possible novel clock mathematics

[Radical Edward]

does anyone here know anything about clock mathematics? I have come across it a few times, and it seems simple enough;

 

rather than the numbers being on a line, they are on a ring, like a clock is 1-2-3-4-5-6-7-8-9-10-11-12

 

so when we are at 10 on a 12 hour clock, and we add 4 (hours), then the time we get is not 14, but 2, and so on. I believe this is used in encryption, and for solutions to elliptic equations (and probably other things now that wiles solved fermat's theorem)

 

however I was wondering about this, has anyone done this before:

 

instead of numbering from 0 or 1 to n, how about numbering from -n to 0 or -1 (depending on if you want a zero or not. the neat Idea I had about doing this would be for roots, since the root of a negative number gives an imaginary number we would need another axis. so rather than a clock, you could have a tube and do maths on that. or, if you wanted to be really neat, you could convert the i-axis into a clock too, and get a torus out of it.

 

what would the mathematical implications be of trying to perform maths on this construct? are there other possible topologies, other than tubes and toruses? how about a twist in the torus, so that say we have our i-clock starting at i=0 on the real number n, and it ends on n+1?

 

I just thought this would be fun to play with anyway if anyone wants to think about it.

[JaKiri]

You're right, it is used in encryption. I'll tell you about elliptics in a couple of years time.

 

You're wrong, however, about the shape of the imaginary clock. It wouldn't produce a tube (given that effectively, the clock is representing numbers as a bearing), it would produce a sphere, with negative imaginary numbers on one side and positive ones on the other (it would of course be symmetrical for most calculations)