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  • Brady.

  • The title of this video is Tentacles, Kimbo.

  • Just because I've wanted to do something that sounds not mathematical but is glass blower Lucas Clark comes over to my house and says, Cliff, I made something and I can't understand it.

  • Then he shows me this.

  • It's to class tubes.

  • Hooked is a ring.

  • Yeah.

  • Are you trees, eyeglasses or you're treated as two rings linked together like this?

  • He says to me, This is two rings connecting, I say, Yeah, it's mathematically a to hold tourists, He says.

  • Okay, they reaches over, is their bag and he pulls out this.

  • They says, Isn't this the same thing?

  • And I said, Yeah, yeah, you've just taken this stretched it And so this is the same.

  • Is this still a to hold tourists with two holes in it?

  • Topology does not care about distance.

  • It doesn't care about size.

  • It says if you make it out of stretchy rubber.

  • OK, so he says, What if I I inflate the middle of this?

  • I'm good.

  • Just blow Aaron inflate.

  • This, they say, should make no difference in its properties.

  • So he pulls out this okay from here.

  • Thio here.

  • It still has 12 holes and connected here.

  • It would be called to hold tourists or could also be called handle body with two handles on it.

  • Okay, No problem.

  • So I'm looking at thinking about him.

  • He pulls up the next day, says I can take this handle regal and bring it over there.

  • And I say, Yeah, that should be no problem.

  • So he does.

  • So he goes, Look over to there.

  • So the next thing this glass blower doesn't say, what happens if I move this connection here, just carry it around over to there in this connection over here, there's a perfectly legal according to operations in topology, you could move the same.

  • Where you want is lying.

  • It's still connected.

  • So he says, I'm going to take that connection in this one.

  • Go OK like that.

  • Okay, so he does.

  • So he moved those two ears from being next to each other parallel to so that they're connecting like this.

  • Ah, Okay.

  • Yeah.

  • Illegal, safe.

  • Everything's legal.

  • No problem at all, he says.

  • Suppose I shrink this sphere part now?

  • Oh, that's easy.

  • I shrink it from that to this.

  • What have you done now?

  • So that becomes that and this one becomes this one here, hopes to have a big nose.

  • And so this fear part becomes this wide part here, where that new hole come from.

  • What new hole?

  • This new hole here.

  • Where is it from?

  • Hey, starts asked me, where is that from?

  • And then he goes one step further and fully shrinks that into this.

  • Uh, wait a second.

  • He's telling me that this can be transformed into this following ordinary rules of topology.

  • I'm looking at all this.

  • He's saying, Can you explain it?

  • And I'm saying will go back to this.

  • This is a lot like a human being.

  • It's like me standing with my arms like this.

  • There's a hole there in a hole there.

  • This is Kimbo here.

  • I am a Kimble, and this is the same as me with my fingers linked together like this.

  • Yeah, there's a hole here.

  • There's a hole here and there.

  • This space here that my head's waggling around in the same Is this space here, Right here is that space is the same as the space here.

  • Okay, Yeah, my fingers are like this.

  • And so I say, somehow this has been transformed to this, which is the total logically the same as going from Ah, Kimbo, two interlinked fingers.

  • So I'm sitting there and thinking ought to be able to go from here back to this.

  • And that night I'm in bed trying.

  • Go.

  • But you live like this.

  • The wife nudges me and says, Cut out, Cliff, go to sleep, all right.

  • And I keep going like this, waggling my fingers around.

  • It's not working right, and I'm saying, What's wrong with us?

  • And and and and and a couple days later, visitor comes by three visitors from Denmark.

  • People are often times coming over my house.

  • Check out topology and things, and I show this to them.

  • And these three grad students, I think from Denmark, came through and I showed this to him, and I said, I'll give you a client bottle if you could solve it.

  • They sit around thinking about it, talking about it.

  • Couple days later, they show me the answer and I'll show it to you know, I'm going to need a little bit of help.

  • I'm going to need a couple tentacles.

  • Can I go from one arm?

  • Kimbo, to this Well, I'll try it.

  • The way I'll do it is I'll put off put my finger here.

  • And I claim that going like this is the same top.

  • Logically is going like this.

  • This, this tentacle is to just give me a longer finger so I can go like this and round like this over here to my thumb, and then move my thumb along to this.

  • I got it.

  • Thanks to the wonderful miracle of tentacles, I can show that I can go from here to here.

  • Okay?

  • On my left hand, I could do the same thing, but the room with the blue got it with two hands.

  • I can go from here to here.

  • So this is a preserve.

  • You know, the number of holes.

  • One whole, one hole has been preserved.

  • So what about what about with two hands going to this?

  • I'll start with this and I'll start over here and this hand here.

  • I'll go around over to my nose.

  • Reagan, there's my nose.

  • I'll now take this finger over here and bring it to my shoulder like that.

  • I'll now read your own around this way.

  • See the end of this.

  • I have to keep this guy touching, but I could move around till it gets no thumb.

  • Get it like this.

  • See, I've done that.

  • Now I could move my fingers together.

  • They've got get rid of that.

  • I know.

  • Have this shape right here.

  • I've managed to bring my fingers around to enclose this one finger.

  • Similarly, having done that, I can't take this finger My left index finger around and around this way.

  • Spring like this or you wear like that.

  • No.

  • Is that cool or what?

  • In other words, I can transform from arms a Kimbo into interlinked fingers with the aid off a couple tentacles and by extrapolation, Aiken, do it.

  • If only I had longer fingers defied to longer fingers, I could do it entirely off which to me says Topol logically.

  • Oh, there's cool things you can do with tentacles.

  • A Kimble.

  • But wait, there's more freaky.

  • There's more.

  • Go.

  • Okay, First, I'll show the lemon.

  • If you start with your finger on your chest, you can extend to your thumb by falling a woman arm and this pointer finger can go all the way there in here, up here and connect right here with this sum to make this.

  • This is very what you have.

  • This We can extend this to just fingers just like the bone and get to this.

  • Then I'm buying 11.

  • I just showed you could go all the way off your arm to get this.

  • This can then be a flight on the other arm by falling your fingers all the way up and in connecting with your thumb, and then you have the desired result.

Brady.

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A2 初級

触手アキンボ(クリフ・ストールと) - Numberphile (Tentacles Akimbo (with Cliff Stoll) - Numberphile)

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    林宜悉 に公開 2021 年 01 月 14 日
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