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I've just seen the wonderfully done movie Sphere Inside Out, one about the Smale's paradox.

And the first question came in mind is that, why it has to be so ugly? Why turning an ultimately simple sphere inside-out is so complicated? Although this movie has demonstrated in so many view points and a variety of ways, I still cannot fully accept this truth in my mind. What's the critical point in this whole pack of steps, what exactly did Smale find to solve this problem? And are there other methods that is also easy to understand?

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