Практика Shadowing: The Professor Who Taught People How To Think (1962) - Изучайте разговорный английский по видео

I am Julia Sumner Miller.

I teach physics.

Consider this astonishing thing.

I have here a wheel resting on the tabletop and on the bottom of the wheel a spot.

Now when I roll the wheel in this fashion, the spot describes a very special curve.

This curve is called a cycloid and it has dramatic and astonishing properties about which we shall shortly learn.

What we must now ask is, why is it so?

Hello there.

Another programme, Why Is It So?, with Professor Julius Sumner-Miller.

And again, some rather fascinating experiments.

I think I must begin by asking again, why is it so?

Isn't this a beautiful thing, what this point does?

Now, the beauty lies not alone in this rolling wheel and what the point does, but in the implication of the motion of this point.

Let me show the people again what this point is doing.

So if we can get a shot again, you see?

See what the point is doing?

It comes up to the top, and then it goes down to the cusp, and then it starts up and goes over again.

Now come to the board, and I will tell you the story.

Here is the rolling wheel.

And here is the surface on which it rolls

and here is the point say at the top and this is what the point does

That's what the point does now in itself There isn't much to this

but it has a history which is absolutely enchanting and I want to tell you the history

In the middle of the 17th century there was a young Swiss by the name of Bernoulli

Indeed he was one of a family of hundreds of Bernoullis all of whom were geniuses

Now this one in the middle of the 17th century raised the problem.

Here's the problem Given two points a and B

In a vertical plane But not in a vertical line that is I don't want B underneath A

Put a wire let us say between A and B and let a bead slide on the wire

In such a fashion

that the bead gets from A to B in the least possible time We call

that the path of least time now would not reason alone dictate an obvious answer a straight line

So right so you put a bead on here

and let it slide and it gets from A to B in the briefest shortest possible time

That is not right the path from A to B of the shortest time is this and

And do you see that that looks like a piece of that cycloid tipped over?

It is, but Julius, this surely can't be right because the distance is...

This is so.

This is the path of least distance, and this is the path of least time.

Now I'll tell you the history of this problem.

Bernoulli posed it in the middle of the summer, and he gave until Christmas for a solution.

See, half a year he gave the mathematicians.

Promptly he received a letter from Leibniz, Gottfried Wilhelm Leibniz.

I have cut the knot of that beautiful problem and

then Leibniz suggested to Bernoulli

extend the time for a year from Christmas so as So

that the French

and Italian mathematicians have no reason to complain of the shortness

of the period You see Leibniz with his German intellectual arrogance felt that the French and Italian mathematicians were boys

So Bernoulli extended the problem for another year

Now it came the turn of the new year And Bernoulli received a solution in the mail

No signature attached But Bernoulli recognized the writing He said in this way Tanguam ex ungue leonum How's your Latin?

Not very good Just as the lion is known by its claw The solution had come from Newton

Have we heard from Newton before?

We have indeed So Newton solved the problem in a manner unbelievably shrewd.

Now, this quick solution by Newton angered Leibniz.

You see, a man does the problem too quickly.

So Leibniz posed another problem.

For the purpose, he said, of testing the pulse of the English analysts.

Now, there was only one English analyst that Leibniz had to worry about, and that was Newton.

Now, Newton received word of the problem in a letter

on his return home from his job as a clerk at the Mint.

Notice I've learned to say that, clerk.

In Yankee country, we say clerk, you know.

And after supper, Newton solved the problem recreationally.

Do you see the contest now that must exist between Leibniz and Newton?

But I want to show you more about this curve.

This curve, which is now the shortest possible time from A to B,

is called a brachistochrone.

Now, if you had some Greek, I would tell you that brachistos means shortest and chronos means time.

You see how beautiful the Greek is?

That's why I have suggested the return of Latin and Greek to the public schools.

See, brachistochrone.

Now, this brachistochrone, which is this path here, has astonishing properties, more than I've yet narrated.

And what are they?

Let me draw the curve bigger still.

A, B.

Watch it.

There's the curve.

Now, if I put a bead here and let it slide on this wire, it gets from A to B in a certain time.

