Matti Pitkanen (matpitka@pcu.helsinki.fi)
Tue, 25 May 1999 14:56:44 +0300 (EET DST)
On Mon, 24 May 1999, Stephen P. King wrote:
> Dear Matti,
>
> I got my brain in gear for a little while... ;)
>
> Matti Pitkanen wrote:
> >
> > On Fri, 21 May 1999, Stephen P. King wrote:
> > > I am still struggling with the meaning of your concepts, but I am
> > > trying. :) Are "thoughts" information? Do we consider them as existing
> > > "sharply", e.g. with well defined finite properties prior to the
> > > subjective experience of them? We must not assume that we can fix some
> > > "external" point of view of the Totality and construct a toy model of it
> > > and then say this "is absolutely how Nature works"! Our models and
> > > formalisms are methods of communicating our subjective experiences, and
> > > we try to build models that a maximum of communicators can agree upon
> > > and use.
> [MP]
> > Thoughts are not information for me at basic level.
> > I regard thoughts at *classical level* as physical representations for
> > external worlds. Simulations. Evolutionary pressures select logically
> > consistent thoughts and also takes care that representations become more
> > and more detailed.
>
> I am distinguishing the information from the "physical
> representations", the former is "independent" from the latter in the
> sense that a given set of information can be physically represented in
> many different ways, alternately a given physical state can be described
> in many different forms of information, e.g. languages. This is the
> essence of the matter-information duality.
[MP]
On the other hand, same binary sequence can have infinite
number of different interpretations. Is it really possible to speak
about information as something absolutely existing quantity?
Examples:
a) I thought that negentropy gain (entanglement
entropy) in quantum jump could be regarded as a measure
for information gained in conscious experience. It however seems
that this number measures the 'catchiness' of conscious experience
and not its information content.
b) The number of degenerate absolute minima of Kaehler action associated
with given 3-surface gives measure for cognitive resources of
3-surface/subsystem. But also this measure fails to be measure for real
information: rather, it is kind of intelligence quotient.
Measure ability to simulate.
c) I can also imagine that by gluing cognitive spacetime sheets
of finite duration to material spacetime sheet, I obtain
cognitive representation for material world. By reducing the
average temporal and spatial distances between these tiny cognitive
spacetime sheets are, I can make the cognitive representation
more and more precise and it is natural to introducestemporal
and spatial resolutions for conscious experience as
average temporal and spatial distances between the cognitive
spacetime sheets. For instance, in vision resolution is about .1 seconds:
movies of course use this fact. But again, I do not have any measure for
information but something like intelligence quotient.
So is it at all possible to speak about information as something
absolutely existing quantity? Is information perhaps
remnant of Cartesian thinking: no continuous streams of
consciousness - no information.
Could it be that information does not exist in absolute sense since
a) physics does not give rise to information as a basic
physical concept (GCI would suggest the generalization of
information to conserved information current with time component
interpretable as information density: this does not look
promising idea)
and
b) we cannot describe the contents of our mental states using binary
sequences.
> Ah, you used a favorite word of mine! :) "Simulations". When two (or
> more) physical systems communicate they are in effect simulating each
> other's behavior internally, the behavior is equivalent to a computation
> of the system's information content. We say that they can an communicate
> to the degree that they simulated each others behavior. This is the
> essence of bisimulation. (See section 7 of
> http://www.cs.brown.edu/~pw/papers/math1.ps)
[MP] This idea I like. Could it be that simulation could be more
fundamental concept than communication. Communication as simulation
rather than exchange of this problematic information, which possibly
has property of non-existence?
> The evolution of larger and larger sets of mutually consistent
> "thoughts" is derived from the "forces" of mutation (of the individual
> system's propagators) and selection (of the most efficient computational
> sequences that simulate the behavior of other systems). Thus we say that
> evolution drives interacting systems toward maximal mutual consistency.
> Pratt's ideas (in http://boole.stanford.edu/chuguide.html#ratmech) are
> the computer science versions of this, well, as I interpret them. ;)
>
> > Geometric realization is in terms of snapshot: nondetermism of variational
> > principle implies that multitime snapshot is needed to fix initial value
> > problem and this multitime snapshot is like a movie giving representation
> > for the history. In TGD multime snapshot is just union of 3-surfaces
> > with time like separations. In strictly causal theory one would have
> > only single time snapshots: no simulations, no cognition, no thoughts.
>
> I understand the use of "snapshots" (call them T) and I think I
> understand how you avoid the problem of Uncertainty by using a
> probability density (?) or ensemble of Ts.
