Infinity

[Niflmir]

And just to tie off any possible loose ends, so to speak, no you can't tie a granny knot in an infinitely long string. You have to fold the ends over and under each other to make a granny knot, and an infinite string has no ends. But you can tie other kinds of knots in it.

Arrange your infinitely long string into a Cornu spiral (or something similarly compactified), tie whatever knot you like.

 

[Dexter Sinister]

I bow to your superior knowledge of mathematics. :smile: I know what you mean, but I was trying to keep the mathematical formalism out of this in discussing it with SJP, who's not a mathematician. I did, however, acknowledge in a later post that I was wrong about the knots after thinking it over for a while.

 

[Niflmir]

I bow to your superior knowledge of mathematics. :smile: I know what you mean, but I was trying to keep the mathematical formalism out of this in discussing it with SJP, who's not a mathematician. I did, however, acknowledge in a later post that I was wrong about the knots after thinking it over for a while.

The wikipedia articles on all of those are pretty good. I was hoping people would go read them to decypher what I said (its not as complicated as it may sound) since I find those things so interesting and hope other people would too.

Yeah, your correction was what made me look back to that. I just thought arranging the infinite string into a Cornu spiral made it conceptually simpler to consider the things you could do with it. (Simple if you don't mind the Cornu spiral.)