Huh?

Certain time.

Supposing I start the bead right here instead of at A, supposing I started at C, it takes the same time to go from here as from here.

Supposing I started at D.

It takes the same time to go from here as from here as from here.

Isn't this beyond belief?

It is indeed.

Indeed, let me start it right here.

It takes the same time from here to here as from here to here as from here to here.

Is not that beyond...

That is astonishing.

Of course it is.

And there lies the beauty of the point on the rolling wheel.

Are you agreed that there is some drama in this history?

And I know I've probably risked a certain amount here by asking, how is this used?

Oh, oh, the cycloid.

The cycloid has astonishing properties in the making, say, of gears and how they mesh and lots of things.

You don't really care.

100

I don't care.

101

I don't care.

102

All I am interested in is the beauty and the drama and the elegance of this intellectual gymnastic, which Bernoulli gave rise to in the problem.

103

Mm, yes.

104

Isn't it something?

105

Do you see now a little kid gets hold of this, and he needs to learn the mathematics to do this, which is at the highest flight.

106

One needs what is called the calculus of variations.

107

But I've spent enough on Bernoulli, on Leibniz, on Newton, on the Brachistochrone, Brachistos Kronos.

108

And the most fascinating story.

109

But now what about these problems you gave to people at home to worry about?

110

Last time.

111

The two eggs, one of them bad.

112

No, we have an assemblage of eggs in the refrigerator.

113

In some, we speculate are good, in some, we fear are bad.

114

We wish to, what shall we say?

115

Distinguish them.

116

Yes.

117

So we put them in a great tank of water, in some float, in some sink.

118

You remember the little conundrum now?

119

Which is it that sink and which float?

120

You remember the old lady who threw them all out in despair?

121

I should not really tell you this, but which ones do you think float?

122

I think probably the bad ones.

123

Oh, you have passed the course again with some hope.

124

The bad ones float.

125

Now, why it is so, we do not explore.

126

See, we're just giving the answer to make those who wish to know happy inside.

127

I told you what Marcus Aurelia said, you know at the turn of the Christian era All wish to know but few the price will pay

128

This is the disease in the world All right, so the eggs now what happens first you remember that one we had a flask

129

Filled with water Which is at a certain level?

130

Oh, I guess we better look at it here on the table Yeah, a round bottom flask the water is at a certain level and what did I ask you?

131

I put this flask in a great vat of hot water, right?

132

A great flask of hot water.

133

And what does the water level in the tube do?

134

Remember, I'm asking you, what is seen to happen first?

135

And you whispered a solution last time, which I was emboldened to say was...

136

Wrong.

137

Yes.

138

You said, it goes up.

139

Why do I raise this question?

140

Have I not said to you that few, many look, but few see?

141

Indeed, when this is put into a vat of hot water, the first thing one observes is that the level goes down.

142

Indeed, this is what thermometers do.

143

Consider this a mercury in glass thermometer.

144

It reads the room temperature here.

145

I now put it into a glass of hot tea, a cup of hot tea.

146

What does the mercury first do?

147

Wouldn't you say again that it goes up?

148

I wouldn't say.

149

No, it does not go up.

150

It goes down.

151

But why is it so?

152

Oh, you wish to know, but you do not wish to pay the price.

153

Supposing we just leave it at that.

154

I have given you the answer.

155

Why is it so?

156

It's enough for me to work it out.

157

Right, right, right.

158

What happens first?

159

Remember, it goes down first.

160

The double bubble, remember?

161

Oh, this is a beaut.

162

We had a T-tube.

163

A T-tube with two funnels, so.

164

And a tube here, which permits me to blow some air into.

165

And then I blew up two bubbles.

166

I blew a small bubble and I blew a big bubble.

167

And then I shut off the connection with the outside air so that the bubbles are connected with each other, but not with the outside air.

168

Question, what now ensues?

169

What do the bubbles do?

170

What happens?

171

I think my answer was that they equalize.

172

Right.

173

Everybody says they equalize.

174

An astonishing thing takes place.

175

they don't equalize.

176

Watch.

177

We will discover, incredible isn't it, Sanders, that the small one gets smaller.

