[time 581] Re: [time 575] Time and dualism

Stephen P. King (stephenk1@home.com)
Fri, 20 Aug 1999 08:50:01 -0400

Dear Matti,

        This response was not written chronologically from beginning to end...
I try to think and revise as can. :-)

Matti Pitkanen wrote:
> On Wed, 18 Aug 1999, Stephen P. King wrote:
> > Have you read Stuart Kauffman and Lee Smolin, "A possible solution for
> > the problem of time in quantum cosmology,"
> > http://www.edge.org/3rd_culture/smolin/smolin_p2.html, gr-qc/9703026)
> > and Hitoshi's response? My thinking about "geometric time" is very
> > reflected in Smolin & Kauffman's article, particularly
> > http://www.edge.org/3rd_culture/smolin/smolin_p3.html.
> No.

        If you get a change, could you? It would help us to understand each
other! :-)

> > It is impossible
> > for there to exist a clock external to the configuration space and thus
> > it is impossible to associate any particular "time" or history ordering.
> Geometric clock is impossible and is not even needed. Subjective clocks
> are needed. I have suggested in 'Self and Binding'
> (http://www.physics.helsinki.fi/~matpitka/selfbind.html) a model
> of clock as a subself waking up periodically. The model explains
> why subjectively experienced time runs slowly when we get bored,
> why time disappears totally in whole-body consciousness (there is
> no subselves awake and hence no clock and hence no time!), what might be
> involved in those states of mind in which time stops (for instance,
> you are in car accident: by the way, there is a book of Oliver Sacks
> telling from persons who lived in this state for decades:'Man who
> mistook his wife for his hat').

        Ok, what Hitoshi and I are contending is that if it is impossible to
define a clock, there is no such quantity as time! You said: "Geometric
clock is impossible and is not even needed.", thus the notion of a
"geometric time" is meaningless! Unless we are referring to the M^4-
past light cone, them I agree with you...

> > What Hitoshi and I are arguing is that Local Systems, which map into (?)
> > subsets of the Universe, and thus into (?) its configuration space, have
> > a scattering propagator that allows for the association of a clocking
> > act with the local system. Thus LSs can have time, but with the caveat
> > that their is only subjective time. The notion of an objective time is a
> > logical contradiction, it fails to pass the CE requirements!
> Objective/geometric time is logical contradiction if you require it to
> have the properties of subjective time (arrow, 'clockability',
> irreversibelity). This requirement is perfectly natural if you
> dualistically insist that universe is computer in the sense that its
> hardware is dual to its software. I however assume that only geometric and
> informational time development correspond to the dynamics of reading
> head of Turing machine and the problem disappears.

        If "geometric time" does not have the qualities of "[an] arrow,
'clockability, [and] irreversibility", what qualities does it have that
allow us to think of it as time? I really don't understand! :-( The
"dynamics of reading [writing] of the Turing [machine] head", for me,
speaks to the interaction of matter and information; it is the
operations of record generation that are an essential aspect of any
observation. H. H. Pattee's work gets into the specifics of this.

> > > Second reason is that in the world without geometric time we could
> > > not have any emotions: a world without possibility to get
> > > frustrated now and then would be a dull place. The reason is that most
> > > emotions result from the comparison of geometric time development
> > > providing expectation for what will happen with what happened, that is
> > > subjective time development.
> > > *******
> > I do not feel that appeals to emotions are useful for we do most
> > understand them; all we can do is "feel" them. We can at least say that
> > they are subjective. :-)
> I think we can say something about emotions. Many
> of them involve comparison of what was expected to happen and what
> happened. This differentiates them from pure sensory experiences.
> By the way, this is the reason why computationalism is able to
> model intentional things like desire and goal in brute manner.
> Emotional intellect is now realized to be decisively
> important for survival. Persons who have only rational intellect
> are no values are victims of combinatorial explosion! Think
> about person busily computing whether to kill or not to kill the person
> sitting nearest in the bus.

