Ben Goertzel (email@example.com)
Thu, 1 Apr 1999 18:16:18 -0500
>The amount of entanglement is measured by entanglement entropy
>S= Tr(rho*log(rho))= SUM p(m)log(pm)
>and is of same form as Shannon entropy characterizing how far subsystem
>is from pure state.
OK, I understand. Thanks.
>TGD based QM measurement theory postulates that density matrix rho is the
>universal observable measured in quantum measurement and that subsystem
>goes in quantum jump to eigenstate |m> of rho with probability p(m)
>and thus ends up to pure state without any entanglement.
This is really not far from the standard von Neumann interpretation
>> I don't understand this. How do we get from this mathematical measure
>> to "cognitive resources"??
>This is a long story told in my homepage
>In TGD quantum states are replaced with quantum *histories* and moments
>of consciousness correspond to quantum jumps between them. Contents of
>conscious experience are assumed to localize into region where
>nondeterminism of quantum jump is localized: consciousness is where the
>free will is.
I think this ties in with my theory that "consciousness is randomness"
>c) The concept of local system has as its TGD analog spacetime sheet of
>finite size. The idea of local system is however realized quite
>differently in TGD. Hitoshi introduces clock at every point (I
>apologives if I have not understood correctly!). In TGD approach
>spacetime sheets representing elementary
>particles, nuclei, atoms,...ourselves,.... , galaxies,... are
>local systems realized as spacetime sheets which have contact to larger
>spacetime sheets via extremely tiny wormholes.
Perhaps the wormholes constitute a clock in some way?
Just daydreaming ;)
> Quantum jumps between
>quantum histories give rise to moments of consciousness creating
>the experiences of separation.
I think that this general concept is compatible with Hitoshi's theory, but
he realizes the evolution of histories by a different formalism, and he
the "jump leading to a moment of consciousness" as the classification of a
of quantum particles as a local system (center of mass, category)
>There is no unique objective reality/whole
>as in materialistic world view since quantum jump replaces the cosmology
>with a new one: as conscious beings also we are (mini)Gods(;-).
>A different aspect to whole/part distinction is related to the
>manysheeted spacetime concept. Different spacetime sheets correspond
>to different branches of physics: at nuclear spacetime sheets nuclear
>physics applies and at atomic spacetime sheets atomic physics is
>satisfactory description. The reason why these physics are practically
>separate is that interactions between different spacetime sheets are
In a discrete view your sheets become lattices, and we have multiple weakly
Different sets of links on the same set of nodes, perhaps?
if you could present a discretized version of the many sheeted theory it
would make it more clear to
everyone and might make correspondences with Hitoshi's and other theories
more clear --
just a pie-in-the-sky suggestion ;)
>I do not believe in mathematical tricks (although I have tried them
>occasionally(;-)). My basic philosophy has been to construct quantum TGD
>using only the basic classical spinor-geometry generalized to
But it's all bits and bytes ultimately, Matti. Infinite dimensional math is
a shortcut for some purposes,
but also obscures things sometimes IMO. I say this as a mathematician who
spent many years studying
functional analysis etc.
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