178

Come.

179

Oh, this is really enchanting.

180

Watch it.

181

Watch.

182

Do I have a small one here?

183

Yes.

184

And a big one there.

185

Now let us watch them closely.

186

And if there's, oh, Oh, we had a little trouble.

187

Some blow in the studio, I fear, is going to mess me up.

188

Watch it now.

189

I've shut off this tube.

190

Watch the small one.

191

Just watch the small one.

192

We have a frightful blow in the studio, but do you see the small one getting smaller?

193

Do you see it, Sanders, getting smaller?

194

Tell me, do you see it?

195

It is.

196

Good.

197

And notice another fantastic thing, that the smaller it gets, the faster it gets smaller.

198

Watch it.

199

Watch it now, watch it.

200

I'll try it once more.

201

Watch it now, watch it.

202

Do you see it getting smaller, Sanders?

203

And notice, the smaller it gets, the faster it gets smaller.

204

Isn't that fantastic?

205

Presumably, this one is getting bigger.

206

Yes, but it's so large already that any change in it is hard to see.

207

Yes.

208

The calculus would tell you that.

209

But I want to do it once more for another reason.

210

What do I wish to point out here?

211

I want you to make the observation that I would point out myself.

212

What are you observing that should be observed?

213

Is there anything I can think of as the colors?

214

Now you have come to it, young man.

215

Another hope to pass the course.

216

Notice the pretty colors in thin films.

217

We have some blow in the studio.

218

You remember, Newton first observed these colors in white light.

219

You know what he said?

220

In the year 1665 I procured me a triangular glass prism with

221

which to try the celebrated phenomena of colors

222

So he cut now a slot in his window shut You know

223

and he let the sunlight in and then he saw her on yonder wall red orange yellow green blue and violet

224

And you know how he appraised that

225

the most remarkable observation in all of his lifetime and regarding nature What did he say?

226

The oddest, if not the most profound, in all the operations of nature.

227

Imagine looking at white light.

228

Red, orange, yellow, green, blue, and violet.

229

Isn't that staggering?

230

So, the double bubble paradox.

231

Now, free fall and horizontal projection.

232

Oh, this one is enchanting too.

233

You remember what we did.

234

We had an apparatus.

235

Two ping pong balls.

236

Two ping pong balls.

237

One was released to fall so, and the other was projected so as to take that path, right?

238

Right.

239

And you are of the view that why this is a longer way to go and should take longer.

240

But Galileo disposed of that, so you see, you should have been a student of Galileo's and done better with the problem.

241

Why is it so?

242

Well, I'll simply suggest the line of thinking and let the viewers handle it for themselves.

243

The instant this is released, gravitational forces take it down.

244

So in a certain length of time it has fallen so from here to here.

245

Now the horizontal motion that this one has makes no contribution to the vertical motion.

246

So after the same elapse of time, gravity has taken this one down to the same place, but clearly its horizontal motion has brought it to here.

247

So isn't it in the same horizontal plane?

248

And so it is always in the same horizontal plane.

249

Now Galileo did this beautifully, you see, in the 16th century.

250

Do you see how far behind you are?

251

No, 500, yes.

252

400, see?

253

All right.

254

Now, finally, the holes in the metal plate.

255

I like to show it like this.

256

I have a metal plate.

257

I'll hold it in hand in a minute.

258

And I have a teeny weensy hole.

259

Notice, ever so tiny.

260

Let's go look at the plates.

261

Teeny weensy hole.

262

You know how much time we have.

263

You know how that plates make.

264

Don't worry about it yet.

265

Yeah, notice.

266

A plate with a hole.

267

This happens to be a round plate with a round hole.

268

But this happens to be a square plate with also a tiny hole.

269

Right?

270

Are we agreeing?

271

Yes, yes.

272

Question.

273

I heat the plates uniformly.

274

Could I not do that by putting them in an oven?

275

Is not the question, what happens to the holes?

276

Now, what's your view of it?

277

My view would be that the holes would shrink.