        I really don't understand how you relate emotions to "geometrical
time". From what the neurophysicists tell us, emotions involve
variations in neurotransmitters and seem to involve specific areas of
the brain, the limbic system (I think). Emotion seem to be "valuations"
that weigh sense impressions in the short term memory, associated with
the limbic system, in a way that looks like the creation of a basis and
inner product for vectors.
        Emotions are usually not "chosen", that would require the ability to
choose the valuation and it appears to be out of the reach of the
awareness. Persons are very rarely "aware of themselves being aware".
This takes a lot of effort!
> > >
> > > For geometry, we
> > > only need a 3+1 manifold, M^4. As it is, as you say, static, it has no
> > > "change" related to it. Time is a subjective measure of change.
> > > My problem is that you seem to assume the existence of an "outside"
> > > observer that can tell the difference between a Planck length of
> > > duration h and \infinitesimal + h. What does this entity use to measure
> > > the difference?
> > > [MP] M^4_+xCP_2 is completely static. Spacetime surface
> > > X^4 is dynamical in the sense of classical physics and is absolutely
> > > necessary but from spacetime view point could be said to be static.
> > > Quantum average X^4 changes in each qjump.
> > Let me be sure I understand your concept here! Are all curves
> > (geodesics) embedded in X^4 surfaces invertible? This is what I take
> > "dynamical in the sense of classical physics".
> I meant 'dynamical in sense of classical physics' in sense of classical
> field theory: classical physics is specified by the time evolution
> of induced metric (gravitational field) and induced spinor connection
> (classical electroweak fields) and classical color field.

        Huh? I had the impression that spinors and "color" (in QED and QCD) are
purely quantum, e.g., having no classical version... I am confused!
> Besides this the topological inhomogenities representing particles
> (CP_2 type extremals) and cosmic strings (galaxies) are present.

        Umm, I am skeptical of the "cosmic strings"... I find the plasma
physics model of galaxies to be more tenable, at least it is testable in
the laboratory!
> 'Geodesics are invertible' requirement is based
> on the idealization based on the point particle limit: in TGD
> framework geodesics would give approximate description for cm mass
> motion of em neutral spacetime sheets glued to larger spacetime sheets and
> idealized to points. Actually these spacetime sheets can get glued
> and decay: this would correspond to Feynmann diagrams describing
> particle emission and absorption (CP_2 extremals). All this is
> 'classical physics' in TGD framework.

        Interesting, this picture looks similar to Hitoshi's, except for the
details about CP_2 extremals and "em neutral spacetime sheets"... In
Hitoshi's model all "direct" observations give classical situations, QM
behavior can only be inferred from "corrections". This corresponds to
your statement that the self can not be modeled, we can only infer its
properties, bounds, etc. ...

> > This makes the dynamics
> > of such incapable of manifesting time! See M. C. Mackey's Time's Arrow:
> > The Origin of Thermodynamic Behavior for the proof.
> This proof is based on identification of geometric time with subjective
> time, which is what standard physics does. But in TGD situation is
> completely different. Subjective time measured
> by quantum jumps has in principle nothing to do with geometric time.
> Subjective time is irreversible, geometric time is not.
> In statistical sense click of subjective clock corresponds to
> 10^4 Planck times of geometric time but only in statistical sense.

        No! Mackey works from a reinterpretation of thermodynamics based on
"densities". It occurs to me that there is something strange about your
definition of "subjective time"! Since you associate q-jumps with, what
I would call "moments of consciousness" (MC), the observer associated
with a particular poset of q-jumps can not separate one MC from another!
In other words, an observer will never be aware of its own clock's
reading directly. Observers get around this by making records of events
that are observed and the recordings are arranged in posets, thus the
observer can infer its "clocking rate", but it can not observe it
directly. This is directly related to an observer's inability to
directly observe itself. "I can only see a reflection of my face, not my
face it self."
> Besides this, every cognitive spacetime sheet has its own
> subjective time. Cognitive spacetime sheets are the counterparts of clocks
> associated with LS:s. Geometric spacetime is full of cognitive
> spacetime sheets, from Big Bang to infinite future, and each is measuring
> time consciously! Life is 4-dimensional phenomenon: entire spacetime
> is alive at this subjective now, not only this snapshot of cosmic time,
> this is dramatic deviation from standard view.

        Yes! Just as LSs each have their own "subjective time", but this, as I
just explained, is an action, a clocking action. Each LS, or cognitive
spacetime sheet in you model, has its own "measure of change". If there
is no change in a system, e.g. it is static, it was neither a time
associated nor the ability to observe change!

