**Matti Pitkanen** (*matpitka@pcu.helsinki.fi*)

*Fri, 2 Apr 1999 14:32:28 +0300 (EET DST)*

**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]**Next message:**ca314159: "[time 100] Re: [time 92] Entanglement"**Previous message:**Matti Pitkanen: "[time 98] Re: [time 92] Entanglement"**In reply to:**ca314159: "[time 92] Entanglement"**Next in thread:**Stephen P. King: "[time 102] Re: [time 99] Spacetime& consciousness"

On Thu, 1 Apr 1999, Ben Goertzel wrote:

*>
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*> >The amount of entanglement is measured by entanglement entropy
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*> >
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*> >S= Tr(rho*log(rho))= SUM p(m)log(pm)
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*> >
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*> >and is of same form as Shannon entropy characterizing how far subsystem
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*> >is from pure state.
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*>
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*>
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*> OK, I understand. Thanks.
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*>
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*> >TGD based QM measurement theory postulates that density matrix rho is the
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*> >universal observable measured in quantum measurement and that subsystem
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*> >goes in quantum jump to eigenstate |m> of rho with probability p(m)
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*> >and thus ends up to pure state without any entanglement.
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*>
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*> This is really not far from the standard von Neumann interpretation
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Actually the recent picture about quantu jump provides generalization for

von Neumann's intuitions about brain as ultimate reducer.

In TGD framework cognitive spacetime sheets, which are nearly vacuum and

have finite time duration. [Energy and other conserved quantities flow

from material spacetime sheets to cognitive sheets when they are formed

and back to material spacetime sheets when cognitive spacetime sheets

disappear.] The entanglement of cognitive spacetime sheets, 'Mind' with

spacetime sheets carrying matter, 'Matter' is reduced in allowed quantum

jumps.

*>
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*> >> I don't understand this. How do we get from this mathematical measure
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*> >> to "cognitive resources"??
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*> >
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*> >This is a long story told in my homepage
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*> >(http://www.physics.helsinki.fi/~matpitka/cbook.html).
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*> >In TGD quantum states are replaced with quantum *histories* and moments
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*> >of consciousness correspond to quantum jumps between them. Contents of
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*> >conscious experience are assumed to localize into region where
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*> >nondeterminism of quantum jump is localized: consciousness is where the
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*> >free will is.
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*>
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*>
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*> I think this ties in with my theory that "consciousness is randomness"
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*>
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I would not use the world randomness. After all, in quantum jump selection

between eigenstates of subsystem density matrix occurs: final state is not

at all random. Secondly, the probabilities for final states are not

in general same. And thirdly, strong form of Negentropy Maximization

principle selects unique subsystem which can perform quantum jump: the

system is the one giving maximum negentropy gain and thus having largest

entanglement.

[Entanglement corresponds to attention 'psychologically' so that the

most alert subsystem has moment of consciousness). The most alert

subsystem can of course decompose to mutually unentangled subsystems

having their own separate conscious experiences].

*> >c) The concept of local system has as its TGD analog spacetime sheet of
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*> >finite size. The idea of local system is however realized quite
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*> >differently in TGD. Hitoshi introduces clock at every point (I
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*> >apologives if I have not understood correctly!). In TGD approach
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*> >spacetime sheets representing elementary
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*> >particles, nuclei, atoms,...ourselves,.... , galaxies,... are
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*> >local systems realized as spacetime sheets which have contact to larger
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*> >spacetime sheets via extremely tiny wormholes.
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*>
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*> Perhaps the wormholes constitute a clock in some way?
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*> Just daydreaming ;)
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I think that any periodic phenomen provides a clock: the basic

problem is to find someone to perceive the reading of the clock(:-).

In quantum jumps between quantum histories picture the nondeterminism of

Kahler action comes at rescue and makes possible conscious experiences

with time localized contents.

The oscillations of Josephson junctions formed by wormhole super

conductors indeed generate clocks if one believes that EEG is a clock.

Amusingly, simplest EEG clock corresponds to sequence of solitons of Sine

Gordon, which is mathematically nothing but gravitational pendulum

rotating. Also EEG oscillations equivalent with oscillating

gravitational pendulum are possible. In latter case EEG is equivalent

with the clock in the wall!

