Matti Pitkanen (matpitka@pcu.helsinki.fi)
Thu, 12 Aug 1999 10:31:26 +0300 (EET DST)
Dear Stephen and all,
I have snipped of text quite a lot since mail would have become very long
otherwise.
On Wed, 11 Aug 1999, Stephen P. King wrote:
> Subject: [time 516] Rational mechanics and payoff matrix
>
> Date: Thu, 5 Aug 1999 09:47:12 +0300 (EET DST)
> From: Matti Pitkanen <matpitka@pcu.helsinki.fi>
> To: "Stephen P. King" <stephenk1@home.com>
> CC: time@kitada.com
>
>
> Dear Matti and Friends,
>
>
> Please forgive the slowness in my response and the miserable condition
> of my grammar. I have not been myself lately! :-(
>
> On Wed, 4 Aug 1999, Stephen P. King wrote:
>
> > Dear Matti,
> >
> > Matti Pitkanen wrote:
> > >
>
> [MP]
> Certainly in real life: but does not strategy mean a rule which fixes
> the move and make thing predictable?
>
> [SPK]
> This "fixing" is contextual; it only applies for the particular history
> and the available information. I call this "contextual definiteness",
> contrasted with the "contrafactual definiteness" of classical logic. It
> is easy to forget, and slip back into the classical mode of thinking. We
> must constantly be on guard against this, for it clouds our
> understanding. For example, when we say that a "rule is fixed", is it
> necessary that this "fixing" be such for "all time"? The grue paradox
> shows the serious problem that this creates!
> http://bayes.phil.uiuc.edu/417/grue.html
If the strategy and rules telling when strategy is changed predetermines
everything. If free selection and unpredictability is involved situtation
of course changes. But this is trivial.
> >[SPK]
> > Matti! Are not the formal representations of Heisenberg's matrix
> > mechanics and Schrodinger's Waves and Feynman's path summations
> > mathematically
> > equivalent? Your point that "calculation of all these histories would
> > involve huge amount of computational work" holds for all of these
> > methods and is exactly why I am making a big fuss about computational
> > issues! Your point here is an example of my reasoning!
> [MP]
> What I am saying that only the sum over amplitudes is actually
> calculated. This would be like weighing a kilogram of matter by
> measuring the energy of every quark, electron and neutrino,
> separately
> and summing up the results. Something like 10^27 protons for instance.
> It is easier to put the matter in ordinary scale, takes five minutes,
> no need for building particle detectors and atomic smashers(;-).
> **
> But, you would admit that somehow Nature is doing this! The reality
> that is represented by an n-body Lagrangian is computed by Nature
> somehow, else the orbits of planets would instantly dissolve!
Here my philosophy is so different that I cannot follow your argument!
You claim that only possible realities are calculable realities and Nature
computes them somehow. I claim that the only restriction is internal
consistency and maximal generality (infinite-dimensional configuration
spaces with unique Kahler geometry and spinor structure..)
In any case, I understand that the idea about computer sitting at
its own terminal is extremely attractive. If my personal life
history were different I might defend this idea passionately!
> Then we
> think of time passing for a system, be it of planets or dust or a living
> organism, we must consider how it is that each event that could be
> measured of such by another system is selected. You speak of q-jumps an
> their initial -> final aspects, with this I concur, but I am saying that
> we are missing something. The logical implication or entailment
> relations that can be drawn from the information encoded in the events
> plays a strong role. It is insufficient to claim that event A physically
> causes event B without considering that the information state of B
> (represented by B*) be necessarily implied or entailed by the
> information state of A (represented by A*). Thus we say that A causes B
> iff B* entails or implies A*, thus time is dual to logic, they "flow" in
> opposite directions. What makes the difference in this line of thinking
> versus that of the traditional thinking is that it takes into
> consideration the information content of a given configuration of
> matter, the latter classical model only considers matter, its
> information content, and thus a mind, is a meaningless epiphenomena at
> best.
I understand this. You have dualistic theory. In my approach A=A*
(objective realities=ideas) and the new element is subjective causality
A--> B by quantum jump. Situation is different. A--UA-->B is quantum
computation (U is unitary evolution). In this vague sense I could of
course say that quantum jump computes itself but this would
perhaps be game with words.
>
> [MP]
> It is true that path integral in practice reduces to standard
> perturbation based on Gaussian integrals: but in this case it is only a
> formal and very elegant trick to derive the standard perturbation
> expansions. For instance, gauge invariant systems can be treated
> in very elegant manner unlike in Hamiltonian formalism: for instance,
> the calculation of infinite dimensional Jacobians reduces to
> perturbative
> calculations of diagrams involving fictive particles called
> Faddeev-Popov
> ghosts. The connection of infinite-dimensional integral with particle
> physics language is fascinating. But not even
> attempt is calculate path integral as a real integral defined by
> measure in this practical approach.
> **
> Exactly why do we do perturbation? Because we do not know how to solve
> n-body problems using infinitesimal calculus! This fact is forced upon
> us because the n-body problem has strongly non-integrable situations!
Yes. In quantum field theory infinite-dimensionality of the problem makes
perturbation theory the only sensical approach. Even more, perturbation
theory actually *defines* the theory. There is simply now other definition
of theory since path integral does not define integration measure
(exp(iS) appears instead of real exponent: this is the problem).