> > You say that the
> > q-jump is, in effect, an alteration of X^4's "quantum average. Ok, how
> > is this an observable? Where is the "change" coming from?
> Dissipation is one signature. Fundamental physics predicts reversible
> world. World is however irreversible. This forces to introduce
> besides reversible World I the not so beautiful World II.
> In TGD World II is envelope for the sequence of reversible World
> I:s. For instance, an interval of one second about World II is
> like envelope for 10^40 curves representing World I:s.

        Can you isolate why "Fundamental physics predicts reversible world"? Is
it because of the use of infinitesimal calculus and the association of
"time" to an absolute external parameter of change? Mackey conclusively
proves that a reversible world is NOT the world that we experience. If
it has any reality, it is solely in our minds! I have issues with the
whole Platonic Ideals notion! The idea that there exists a static realm
of pure qualities (and quantities, for mathematics!) seems to be at odds
with both thermodynamics and QM!
        Umm, I find Jerome Rothstein's ideas helpful! and my paper
        I need more information to understand you World I and II concepts...
> Second signature is the prediction that also geometric past changes
> in quantum jumps between quantum histories. The experiments of Libet,
> Kornhuber and recent experiments of Radin and Bierman, in which
> time direction of causality seems to change, find nice
> explanation in this framework. For instance, when person decides
> to raise his finger, EEG activity in brain starts before the person
> raises the finger. What happens that person jumps to new history in
> which EEG activity (no quantum jumps!) starts before the decision.

        It look to me that what is changed in a q-jump is the
information/material configuration of the LS. The LS, as an observer,
could imagine that there is an actual one-to-one isomorphism between its
internal configuration that encodes its history dependent memory and
some "external" space-time, but this is only an illusion. Your point
about Libbet et al's experiments seems to support Pratt's dictum
"cognito, ergo eram" (I think, therefore I has").
        We can model "geometric time" as the time that multiple observers can
communicate consistently to each other about, and that boils down to
cross-entropy or overlapping in their subjective histories and thus
their clockings.

> > The problem is that it is impossible to define change "from within" a
> > static system or its spaces. I get around this by showing that subsets
> > of a totality that is static are not necessarily static, so long as the
> > totality is unknowable (and/or undecidable, see Smolin's comment!), e.g.
> > that the whole can not be mapped uniquely to any particular subset in a
> > constructable in finite time manner. Both Hitoshi and Mackey have proven
> > theorems that show similar concepts to this!
> You are probably right: the measurement paradox of quantum theory is
> example of what you claim. But we have different assumptions. You assume
> that entire system is static. I assume quantum jump: this is the change!
> Quantum jump does not occur within the world: it replaces entire world
> with a new one!

        Sure, but one observer's "entire world" is not necessarily every
observers world! It is consistent for there to exist "entire worlds"
that have different "physical constants" and the observers of them would
be unable to communicate effectively with us. It seems that we both
agree that observation is change. I agree with your claim that a q-jump
"replaces entire world with a new one". I am only saying that the
Universe, the totality of Existence, is static. We are never aware of
it. All q-jump computations are only mappings or identifications between
subsets of the Universe. Hitoshi's definition of time uncertainty gets
into the details of this...

> > > Selves are observers and correspond geometrically to cognitive spacetime
> > > sheets. They drift quantum jump by quantum jump to future since
> > > the macroscopic spacetime changes in each quantum jump (the location
> > > of cognitive spacetime sheet of self on it changes). Therefore selves
> > > 'see' different temporal cross section of the *material* spacetime
> > > sheet in each quantum jump. This material spacetime sheet does not
> > > change much in quantum jump: cognitive spacetime sheet shifts its
> > > temporal position.
> > Is a "cognitive spacetime sheet" static? How is a cs sheet different
> > from a ms sheet? Its vacua values? I really do not understand this at
> > all.
> This would require visual thinking: words are practically useless.
> There are two-dimensional illustrations about cognitive spacetime sheets
> on my homepage. (http://www.physics.helsinki.fi/~matpitka/illuab.html, I
> think)

        I found it: http://www.physics.helsinki.fi/~matpitka/illua.html Umm,
looking at it, it struck me that you say "There is rather precise
metaphor making possible to understand the concept of induced gauge
field intuitively. The shadow (projection!) of a nondynamical solid
object ( < --> metric and spinor connection of H) with time-independent
size and shape to a surface (<--> 3-surface) changing its size and shape
is dynamical." I agree, but, as my friend Al asks, *what is altering
the object such that the shadow can change*? I see interactions are
driving q-jumps which alter what is projected. This is how I see
interactions as "act-ualisations" of the subsets of the Universe.
Specific properties are condensed by observational acts and recorded
into matter.
> a) Cognitive spacetime sheet is piece of M^4 slightly deformed
> in direction of CP_2.
> b) CS is glued to MS or possible larger CS.
> c) CS has FINITE time duration. MS has INFINITE
> time duration (forced by the presence of conserved energy, momentum etc).
> When CS begins, the tiny energy possessed by CS flows to it from MS and
> back to MS when CS ends.

