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  • From a recent trip to Japan, my home country, I brought back a little present.

  • It's a traditional toy. A Japanese toy called "Kamifusen", which means paper balloon.

  • [robot pumping air]

  • And as you can see, it's a balloon made of paper, and there's a hole in there, yeah?

  • So the way you inflate this paper balloon, when you squash it, is to blow into this hole...

  • [Tadashi blowing up balloon]

  • And make it rounder. Okay, but there is another way to make it rounder.

  • [balloon crinkles]

  • You can squash it, and then you can start tossing it around.

  • [Tadashi hitting balloon]

  • You hit it from all sides at random... oops!

  • Now, when you hit something, don't you have the impression that you are denting it and therefore making

  • it less and less round and you're denting it, right, from both sides?

  • But look at what's happening as I toss it and hit it from all sides. I'm doing it completely randomly.

  • You can hit it quite hard.

  • [Tadashi hitting balloon]

  • What was shriveled to a little crumple

  • is now getting rounder and rounder

  • and becoming more and more spherical.

  • And look! I ended up with a round sphere.

  • So, this is a really strange way of making something round by denting it repeatedly from all sides.

  • How does this trick work?

  • I think the key to this behavior,

  • which all Japanese children know instinctively, is really in the following behavior of the balloon. When I

  • shrivel it to a little crumple,

  • watch what happens when I release it.

  • You see, it starts fighting its way back...

  • ...at least initially. It doesn't inflate all the way back of course, but it has some memory.

  • And it wants to come back to where it started. It fights its way back as I said.

  • [Brady] Why is it even doing that? What's causing that?

  • That's... that's an interesting question. Um, I have to think about this.

  • [laughter] Okay.

  • So let's imagine the following toy model. Let's say that you have a state of this balloon, which is

  • crumpled on both sides: on the left as well as on the right,

  • and I'm going to strike this balloon at this moment.

  • Pafff!

  • From the left, let's say. What happens,

  • to a good approximation,

  • I think, is that the side that you hit gets over crumpled because I just hit it.

  • You know, you introduce a lot of crumples.

  • But the other side gets puffed out literally because there is this force which

  • Pushes it rightward. But, you see, then something interesting happens.

  • That "fighting back" effect means that the left side which was over crumpled,

  • starts fighting back, so it starts expanding to roughly the

  • degree of wrinkliness that it had in the beginning, whereas the right hand side stays puffed out.

  • So, per this cycle, you see, what happened is that

  • I increase the overall smoothness a little bit. The other side which got puffed out, whereas this side that I over wrinkled

  • fought back by itself. So, if you keep hitting it from all sides gradually you are making the thing rounder and rounder.

  • So let's plot the evolution of the volume against time, and let's say in time

  • I'm hitting the balloon at various regular intervals. It doesn't have to be regular intervals.

  • Okay. So the volume of the balloon starts like this and

  • as soon as I hit it, of course,

  • instantaneously, I suddenly decrease the volume. I just shrivel it. So, a hit

  • gives you this dip. But then, the thing fights back.

  • Yeah? This is the fight back. And then the next hit will decrease the volume.

  • And then it will fight back, fight back and so on, and gradually it asymptotes,

  • or it approaches this spherical shape

  • from below like this. So it never becomes completely spherical, but it grows like that. So I think there is a process of

  • "grow, shrink, grow, shrink, grow, shrink, zig, zag, zig, zag" and then goes back then. That's why you can do this strange thing of

  • hitting it, or denting it, repeatedly, and yet the result outcome is that it becomes rounder and rounder.

  • Okay, this will probably take a long time.

From a recent trip to Japan, my home country, I brought back a little present.

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風船を膨らませる意外な方法 - Numberphile (An unexpected way to inflate a balloon - Numberphile)

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    林宜悉 に公開 2021 年 01 月 14 日
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