Stephen P. King (stephenk1@home.com)
Mon, 24 May 1999 23:23:55 -0400
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.
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)
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. 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.
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.
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! 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.
> 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... ;)
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...
> 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.
> > We first need to figure out exactly what we mean by "free will" and
> > "causality"!
>
> I already did it, see above(;-)!
:)
[MP]
> > > If one wants to describe observer in manner consistent with physical laws
> > > one ends up with identification of consciousness as a property of physical
> > > state or as a process and this in turn leads to conclusion that
> > > consciousness is epiphenomenon, no free will. This of course assuming that
> > > physics is deterministic. Quantum nondeterminism does not help since
> > > the concept of observer is equally problematic in
> > > standard quantum physics context, to say nothing about quantum
> > > nondeterminism itself. My impression is that talking about observer
> > > involves assuming too much.
[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...
[SPK]
> > You say that "consciousness is epiphenomena", what do you mean by that?
> > We really need to have a model of "free will". I find Pratt and Wegner's
> > notions to provide a natural way of thinking of "free will", explicitly
> > in the notion of "branching time". We remove the artificial notion that
> > all possible is available at the beginning and model process as able to
> > update and adapt to new information as it becomes available.
> > This, in my opinion, makes all the difficulties and hard problems of
> > consciousness and free will disappear! :) BTW, quantum nondeterminism is
> > just stochastisity, the absence of causality. It is a wrong notion also.
[MP]
> By epiphenomenon I mean something derivable from the properties of
> physical state alone.
Ok. :) That is what I thought but I have to be sure. :)
> 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
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. 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!)
> 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? 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! :)
>
> c) One model is very simple and related to a model of genetic code
> in terms of so called Combinatorial Hierarchy. It is somewhere at
> my homepage. Statements are taken to be Boolean valued maps.
> One starts with two element set, basic statements, and forms all possible
> maps. 2^2 alltogether. One throws one away and gets 3. At next stage one
> forms all statements about these statements: 2^3 allogether and throws
> one away. 7 alltogether. By continuing one obtains 3,7, 127, 2^(127)-1,
> statements. These are Mersenne primes forming so called combinatorial
> Hierarchy at level 127 the number of mutually consistent statements
> is 64, number of DNA:s. Also the number of amino acids +stopping sign (21)
> can be identified by closer inspection of this structure formed by
> finite fields G(n,1), n= 3,7,127,.. and their coset spaces.
> One can identify general form for genetic code as a map (not unique).
This is very interesting! :) I can see how p-adic are so useful! :)
snip
> > > I love to disagree! Do conscious observations really involve
> > > computation? I tend to believe that something much much simpler is in
> > > question (no need to say, quantum jump, the miracle!). Thoughts as
> > > associations or sensory experiences. . 2+2=4 as learned association of
> > > symbols rather than computation. Somehow I feel that computationalism
> > > is modern version of the clockwork models of mind based on gears and
> > > springs.
> >
> > 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...
Onward!
Stephen
This archive was generated by hypermail 2.0b3 on Sun Oct 17 1999 - 22:10:32 JST