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
so aren't you basically asking if there's some way to do math
without form?
Forgive me if I'm being an idoit. ;)
~Simon
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