On Sunday, February 10, 2013 1:55:15 PM UTC-5, John Clark wrote:
>
>
>
> On Sat, Feb 9, 2013 at 2:16 PM, Craig Weinberg 
> <whats...@gmail.com<javascript:>
> > wrote:
>
>>
>>  
>
>> > They [mathematicians] are just elaborating existing concepts of 
>> geometry, not creating it from mathematical scratch.
>>
>
> But all those concepts of geometry, like the trigonometric functions, can 
> be derived from one dimensional numerical sequences with no pictures or 
> diagrams involved and if told that a particle with N degrees of freedom 
> changes in a certain way and then changed again in a different way but one 
> that is still consistent with those functions a one dimensional geometer 
> could still specify what the coordinates of that particle will now have in 
> N space.  
>

That's my point. There is never any need to have more than one dimension. 
All there need be is numerical sequences.

>
> > It doesn't matter how many dimensions you make the machine, the tape is 
>> still one dimensional
>
>
> Yes but it can make calculations in N dimensional space, and a Turing 
> Machine might not even know that it is one dimensional, or even that it is 
> a Turing Machine.  
>

The N dimensions are figurative though. Literal geometric dimensions are 
inaccessible to mathematics unless we correlate them ourselves. We have 
access to multiple spatial dimensions of geometry through our sensory-motor 
participation as a body in a universe of bodies, but mathematics has no 
such access. Thus comp fails by overconfidence.

Craig
 

>
>   John K Clark 
>
>

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