Entry 21: in which We kick around a hypersphere

"Pater" says the boy.

"Hmmm?"

"This pink string disc thing ... hey I like it, it's got a ring! Pink string disc thing! Or we could ping pink string, or ... "

"Yes, yes, what about pink string?"

"Well you know how there's this 2D chap that we plop onto a 3D world and then first he's outside his pink string disc thing and then suddenly he's inside it and it all seems very magical ..."

"Yesss ..."

"Well you said to extend that by another dimension and Bob would be my uncle, who is Bob by the way?"

"Never mind Bob!"

"Yes, well anyway I've given it a lot of thought and can you explain it to me please?"

Good grief, what is the point of planting seeds of wisdom when they wither on the vine if I may mix my metaphors a bit. I sigh but continue:

"Right, so essentially we have our magical ball of pink string, the one that won't run out, and this time we plonk Mr 3D on a small 4D hypersphere. Well just as Mr 2D on the north pole of a 3D planet looked around him and thought he was on a familiar 2D plane, so Mr 3D looks around him and concludes he's on a familiar 3D sphere.

"His job is just to walk around and around the (initially small) sphere, playing out the pink string as he goes. As he does so, the sphere gets covered with pink string and starts to get bigger and bigger, just like one of those 'biggest ball of string in the world' things.

"He keeps going and the sphere gets bigger and bigger, huge in fact, so that the horizon is a very distant thing. But he just keeps going.

"After a very long time he gets a very big surprise; one that is possibly in 'nasty shock' category. He was on the outside of a very large pink sphere, but suddely he finds himself on the inside of a pink hollow, and what's more, a hollow that gets smaller and smaller the longer he continues.

"Just as Mr 2D could not understand how he went from being on the outside of a disc to being on the inside of the same disc (which to us, from a 3D persepective, was perfectly obvious), so Mr 3D simply cannot understand how he went from being on the outside of a sphere to its inside".

A long pause.

"Which to us, from a 4D perspective is perfectly obvious".

Another long pause.

Finally he pipes up "I'd give a lot to see one of those 'biggest ball of string in the world' things."

Wouldn't we all? Mercifully I am almost certain I hear Mrs G's dulcet tones requesting my presence and exit stage left.