My proposal, actually much more than proposal, is configuration space
Kahler geometry and geometrization of physics (sounds
like final solution of certain problems proposed by certain
persons, huh;-). In this approach path integral does not appear.
Functional integral over 3-surfaces is defined by a genuine measure.
Path integral appears only at QFT limit of the theory as an elegant
book keeping trick, nothing more.
These problems are not just technical problems: they are
are related to fundamental philosophical problems. The origin of path
integral is Hamiltonian formalism basically as one learns by reading
Feynman's paper and Hamiltonian formalism relies on Newtonian concept of
time. It is not an accident that TGD leads to radical rethinking of time
concept.
> Why do we continue to "kick against the prick"? I admit that the
> integration problem may not be easy to deal with, I am not a
> mathematician so do not have a solution for such, but I have read of
> formalisms such as "interior set theory" that may help us in this
> endeavor.
> http://link.springer-ny.com/link/service/journals/00153/bibs/5034004/50340269.htm
> http://atheism.org/library/modern/graham_oppy/t_finite.html#fn4
> http://www.friesian.com/calculus.htm
> And Prigogine's Brussel's school is making bold attempts in this
> direction!
>
I try to find time to read this material.
> [MP]
> To put this in perspective from my side: the path integral is formal
> construct. In TGD it would mean summation of all paths in the space of
> configuration space spinors to calculate S-matrix elements and would
> be useless construct.
>
> In TGD however configuration
> space integral over 3-surfaces appears. It is integral in a sense
> of actual integration measure and involves
> delicate cancellations of standard infinites and nonlocality of
> Kahler function with respect to surface to avoid divergences. Using the
> language of Feynmann, the task of the demon calculating this
> integral would be to sniff the value of absolute minimum of Kaehler
> action for each 3 surface Y^3 on lightcone boundary. I believe that it
> is
> possible to sniff the value by symmetry arguments: infinite-dimensional
> group of isometries for configuration space.
> **
>
> Sure, but this Demon can not violate the second law in the meantime!
> The problem that I see, and I could be seriously wrong, is that pleading
> symmetry arguments is equivalent to postulating a priori synthetics. If
> we assume that particular values are given a priori (synthetics) then we
> are saying that these values are somehow calculated for free by the
> Universe! If we postulate the existence of an Oracle, such as a Platonic
> Form, (the quintessential a priori synthetic!), then we are required to
> explain how we communicate with such. Either way we are required to
> generate entropy (loose free energy) to gain knowledge.
> Please look at my link to Maxwell's demon:
> http://members.home.net/stephenk1/Outlaw/maxdemon.html
I think that your argument applies when one talks about how universe
becomes consciuous about laws governing its evolution.
The basic result in quantum theory of self-organization is that
self-organization, since it requires generation of new subselves
by quantum jumps reducing maximal quantum entanglement,
and also generation of larger selves by quantum entanglement,
requires entanglement feed and thus feed of entanglement entropy.
I would be that this just loose of free energy.
You are quite right in that Universe definitely calculates something.
We disagree on what it calculates. I could say that calculation is
quantum computation associated with each quantum jump. To gain
consciously experienced, subjective information, universe must quantum
calculate each quantum jump: A-->UA!
The objective information associated with the quantum states is not
calculated, it is there and is fixed by the uniqueness of
infinite-dimensional geometry.
>
> [MP]
> I have the feeling that integration over non-zero modes could be done
> explicitly. There is 'theorem' stating that any path/functional
> integral can be reduced to a Gaussian integral around classical
> saddle points/maxima of exponential of action. The 'theorem' of course
> fails in reality but works for completely integrable systems. I have the
> feeling that 'theorem' might work in p-adic context. Integration would
> reduce configuration space integral to sum of integrals around
> maxima of Kahler function for given values of zero modes. Note that one
> needs to consider only fixed values of zero modes since quantum jump
> involves localization in zero modes.
> [For the actual theorem see: Duistermaat, J., J. and Heckmann, G., J.
> (1982), Inv. Math. 69, 259.]
> **
> The serious lack of integrability in n-body systems makes this a
> serious problem! Have you ever read Poincare's discussion of the n-body
> problem? Or read Prigogine's The End of Certainty : Time, Chaos, and the
> New Laws of Nature?
>
Yes. Lack of integrability destroys makes the theorem only 'theorem'.
I hope I would have time to really look whether and how p-adics could
somehow help to make 'theorem' a theorem. I have not read Poincare's work.
I might have seen Prigogine's book. In any case I would feel great
sympathy since I have been talking about p-adic evolution and strong
NMP for years now: and I enthusiastically suggest that they are New Laws
of Nature(;-)!
> [SPK]
> > The "classical world" is a mental construction. It is NOT "out there",
> > it is in our head! So we are faced with the question: How does the self
> > "calculate" the path that minimizes the action? We know that the q-jump
> > is just such a computation; now we need to look more carefully how the
> > "measures" (Wiener integrals, etc.) are defined by the "way" that the
> > observation is made.
> [MP]
> Our philosophies are different.
>
> I believe that our mental constructions are much more than
> constructions, they are sensory perceptions, subject to all kinds
> of mis-interpretations and errors, but perceptions in any case.