        Here we have great differences in notions, maybe... ;-) I can think of
a cognitive spacetime sheet, in my way of (dualistic) thinking as that
*space-time sheet* identified by the information collected by a mind
during a "moment" (which I am identifying with your notion of a q-jump).
This assumes a residuation type relation between a mind's information
content and a configuration of matter/energy. It does have a finite
duration/extension as you point out. I do not see "energy" as a quantity
applicable to the mind, it is a material aspect not a mental aspect. The
similarity between thermodynamic and information entropy (they differ by
a sign) manifest the way that the duality works. Generation of thermal
equilibrium <=> gaining of knowledge
> Everything is static in 4-dimensional view.
> With respect to subjective time the temporal position of CS at MS is not
> static. In each quantum jump it changes and this gives rise
> to arrow of psychological time.

        Sure, each observation in a "moment" is 4-dimensional. Hitoshi's
discussion of the apparent Hubble expansion involves this!
> Think just a sphere, CS, 'glued' to planar surface (MS). Call x-axis
> time axis. In each quantum jump this world is replaced by a new one and
> x-coordinate of the sphere increases on the average.

        But, this is inherently problematic as it tacitly suggests that the
"increases on the average" are just stochastic. How do we consistently
represent the alteration of the quantum history due to interactions
(measurements)? This picture of yours is too a priori synthetic for my
taste... :-(

> :-( Umm, you say " selves 'see' different temporal cross section of
> > the *material* spacetime sheet in each quantum jump", this is very
> > similar to saying that an observer's consciousness observes different
> > "slices" of space-time as "it moves along the direction t"... This is
> > part of the "4-dimensional block o' space-time" model that also says,
> > explicitly, that time's is an illusion, that "it is in our mind".
> No!! The whole point of the argument is that quantum jump replaces
> spacetime surface containing material and cognitive spacetime sheets
> with a new one.

        Sure, we agree; but it difficult for me to understand how... I believe
that space-times are defined by the range of motions and transformations
of cm points of LSs, space-times that "contain" no matter are impossible
to define. They are, to me, like "free particles", just convenient
mental fictions.
> The temporal position of cognitive spacetime sheet changes in this quantum
> jump, material spacetime sheet does not change much. Therefore cognitive
> spacetime sheet 'sees' different small temporal portion
> of material spacetime sheet, for instance a new reading of purely
> classical clock ticking on the wall. I suggest direct visualization
> of the idea: it is extremely simple.
> Cognitive spacetime sheet gives actually about small time interval,
> I was just simplifying things to make the connection with standard
> picture clear.

        Umm... :-( I see the "standard picture" as deeply wrong. We must
consider the subject-object relation as fundamental in physics, we can
not maintain that the world just exists. It does, indeed, exist, but in
what particular state and what particular event? That is not an
existent. We could say that the specific content of an experience does
not precede the experience itself!

> > Ok, we agree that "time is in our mind"! The problem is that there
> > seems to exist more that one mind, and there does not seem to be any
> > particular a priori ordering of space-time "slices" "out there"! What to
> > do?
> I think that you misunderstood my argument.
> There is no ordering of geometric time and no ordering of geometric time
> is needed. The ordering of geometric time is misconception
> induced from the failure to distinguish between subjective and geometric
> time.

