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

*Thu, 1 Apr 1999 07:42:11 +0300 (EET DST)*

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Below answer to your questions. It happened as it often happens: the

posting became very long. I apologize.

On Wed, 31 Mar 1999, Ben Goertzel wrote:

*> Hi,
*

*>
*

*> >In TGD the entropy associated with density matrix of subsystem is in
*

*> >key role: strong form of Negentropy Maximization Principle states
*

*> >that in a given quantum state quantum jump is performed by the subsystem
*

*> >for which the negentropy gain is maximum in quantum jump reducing
*

*> >entanglement entropy to zero. The 'physical' interpretation is following:
*

*> >entanglement is measure for attentiveness not yet involving consciousness.
*

*> >Entanglement entropy measures, not the information content of
*

*> >conscious experience, but how 'catchy' the potential conscious
*

*> >experience is. The most catchy consciouss experience is experience.
*

*> >Mass media people would certainly agree with this!
*

*>
*

*> I don't know what "entanglement entropy" is, sorry. What is the formula
*

*> for this? --
*

*> in the discrete case (to keep things simple)
*

In QM entanglement is one of the most QM:eish phenomena and plays key

role in quantum compute sciencer. Schrodinger cat provides the standard

example of entanglement. The state of cat and bottle of poison is

superposition of cat dead-bottle open and cat alive-bottle closed states.

In TGD inspired theory of consciousness these kind of superpositions

appear at macroscopic level and our volitional acts select one branch

in the superposition.

Entanglement entropy serves as a measure for entanglement.

Let entangled state be

Psi = C _Nn |N> |n>

where summation occurs over M and N

In entangled state one cannot associated pure quantum state to subsystem

and density matrix provides the description of subsystem. Density matrix

is obtained from formula

rho_mn= C_MmC_Mn^*, (sum over M)

One can clearly integrates away external world states labelled by M.

Density matrix can be diagonalized and eigenvalues have interpretation

as probabilities p(m) for occurrence of particular state m in the

entangled superposition.

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.

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. In this quantum

jumps S goes to zero and negentropy gain is just S: one could perhaps say

that subsystem gains self knowledge (or rather is conscious). The

original interpretation of S was as a measure for information content of

conscious experience but the interpretation as a 'catchiness' of conscious

experience has turned out to be a more natural interpretation.

There are some interesting and very important delicacies related

to the definition of S in p-adic context but I will not go to them here.

*>
*

*> >The problem is to find also a measure for the information content
*

*> >of conscious experience and there are quite explicit ideas also about
*

*> >this. The modification of Roy Frieden's ideas to TGD context lead to
*

*> >the idea that the number of degenerate absolute minima of Kahler action
*

*> >going through given 3-surface X^3 (there are several of them by classical
*

*> >nondeterminism) is entropy typ measure for the cognitive resources of
*

*> >3-surface.
*

*>
*

*> 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

(http://www.physics.helsinki.fi/~matpitka/cbook.html).

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.

The problem is following: since entire quantum histories are in question,

the *contents of conscious experience should depend on the initial and

final history only*: spatial localization of contents of conscious

experience is possible but there seems to be no time localization

and hence no psychological time.

The solution of problem is provide by TGD and relates directly to General

Coordinate Invariance. 3-surface in M^4_+xCP_2 is

basic dynamical object of TGD and the so called

Kaehler action associates to every 3-surface X^3 a four-surface X^4(X^3):

this makes possible *4-dimensional* general coordinate invariance in

space of *3-surfaces* X^3 since Diff^4 can act on this 4-surface.

The unique property of Kaehler action is its *classical

nondeterminism*: there is large number of 4-surfaces X^4_i(X^3) going

through X^3 and having same absolute minimum value of Kaehler action.

For instance, one can have situation in which spacetime surfaces differ

in a finite time interval only: nothing like this occurs in standard

physics based on strictly deterministic action principles.

This classical nondeterminism makes possible quantum nondeterminism:

many particle states can get quantum entangled with various

classical branches X^4_i(X^3) of spacetime surface and if these

branches differ in a finite time interval, the nondeterminism of quantum

jumps selecting one of the branches is located in finite time interval.

Hence the contents of conscious experience give dominantly information

about physics in that time interval and psychological time emerges.

The number N_d of different absolute minima X^4_i(X^3) clearly

tells how many possible alternative choices subsystem defined by X^3

has. The larger the value of N_d, the larger the amount of free will.

