On 07 Nov 2012, at 19:04, Craig Weinberg wrote:
On Wednesday, November 7, 2012 10:49:35 AM UTC-5, Bruno Marchal wrote:
On 07 Nov 2012, at 13:42, Craig Weinberg wrote:
> Can anyone explain why geometry/topology would exist in a comp
> universe?
The execution of the UD cab be shown to be emulated (in Turing sense)
by the arithmetical relation (even by the degree four diophantine
polynomial). This contains all dovetailing done on almost all possible
mathematical structure.
This answer your question,
It sounds like you are agreeing with me that yes, there is no reason
that arithmetic would generate any sort of geometric or topological
presentation.
"Generating geometry" is a too vague expression.
Keep in mind that if comp is true, the idea that there is more than
arithmetical truth, or even more than some tiny part of it, is
(absolutely) undecidable. So with comp a good ontology is just the
natural numbers. Then the relation with geometry is twofold: the usual
one, already known by the Greeks and the one related to computer
science, and its embedding in arithmetic.
Or are you saying that because geometry can be reduced to arithmetic
then we don't need to ask why it exists? Not sure.
Geometry is a too large term. I would not say that geometry is reduced
to arithmetic without adding more precisions.
but the real genuine answer should explain
why some geometries and topologies are stastically stable, and here
the reason have to rely on the way the relative numbers can see
themselves, that is the arithmetical points of view.
In this case it can be shown that the S4Grz1 hypostase lead to typical
topologies, that the Z1* and X1* logics leads to Hilbert space/von
Neuman algebra, Temperley Lieb couplings, braids and hopefully quantum
computers.
No need to go that far. Just keep in mind that arithmetic emulates
even just the quantum wave applied to the Milky way initial
conditions. And with comp, the creature in there can be shown to
participate in forums and asking similar question, and they are not
zombies (given comp, mainly by step 8).
The question though, is why is arithmetic emulating anything to
begin with?
Because arithmetic (the natural numbers + addition and multiplication)
has been shown Turing complete. It is indeed not obvious. In fact you
can even limit yourself to polynomial (of degree four) diophantine
relation. But you can use any Turing complete system in place of
arithmetic if you prefer.
I will give a proof of arithmetic Turing universality on FOAR, I will
put it here in cc.
Bruno
http://iridia.ulb.ac.be/~marchal/
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