Subtracting Paperclips - Numberphile

Key Takeaways

you can try many many other variations depending on where to put the rub bands and also using more paper clips let me show you one or two examples we have tried the position number one or position number two but one position that we have never tried this is quite interesting rub band in the middle and it has to stay on the paper and you can put uh paper clips and see what happens rub band now in the middle here and paper clips 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 bone that's okay but those two paper clips got linked against each other but each one of them is linked with the rubber band so there are all three if you like three circles are meeting in the middle and any two of them being linked not Bor it's not borium because even if I make for example the rubber band disappear the two paper clips are still linked and so on you can probably guess at this stage what's going to happen if I put the rub band in the same position but one paper clip at the top but the other paper clip at the bottom so paper Clips are on the wrong sides 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 paper clips is link to band but not between themselves let's finish with something that is work in progress so far we have been linking paper clips together and sometimes we refer to this as addition I mean you know two paper Clips coming together so it's like adding what about subtracting by which I mean can we start from two paper clips that are linked already and slotting them in some configuration on bent paper can you take them apart now I tried many many different possibilities and it turns out that this time the orientation matters you know you can link paper clips 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 paper clip around and you can link them right like this it's very very confusing so let's try to link them here and see how we Fair it turns out that this kind of link will end up tearing the paper and just distorting the paper clips and it ends up in disaster also I think because you see I haven't done this many times so I have to be very careful each time but if I change the orientation of the paper clips 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 two paper clips are already linked I bend the paper in that standard position but I slot the paper clip 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 paper clips 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 okay let's see will be able to do it they came apart so we can now subtract you like that don't you yeah yeah no that's very nice they come up you can make them come apart yeah yeah computation or calculation in general we always think naturally because that's how we learn these things in school um about numbers calculating with numbers or perhaps at the more advanced level calculating with the 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 he hasn't written any numbers or formulas has effectively computed