On Thursday, November 8, 2012 2:57:35 AM UTC-5, Bruno Marchal wrote:
> 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.
Create? Discover? Utilize?
> 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.
If the idea of comp is that the origin of consciousness can be traced back
to digital functions, I am saying that lets start with an even simpler
example of why that isn't true by trying to trace the origin of geometry
back to digital function. What specifically does geometry offer that the
raw arithmetic behind geometry doesn't? Why the redundancy to begin with?
What is functional about geometry?
> > 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.
Can't any computable geometry be stored as numerical codes in digital
memory locations rather than points or lines in space?
> > 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.
Why would a Turing complete system emulate anything though? It is what it
is. Where does the concept that it could or should be about something else
> I will give a proof of arithmetic Turing universality on FOAR, I will
> put it here in cc.
My point is precisely that this kind of universality invalidates Comp. If
you have a universal machine, you don't need geometry, don't need feels and
smells and hair standing on end...you just need elaborately nested
sequences which refer to each other.
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