        So why do we have a geometric time at all? Is it because of your use of
a "M^4_+ future light cone"? I must say that I have a serious problem
with this! All that an observer can "see" is within a M^4- past light
cone, the M^4+ is not "out there" any more than "tomorrow" is out there
waiting for me to get to it. Actually, the "past" only is actual in that
records can be found of its events, it is not "out there" either! The
events that are experience by observers are "put together" by their
observations, each observer's acts select from the infinite potential
(of Existence) to actualize an observation. The recording of such is
dual to the selection.
> The apparent ordering of geometric time induced from ordering of
> subjective time measured by quantum jumps. In statistical sense the
> geometric time observed by cS=temporal position of CS, increases by
> 10^4 Planck times in single quantum jump. In hope of making things clear
> I use the phrase 'psychological time' instead of geometric time
> when I talk about time experienced by us.
> Each cognitive spacetime sheet experiences its own psychological time.
> Cognitive spacetime sheets are perhaps a realistic version for
> a continuous distribution of clocks around spacetime, which, at least
> to me, is too hard an idealization.
        The idea of a "continuous distribution of clocks around spacetime" is
impossible if we require the spacetime to be Diff^4 invariant! This is
one of the key points that led Hitoshi to his model.
   "a cause of the problem of time seems to lie in associating time to
each point which has no positive size. No clocks can reside in a
sizeless point. At the stage of special theory of relativity, this
difficulty does not appear: Time is associated to each inertial frame
which can accommodate actual clocks. At the stage of general theory of
relativity, the field equation with the invariance postulate with
respect to diffeomorphisms requires one to eliminate the size of the
frames in which clocks reside." http://www.kitada.com/#pre

> > > Only subjective experience tells differences
> > > and these temporal differences are on the averages of order 10^4
> > > Planck times if the simplest guess is correct.
> > > I hope this is answer to your question: I am not quite sure whether
> > > I understood the question properly.
> > It is most important that we continue this conversation such that we do
> > reach an understanding! :-) I apologize if I seem to need some humility!
> I think that you might catch the idea just by looking the illustrations
> of cognitive spacetime sheets on my homepage. The idea trivializes in
> whole-body consciousness mode and this mode communicates with
> figures(;-).

        I am having a hard time interpreting your illustrations... :-( I have
pictures of my own that give me fits! I think I understand this
whole-body consciousness. :-) I have pictures, more like immersion
experiences that overwhelm me. I had one the other day about loop spaces
defined by CTL's (closed timelike loops) and was looking at the behavior
of electromagnetic fields and light rays...

> > It is just so frustrating to see an obvious problem to be completely
> > ignored by the majority of persons that profess to be interested in the
> > situation at gives rise to the problem in the first place! Time requires
> > a means to define it, without a constructable clock, it is a
> > contradiction to say that there is a parameter t such that motion is a
> > function of t.
> I agree partially: there is deep problem! I however see the problem as
> confusion between subjective and geometric time. Subjective time ticks and
> is consciously measured and something quite new is needed to achieve
> this: you call this new LS:s, I call it CS. Geometric time just
> continuously and majestetically exists just like space (and reading head
> of Turing machine(;-).

        OK. I just wish I could see it like you do... So long as we are careful
about a priori synthetics...

> > Newton postulated a divine entity outside of the Universe to give
> > himself an absolute measure of time. With the advent of Special
> > Relativity, we see that space and time can not be considered separately,
> > but we now have an absolute space-time, requiring an already burdened
> > metaphysical entity to also constantly carry a ruler so that its "laws"
> > remain inviolate. Is such an entity subject to the Uncertainty
> > principle? If it is, that it has a serious problem!
> Depends on which is the framework from which you start. In any case,
> special relativity already shows that time is like space and geometric
> time and subjective time are different: we do not experience
> subjective time as 4:th dimension! Therefore geometric and subjective
> time must be basically two different things! The question
> becomes: why the contents of our conscious experience are
> located around definite value of geometric time and why this
> values seems to increase?