> **
>
> I am talking about space-time as being a "precondition of experience",
> to quote Von Weizacker! A perception is an act of selection from an
> equivalence class (if we can use that notion) and we cannot assume that
> the particular properties are given prior to the perception, this is a
> clear case of the Einstein-Bohr disagreement. The fact that perceptions
> are prone to errors is the proof that objects do not have particular
> properties in-themselves, it is the subject-object interaction that
> defines the properties, and since we include dynamic behaviors in the
> class of properties, we are saying, with Erieden, that the observation
> defines the physics!
This I full heartedly agree. What we call reality are the
experiences which always are determined by initial and final realities of
quantum jump. Only in quantum statistical sense quantum history can remain
unchanged in quantum jump. But this does not mean that
this space of objective realities would not exist and would be
determined by uniqueness of infinite-dimensional geometry.
>
> [MP]
> Q-jump is computation but not in the classical sense. I must
> be able to mimick quantum jump in order to calculate something from
> my theory that is simulate what Universe is doing without slightest
> computational efforts. Computation begins when universe
> begins to simulate itself.
> **
> Yes, that is what I am saying! But, the act of the Universe simulating
> itself has a thermodynamic price! To be sure, the Universe, qua the
> totality of existence, does not "simulate itself", it merely "is"
> itself.
Ee agree. The differences result from the fact that you are dualists
and I am tri-partist.
> It is the acts of mutual simulation among the subsets of the
> Universe that is the subsets evolving toward equilibrium relative to
> each other. This equilibration, from the physical aspect, gives us
> thermodynamics and this translates over to a sense of flow, an arrow of
> time. The duality picture then explains how, for each subset of the
> Universe (an LS), the particular configurations that are taken along the
> way are selected by the logical entailment requirements of the mutual
> simulations of the LSs.
OK
> The bi-simulations occur between the subsets of the Universe, and it is
> they that constitute all interactions, and thus the act of observation
> is complementary to the maximization of thermodynamic entropy.
Here we disagree. I think that they do *not* constitute all interactions.
Cognitive spacetime sheets provide the geometric basis of simulations
and in standard physics there is nothing like cognitive spacetime sheets
and every standard colleague would claim that standard physics
explains everything except why someone can consider the possibility
that this might not be the case.
The phenomena of phantom DNA and homeopathy support the concept of
cognitive spacetime sheets but it would be waste of time
to try to convince any 'serious' colleague abou reality of
these phenomena. Non-undestood phemomena are not existing phenomena,
to paraphrase Wheeler.
> We must look carefully at what we mean by "classical computation"! If
> we are speaking of Turing Machines, we can easily prove that any
> classical differential equation can be matched to an equivalence class
> of TMs (differentiated by language) and so we can see that the Newtonian
> "clockwork" can be well-represented by a TM.
Is is true that continuum limit can be achieved or is the calculation
always approximation based on discretization to difference equation?
>Peter's discussion of the
> differences between well-founded and non-well-founded sets points out
> the essence of this argument. TM's are defined within precise initial
> (or final) Cauchy boundary conditions and are invertible. (On a side
> note, the halting problem of TMs seems to represent classical chaos! It
> is deterministic, but its simulation time is irreducible!)
>
> [MP]
> But we can forget our different philosophies. We have a common problem!
> You are talking about the path minimizing the action.
> I would be happy if I could calculate the absolute minimum of Kaehler
> action for given Y^3 exactly to simulate the universe.
> ********
>
> Ok, (Y^3 is the light cone surface?
Y^3 belongs to 7-dimensional manifold lightcone boundary xtimes CP_2.
Every point of lightcone boundary replaced by CP_2. Lightcone
boundary is moment of big bang in standard empty Robertson
Walker cosmology.
> I forget)… if so then we indeed
> have a common problem, but I am wondering if your requirements of
> "absolute minimum" and "exactly" are too strong! Where is the \epsilon
> of error fit in?
It enters the stage when one p-adicizes the theory (which is necessary
to calculate S-matrix). Errare humanum est. Only conscious selves have
the gift of making needed and the mapping of reality to
personal p-adicities of selves, bring in epsilon. Realities are precise
but experiences about them are not.
Your argument is correct in dualistic approach but my approach is
tri-partitistic. In dualistic approach epsilon of subjective experience
presumably requires similar epsilon at the level of material reality.
> I see a situation were the finite bound on the ability
> ("expressiveness") of a Local System allows for local minima and
> approximations, not absolute (global) minima and exact bi-simulations.
> Pratt's example of the strict binary involution of a Chu spaces give us
> a model that satisfies your strong requirements, but it is obvious (from
> the fact that error and irreversibility are experienced) that exact
> simulations are not realistic!
Exact simulations are not realistic, yes. But again tripartistic approach
comes in rescue: in TGD quantum histories are the basic realities,
which are simulated by various p-adicities.
One could also say that simulation is possible only if there is something
real which is simulated.
>We should say that it is the errors in
> the bi-simulations among the LSs (as subsets of the Universe) that given
> us time, for if exact bisimulations could occur, there would be no time
> or motion at all. Every action that could occur would occur in an
> arbitrarily small duration and such a situation converses to 1/
> \infinity or zero. Thus I say that time exists because everything can
> not happen at once. And this discussion does not get into the subtleties
> of non-commutativity and concurrency.
