Shadowing Practice: The Professor Who Taught People How To Think (1962) - Learn English Speaking with Video

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.

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I don't care.

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I don't care.

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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.

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Mm, yes.

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Isn't it something?

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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.

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One needs what is called the calculus of variations.

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

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And the most fascinating story.

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

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Last time.

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The two eggs, one of them bad.

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

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

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We wish to, what shall we say?

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Distinguish them.

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Yes.

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

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You remember the little conundrum now?

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Which is it that sink and which float?

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

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

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I think probably the bad ones.

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

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The bad ones float.

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

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

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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

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

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Filled with water Which is at a certain level?

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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?

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

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A great flask of hot water.

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And what does the water level in the tube do?

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

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

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Wrong.

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Yes.

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You said, it goes up.

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Why do I raise this question?

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

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

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Indeed, this is what thermometers do.

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Consider this a mercury in glass thermometer.

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It reads the room temperature here.

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

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What does the mercury first do?

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Wouldn't you say again that it goes up?

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I wouldn't say.

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No, it does not go up.

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It goes down.

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But why is it so?

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

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Supposing we just leave it at that.

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I have given you the answer.

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Why is it so?

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It's enough for me to work it out.

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Right, right, right.

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What happens first?

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Remember, it goes down first.

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The double bubble, remember?

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Oh, this is a beaut.

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We had a T-tube.

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A T-tube with two funnels, so.

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

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And then I blew up two bubbles.

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

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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.

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Question, what now ensues?

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What do the bubbles do?

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What happens?

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I think my answer was that they equalize.

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Right.

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Everybody says they equalize.

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An astonishing thing takes place.

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they don't equalize.

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Watch.

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

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Come.

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Oh, this is really enchanting.

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Watch it.

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Watch.

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Do I have a small one here?

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Yes.

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And a big one there.

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Now let us watch them closely.

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

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

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Watch it now.

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I've shut off this tube.

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Watch the small one.

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Just watch the small one.

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

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Do you see it, Sanders, getting smaller?

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Tell me, do you see it?

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It is.

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Good.

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

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Watch it.

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Watch it now, watch it.

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I'll try it once more.

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Watch it now, watch it.

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Do you see it getting smaller, Sanders?

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

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Isn't that fantastic?

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Presumably, this one is getting bigger.

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

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Yes.

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The calculus would tell you that.

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

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What do I wish to point out here?

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

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What are you observing that should be observed?

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Is there anything I can think of as the colors?

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Now you have come to it, young man.

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Another hope to pass the course.

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Notice the pretty colors in thin films.

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We have some blow in the studio.

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

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You know what he said?

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

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which to try the celebrated phenomena of colors

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

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

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And you know how he appraised that

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

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

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Imagine looking at white light.

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

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Isn't that staggering?

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So, the double bubble paradox.

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Now, free fall and horizontal projection.

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Oh, this one is enchanting too.

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You remember what we did.

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We had an apparatus.

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Two ping pong balls.

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Two ping pong balls.

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

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Right.

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

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

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Why is it so?

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

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

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

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

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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.

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So isn't it in the same horizontal plane?

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And so it is always in the same horizontal plane.

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

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Do you see how far behind you are?

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No, 500, yes.

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400, see?

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All right.

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Now, finally, the holes in the metal plate.

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I like to show it like this.

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I have a metal plate.

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I'll hold it in hand in a minute.

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And I have a teeny weensy hole.

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Notice, ever so tiny.

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Let's go look at the plates.

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Teeny weensy hole.

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You know how much time we have.

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You know how that plates make.

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Don't worry about it yet.

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Yeah, notice.

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A plate with a hole.

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

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

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Right?

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Are we agreeing?

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Yes, yes.

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Question.

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I heat the plates uniformly.

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

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Is not the question, what happens to the holes?

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Now, what's your view of it?

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My view would be that the holes would shrink.

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shrink

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that is close up get smaller you know yes notice all

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the virtue you demonstrated earlier is now taken away is gone

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

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

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

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is nothing but a plate with a big hole.

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

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

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How do you like that?

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That's strange.

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It's a good sentence.

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The hole gets bigger.

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

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So this is a plate with a big hole.

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This happens to be a plate with a small hole.

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

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I'm wrong too often.

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Oh, right.

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

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Yeah.

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Sure.

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Now, where do we go?

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Well...

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Oh, yes.

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The beauty of the pendula.

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The beauty of the pendula.

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Here again, some motion explored by Galileo.

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I want you to see what we have here.

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Do you see?

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I have three simple pendula.

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Singular pendulum.

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

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Three pendula.

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

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

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Oh, put this up here. So, good.

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Yes.

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Some of these.

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Requirements for the camera escape my mind.

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

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

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So, what am I going to do with these?

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I am going to make an adventure

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that should make us feel jointly as Kepler felt after 26

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

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You know that story?

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None.

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Copernicus.

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

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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.

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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.