278

shrink

279

that is close up get smaller you know yes notice all

280

the virtue you demonstrated earlier is now taken away is gone

281

the holes get bigger now let me give you an argument to help you do you remember this ring

282

which does not allow the ball to pass and then we agree that

283

if we heat the ring the ball then does pass yes as a point of departure for your thinking this ring

284

is nothing but a plate with a big hole.

285

I would say it's a plate, mostly hole.

286

And holes in metal plates behave exactly as they would if they were not holes, but filled with the stuff which is not there.

287

How do you like that?

288

That's strange.

289

It's a good sentence.

290

The hole gets bigger.

291

Wouldn't the plate get bigger if there was no hole in it?

292

So this is a plate with a big hole.

293

This happens to be a plate with a small hole.

294

and generically then, all holes in plates get bigger when the plates are heated.

295

I'm wrong too often.

296

Oh, right.

297

Do you see, are not these old-fashioned primitive things quite enchanting to engage in?

298

Yeah.

299

Sure.

300

Now, where do we go?

301

Well...

302

Oh, yes.

303

The beauty of the pendula.

304

The beauty of the pendula.

305

Here again, some motion explored by Galileo.

306

I want you to see what we have here.

307

Do you see?

308

I have three simple pendula.

309

Singular pendulum.

310

And this case, this calls for A in the plural.

311

Three pendula.

312

Notice a short one, a longer one, and a longer one still.

313

Do you want to put this up on the...

314

Oh, put this up here. So, good.

315

Yes.

316

Some of these.

317

Requirements for the camera escape my mind.

318

And that's what you are here for, to remind me.

319

You know I'm old and senile and forget quickly.

320

So, what am I going to do with these?

321

I am going to make an adventure

322

that should make us feel jointly as Kepler felt after 26

323

years of labor in looking at the pages of data which Tycho Brahe had gathered.

324

You know that story?

325

None.

326

Copernicus.

327

Copernicus and his manuscript, De revolutionibus orbium celestium, which revolutionized the thinking about the world,

328

and then the data which Tycho Brahe gathered over 30 years, with which he could do nothing because he was a very good observer, but a poor mathematician.

329

And along came Kepler, who spent 26 years looking at 10,000 pages of numbers, and from it got Kepler's laws of motion with which the world goes round.

330

So I'm going to be with Kepler.

331

Watch me.

332

Come.

333

Come here.

334

Here is the support.

335

And here is a pendulum.

336

And here is another pendulum.

337

And here is another one.

338

And I have made this one 10 centimeters long.

339

And I have made this one 40 centimeters long.

340

And I have made this one 90 centimeters long.

341

Notice the numbers.

342

10, 40, 90.

343

Now I start this one swinging.

344

And I clock so many swings.

345

supposing with a stop clock I count the time required for

346

20 swings the length of the bobs are 10 40

347

and 90 centimeters right now the time I will say for 20 vibrations T sub 20 I could count 15

348

or I could count 41 11 doesn't matter the time for

349

20 vibrations of this one in my laboratory now I knows how I said

350

that in in my home I say laboratory

351

and I tell my students look much labor and little oratory you like

352

that all right now the time for 20 vibrations is as follows in my home 13 seconds 26 seconds

353

and 39 seconds do you see anything beautiful and pretty about those numbers?

354

Well, 13 added to 13, 26 added to 13, 26, 39.

355

Yes, you've got a feel for it.

356

Here is what is uncovered.

357

These numbers are in the ratio, dividing all by 10, in the ratio of 1 to 4 to 9.

358

Correct?

359

These numbers, I hope you see are in the ratio of 1 to 2 to 3.

360

And now do you see any relation between this number and that one, and this one and that one, and this one and that one?

361

Yes.

362

1 is the square root of 1, 2 is the square root of 4, and 3 is the square root of 9.

363

So it looks as if the time of oscillation or the times, which for one oscillation we call the period,

364

is proportional to the square root of the length.

365

And here we have uncovered in a beautiful Keplerian fashion how the period of a pendulum is governed by its length.

366

Now, there's some more stuff in there.

367

When the mathematics is done, it comes out like this.

368

And for those who know a little physics, I remind them that this and this comes out of mathematics.