Time exists because everything cannot happen at once is nice argument
but does it still rely on (implicit) attempt to identify subjective time
development with geometric time development. Perhaps I am preaching
but I think that the realization that subjective and geometric times
are different, is a bottle neck idea. It resolves the standard paradoxes
of standard physics (nondeterminisn/determinism paradox, what were
the initial values, why reversible world of basic physics and dissipative
world of everyday experience,..) and leads to tripartism.
>
> [SPK]
> > That is ok, we learn from each other as we go! :-) Could you point to
> > a particular statement here that is difficult?
>
> [MP] DNF. Each exponentiation dualizes. We interpret.... proposition.
>
> Ok, I will try! :-) Pratt gave me this definition in response to my
> query: "DNF is disjunctive normal form. A logical formula is in DNF
> when it is a disjunction of conjunctions of literals. (A literal is a
> propositional atom or its negation.)"
> The notion that "each exponentiation dualizes" relates to how
> residuation works, thus if we take the power of a SET we get an
> anti-Set, and if we that the power of it in turn, we get back a Set.
Here I am not sure whether I can follow. I will look at the paper.
> His definition of "truly mental propositions" seems to relate to the
> use of Complete Atomic Boolean Algebras (CABAs) which completely
> describe the logical relations of a closed system, I think. :-)
> It is best to read and re-read ratmech.ps, Pratt's paper to understand
> his subtle notion. This is a paradigm shift, and a big one! We can not
> understand Pratt (or Wegner) when we use the old paradigm…
> [MP] Yes this of course also my view an standard view
> but this was my interpretation of 'The former is physical causality or
> $impression$, flowing forward in time from events to states'. 'From
> events to states'! Events correspond to 'physical plane' and states
> correspond to 'mental plane'. This causation would be from mental to
> physical or vice-versa rather than mental to mental or physical to
> physical.
>
> Yes, that is the whole point of the Pratt's duality. Look at the first
> paragraph of section 2, pg. 3. "A physical event a in the body A
> impresses its occurrence on a mental state x of the mind X" and "dually,
> in a state x the mind [X] infers the prior occurrence of [an] event a".
> After thinking more about your point here, I see what you are saying and
> I can only conclude that your reading of ratmech is incomplete!
Certainly! But impressing and inferring is from physical to mental and
vice versa and Pratt is indeed talking about causal interaction *between*
the planes.
> Pratt clearly says in the abstract: "We apply Cartesian logic to reject
> …an assumption that Descartes somehow himself neglected to reject, that
> causal interaction *within* these planes is an easier problem than
> between." I would agree with the criticism that Pratt is not a good
> philosopher when it comes to arguing his idea to death, like most
> professional philosophers, but I can forgive that and "read between the
> lines" and grasp the implications of his words, couched as they are in
> the jargon of computer science.
> It is when we try to model the physical interactions (Body <-> Body) or
> model the mental interaction (Mind <-> Mind) that we must use the
> algebra (if it could be called that) of residuation. The mechanics" of
> bisimulation make this point obvious! Common sense aside, my physical
> body does not interact directly with your my body. The choice of my
> body's next event that would appear to the material monist as a
> "reaction" by considering all possible mental states that would be
> entailed by such a change, the one state that best encodes the logical
> entailment has a dual event, which is the one that is chosen as the next
> event of my body.
I believe that I understand this. Reaction is in this approach something
which best encodes the logical entailement and determines reaction.
I also relate this to earlier discussions about conduction/inductions.
Is this reaction always unique and if not, is this nonuniqueness
identified as explanation quantum non-determinism and free will?
I also understand why universe must calculate itself into existence
in this approach.
In my approach, it is quantum computation which occurs,
at each step and leads to some final state when computer computer halts.
Quantum computation and Psi_f is in well defined sense reaction to the
final state Psi_i of the previous quantum jump since that state appears
as initial state for U: Psi_i--UPsi_i. Probabilities for
various Psi_f are however determined by quantum measurement hypothesis,
strong NMP and by Born rule. I do not attempt to determine Psi_f by any
consistency requirement.
> You see, we adapt to our expectation or prediction of each other's
> behavior, not the actual behavior, since "actuality" is not "out there"
> in some unique absolute space-time, it is contextual, tensed, contingent
> and local. This is obvious since we can not perceive each other
> directly, we can only perceive our own subjective version of each other.
> This follows from the notion that knowledge of the In-itself is not
> obtainable, be it the Universe or any of its subsets. All we can do is
> to choose a "next" event and state that best fit the context. Exactly
> what the mechanism is still a mystery, but there is evidence that
> somehow consciousness influences the probability distributions of
> "random" events, http://www.fourmilab.ch/rpkp/pk-rad.html , and it need
> not be that of a human!
>
I would bet that quantum entanglement is the mechanism(;-).
>
> [SPK]
> > The neuro-motor
> > activity follows physical causality, the particular action that results
> > follows from the selection of one particular physical movement out of
> > the many possible by the action of mental inference, the mental
> > (information) state dual to the neuronal pattern "consults" all possible
> > physical events and select the one that closest one to the movement
> > required. (We need to frame this in the mathematics of bisimulation, my
> > wording here is merely metaphorical!)
> >
> [MP] I think this is roughly my view: quantum jump
> selects between degenerate branches of multifurcation of
> spacetime surface: this is volitional action. And the ordering of
> quantum jumps automatically fixes the time ordering.