[MP]
The failure of standard causality only forces to generalize
the concept of initial values by allowing association sequences
(unions of 3-surfaces with timelike separations): this
means only an extension of configuration space which is analogous
to configuration space E^3 for particle in quantum mechanics.
There are no problems with Uncertainty Principle.
>But the movie analogy is, in
> my opinion, deceptive since it tacitly assumes that the snapshots have
> an a priori ordering. I think that you do have a way of showing how the
> Ts are sequenced, but I do not understand it.
Good and troublesome question!
a) The lightcone proper time of imbedding space induces the ordering
in geometric sense.
b) Multisnapshot/association sequence determines the contents single
conscious moment.
b) That geometric time ordering corresponds to order of logical
implications seems to be a hypothesis about how contents of conscious
experience are determined. This is all what I can say about this.
> I see the Ts as being ordered in a dual fashion (forward and backwards)
> by the evolutionary process described above and specifically by Pratt's
> "residuation". The "forward" ordering is that of temporal causation
> (->) of the physical system ("body") and the "backwards" ordering is
> that of logical precedence (<-) of the information content ("mind").
> This is stated as: A causes B iff B* implies A*.
> We can chain this rule to get any length of causation/precedence, e.g.
> ... -> A -> B -> C -> ... iff ... <- C* <- B* <- A* <- ..., etc. Thus
> your above statement: "In strictly causal theory one would have only
> single time snapshots: no simulations, no cognition, no thoughts." would
> only hold in the special case of infinite efficient bisimulations and/or
> no possibility mutation. See Pratt's paper!
>
> > Conscious thought is quantum jump selecting from quantum superposition of
> > multitime snapshot 3-surfaces one.
>
> I agree! :)
>
> > I believe that great stories are possible although they always reduce
> > to models inspired by them. By Great Stories I mean principles like
> > General Coordinate Invariance, Geometrization of Physics, Consistency
> > Implies Existence, and so on.... They do not tell how nature works
> > absolutely but are necessary for model building.
>
> I also agree!;)
>
> [MP]
> snip
> > > We can easy see that the classical notions of determinism are plain
> > > wrong! The idea that an isolated system's properties exist in a sharp
> > > state independent of observation is wrong! QM forbids the construction
> > > of a sharp Cauchy hypersurface of position and momenta with arbitrary
> > > sharp values and thus the very idea of determinism is flawed! (thus we
> > > have to use operators!) We are thus in a position to wrestle with some
> > > notion that explains for both "free will" and "causality" (as opposed to
> > > determinism).
> >
> > One can however formulate initial value problem for Schrodinger amplitude
> > with difficulties and I see this as the relevant initial value problem in
> > QM.
[MP] Sorry! I meant *without difficulties*!!
>
> Is it really necessary to assume absolute initiality? In Peter's work
> we see that we can drop initiality and get more expressive models of
> computation!
[MP] Also quantum TGD gives up the absolute initiality:
initial values as single snapshot are replaced with association
sequences, multisnapshots. This is what makes cognition possible
in TGD framework! In p-adic context also p-adic nondeterminism is
present.
But this does not solve the problem of free will. If only single
(geometric) time evolution, deterministic in strict
or limited sense, there is no free will.
> See the parts on non-well founded set theory in:
> http://www.cs.brown.edu/~pw/papers/math1.ps By using "streams" we can
> bypass the initiality problem, but there remains the problem of putting
> together a way of communicating how streams "sample" from each other. I
> believe that the use of the term "window" would be appropriate... It
> allow for the definition of a local sense of how interactions start and
> end without imposing absolutist initiality and finality.
[MP] I read article about non-well founded set theory and found it
very stimulating.
>
> > Certainly I agree with you that 'determinism' is the key word.
> > My conviction is that the confusion is caused by the belief that
> > nondeterminism occurs at spacetime or state space level. It need
> > not occur and this could make possible the peaceful coexistence of
> > nondeterminism of state function collapse and determinism of Schrodinger
> > equation. My suggestion is to jump out of the system. ....jumps between
> > quantum histories, etc, etc...
>
> The difficulty I find the works of most physicists in reconciling the
> way that the Schroedinger wave is defined in a "isolated system" sense
> and the way that the jump ("collapse of Phi") is defined as the
> violation of the "isolateness". I see these reconciled in Hitoshi's
> model by having the Phi propagate internally in the LSs and the jumps as
> finite duration mappings between the exteriors of LSs. But remember that
> Hitoshi is coming from a QM primitive perspective and you are
> considering space-times as primitive, I think... ;)
Yes. I regard geometry as primitive and quantum jump even more primitive,
even non-modellable(;-)...
