On Saturday, February 9, 2013 1:31:55 PM UTC-5, John Clark wrote: > > On Mon, Feb 4, 2013 Craig Weinberg <[email protected] <javascript:>>wrote: > > > If geometry did not exist. Could you invent it with mathematics alone? >> > > Mathematicians have invented geometries of 5, 6, 7, or even a infinite > number of dimensions as in Hilbert space even though they have no tactile > experience of such things. >
But geometry exists the universe that mathematicians inhabit. The whole idea of dimensions already exists as a geometric concept, and that is what Hilbert space is based on. My question requires that you imagine, with scientifically rigorous intent, that you are in a universe which completely pre-figures geometry. You haven't done that. > They do this by increasing the number of independent parameters that are > needed to define a point particle. Then they specify a few simple logically > consistent rules by which one set of parameters can morph into another set > of parameters and call this process "movement". > Exactly. They are just elaborating existing concepts of geometry, not creating it from mathematical scratch. > > A Turing Machine could do the same thing, but I do admit that It a Turing > Machine requires the existence of at least one dimension, I don't see how a > zero dimensional point brain could work because you need things to be able > to change in it. > You are conflating the body of the Turing Machine with the presumed computational experience generated by it. It doesn't matter how many dimensions you make the machine, the tape is still one dimensional (or however many dimensions you want it to be). Regardless, there is no number of abstract mathematical dimensions which suddenly must translate into a visual/tangible matrix of points in space. You can have a billion dimensional machine with a trillion dimensional tape, making quadrillion dimensional programs without ever stumbling upon or inventing any geometric presentation whatsoever. This is the true Turing test: If you have a computer that is designed specifically to have no experience of geometry (like it has blindsight for geometry), but you can't prove that it doesn't have geometric experience by interrogating it, then you cannot assume that geometry can arise from computation. 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.
