字幕表 動画を再生する 英語字幕をプリント You can try many many other variations depending on where to put the rubber bands, and also using more paperclips. Let me show you one or two examples. We have tried the position No. 1 or position No. 2, but one position that we have never tried- This is quite interesting, rubber band in the middle, and it has to stay on the paper and you can put the paperclips and see what happens. Rubber band now in the middle here and paperclips at the top. So, now what's going to happen when I pull... This is what happens. So rubber band is hanging from the paper but it's ok. but those 2 paperclips got linked against each other, but each one of them is linked with the rubber band. So, they're all 3, if you like 3 circles meeting in the middle and any 2 of them being linked. - [Not Borromean?] - It's not Borromean, because... even if I make, for example, the rubber band disappear the 2 paperclips are still linked, and so on... You can probably guess at this stage, what's going to happen if I put the rubber band in the same position that one paperclip at the top, but the other paperclip at the bottom, so paperclips are on the wrong side of each other. So, now what's going to happen when I pull... Do you have a guess? Interesting, let's try this. That's interesting, it looks like the previous one. But this time, each paperclips is linked to the rubber band, but not between themselves. Let's finish with something that is 'work in progress'. So far, we have been linking paperclips together, and sometimes we refer this as "addition". I mean those 2 paperclips coming together, so it's like adding. What about subtracting? By which I mean, can we start from 2 paperclips that are linked already and slotting them in some configuration on the bent paper, Can you take them apart? Now, I've tried many many different possibilities, and it turns out that this time the orientation matters. You know, you can link paperclips in many many different ways. For example, you can link them here, or you can link them, for example, here, or you can link them here, and so on. So the position matters, and also, you know, you can link them like this, or you can turn the paperclip around and you can link them like this. It's very very confusing. So, let's try to link them here, and see how we fare. It turns out that this kind of link will end up tearing the paper, and it just distorting the paperclips and it ends up in disaster, or so I think, because, you see, I haven't done many times so... I have to be very careful each time. But if I change the orientation of the paperclips, and put them in this configuration, that's the right configuration. You may not see much of a difference, but the key is how those are linked at the top. Let's do it very very carefully. Those 2 paperclips are already linked. I bend the paper in that standard position, but I slot the paperclip here and here, by allowing this linked pair to straddle over the paper like so, here and here like this, okay. And then I slot them very carefully. And here is the preparation; paperclips were linked. Now I pull the ends, and... hopefully this works, if it doesn't, we'll be very sad, and something... some disaster happens. OK let's see, will it be able to do it? They came apart, so we can now subtract. - [You like that, don't you?] - Yeah, yeah, yeah that's very nice. Because you can make them come apart, yeah, yeah... [from Part One]: —computation, or calculation in general. We always think naturally, because that's how we learn these things in school and about numbers - calculating with numbers - or, perhaps, at a more advanced level calculating with formulas. And, you know, you do some algorithm, you do some recipe, and then the expected results come out. But here, your brain, although it hasn't formalized anything, - you know, it hasn't written any numbers or formulas - has, effectively, computed.