On Sat, Feb 9, 2013 at 2:16 PM, Craig Weinberg <whatsons...@gmail.com>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 everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list?hl=en. For more options, visit https://groups.google.com/groups/opt_out.