On 07 Feb 2013, at 00:12, Simon Forman wrote:
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?)
Craig
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.
(*)
http://iridia.ulb.ac.be/~marchal/publications/SANE2004MARCHALAbstract.html
Bruno
That paper is fascinating. If I can understand it and come up with
anything to say I will. :) Thank you for sharing it.
Thanks for saying. If you can't understand it, don't hesitate to ask
any question.
The first part (the UDA, Universal Dovetailer Argument) requires only
some passive understanding of elementary computer science, and it
makes the main point. The second part requires some knowledge in
mathematical logic. It makes the same point, more constructively, and
in a language accessible to all sufficiently rich (Löbian) universal
machine.
Bruno
~Simon
--
"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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