>
> Sure, but the total ordering of the q-jumps is NOT a priori given, it
> simply can not be as such a notion would directly contradict the
> experimental evidence of QM, such as interference of electrons "fired"
> one at a time through a two slitted barrier and particularly, "quantum
> eraser" experiments.
>
But quantum jump order themselves automatically!
If I had just pairs m-->n , r-->s , k--> l, there would
be no ordering. I have however m-->n, n--> p, p-->s!
n-->p cannot occur before m-->n!
Your argument holds probably true in the framework based on standard
time concept. But subjective time, geometric time and time parameter
appearing in the informational time evolution are
different in TGD framework!
The predictions of TGD for transition probabilities are exactly
of same general form as in standard QM.
The reason is that in standard physics S-matrix is calculated
assuming infinite interaction time (this is done for calculational
purposes, but *completely* routinely!). In TGD infinite interaction time
associated with U is actual (and has nothing to do with our
psychological time).
I want to emphasize the fact that all paradoxes of standar QM
and its 'craziness' are due to the fact that one does not make
distinction between these three time evolutions and tries to understand
all three time evolutions as single time evolution. When new
time concept is introduces, the craziness of QM disappears.
>
> [MP]
> Does the duality between matter and mind imply that the two spaces
> are more or less isomorphic from the requirement that
> it presevers some basic structures? Is the mapping matter to mind
> one-to-one mapping?
>
> OK. Let's forget this and ask what 'description' really means.
> Is it possible to describe system as such? Or are all descriptions
> only comparisons as they seem to be in my own approach (contents
> of cs depend on initial and final states of qjump).
>
> Is the number of descriptions of the system same as the number of
> configurations of system? I think one should ponder this problem first?
> ***
>
> Let me address the first question: "Does the duality between matter
> and mind imply that the two spaces are more or less isomorphic from the
> requirement that it preservers some basic structures?"
> To be honest I fail to see the connection between the isomorphism
> (which they are not, they are "complementary" like a directed graph and
> another graph with the directions reversed) and the "requirement that it
> preserves some basic structure". What structure? There is no "inherent"
> structure in a so called "objective" sense! We only have all possible
> events and all possible states as the constituents of the Universe. The
> distinction between the two is only a subjective one, dependent on the
> relational structure that the LS, as a subjective observer, imposes due
> to its history of bisimulations with other LSs. Thus the duality only
> holds between the LS as their relational structures, there can be no
> particular relation outside of these.
> Your second question: "Is the mapping matter to mind one-to-one
> mapping?" When it has that property, in the sense that the residuation
> generates a greatest fixed point under the Chu transform, an example of
> which is the exponentiation operation, between the set of possible
> events of a LS as a body, and the anti-Set (or Set^op) of possible
> states of the LS as a mind.
> Your third question relates to the nature of a description. What is a
> description? Could be say that a description of a system is an internal
> relational structure that "represents" for the observing system. This is
> what is happening when a perception occurs! When we generate a poset of
> symbols that is a physical implementation of the information inferred
> from the bisimulational observation. Let's say that the poset in
> question is a book. When another observer "reads" this book, what is
> going on? First, the producer and the reader of the book must share
> sufficient similarities in their posets of observations such that a
> third observer could bisimulate both of them within a single maximally
> self-consistent observation.
> Your fourth question: "…are all descriptions only comparisons, as they
> seem to be in my own approach (contents of cs depend on initial and
> final states of q-jump)." Well, your model seems to say that minds are
> given as "cognitive space-time surfaces", so if the residuation
> formalism, when applied to your model works, then we are only differing
> in semantics. :-)
> Your final question is interesting: "Is the number of descriptions of
> the system same as the number of configurations of system?" Well, it
> appears that there is a connection between these two since each distinct
> (disjoint?) description has to be implemented or encoded in a distinct
> configuration of the system. Thus, when we consider a "quantum
> computation" with its superposition of state vectors, we are superposing
> the information content thereof also, if we think of state vectors as
> being physical. If we think of quantum state vectors as "information",
> then we expect a complementary superposition of the physical events
> entailed by such. I see Penrose's "one graviton criterion" notion as an
> example of this! Umm, this does smell like TGD!
Thank you for thorough explantion. I must consider your comments in detail
later.
> [SPK]
> > Yes, we agree on this. I am saying that the mathematics of bisimulation
> > that Peter discusses are the best way to think of this. Peter's
> > "expressiveness" captures your thinking about "Higher selves can have
> > only abstracted..." :-)
> [MP]
> > > This forces selves to build simulations of the subsub...selves
> > > on their on spacetime sheets. We are indeed doing busily
> > > Monte Carlo calculations on elementary particle physics.
> [SPK]
> > That does this tell us, that we resort to random samples to model
> > particle properties?!
> >
> [MP] Yes. We simulate statistical determinism. Probability
> distributions for the configurations of outcoming particles.
>
> Also discretized functional integral is evaluated by Monte
> Carlo. This is like measuring the are of lake by surrounding
> it by square of 10 kilometers times 10 kilometers and bombarding
> it and counting the hits per the total number or bombs
> in this area to get the area of the lake. Very simple computationalism!
> Very far from construction of infinite-dimensional geometries but those
> who have the money can understand what is done and find these activities
> rather rational as compared to playing with infinite-dimensional
> spaces!
