On Thursday, November 8, 2012 11:36:18 PM UTC-5, John Clark wrote:
> On Wed, Nov 7, 2012 at 7:42 AM, Craig Weinberg 
> <whats...@gmail.com<javascript:>
> > 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. 

I'm saying that there would be no such thing as objects, movement, space, 
or rotation in a comp universe. You can prove this by understanding that 
there are no objects or spaces actually moving around in the chips of your 
computer. Everything that you want to do with arithmetic can be done with 
numbers alone, no points, spaces, lines, forms, or objects are ever needed, 
nor could they add anything to the functionality.

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. 

Do you understand why computers don't need to do that? This is my point, we 
have visual intuition because we have visual sense as a method of 
participating in a universe of sense. It would be meaningless in a universe 
of arithmetic.

> 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.

I'm not talking about why human beings find geometry useful. I am saying, 
IF the universe were purely functional, with no human beings, no 
consciousness even, why would geometry be useful to mathematics? Why would 
there even begin to be a theoretical underpinning for a universe which 
remotely resembles this one?


>  John K Clark  

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