# Re: Arithmetic doesn't even suggest geometry, let alone awareness.

`On Wed, Nov 7, 2012 at 7:42 AM, Craig Weinberg <whatsons...@gmail.com>wrote:`
```
> Can anyone explain why geometry/topology would exist in a comp universe?
>

If numbers exist then so does geometry, that is to say numbers can be made
to change in ways that exactly corresponds with the way objects move and
rotate in space. For example, make the Real numbers be the horizontal axis
of a graph and the imaginary numbers be the vertical axis, now whenever you
multiply a Real or Imaginary number by i you can intuitively think about it
as rotating it by 90 degrees in a counterclockwise direction.

Look at i, it sits one unit above the real horizontal axis so draw a line
from the real numbers to i, so if you multiply i by i (i^2)  it rotates to
become -1, multiply it by i again(i^3) and it becomes -i, multiply it by i
again (i^4) and it becomes 1, multiply it by i again (i^5) and you've
rotated it a complete 360 degrees and you're right back where you started
at i.

It is this property of rotation that makes i so valuable in dealing with
things that rotate in space, the best example may be electromagnetism where
Maxwell used it to describe how electric and magnetic fields change in the
X and Y direction (that is to say in the Real and Imaginary direction) as
the wave propagates in the Z direction.

John K Clark

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