>
> I wonder why this is so? :-) Are we using a method that Nature uses to
> "compute" what "locally happens next"? I think so! I see something
> similar in the way that the Hausdorff dimension of a fractal is
> calculated… Umm, I would like to hear more about the Monte Carlo method,
> as you see it. :-)
>
You already heard my opinion(;-)! Of course, it is necessary to calculate
and computational phyhsics is needed. My point was that human mind
(and minds with which it can get entangled) is much much more intelligent
and has huge intuitive powers: it is sad that decision makers try to
reduce physics to calculations allowed by our primitive computer
technology. A good example is the attempt to reduce the path
integral of QCD to lattice. Minkowski space is replaced by
Euclidian space in the first step (just a calculational trick, as they
say). At the next step infty^4 points of M^4 are replaced by something
like 10^4 points of lattice. Approximations of this nature might
destroy the original theory totally but they do not care.
> [SPK]
> > The idea that Natural Selection is a Universal Principle is becoming
> > more tenable. Lee Smolin and Loius (?) Kauffmann and advancing it in
> > their books... Again, we see this reflected also in Peter's model of
> > computation; interactive computers "evolve"!
>
> [MP] I found that Pinker (computationalist) was rather near to my
> views about Natural Selection, whatever it really means.
> He did not agree with those who claim that it reduces to say
> self-organization in classical sense (no
> quantum jumps so that everything is determined from the initial
> values). Or that complex determistic systems automatically generate
> something which might be called life. There must be some local
> principle
> leading to selections and selection must be something absolutely real.
> **
> Sure, I agree. I see this happening in Hitoshi's LS model, but I am not
> sure what you mean by: "absolutely real". Do you mean that selection is
> not "subjective"?
Selection really occurs, it does not only seem to occur.
I use 'subjective' when I talk subjective experiences, not as something
which can be 'illusory'. Subjective experiences are one aspect
of existence. Illusions are created by unfaitful cognitive representations
and poor simutations.
> If so, that we would seem to not understand each
> others definition of "subjective"! For me "subjective" refers to the
> observations that can be had by actual LSs
OK. We agree.
. This is equivalent to saying
> that "as I write these words on this keyboard, I have the subjective
> experience of being in a room, with children making a racket in an
> adjoining room, with a TV showing some SciFi show, etc.". This is an
> experience that I am perceiving and I expect that another observer, that
> I can communicate meaningfully with, would have a similar subjective
> experience. When someone writes or says "absolutely real", I wonder: "to
> whom?" How is it "absolutely real"? How could it be otherwise, e.g. what
> would falsify such a statement? Against what "standard" would I compare
> it to? The funny thing is that "absolute standards" involve by their
> very nature infinite regress!
I was just saying that selection occurs: materialist would argue
that no actual selection occurs and that our conscious experiences
only cheats us.
>
> [MP]
> I identify the basic principle as p-adic evolution automatically
> forcing evolution and implied by localization in zero modes implying
> classicality of observed world. Strong NMP is second principle involved.
> And self-organization by quantum jumps. Self-organization
> could be understood as SELF-organization: selves are indeed generated.
> Selves within selves within ...
> **
>
> So are you saying that the ordering of primes decides in an a priori
> way the phylogenic order of organisms?
Also that. Ontogeny repeats phylogeny is just a metaphor. p-Adic
topologies form natural hierarcy: the larger the p the fine is the
topology. Also maximal information gain in quantum jump increases
with p: p*log(p) or at least as log(p). Complexity theorist would
say that the prime characterizing effective p-adic topology
measures the degree of complexity of system.
> I can see that this would follow
> from a Platonic philosophy of mathematics, but does not the fact that
> many distinct and mutually exclusive geometries and number systems and
> be shown to be consistent makes us wonder if maybe we are taking our
> ability to imagine a bit too seriously? The anthropic principle is one
> example of this!
>
There are actually not too many finite or finite-dimensional number
fields about which I know(;-). Reals, p-adics, finite
fields, quaternions, octonions. Function spaces are local number
fields but if function has zero inverse is not everywhere finite.
Any other? Also quaterions and octonions
could have very natural place in TGD (dimensions of
spacetime and imbedding space contra dimensions
of quaternions and octonions). Finite fields emerge
naturally also: p-adic integers modulo p form finite field.
Consistency in finite-dimensional context is of course very mild
principle. As I have repeatedly mentioned, it is infinite-dimensionality
which makes things nontrivial. A good example is the paper about
noncommutative geometries and divergencies by Chaichian et al: again
on dream for infinite-dimensional calculus seems to have collapsed.
I can only tell that if follows from the basic structure of quantum TGD.
TGD is certainly not the only possible theory of universe one can imagine
but it is unique on very general grounds
Of course, mathematics is not enough. I would not spend 8 years
with p-adicization of quantum TGD unless I p-adic mass calculations
had not been so succesfull.
> [SPK]
> > To be honest, I looked at the first chapter of your (on-line) book and
> > I wonder how phenomena can be calculated easily with it! I am looking at
> > the philosophical aspect of Quantum gravity, I firmly believe that
> > Nature is performing computations that make our miserable machines look
> > like stone age tools! :-) I believe that physics is really about
> > figuring how Nature works so that we can aim the cause-effect in a
> > direction more friendly to our human needs.
