Hitoshi Kitada (firstname.lastname@example.org)
Sat, 3 Apr 1999 00:53:21 +0900
Thanks for an interesting post. Let me make a comment and some questions...
From: Matti Pitkanen <email@example.com>
To: Ben Goertzel <firstname.lastname@example.org>
Cc: Stephen P. King <email@example.com>; firstname.lastname@example.org <email@example.com>
Date: Friday, April 02, 1999 8:40 PM
Subject: [time 99] Re: [time 89] Re: [time 77] Re: [time 75] Re: [time 69]
>On Thu, 1 Apr 1999, Ben Goertzel wrote:
>> >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
>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
The difference here between your view and mine seems to be in that you think
one sheet disappears when another sheet comes in, while I think both sheets
(local systems and the outer classical world, in my case) exist at least on
the unobservable level. But this seems just a difference in expressions: In my
formulation, all possible local systems "exist," and the classical world
appears according to the requests of observers, at which instant a particular
set of local systems are selected. This corresponds to your "... quantities
flow from material sheets [disappearance of material sheets] to cognitive
sheets [apperance of cognitive sheets]" (and vice versa).
In the sense that observer (or its brain) is the ultimate reducer, our views
are on the same ground (althought there seems a difference in geometries as
Stephen pointed out in [time 102]).
The entanglement of cognitive spacetime sheets, 'Mind' with
>spacetime sheets carrying matter, 'Matter' is reduced in allowed quantum
>> >> 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"
>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 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
>> >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 ;)
>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.
Does "the nondeterminism of Kahler action" continue only for a _finite_ time
in an exact sense? My question is if it ends precisely in a finite time length
or in some approximate sense of "finiteness."
>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
>> >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)
>Subsystem corresponds to local system clearly.
>> >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
>> coupled > lattices
>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
>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
Could you give any calculation procedures of the quantities physicists want to
calculate on the basis of your infinite-dimensional mathematics?
>> 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
>> >infinite-dimensional context.
>> But it's all bits and bytes ultimately, Matti. Infinite dimensional math
>> 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.
>p-Adic approach fits very naturally with bits and bytes philosophy.
>For instance, even infinite-dimensional configuration space integral
>reduces to a discrete sum.
Could you explain the machinery that reduces the infinite-dimensional
configuration space integral to a discrete sum? If so, it seems to me that you
can define e.g. the (problematic) Feyman's path integral rigorously by your
formulation. Is my expectation true?
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
I suspect that each of your infinite hierarchy of consciousness is still
finite. If this is the case, each God on each hierarchy looks like being able
to play just with "bits and bytes."
Also would you explain the meaning of the second sentence of what you wrote in
>d) Note that M^4 metric is of standard form dt^2 -dx^2-... in p-adic
>context. Now however there seems to be no sharp difference between
>Euclidian and Minkowskian signature of metric.
This archive was generated by hypermail 2.0b3 on Sun Oct 17 1999 - 22:31:50 JST