Math: turning a sphere inside-out

Marcelo found the full video.

Update:
Philocalist said:
On the subject, several years ago, probably 10 years or more, I was doing a lot of reading and research about savants, specifically autistic savants, and some of the things these people could accomplish were absolutely mindbending: one little girl (before her third birthday!) was found and filmed riding her bicycle, unassisted.
Nothing much very strange about that, agreed ... apart from the fact that she was almost two metres off the ground, riding along the top of a fence less than an inch (2cms) wide, completely relaxed, totally balanced and in full control! Think about it ... HOW did she get up there (WITH her bike!) in the first place, let alone perform such a balancing act? The ride itself was later repeated in front of scientific investigators, at a much lower level, so is a matter of record, but there was never an explanation given for her appearance on top of the fence .....

However, my favourite bit ... as part of a carefully controlled observation / experiment (held in London, under laboratory conditions, in front of film cameras) several children were being 'observed' ... a mix of nationalities.
Several 'unusual' occurences were observed / recorded, though one little boy (of Iraqi descent) spent the entire time apparently very withdrawn, simply sat bouncing a tennis ball off the floor, onto a wall and then catching the rebound.
After the 'subjects' had left the area, the ball was found as the room was tidied up ... it was inside out!
Totally intact, without any puncture or damage, but inside out ... and this was attested to by both Dunlop (the manufacturer of the ball) and the scientists present ... it was all a metter of certified public record then, so I guess it still exist today in some archive?
And the little boy? Not found at the address given, and untraced ever since ...

Thanks, Peter. I love things that show that the universe is not what it appears. My friend author Carol Howe told me about how she and a friend were in a long car ride, and they were admiring and talking about a beautiful full harvest moon coming up behind the car for a good part of the ride. The next evening they took out deck chairs to admire the moon again, but... it never came. They checked the calendar, and there was no full moon that week!