> [MP]
> The point is that computations are not involved.
> Symmetry principles dictate almost everything. What can be done
> at this stage is to derive theorems (actually 'theorems'): numerical
> calculations are completely out of question at the level
> of infinite-dimensional configuration space.
>
> For instance, particle mass squared spectrum is fixed completely from
> Super Virasoro invariance. The masses of light particles can be
> calculated from p-adic thermodynamics: symmetry
> dictates again almost everything. The calculations are
> extremely simple since perturbation theory in powers of 1/p
> converges extremely rapidly. Predictions are excellent, which
> made me to take p-adics deadly seriously.
> **
>
> Umm, I don't have a good argument to write here now about using
> "symmetry principles" to argue "why things are as we perceive them", but
> I think that we must be very cautious about doing that!
Things are not as we perceive them using only our five senses! The world
of CP_2 length scale is something which we do not certainly perceive
by direct sensory experience. Experiences of selves involve something like
10^40 subsequent quantum jumps typically and average about these! The
world of Super Virasoro representations is what one encounters at single
quantum jump level.
I think that the success of abstract theories of physics demonstrates
to me invincibly that there is something behind our experiences.
The Platonic realm of objective realities, not only single objective
reality.
> For example
> circular orbits are more symmetrical that any other shape of orbit, and
> this example was used to defend the Ptolemic model of the cosmos! Just
> because our model has beautiful epicycles does not necessitate its
> "actuality". In fact, all physics is about the intellectual pursuit of
> the means by which to predict and control Nature. We must NEVER forget
> that our models, no matter how esthetically pleasing, are just models,
> and not IT!
You are right about esthetics. The only defense for the
huge symmetries of configuration space geometry is that without
these symmetries it simply does not exist. Riemann connection
is divergent, curvature tensor is divergent, etc...
If cancellation of infinities requires symmetries, I must accept
symmetries. It is of course nice that symmetries are also
esthetically satisfying and that these symmetries lead to
predictions which agree with what I can find from particle data
tables.
Models and theories are different thing. Theory-world separation
is one aspect of dualism. In my tripartistic approach theory is the
the world: objective realities= ideas. Subjective existence involving busy
construction of models is which occurs between two worlds, two ideas.
> [MP]
> My strong belief is that physics at this level cannot be done
> by computing but using symmetry arguments to guess the result and
> then proving it. Calculation of S-matrix elements (have not even tried
> that although I know from symmetry arguments that string model
> type formalism results) should
> also reduce to symmetry principles.
>
> I already mentioned the p-adic version of Duistermaat-Heckmann theorem
> could make it possible to calculate the functional integrals involved
> analytically: the 'theorem' of real context would be theorem in
> in p-adic context.
> **
>
> You do not understand what I mean by "compute"! :-) Computation, to me,
> is the process by which, given a situation representing a question, lack
> of knowledge etc., a system undergoes a selective act that desides the
> answer, solution, etc. What a IBM microcomputer or Gateway 2000 system
> does is an example of this. I am claiming that each time a q-jump
> occurs, it involves a computational act. Please understand that my
> definition here of "computation" is not a theorem, it is just a
> definition that came to mind as I considered your staements… :-)
>
There are of course many different manners to define computation.
I can quite well say that each quantum jump is quantum computation.
I do not believe that it would be useful
to try to somehow model this quantum computation by cutting it into
pieces. This is microscopic level. At macroscopic level
self cascades have same hierarchical structure as computer programs
and would provide a model for cognition and conscious thinking.
It resembles computation although it is not deterministic.
For instance, logical deduction is a sequence in which the
generation of new selves also changes the premises so that
logical consistency is always achieved!
> > > ********
> [SPK]
> > Of sorts, but we are taking category theory, so we have equivalence
> > classes of each. Infomorphisms (or residuations, same thing) are
> > identifications between subsets of the the two equivalence classes. So
> > we match a particular mind with a particular body by considering the
> > duality: what mind best describes the body that best implements the
> > mind. So the notion of MNP is very close to my thinking! :-)
> [MP]
> Amusing coincidence. I am just pondering the following problem. How
> on Earth do I know that the me of today is the me of yesterday if my
> self has slept over night (not existed). How do I even know
> that the me of yesterday existed subjectively: perhaps I was
> born when I woke up?(;-)
>
> Umm, it could even be said that you came into existence five minutes
> ago, with a full set of memories (encoded in your brain's neural
> topology), and that all that you can infer subjectively is just what can
> be entailed from this.
Actually I would say just this: short term memory is naturally identified
as subjective memory. We wake-up and fall asleep all the time.
> We can dismiss this conundrum, by understanding
> the computational power required to generate the poset of information
> involved in the subjective experience far exceeds what is available in
> the brain of the individual at the moment of the earliest memory.
> William Poundstone's discussion in Labyrinths of Reason; Paradox,
> Puzzles, and the Frailty of Knowledge (January 1990, Anchor; ISBN:
> 0385242719) is excellent.
>
I whole-heartedly agree. It is known that autobiographical memory seems
to be practically unbounded (as I read from some paper on page
of Chalmers). This is one objection about standard computationalism.
