On 2/6/13, Bruno Marchal <marc...@ulb.ac.be> wrote:
> On 05 Feb 2013, at 11:19, Simon Forman wrote:
>> On Monday, February 4, 2013 12:22:53 PM UTC-8, Craig Weinberg wrote:
>> On Monday, February 4, 2013 3:09:16 PM UTC-5, Alberto G.Corona wrote:
>> but there is a self reference when we try to imagine how the brain
>> or a computer process geometry, and we imagine them embedded in the
>> space and time that they create, which is not a correct intuition.
>> we must imagine it in no time and no space. IMHO.
>> That's what I think too, geometry without space isn't geometry, so
>> that there is no reason to assume that mathematics produces
>> geometric presentations, or that it could possibly produce them. If
>> we want mathematics to occupy space, we have to pull that
>> possibility out of thin air, as well as the capacity for numbers to
>> suddenly do that (and why would they need to?)
>> Doesn't the quantum physical reality of information mean that all
>> math *is* geometry?
>> Put another way, math without a substratum would be in some platonic
>> world, and not the real one,
> How do you know that? See the paper below(*) for an argument showing
> that if we are machine, then the physical reality is *only* emergent
> from arithmetic. Moon and stars are coherent "number's dream", and
> this can be tested. So if you want a material substratum, you need to
> assume that you and your brain are not Turing emulable.
That paper is fascinating. If I can understand it and come up with
anything to say I will. :) Thank you for sharing it.
"The history of mankind for the last four centuries is rather like that of
an imprisoned sleeper, stirring clumsily and uneasily while the prison that
restrains and shelters him catches fire, not waking but incorporating the
crackling and warmth of the fire with ancient and incongruous dreams, than
like that of a man consciously awake to danger and opportunity." --H. P.
Wells, "A Short History of the World"
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