369

So, what is my suggestion?

370

I put this on the board, and I put this on the board and I let it stand

371

and some little fellow who has the hope of Faraday suddenly sees the light of this

372

and he certainly must feel as Kepler felt after 26 years

373

uncovering the mystery of the behavior of the world one more remark suppose

374

and I took any other length at random see 10 40 90 centim suppose I took 176 centimeters

375

or 1132 centimeters would not the time here bear the same ratio to

376

that number as this does to that and so on which I invite a young observer to pursue.

377

Isn't this beautiful?

378

It's fascinating.

379

Sure it is fascinating.

380

This is the word that we must have always.

381

Dramatic.

382

Alright.

383

Where are we going now?

384

We are going now to explore why a lariat works.

385

You know, the Texas...

386

Do you have it here in Australia?

387

Not to use very much, except trick...

388

Oh, no. Well, all right.

389

Why do they work?

390

Well, I'm going to show you why they work.

391

I have a disc, mounted with a.. fixed with a string, and a little.. a little screw I here.

392

And I'm going to fix this screw I...

393

Hold that in there, will you, for me?

394

Thank you.

395

I'm going to fix that into the chuck of this rotator.

396

Uh-oh.

397

Uh-oh.

398

Get there. That.

399

Thank you.

400

I'm going to get it in there.

401

And now what am I going to do?

402

Is it not really some mystery here?

403

How am I going to show how a lariat works with this rig?

404

But do you see how primitive my apparatus?

405

Now watch what I'm going to do.

406

I'm going to turn the crank of this

407

of this egg beater drill and this thing is turning about an axis for

408

which we say the moment of inertia is so much and now watch what the disc does.

409

What do you think the disc will do?

410

What do you think it'll do?

411

It seems to be speeding up.

412

Yes Now we're having a little trouble I'm having a little trouble now.

413

Do you see?

414

There we are I had a little trouble what happened to the disc

415

Did it not come up to rotation in a horizontal plane could I use an American expression that flipped its lid?

416

Yes, yes, yes, very good.

417

Do you see now?

418

You're going to say Julius How does that throw any light on how a lariat works?

419

Well, a word about it.

420

The rotation about this axis, this axis has a certain moment of inertia.

421

This disk has for this axis.

422

Now when it comes up like that, it has a different moment of inertia.

423

And we uncover a beautiful theorem in mechanics, which says that a system in stable rotation tends to rotation about an axis for

424

which the moment of inertia is a maximum.

425

That's a pretty heavy sentence.

426

Let me do it, however, with the chain.

427

How much time do we have?

428

Oh, about eight minutes or so.

429

Oh, do we?

430

All right, get that in there now.

431

And I'm going to show you a lariat.

432

There, I'm going to show you a lariat.

433

Watch it now.

434

There's a chain.

435

Do you see?

436

It hangs limp.

437

It's a closed loop.

438

Indeed, it's a lariat.

439

Watch me put it into a horizontal plane.

440

I have to do this gently.

441

Watch.

442

It's turning.

443

It's turning.

444

if I get impulsive with it, it will tangle up and not do what I want it to do.

445

Now, do you see it shaping up a little bit?

446

And there, oh, there we are.

447

Pretty nearly.

448

I'm in a little trouble.

449

Let me start again.

450

That was very clear.

451

Yes, but notice it's tangled and there we are.

452

Do you see that any impulsive behavior with nature, Nature will get angered and thwart you every time You must do exact...

453

There we are Isn't that better?

454

How do you like that?

455

That's tremendous Oh, yes Do you see?

456

What I have done is gone from a disc Indeed, if I did a hoop, it would do the same Indeed, if I did a stick,

457

it would do the same And from these simple things, you see I have advanced stealthily upon the case of the rope of the chain.

458

But if I try to do the problem of the chain first, it is too difficult.

459

So here is a line of endeavor for the human intellect.

460

When it attacks a problem, it must make things simple first.

461

Progressively.

462

As Einstein said, in the beginning, things must be made as simple as possible.

463

Einstein.

464

Now, if then we understand what these things do, I have a problem.

465

Here is a football.

