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 > <[email protected]<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 > > -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/everything-list?hl=en. For more options, visit https://groups.google.com/groups/opt_out.