        Umm... why then do people identify the reals with temporal events? Your
idea of "values seem to increase" is usually associated with "the
thermodynamic arrow" in the literature...
        Thinking further as I talked to Al last night, I can see geometric time
as the M^4- lightcone structure of events that is illustrated by looking
out into the night sky and considering that the further away a point of
light is from my "moment of now" the "further back in time" it is. SO I
think that I am softening my thinking about geometric time, but with the
caveat that each observer has a version of geometric time (M^4-) thus
making it subjective. The idea of an "objective geometric time" can be
derived from the overlapping of subjective geometric times. The
discussion of the Robertson-Walker metric by Hitoshi as giving an
appearance of a expanding 'universe' follows logically...
> > > The problems are created if I assume that entire time development
> > > is computing. I however assume that classical physics, classical
> > > spacetime and unitary time evolution U belong to hardware, the
> > > quantum computer itself: only the subjective time development involves
> > > activities like computation.
> > Why is "entire time development is computing" a problem? If the
> > "classical behavior" is the hardware, the "Body", we naturally associate
> > the "subjective time development" which "involves activities like
> > computation" with the "Mind". What is crucial is that there is not a
> > single unique and absolute "Body" just as there is no single unique and
> > absolute "Mind", unless, of course, we continue to appeal to
> > metaphysical entities to prop up our equations!
> > The key understanding is that the Universe in itself, qua existence
> > itself, is neither Mind or Body, it is Existence. Mind and Body are dual
> > aspects of its subsets. To posit that the Universe has such is to assume
> > that existence is finite, and this is a contradiction! It fails to pass
> > the CE test!
> I would say something resembling this: subjective existence is in
> quantum jump. Universes/quantum histories themselves are LOGOS=COSMOS
> but without consciousness.

        To me LOGOS is a verb, an act... I do agree that Universes/quantum
histories themselves have no consciousness, but only when we are
considering them from the perspective of observations. The
Object-Subject relation is, I believe, symmetrical. Every object that I
can perceive is, in a sense of interactions, perceiving me.
> > > I believe that classical computation is one of the most recent
> > > evolutional developments in biosphere. If this is the case
> > > then it is wrong to assume that basic cognition, and even more, entire
> > > physics would rely on classical computation.
> > Our definitions of computation are completely different! It has been
> > proven that a system of billiard balls can implement any computation
> > that can be implemented by a so-called universal Turing machine
> > (UTM).(http://www.cs.berkeley.edu/~jimlin/bball/whatis.html).
> [MP] But the problem is that classical Turing machine is too restricted
> model for computation as conscious beings do it.
> That one can model classical physics by Turing machines (forgetting
> now the problems caused by initial value sensitivity) does not
> mean that classical time development is actually a computation.
        If any classical system's behavior can be modeled by a UTM and a UTM
can be implemented in a classical system, I see a connection between
time and computation! (Noting that this particular model assumes unique
initiality conditions) Now that we have good models of quantum
computation, such as Peter's, we can understand better how time works in
a quantum context... It is just a model, a way of thinking after all...


> > > [MP]
> > > I would say that it is impossible to code all information about say
> > > real valued function on real axis to single real.
> > Why not? That does see to be what Calude et al are saying... It has
> > been proven that the set of all UTMs is isomorphic to the set of Reals;
> > I could be wrong! :-)
> The point is that the values of function are set of reals with
> cardinality or reals, call it C. You should put C infinitely long
> decimal expansions to row and get still real, is this possible?

        Yes, I think so. A diagonalization of a R x R matrix is within R,
unlike the integers...

> Calude speaks of *rows of integers* having finite expansion.
> Also rationals have periodic decimal expansion and information
> about rational can be coded by finite number of decimals (right?).
        Let me see... "Any finite sequence [of symbols] can be unambiguously
coded in binary (or decimal) and thus corresponds exactly to some
rational number." What I am making noise about is that "symbols" are
matter codings of information. (Without matter it would be impossible to
make records, thus disproving Idealism...) Umm, another thing about
Calude's Lexicons are like programs, they need material configurations
to be read, e.g. reading heads - tape, etc.
> > > The only manner to
> > > achieve this is to perform discretization. Pinary cutoff would
> > > be this discretization in TGD. Reals would be replaced by subset
> > > consisting of rationals and function would have values in subset
> > > of rationals. In this case single real would code the whole function.
> > I don't understand. :-( How is the subset chosen? What role, if any,
> > are played by the irrationals?
> >
> Single very important word was missing : '...code the whole function
> *approximately*! Pinary cutoff!

        Yes! The finiteness of the observations (experiences) are an effect of
the finiteness of the result of a pinary cutoff?!
> > > Interesting possibility is that generalized rationals defined
> > > as ratios of generalized integers having infinite primes in their
> > > decomposition to powers of primes could help somewhat.
> > I don't understand the rules or principles here. :-)
> >
> I generalize integers by starting from the decomposition to a product
> of powers of prime.
> N= Prod_k p^(n_k).

        Could you give me a specific numerical example? The algebra symbols
give me no pictures. :-(
> Usually only finite primes appear in this product. Now I allow also
> infinite primes and their powers and get infinite integers. I believe that
> the construction for all infinite primes exists.