> I am trying to better understand how information is encoded on the
> "surface" of LSs; I am thinking of this in terms of how information is
> encoded on the event horizon surface of a black hole...
[MP]
There are attractive analogies. My own favourite is elementary particle
blackhole analogy. Entanglement entropy which for thermal entanglment
(entanglement probabilities given by p-adic Boltzman weights coming as
powers of p) is proportional to the surface area of elementary particle
horizon. But entanglement entropy seems to measure the catchiness of
potential conscious experience, not its information content.
It seems that we never catch the information: is it there at all(;-)?
>
> > Or another manner to see it is to realize that there are two time
> > concepts and two causalities. Time ticking as quantum jumps and good
> > old and well tested geometric time. Causality associated quantum jumps,
> > deeds, acts of free will and causality associated with classical physics
> > as passive obeyiance of field equations.
>
> Can we think of "classical physics" and "geometric time" as
> idealizations that, at best, model the average situation when velocity
> and energies are low and resolvability is arbitrarily accurate, e.g. c =
> \inf., hbar = 0? It is useful to make such tacit assumptions in our
> "common sense" toy models, but we do know that such are not factual. We
> should just drop the pretense.
>
[MP]
You could be right. This actually makes clear the difference in our
approaches. I base my approach on the assumption that
infinite dimensional Riemann/Kaehler geometry
is part of the ultimate reality. Riemann
geometry does not involve any idealizations related to hbar or c.
There have been attempts to construct quantum geometries
as noncommutative geometrics but
in these approaches some new constant analogous to hbar is introduced.
It might be that p-adic geometry is closely related to noncommutative
geometries: in fact. Haar measure in quantum group SU(2)_q can
be interpreted as p-adic Haar measure for q=1/p.
In fact, the mapping of real spacetime surface to p-adic spacetime
surface is very 'quantal'. There is direct parallel with quantum
measurement theory: as I told earlier, the mapping can be said to commute
with maximal commuting set of isometry charges. Furthermore, the
coordinates of imbedding spaced decompose to 4+4 such that mapping
is continuous in first four but discontinuous in last 4.
This reminds me of geometric realization of Uncertainty Princple.
snip
> [SPK]
> > > But exactly what are "physical laws"?! Can we affirm that such are
> > > independent of any observation? NO! I believe that "physical laws" are
> > > the patterns of regularity that are imposed on sense data by the very
> > > act of observation and thus do not exist as such independent of
> > > observers! Thus I find Frieden's notions, as I have read about them so
> > > far, attractive.
> [MP]
> > Perhaps Consistency Implies Existence comes in rescue here!
> > Infinite-dimensional mathematics does not allow too many internally
> > consistent patters of regulatity!
>
> I don't think so. :( It looks like only if we restrict mathematics to
> finite realms of applicability do we get consistency, but locally
> bounded consistency. We can not have absolute completeness within
> systems that "count" but we can not have time to count within isolated
> systems ("bound state"), so we tread the middle path. :) I am assuming
> that a physics that does not allow for distinguishing states does not
> allow counting and since Goedel's incompleteness involves the encoding
> of arithmetic in a theory...
[MP] You might be right, of course. I feel however that you miss
the basic point: infinite-dimensional geometries do not exist
unless they have infinite dimensional groups of symmetries (Riemann
connection fails to exist). This is *horribly* strong result.
The construction of metric reduces to single point of the
infinite-dimensional space. This is nothing but the realization
of the good old 'the laws of physics are same everywhere', now
in infinite-dimensional space and implied by mere
mathematical existence.
snip
>
>
> > About what you say quantum nondeterminism I do not agree.
> > Unfortunately I do not know enough about Pratt's and Wegner's notions
> > to comment.
>
> Umm, I did not imply by my statement that "quantum nondeterminism is
> just stochastisity" is objective, i.e. independent of observation! I
> meant to say that it is considered by most to be such. I agree with
> Peter's notion of secondary observers as the "cause" of nondeterminism.
> See his section 11 on Subjective Nondeterminism in
> http://www.cs.brown.edu/~pw/papers/math1.ps
>
[MP]
Cause of 'nondeterminism' or nondeterminism?
> snip
> [MP]
> > I have been pondering the notion of abstraction from many points of view.