Situation changes if there is hierarchy of selves having longer and
longer subjective memories, extending over entire lifetime, entire
hierarchy of short term memories. These memories
are not coded to wiring of neural network. We can perhaps
communicate with higher selves and get access to
these higher level short term memories: when I am not in
wake-up state I am entangled with larger self and communication of long
term memories occurs during this period.
There is also geometric 'memory' making possible intentionality
and same applies to it.
> [MP]
> I think that the solution relies on two kinds of memories:
> 'memory' with respect to *geometric time* and memory
> with respect to subjective time (memories about
> previous quantum jumps).
>
> Geometric 'memory' is made possible by
> the temporal duration of cognitive spacetime sheet represeting
> me: might be of order lifetime.
> Geometric memory can be also about geometric future and is more
> like temporal intentionality, plans, beliefs, expectations about
> what happens if there were no selves around making quantum jumps
> and replacing spacetime with a new one and spoiling everything.
>
> Second memory is subjective memory: self experiences all
> the quantum jumps it has made after wake up
> as single whole and is thus an extended objected in
> subjective time (measured by quantum jumps).
> **
>
> Matti! How can "temporal intentionally, plans, beliefs, expectations"
> have any meaning whatsoever independent of an actual observer?
It cannot. Observer, self of course experiences.
'Geometric memory' only realizes intentionality as one aspect of conscious
experience! Without quantum jumps and selves there would be absolutely
nothing intentional!
> Do we
> have to repeat the Einstein-Bohr debate? What does the Heisenberg
> Uncertainty imply to you? To me it implies that subsets of the Universe
> have no properties what so ever in an objective sense. Only when a
> subjective act of observation occurs, be it "directly" with eyes or
> "indirectly" with a computer controlled sensor, can we say that X has
> properties A and none other.
I think we agree about Uncertainty Principle: I have already earlier
explained this. By the way, the fact is
that Bohr mis-applied it to explain double slit experiment: this
was proved experimentally for some time ago. The reduction of quantum
entanglement explains the results of experiment just as TGD predicts
The experiments strongly indicate that it is brain or some macroscopic
subsystem which is entangled and quantum jumps.
It is perhaps good to go through Einstein-Bohr debate briefly.
It was just the quantum jump concept what Einstein could not accept. His
motivations where completely reasonable: the determinism-nondeterminism
paradox. TGD solves this paradox and shows that Borh and Einstein were
both right in their own ways. Quantum histories are deterministic as
Einstein argued and quantum jumps occur as Bohr argued: the solution of
dilemma is that quantum jumps occur between quantum *histories*,
not between time=constant snapshots.
> And, its even more complicated, since
> "fact" that X has the properties A, only holds during the brief interval
> of time that is involved. When we stop looking at the moon, we can only
> infer that it is still there, to state that it "exists" with such a
> brightness and size, etc. independent of the observation is a serious
> mistake! The tree falling in the woods, does not make a sound! We can
> infer from our memory that it most probably would, but that is not an
> "absolute reality". There is no such thing!
>
> [MP]
> This is new feature in theory: earlier I was forced to believe
> that single quantum jump determines competely the contents of
> cs and that genuine memory about previous moments of cs
> is not possible and results only from simulation of past.
> The notion of self allows however to give up this
> assumption: subjective memory about earlier conscious experiences
> after wake-up is possible.
>
> Subjective memory forms kind of a heap of
> geometric 'memories'= expectations of future and this entire
> heap is experienced. For instance, comparison of subjective
> history (what actually occurred) with geometric
> histories (expectations) should be primitive mental act not
> modellable in any manner. Perhaps all comparison reduce
> to this fundamental act of comparison.
>
> OK. After this lengthy introduction I go to the
> possible solution of problem. Although I have no subjective
> memories about yesterday's me, I have the geometric memory about
> my body existing yesterday and I deduce that this body
> must have been conscious since this body resembles
> my recent, very conscious body. So I indeed identify my yesterday
> me as the best fit to my recent body!
> **
>
> I see this situation of "geometric memory" as the "mental state" of the
> environment that is acting as an observer itself of your body's events.
> The world observes me when I observe it, we define each other as we
> bisimulate each other..
>
Something like this, at least when we speak about purely classical
physics for which quantum jumps are not important. In this
case 'geometric memory'/simulation is reliable.
> [MP]
> BTW, what might be the fundamental irreducible mental
> acts performed by conscious mind (self) and not modellable?
> Also computationalist should answer this question.
> Comparison could be one such act. What other irreducible mental acts one
> could imagine?
> **
>
> The subjective "stance" or viewpoint of another mind can not be had by
> a mind other than that "having" it.
Quantum entanglement with higher self containing me and you
as subselves makes this possible. But can I remember anything of
this experience? Can this higher self only communicate its experiences
to me indirectly?
> This follow from the tacit
> assumptions involved in the definition of "subjectivity", thus I agree;
> the specifics of a particular mental action are not modelable, in the
> sense that it is not possible to "copy" the quantum state (using the
> usual meaning of the word state), but we can simulate "what it might be
> like to experience some act". Umm, I am missing your point here! :-)
> What do you mean by "irreducible mental acts"?
Something which cannot be reduced to something simpler, in
computationalism some basic operations which cannot be reduced
to smaller submodules.
Best,
MP
This archive was generated by hypermail 2.0b3 on Sat Oct 16 1999 - 00:36:29 JST