On Sat, Feb 9, 2013 at 2:16 PM, Craig Weinberg <[email protected]>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. > 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. 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.
