Matti Pitkanen (matpitka@pcu.helsinki.fi)
Fri, 21 May 1999 18:54:15 +0300 (EET DST)
On Fri, 21 May 1999, Stephen P. King wrote:
> Dear Matti,
>
> Matti Pitkanen wrote:
> snip
> > Actually I am speaking about spacetime surfaces in my own approach.
> > Absolute minima of Kaehler action. Imbeddability as
> > smooth surface to M^4_+xCP_2 should make everything rather well defined.
> > I might equally well speak about 3-surfaces
> > with sufficiently general definition of 3-surface since minimization of
> > Kahler action associates to 3-surface spacetime surface.
> > By nondeterminism of Kaehler action, this means allowance of unions of
> > spacelike 3-surfaces with time like separations, and this brings in
> > 'thoughts' interpreted as surfaces of this kind: multisnapshots of
> > classical time development.
>
> 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.
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.
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.
Conscious thought is quantum jump selecting from quantum superposition of
multitime snapshot 3-surfaces one.
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.
>
> > About your hypothesis. Basic problem is that observer with free will is
> > inconsistent with the determinism of physics. Speaking about observers
> > means dualism. The basic problems and paradoxes of various are dualisms
> > discussed by Chalmers in his book: Chalmers was a believer of interactive
> > dualism but quite convincingly showed that it does not work.
> > Hard problem is one of the problems: if contents
> > of consciousness are determined by 'function' of the system, that is
> > by the dynamical development of system, it is very difficult to see
> > how free will could fit into the picture.
>
> I will read Chamers book to try to understand the reason why he thinks
> that interactive dualism does not work. It is this information that I
> need to critique my thinking since I am advocating a type of interactive
> dualism! From my thought so far I would answer "if contents of
> consciousness are determined by 'function' of the system, that is by the
> dynamical development of system, it is very difficult to see how free
> will could fit into the picture" by saying that there is something
> fundamentally wrong with the very concept of determinism!
> 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 Isee this as the relevant initial value problem in
QM.
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...
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.
> We first need to figure out exactly what we mean by "free will" and
> "causality"!
I already did it, see above(;-)!
>
> > 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.
>
> 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.
Perhaps Consistency Implies Existence comes in rescue here!
Infinite-dimensional mathematics does not allow too many internally
consistent patters of regulatity!
> 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.
>
By epiphenomenon I mean something derivable from the properties of
physical state alone.
About what you say quantum nondeterminism I do not agree.
Unfortunately I do not know enough about Pratt's ane Wegner's notions
to comment.
> [MP]
> > > > Various observations given very limited information about
> > > > reality which itself changes in every moment of consciousness. Could
> > > > this be sufficiently general to be free of internal contradictions?
> [SPK]
> > > Yes, each observation involves only finite amounts of information and
> > > the content changes in every moment of conscious! How this changes and
> > > what are the trade-offs is important. The statement "consistency implies
> > > existence" is a two edged sword! We must understand that given finite
> > > information only a lower bound can be placed on the internal consistensy
> > > of observables. Reality, for me, is the Totality and it is, as a whole,
> > > unknowable, e.g. it is impossible to map an infinite set onto a finite
> > > set in a unique manner. Or am I wrong on that? :)
> [MP]
> > You are quite right. Fortunately, it seems that moments of consciousness
> > somehow manage to give very deep and abstract information
> > about Totality: our ability to form abstractions and experience
> > logical consistency is something remarkable. I really believe that
> > basic property of consciousness is formation of abstractions:
> > we cannot solve a simplest differential equation numerically in our head
> > but we can play with infinite-dimensional geometries.
>
> We are getting somewhere! :) Could we consider "abstractions" as traces
> or spanning subsets or finite Hamiltonian paths over the set of point
> \elem Totality or some other formal notion? (I don't know the right
> word.) :(
> Some work has been done outlining the limitations and strengths of
> neural network computers vs. serial computers that deal with these issue
> you raise. It would really benefit us to understand better computer
> science. I am thus requesting for all to study his papers.
>
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.
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.
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).
> snip
>
> > > > Criticizing again the idea of observer (without denying that it is
> > > > certainly very useful approximate concept at practical level).
> > > > Couldn't communication be basically an observation in which communicators
> > > > form larger unit of consciousness?
> > >
> > > Yes! :) Communication acts are mappings from one space-time to another,
> > > if we follow Edelman's line of thinking in "Bright Air, Brilliant Fire"
> > > so your notion are accurate. I am trying to understand consciousness as
> > > a quantum-like action and can be composed to for different sized units.
> > > The information content can vary within the uncertainty trade-offs so it
> > > is not an atom in the classical sense. The closest I have seen this idea
> > > discussed is in Pratt's papers. I wil try to write up this more.
> > > The key understanding needed is that observations involve computation
> > > of the involved minima. Such are not "free"! The computation of the
> > > Lagrangian of a system has a price tag in free energy available to an
> > > observer. When we think about the computations involve in the traveling
> > > saleman problem we see clear example of this notion.
> > >
> > 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....
This archive was generated by hypermail 2.0b3 on Sun Oct 17 1999 - 22:10:32 JST