On Saturday, February 9, 2013 1:31:55 PM UTC-5, John Clark 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
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
> John K Clark
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