*> > Quantum jumps between
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*> >quantum histories give rise to moments of consciousness creating
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*> >the experiences of separation.
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*>
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*> I think that this general concept is compatible with Hitoshi's theory, but
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*> he realizes the evolution of histories by a different formalism, and he
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*> defines
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*> the "jump leading to a moment of consciousness" as the classification of a
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*> collection
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*> of quantum particles as a local system (center of mass, category)
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*>
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Subsystem corresponds to local system clearly.

*> >There is no unique objective reality/whole
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*> >as in materialistic world view since quantum jump replaces the cosmology
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*> >with a new one: as conscious beings also we are (mini)Gods(;-).
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*>
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*>
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*> Agreed
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*>
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*> >A different aspect to whole/part distinction is related to the
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*> >manysheeted spacetime concept. Different spacetime sheets correspond
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*> >to different branches of physics: at nuclear spacetime sheets nuclear
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*> >physics applies and at atomic spacetime sheets atomic physics is
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*> >satisfactory description. The reason why these physics are practically
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*> >separate is that interactions between different spacetime sheets are
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*> >weak.
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*>
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*> In a discrete view your sheets become lattices, and we have multiple weakly
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*> coupled > lattices
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*>
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p-Adicity leads in a natural manner to lattice like structure. You can

form from real axis 1-dimensional lattice by cutting, say decimal

expansion, from n:th decimal. In p-adic context cutting of pinary

expansion of pinary number so that O(p^n) part of p-adic number is put to

zero is analogous procedure but defines equivalence relation in p-adic

context. Hence one can define entire hierarchy of discrete coset spaces

R_p/E_n by this equivalence relation (denoted by E_n).

This hierarchy of lattices defines extremely rapidly converging

approximation procedure for physically interesting primes p (p=2^127-1 for

electron!). Various physical fields become in this approximation fields in

lattices.

What is especially nice is that p-adic counterpart of, say, Poincare group

respects these lattice structures. I told about how p-adic Poincare

group leaves finite p-adic spacetime cube invariant in some earlier

posting few weeks ago. One can quite well say that p-adics are Taylor made

for lattice approximation.

Personally I however believe that geometry is continuous at basic level.

The basic reason for this is that infinite-dimensional geometry is highly

unique: in TGD case the sole requirements that Riemann connection exists

mathematically + some other general requirements fix the entire

geometry and also imbedding space itself essentially uniquely. In TGD

framework this means unique physics also since physics is just

infinite-dimensional spinor geometry. The inability of physicists to

find divegence free QFT:s reflects also this high uniquess of

infinite-dimensional mathematics.

*> Different sets of links on the same set of nodes, perhaps?
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*>
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*> if you could present a discretized version of the many sheeted theory it
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*> would make it more clear to
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*> everyone and might make correspondences with Hitoshi's and other theories
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*> more clear --
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*> just a pie-in-the-sky suggestion ;)
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*>
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*> >I do not believe in mathematical tricks (although I have tried them
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*> >occasionally(;-)). My basic philosophy has been to construct quantum TGD
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*> >using only the basic classical spinor-geometry generalized to
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*> >infinite-dimensional context.
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*>
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*>
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*> But it's all bits and bytes ultimately, Matti. Infinite dimensional math is
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*> a shortcut for some purposes,
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*> but also obscures things sometimes IMO. I say this as a mathematician who
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*> spent many years studying
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*> functional analysis etc.
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p-Adic approach fits very naturally with bits and bytes philosophy.

For instance, even infinite-dimensional configuration space integral

reduces to a discrete sum. My own view is that

objective realities=quantum histories are continuous object but that our

consciousness is able to work with bits and bytes

only. TGD however leads naturally infinite primes and p-adic number fields

associated with infinite primes (which are actually very much like reals):

also infinite hierarchy of consciousnesses is predicted. Perhaps these

Godlike consciousness above us are not limited to play with bits and bytes

only(;-).

MP

**Next message:**ca314159: "[time 100] Re: [time 92] Entanglement"**Previous message:**Matti Pitkanen: "[time 98] Re: [time 92] Entanglement"**In reply to:**ca314159: "[time 92] Entanglement"**Next in thread:**Stephen P. King: "[time 102] Re: [time 99] Spacetime& consciousness"

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