466

That's a Yankee kind, isn't it?

467

We might imagine this football to be an ellipsoid of revolution.

468

You know, an ellipse which is spun on its long axis.

469

So when I spin this football like this, it is spinning about an axis for which the moment of inertia is so much.

470

Now watch what the football does.

471

Watch it.

472

Oh, what do you think it'll do?

473

Will it behave the same as the lariat?

474

Yeah.

475

Well, notice, this is the long axis now.

476

Yes.

477

Watch it.

478

Oh, I'll have to do it again.

479

Oh, no. Oh, oh.

480

Oh, oh.

481

Can I have it?

482

Here we are.

483

Yes.

484

Notice, notice one loses his professional dignity in these experiments.

485

There it is.

486

There it is.

487

It came up on end.

488

Notice, I'm so delighted with this, I'm going to do it again.

489

There it is!

490

There it is!

491

Do you see what it did?

492

First it was rotating about that axis.

493

Then it took rotation about that axis.

494

And this introduces a very serious problem for the physicist, the mathematician, and the student of nature.

495

Why does it do this?

496

Is it violating the theorem which I spoke of before?

497

Or is it not?

498

Suggestion, hint.

499

See, I hint only very little bit.

500

Man must agree with the principles of nature.

501

Hence, there is no violation here.

502

But where the dilemma lies, I leave for the observer.

503

Watch it.

504

There it is again.

505

Up again.

506

Now.

507

Professor, you have about three minutes, two minutes left, I think.

508

Two minutes.

509

Two minutes.

510

We will entitle this adventure The Case of the Notched Stick.

511

Let's get over here and see what an enjoyable exercise we can have with a stick.

512

Now, let me see how it looks on camera.

513

Good.

514

I have a stick, rectangular cross-section, which I have notched with a file.

515

You see?

516

Yes, yes.

517

And on the end of the stick, I have put a little propeller fixed with a little nail in the middle.

518

You see how it is?

519

Yes, yes.

520

Now, what am I going to do with this?

521

I'm going to lay this on the edge of the table, and with another stick which I call the stroker,

522

I am going to make that propeller behave in a manner unbelievable.

523

Watch.

524

Watch.

525

What do you see that propeller doing?

526

Spinning, I can't see much direction.

527

Oh, watch it now.

528

Watch it.

529

Right.

530

Watch it now.

531

Now, the other way.

532

Spinning clockwise.

533

Right.

534

Do you see that I can make this propeller go counterclockwise or clockwise as I please?

535

Watch it.

536

That's this way for me.

537

That's this way for me.

538

Is not this a delight?

539

Now this is a child's toy which every boy and girl in Australia who sees this program can make.

540

See?

541

When he gets into the university and has had five years of mathematics and five years of physics, he is in a position to explore it.

542

What I am saying, Sanders, is this.

543

The toys are designed for child's play, but when one inquires into why it is so, it is no longer child's play.

544

Indeed.

545

Thank you very much, Professor.

546

My pleasure.

547

And we have one more program.

548

One more in the series.

549

Thank you.

550

Thank you very much.

551

Thank you.

552

Thank you.

Что такое техника Shadowing?

Shadowing — это научно обоснованная техника изучения языка, изначально разработанная для подготовки профессиональных переводчиков и популяризированная полиглотом доктором Александром Аргуэльесом. Метод прост, но эффективен: вы слушаете аудио на английском от носителей языка и немедленно повторяете вслух — как тень, следующая за говорящим с задержкой в 1–2 секунды. В отличие от пассивного прослушивания или грамматических упражнений, Shadowing заставляет мозг и мышцы рта одновременно обрабатывать и воспроизводить реальные речевые паттерны. Исследования показывают, что это значительно улучшает точность произношения, интонацию, ритм, связную речь, понимание на слух и беглость речи — что делает его одним из самых эффективных методов для подготовки к IELTS Speaking и реального общения на английском.

Практика Shadowing: The Professor Who Taught People How To Think (1962) - Изучайте разговорный английский по видео

Что вы узнаете

Слушайте за этими звуками

Говорите как носитель

Что такое техника Shadowing?