> >
> > a) As you know many fermion Fock states have structure of Boolean algebra
> > (state occupied =true/state unoccupied =false). N single fermion states
> > gives rise to Boolean algebra with 2^N elements: statements about N basic
> > statements. The hypothesis is that many fermion states correspond to
> > reflective level of consciousness. There would be only single
> > meta level at the fundamental level. This seems to be the case in real
> > world! It is easy to make statements about statements but extremely
> > difficult to make statements about statements about statements. I have
> > experience of seing red but very rarely experience of having experience of
> > seing red. Thus basically only single fundamental, directly
> > experienced level of abstraction seems to be present and higher levels
> > are constructed as representations.
>
> This is why I say that the work of the computer scientists, such as
> Pratt and Peter, is so relevant to our work! Boolean algebras are the
> stuff that they work on all day (and night)! :) I have a paper somewhere
> that discusses this Boolean algebra property in connection with past and
> future states in QM. I have to look for it...
> I agree that there is "only single meta level at the fundamental
> level"! This is the level of the Totality, but any observation of it is
> a finite sampling of it (like the shadow on Plato's cave wall) and thus
> dualistic. I distinguish the 2^N fermions from the 2^2^N (?) bits that
> they can encode.
> Each individual experiences their own "world" with themselves at the
> center. I say that we observe a "common world" because such is the
> weighted intersection of a finite number of "worlds", e.g. observables
> of LSs. It seems that this idea is very hard to understand at first but
> once grasped... EUREKA! :) This is why I keep saying that each observer
> has its own space-time that is, to that observer only, Minkowskian.
[MP] I would only say each LS has its own collection of cognitive
spacetime sheet representing external world.
>See
> Peter's comments about "Observation equivalence' in Section 3 of
> http://www.cs.brown.edu/~pw/papers/math1.ps. I conjecture that special
> relativity is a mathematical physics model of observational equivalence
> for syncronous co-moving observers! What happens when we generalize? :)
> Some would argue that it is "extremely difficult to make statements
> about statements about statements" merely due to the complexity
> involved. There are many books that discuss how to be aware of being
> aware of an event. It is difficult but can be done, I have had to learn
> to do this to overcome my dyslexia! (and use massive spell checkers!)
[MP] Probably it involves constructing cognitive representations (paper
and pencil!): at basic level there would be just only metalevel.
Well, I might be wrong....
>
> > b) I talked about thoughts as simulations, sequences of 3-surfaces
> > with time like separations, which fix uniquely the spacetime surface
> > going through them (generalization of causality concept to achieve
> > classical determinism in generalized sense). One can construct
> > cognitive hierarhies from these 'association sequences'. Take a sequence
> > of these sequences: this is thought about thought. Geometrically this
> > would mean gluing cognitive spacetime surfaces representing association
> > sequences to a larger cognitive spacetime surfaces.
>
> :) I think I am beginning to understand your thinking here! I am
> "bisimulating" you at a higher efficiency level. :) But I need to be
> sure! :) This "fix uniquely the spacetime surface going through them",
> what is its ontological status? Or, is it constructed "as experience" or
> is it a priori "out there", independent of observation?
Quantum histories are quantum superpositions of these spacetime surfaces
and moments of consciousness (observations) give conscious information
about them and create 'I', the illusion about observer as continuous
stream of consciousness.
> This question
> addresses the key difference between TM type computations and IM
> computations that Peter and Pratt discuss at great length in the above
> mentioned papers! :)
>
snip
> > >
> > > We need to carefully consider what is computation! I see these
> > > "associations" as an example of computation! It is the identification of
> > > *output* by a given physical process with some *input*. We think of
> > > "input" as data or equations and variables or signals from arbitrary
> > > sources or ... and "output" as patterns or solutions or messages or ..
> >
> > In this sense you could regard classical time evolution of physical
> > system as computation. But quantum jumps is not a computation: it is
> > not modellable. Or so I believe....
>
> Not modelable in a Turing Machine (TM) sense, yes, but it is modelable
> in an Interaction Machine (IM) sense! The property of
> "nonserializability" of MIMs (see section 10 of Peter's paper) speaks
> directly to this point! :) The key idea is that these "quantum jumps",
> as experiences, are _*NOT*_ a priori synthetics! They are constructed by
> finite local systems in an "on the fly" way! This is a direct
> contradiction to the LaPlacean vision of a 4-dimensional frozen
> universe! Please read Peter's paper. ;)
> also: http://hume.ucdavis.edu/kant/pap1comm.htm for comments on a priori
> synthetics...
I think I understand you point here. My belief (we are
now in dangerous zone(;-)) is that the basic property of subjective
experience is nonmodellability but I could be wrong.
If quantum jump is modellable, the model must
explain why only a discrete subset of all
possible final states (eigenstates of 'measured' observables)
and predict correctly the probabilities of various outcomes.
Here is formidable challenge for IM.
MP
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