        What cardinality does the set of these primes have? Umm, this looks
like a alternative to the continuum hypothesis...
> Then I define generalized rationals as
> R= M/N.
> Depending on M and N they can be infinite, infinitesimals or
> also finite as real numbers.

        Interesting! I like to think of this as a reason why we only experience
rational values. :-)

> > > [MP] You certainly have some practical problems if you believe that
> > > universe does not contain any hardware, which is just given. Even Turing
> > > machine fails to be pure software: its reading head cannot be a part of
> > > program and thus corresponds to 'tacit' information (I know that you say
> > > that dualism might help but I am not sure about this).
> > It is problems like this that lead me to dualism! I don't see the logic
> > of the use of the words "'tacit' information". Is Dennett a material
> > monist? Is "information" an epiphenomena of matter for Dennett?
> > http://artsci.wustl.edu/~philos/MindDict/epiphenomenalism.html This
> > would imply, in combination with the notion that "all observers exist in
> > (embedded in) a single unique space-time), that the "program" could be
> > defined as the behavior of reading heads.
> I really do not know the position of Dennett but as a physicist and
> dedicated tripartist(;-) I see a problem.

        I agree with your assessment of Dennett, he is a bit too smug...
> I admit of course, that I do not understand the delicacies of the
> dualistic approach: perhaps dualist sees software and hardware as duals
> of each other: in this kind of situation itw ould make sense to replace
> reading head with a program. But is our world dualistic?

        Exactly! software and hardware behave dualistically. We can replace the
reading head with a program but we are merely swapping the duality
> Probably I do not understand what computation really means in dualistic
> approach and how it differs from my intuitive notions. Could one consider
> a model of Turing machine as a challenge for dualistic approach?

        No. The Turing Machine is dualism's best witness! Mind is dynamics of
information, software, in the usual sense, is just a linear version of a
mind. Body is the dynamics of matter, hardware... The interaction of the
two is given not by exchange mechanisms but by bisimulation, e.g. the
behavior of matter and mind simulate each other. It is in the actions of
each that they make contact, mental states via logical precedence
chaining and matter events via impression of configurations.

> > I tend to agree with Spinoza and Russell, in that "the mental and the
> > physical are simply two modes of a more basic substance (it should be
> > noted that strictly speaking, Spinoza was not a property dualist as he
> > held that the mental and the physical were two of a possible infinite
> > number of modes of the basic substance, nevertheless he is typically
> > labeled as one). For Spinoza, this basic substance was God. Thus the
> > only real thing is God, who is neither physical nor mental. Spinoza's
> > position is similar to that of Russell's neutral monism, however the
> > latter is not committed to the belief that a supreme being is the more
> > basic substance." http://artsci.wustl.edu/~philos/MindDict/monism.html
> > I see the "basic substance", not as a "substance" or "God", but as
> > Existence itself. (On a side note, Being and Becoming are not
> > fundamental as they are tensed and Existence is tenseless!)
> I understand. Sarfatti is dualist and my bitter enemy, he
> not-even-wrongizes me in every possible instance: what do you
> think about Sarfatti?
        I find Sarfatti to be abrasive and close minded. I do not understand
Sarfatti's version of dualism.

> > > Personally I am convinced that geometry, both finite- and
> > > infinite-dimensional and hence physics apart from quantum jump
> > > in TGD framework is what might be called 'tacit' information: it this the
> > > quantum computer itself, the hardware of it. Quantum jumps define
> > > subjective time development having computational aspects, in particular,
> > > pinary cutoff and (generalized?) rationals emerge at this level.
> > > Universe as a mere program seems impossible for me: also
> > > hardware is needed.
> > We only differ in the choice of words to use in some respects, but it
> > is important to note that the properties of the "hardware" are just as
> > contingent as those of the "software", they depend on each other to be
> > defined! This is what Pratt argues!
> This is what dualistic approach tells. In tripartistic approach software
> and hardware are different things and not mappable to each other. Of
> course, computationalism itself becomes only an ideal since each
> self(!)-organizing time evolutions obey only statistical determinism.
> Having written computer code I know how difficult it is to simulate
> ideal computer. The successes of gene biology (personal histories of
> identical twins) however suggests that statistical determinism works quite
> nicely.

        ok. I am very interested in this notion of statistical determinism. :-)
Could you elaborate on your thinking about it?



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