Also cognition involves free will: we select between thoughts when we

direct attention to something. Thus N_d measures also cognitive

resources, the number of possible thoughts subsystem can have.

Of course, it measures also the ability of subsystem to change the world

since some bracnhes of multifurcations have long lasting effects on the

development of spacetime surface.

*>
*

*> The relation between your very interesting TGD theory and Hitoshi's very
*

*> interesting
*

*> global/local theory is not at all clear to me.
*

*>
*

*> Evidently you all think there is some kind of conceptual correspondence between
*

*> them in spite of the different mathematical vocabularies.
*

I try to list some of the common features.

a) Hitoshi postulates X^4xR^6: R^6 corresponds to phase space of

classical QM and he wants a marriage between QM and General Relativity.

This is what I also want. One can say that Hitoshi separates QM and

General Relativity to Carteisian product to achieve this.

b) I want to get rid of the energy problem of General Relativity

(isometries of spacetime are lost when spacetime becomes curved and it is

difficult to find satifactory definition of energy since Noether theorem

is not at use). I postulate that spacetime is surface in M^4_+xS

X^4 in M^4_+xCP_2

and assume that Poincare symmetries act on M^4_+ (future lightcone)

rather than spacetime so that Poincare is broken only cosmologically.

S=CP_2 is fixed by the requirement that standard model gauge group SU3 xU2

(color group +electroweak group) results from the geometry of S. Also

geometrization of elementary particle quantum numbers and classical gauge

fields results in this manner. TGD can be also regarded as a

generalization of string model: strings are replaced with 3-dimensional

surfaces and the miraculous properties of the 4-dimensional future

lightcone guarantee that Super Virasoro and Kac Moody algebra

structures quintessential to string models generalize.

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. This is like taking

extremely thin 3-dimensional parallel slightly curve membranes or glass

plates of various sizes and gluing them together by these tiny wormhole

contacts. Each plate represents its own sub-universe, local system with

respect to larger glass plates. LS property is relative property.

Every spacetime sheet which is 'General Relativistic' object as such

is LS relative to larger spacetime sheets.

*>
*

*> Maybe it would be useful for you two to articulate what you think the
*

*> points of commonality
*

*> and points of difference between the two approaches are. If you have been
*

*> over this ground
*

*> before in other forums please excuse me for being so presumptuous!
*

*>
*

*> I think that if we arrive at a sufficiently abstract and foundational
*

*> perspective we will be able
*

*> to see exactly where the two approaches coincide, and then where they
*

*> diverge in the process
*

*> of making additional mathematical assumptions to turn philosophy into science.
*

*>
*

*> Matti, does your theory fit into the general framework of
*

*>
*

*> -- one set of laws for parts
*

*> -- one set of laws for wholes
*

*> -- a bridging principle explaining how whole-laws and part-laws interrelate
*

TGD inspired theory of consciousness relies on subsystem-complement

separation. Quantum states=quantum histories =objective

realities (=Platonic ideas somewhat surprisingly) correspond to all

possible wholes: they are unconscious. Quantum jumps between

quantum histories give rise to moments of consciousness creating

the experiences of separation. 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

weak. Many-sheeted spacetime makes possible to explain

generation of structures: in standard quantum field theory basic objects

are point like particles and all geometric structures are ad hoc concepts

introduced as macroscopic idealizations for modelling purposes. In TGD

size and shape of 3-surfaces are completely new degrees of freedom

bringing into physics matter in the sense of res extensa at fundamental

level.

* >
*

*> ??
*

*>
*

*> This seems to be the philosophical structure of Hitoshi's theory...
*

*> If your theory could somehow be cast into this form this would give us a
*

*> way to proceed
*

*> in producing a "conceptual diff" of the two theories...
*

*>
*

*> As I said before, I think that getting the ideas right is the key here and
*

*> that mathematical
*

*> tricks are not going to be the answer. There are too many mathematical
*

*> tricks out there,
*

*> the mathematical universe is full of elegance, but our universe only
*

*> implements a limited
*

*> assortment of the really nice things in the mathematical universe...
*

*>
*

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

infinite-dimensional context.

Matti

**Next message:**Matti Pitkanen: "[time 90] Re: [time 77] Spacetime &consciousness"**Previous message:**Stephen P. King: "[time 88] Re: [time 85] Re: [time 82] discrete models, QM vs. GR"**Next in thread:**ca314159: "[time 91] Re: [time 89] Spacetime & consciousness"

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