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[Music] hey i read somewhere that mathematicians can turn a sphere inside out yes thats true whats the big deal just poke a hole in it and pull it through sure but the point is to do it without making a hole but then it seems impossible youre right you cannot do it with an ordinary sphere like a basketball you have to understand the rules of the game this sphere is made of an abstract elastic material that can stretch and bend and pass through itself but you cannot rip or puncture this material without destroying it and you cannot crease it or bend it sharply if the surface can pass through itself whats the problem do you think allowing self intersections makes it easy try it ill push the two halves right through each other [Music] be careful what about that ring around the equator remember you mustnt tear or crease it ah let me try again thats no good either youre pinching it infinitely tight but then theres no way its impossible youd have to crease or pinch it to turn it i