어 "likly"처럼 들릴 수 있습니다. 또한 "it's not a normal distribution"에서 "it's not a"가 "it's nuh a"로 축약되는 것을 확인할 수 있습니다. 이러한 패턴을 익히면 자연스러운 영어 듣기와 말하기가 가능해집니다.

원어민처럼 말하는 방법: 리듬과 강세

원어민의 리듬을 따라하기 위해선 shadow speech (영어 쉐도잉) 연습이 필수적입니다. 이 영상의 스피커는 주요 정보를 강조하기 위해 단어의 강세를 잘 조절합니다. 예를 들어 "power laws"에서 "power"를 강조하고, "normal distribution"에서 "normal"에 강세를 둡니다. 또한, 긴 문장을 쉼표나 연결사를 이용해 자연스럽게 끊는 방법을 배울 수 있는데, 이는 영어의 리듬을 잡는 데 큰 도움이 됩니다. 쉐도잉을 할 때는 스피커의 목소리와 같은 속도로 따라가며, 강세와 쉼표 위치를 정확히 모방해보세요.

이 영상을 통해 영상 영어 공부뿐만 아니라, 발음 교정과 쉐도잉 연습을 병행하면 IELTS 스피킹 점수도 높일 수 있을 뿐 아니라, 실제 영어 의사소통에서도 자신감을 갖출 수 있습니다. 매일 10분씩 반복 연습하면 빠르게 실력이 향상될 것입니다!

이 영상의 문법

화자가 가장 많이 쓰는 문형을 영상 속 실제 표현과 함께 정리했습니다.

문형	영상 속 표현
수동태 be + 과거분사 — 누가 하는지보다 무슨 일이 일어나는지에 초점	is called · are multiplied · being obtained
현재완료 have/has + 과거분사 — 과거의 일이 지금도 관련이 있을 때	We've had · haven't adjusted · hasn't been
관계절 who / which + 절 — 사람이나 사물에 대한 추가 정보	someone who is · people who earn · people who earned

쉐도잉이란? 영어 실력을 빠르게 키우는 과학적 방법

쉐도잉(Shadowing)은 원래 전문 통역사 훈련을 위해 개발된 언어 학습 기법으로, 다언어 학자인 Dr. Alexander Arguelles에 의해 대중화된 방법입니다. 핵심 원리는 간단하지만 매우 강력합니다: 원어민의 영어를 들으면서 1~2초의 짧은 지연으로 즉시 소리 내어 따라 말하는 것——마치 '그림자(shadow)'처럼 화자를 따라가는 것입니다. 문법 공부나 수동적인 청취와 달리, 쉐도잉은 뇌와 입 근육이 동시에 실시간으로 영어를 처리하고 재현하도록 훈련합니다. 연구에 따르면 이 방법은 발음 정확도, 억양, 리듬, 연음, 청취력, 말하기 유창성을 크게 향상시킵니다. IELTS 스피킹 준비와 자연스러운 영어 소통을 원하는 분들에게 특히 효과적입니다.

섀도잉 방법: 단계별 전체 가이드 읽기 →

쉐도잉 연습: You've (Likely) Been Playing The Game Of Life Wrong - 영상으로 영어 말하기 배우기

연습 모드 선택

앱 다운로드

White holes and wormholes are probably real. Here's why.

Something is jamming GPS over Europe. Here's what we found

No device could prove Einstein wrong... until now

Why It Was Almost Impossible to Make the Blue LED

We're trying something new...

How does light 'know' the shortest path?

Why Cold Drinks Were Deadly Before 1914

Exposing The Flaw In Our Phone System

Our Greatest Delusion

The Most Controversial Problem in Philosophy

We've Been Using The Wrong Science In Court For 50 years

Explaining Pi With Pizza

5 Fun Physics Phenomena

The Absurd Engineering Behind the Internet

The Most Misunderstood Concept in Physics

Falling ladders - why does this happen?

How a slinky falls in slow motion #shorts

We're 99.9% sure this pattern is true, but no one can prove it

What is the secret of a good life? Lessons from the longest study on happiness

How An Infinite Hotel Ran Out Of Room

Why Life Feels Boring (And Skyrim Doesn’t)

How evolution works, in 54 minutes | Sean B. Carroll: Full Interview

We Fell For The Oldest Lie On The Internet

16 minutes of natural conversation | The British Podcast

The World’s Most Average Person

The Modern World Is Designed to Destroy You | Naval Ravikant

TED@NYC: The Power of Negative Thinking

The uncomfortable truth | Yuval Noah Harari

Cosmic Insignificance Theory: A Simple Idea That Will Change Your Life Forever

Game Theory #1: The Dating Game

Things That Are Normal in America But Insane Everywhere Else

Stop Playing Small. Go All In.

이 영상으로 배울 영어 말하기 실력

듣고 주목해야 할 발음 패턴

원어민처럼 말하는 방법: 리듬과 강세

이 영상의 문법

쉐도잉이란? 영어 실력을 빠르게 키우는 과학적 방법