Name: 令人費解的回形針 - Numberphile(數字愛好者) (Perplexing Paperclips - Numberphile)
Uploaded: 2021-01-14T10:15:18.000Z
Duration: 17 min 9 s
Description: 【看影片學英語】數萬部 YouTube 影片，搭配英漢字典即點即查，輕鬆掌握單字發音與用法，長久累積看電影不必再看字幕。

TADASHI TOKIEDA: A strip of paper, a paper ribbon, and two ordinary paper clips.

We bend the paper strip in a Z or S shape, like so.

分詞構句

And, with the help of the paper clips, we shall fix that shape

by slotting the paper clips here and here.

Now, what happens if I start pulling the ends of the paper?

Well, you can see that the paper clips come closer and closer together,

because they are being driven by the paper.

So, if I keep pulling, eventually they'll touch and jam,

they're linked. That's quite interesting.

What we have just done is with two paper clips only, and this what we shall call 'version number zero'.

This is just the beginning. The trick goes back quite a long way;

according to Martin Gardner's Encyclopedia of Impromptu Magic,

this seems to have been discovered by somebody called Bowman in Washington State.

So, we fix the shape of the bending paper like so.

But this time we added a rubber band. You see, the paper has two loops here and here,

and, seeing from your side, we're hanging the rubber band on the left loop.

This is version number 1. Version number 1, then, hanging over here.

What happens? This time what happens is this.

You have the rubber band hanging from the paper ribbon;

underneath clip-clip together from the rubber band.

We have this kind of half-chain—and you will see in a moment why we call it 'half-chain'—

In science, you have to exercise your power of imagination and observation, especially.

You know, you can't just take something and say "Oh, this is not going to matter",

and then reject little differences of innocuous appearance.

Maybe you have to pay a lot of attention to such little differences.

To illustrate that point, let's do something that looks like version number 1,

which we have just tried, but isn't quite.

Number 1 that we have just tried looked like this

The rubber band was hanging from the left loop of those two loops.

The rubber band is now hanging from the right loop instead of left loop,

and that's what we shall call 'version number 2'.

You see, before it was hanging here, and now it's hanging here.

What's going to happen if I pull the ends of the paper?

Well, you know, somebody not observant might say "Well, what's the difference?

Here, here, well, probably doesn't matter."

But you remember that version number 1 ended up having the rubber band hanging from the paper ribbon,

with two paper clips hanging from the rubber band.

This time—version number 2—whole thing falls off the paper ribbon,

so that's different. Nonetheless, when you pick it up,

you still get this clip-clip-rubber band, this half-chain together.

So, in the case of version number 1, we had this,

and, version number 2, this got detached.

Having tried version number 1 and version number 2,

it becomes tempting, indeed irresistible,

to try both at the same time, what is 1+2.

Well, it's very lucky that I have another rubber band here.

I think, and I'm sure you think too, 1+2 should look like this.

You see, because by itself, this rubber band is in the position of version number 1.

This one, by itself, is in the position of version number 2,

so 1+2 should be like this; it's doing 1 and 2 at the same time.

So, the question is what happens if I pull the ends of the paper.

What's going to happen to the two rubber bands this time, and the two paper clips?

Before we do that, however, let me debunk myself a little bit.

The fact that, in version number 1, the rubber band stayed on the paper

and—number 2—the rubber band fell off the paper,

is, in fact, no mystery; we can understand this.

You remember that version number 1 looked like this?

The rubber band was hanging from the paper on the left loop.

If you look carefully, you see that the paper strip goes through the rubber band

In other words, the rubber band is linked with the paper strip.

of course it stays linked, and it has no choice but to stay on the paper.

That is why, in version number 1, the rubber band stayed on the paper.

In contrast, version number 2 looked like this.

Over the two loops in the paper, it was hanging from the right loop.

If you look carefully, you see that the paper comes into the rubber band but goes back out.

So, the rubber band is, in fact, not linked to the paper.

When I pull the ends then, being unlinked, the band is free to fall.

That is why the rubber band can fall off the paper in version number 2.

So, the fact that the version number 1 stays on the paper, number 2 falls off the paper,

That's a purely topological thing that we can understand.

Let's go back then where we left off and try to do 1+2.

So, what's going to happen if we do 1 and 2 at the same time?

BRADY: They're all gonna to be linked, and on the paper.

TADASHI: Good. But, a bit more precisely—

TADASHI: Long chain. Rubber band-clip-clip-rubber band, in that kind of order?

Or, maybe two rubber bands get linked? Well, I do that only for money.

BRADY: I don't know, I picture— my guess is rubber band-paper clip-paper clip-rubber band.

TADASHI: Excellent, OK, so that's quite nice. By the way, it's always important to guess anyway,

because, you know, guessing is really the way to learn and, in fact, advance in science,

both for students and researchers alike, because if you guess right, you are very, very proud you got it right.

And if you guess wrong, you are really shocked; maybe not really, but slightly shocked,

and that engages your thinking, and you can learn what happened,

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令人費解的回形針 - Numberphile(數字愛好者) (Perplexing Paperclips - Numberphile)

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