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So I'm going to be with Kepler.

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Watch me.

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Come.

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Come here.

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Here is the support.

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And here is a pendulum.

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And here is another pendulum.

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And here is another one.

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And I have made this one 10 centimeters long.

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And I have made this one 40 centimeters long.

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And I have made this one 90 centimeters long.

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Notice the numbers.

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10, 40, 90.

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Now I start this one swinging.

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And I clock so many swings.

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supposing with a stop clock I count the time required for

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20 swings the length of the bobs are 10 40

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

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

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

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that in in my home I say laboratory

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

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

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

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

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Yes, you've got a feel for it.

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Here is what is uncovered.

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

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Correct?

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

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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?

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Yes.

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

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

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is proportional to the square root of the length.

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

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Now, there's some more stuff in there.

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

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

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So, what is my suggestion?

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

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

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and he certainly must feel as Kepler felt after 26 years

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

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

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

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

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Isn't this beautiful?

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It's fascinating.

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Sure it is fascinating.

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This is the word that we must have always.

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Dramatic.

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Alright.

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Where are we going now?

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We are going now to explore why a lariat works.

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You know, the Texas...

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Do you have it here in Australia?

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Not to use very much, except trick...

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Oh, no. Well, all right.

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Why do they work?

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

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

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

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Hold that in there, will you, for me?

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Thank you.

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

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Uh-oh.

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Uh-oh.

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Get there. That.

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Thank you.

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I'm going to get it in there.

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And now what am I going to do?

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Is it not really some mystery here?

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

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But do you see how primitive my apparatus?

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Now watch what I'm going to do.

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I'm going to turn the crank of this

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

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

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What do you think the disc will do?

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What do you think it'll do?

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It seems to be speeding up.

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

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Do you see?

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

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

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Yes, yes, yes, very good.

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Do you see now?

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

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Well, a word about it.

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

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This disk has for this axis.

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

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

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which the moment of inertia is a maximum.

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That's a pretty heavy sentence.

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Let me do it, however, with the chain.

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How much time do we have?

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Oh, about eight minutes or so.

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Oh, do we?

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All right, get that in there now.

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And I'm going to show you a lariat.

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

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Watch it now.

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There's a chain.

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Do you see?

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It hangs limp.

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It's a closed loop.

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Indeed, it's a lariat.

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Watch me put it into a horizontal plane.

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I have to do this gently.

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Watch.

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It's turning.

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It's turning.

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

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

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And there, oh, there we are.

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Pretty nearly.

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I'm in a little trouble.

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Let me start again.

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That was very clear.

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

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

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There we are Isn't that better?

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How do you like that?

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That's tremendous Oh, yes Do you see?

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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,

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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.

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

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

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

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Progressively.

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

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Einstein.

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

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Here is a football.

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

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

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

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

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Now watch what the football does.

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Watch it.

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Oh, what do you think it'll do?

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Will it behave the same as the lariat?

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Yeah.

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Well, notice, this is the long axis now.

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Yes.

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Watch it.

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Oh, I'll have to do it again.

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Oh, no. Oh, oh.

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Oh, oh.

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Can I have it?

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Here we are.

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Yes.

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

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There it is.

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There it is.

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It came up on end.

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

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There it is!

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There it is!

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Do you see what it did?

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First it was rotating about that axis.

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Then it took rotation about that axis.

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

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Why does it do this?

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Is it violating the theorem which I spoke of before?

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Or is it not?

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Suggestion, hint.

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See, I hint only very little bit.

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Man must agree with the principles of nature.

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Hence, there is no violation here.

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

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Watch it.

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There it is again.

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Up again.

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Now.

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

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Two minutes.

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Two minutes.

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

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

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Now, let me see how it looks on camera.

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Good.

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

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You see?

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Yes, yes.

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

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You see how it is?

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Yes, yes.

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Now, what am I going to do with this?

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

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

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Watch.

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Watch.

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What do you see that propeller doing?

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Spinning, I can't see much direction.

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Oh, watch it now.

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Watch it.

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Right.

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Watch it now.

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Now, the other way.

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Spinning clockwise.

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Right.

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

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Watch it.

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That's this way for me.

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That's this way for me.

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Is not this a delight?

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

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See?

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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.

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What I am saying, Sanders, is this.

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

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Indeed.

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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.

What is the Shadowing Technique?

Shadowing is a science-backed language learning technique originally developed for professional interpreter training and popularized by polyglot Dr. Alexander Arguelles. The method is simple but powerful: you listen to native English audio and immediately repeat it out loud — like a shadow following the speaker with just a 1–2 second delay. Unlike passive listening or grammar drills, shadowing forces your brain and mouth muscles to simultaneously process and reproduce real speech patterns. Research shows it significantly improves pronunciation accuracy, intonation, rhythm, connected speech, listening comprehension, and speaking fluency — making it one of the most effective methods for IELTS Speaking preparation and real-world English communication.

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What is the Shadowing Technique?