[time 575] Re: [time 560] Zeno paradox, etc...

Matti Pitkanen (matpitka@pcu.helsinki.fi)
Thu, 19 Aug 1999 09:45:48 +0300 (EET DST)

On Wed, 18 Aug 1999, Stephen P. King wrote:

> Hi Matti,
> Matti Pitkanen wrote:
> >
> > Hi Matti,
> >
> > Matti Pitkanen wrote:
> > >
> > > Dear Stephen et all,
> > >
> > > the article about Zeno's paradox was fascinating.
> > > Some comments.
> > >
> > > 1. In TGD context quantum jump Einsteinian solution to Zeno paradox
> > > holds is modified somewhat. With respect to geometric time
> > > there is no motion: tortoise becomes 4-dimensional
> > > geometric object. With respect to subjective time
> > > the observed motion of tortoise is discretized with
> > > average time increment of about 10^4 Planck times per quantum
> > > jump: cognitive spacetime sheet jumps by this temporal distance in
> > > each quantum jump and sees new t=constant section of 4-dimensional
> > > tortoise (in good approximation).
> >
> > [SPK] Ok, but do you see that we have to allow for the existence of an
> > infinite (unenumerable!) number of geometric "turtles"? One question I
> > have is: Why do we have a geometric time at all?! We obviously have a
> > subjective time, but why postulate an "geometric" one?
> >
> > [MP]
> > Physics forces this. The entire physics starting from Newtonian physics
> > and ending to GRT and quantum field theories relies on geometric time.
> > The essential property of geometric time is that it is metric
> > just like space. Subjective time has not metric. The only structure in
> > the set of quantum jumps is that they are ordered. Psychological time
> > provides approximate statistical metrization for the set of quantum jumps
> > but would not be possible unless one had geometric time.
> 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.


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').

> 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.

> > 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.

> > [SPK]
> >
> > 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.

Besides this the topological inhomogenities representing particles
(CP_2 type extremals) and cosmic strings (galaxies) are present.

'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.

> 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.

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.

> 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 beeautiful 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.

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.

> 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!

> > 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

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.

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.

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.

:-( 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.

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.

> 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

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.

> > 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

> 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(;-).

> 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?

> > 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.

> > 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.

> What is
> more classical that a bunch of hard spheres in a box? To say "classical
> computation is one of the most recent evolutional
> developments in biosphere" is missing the point! Yes, our "knowledge"
> and ability to model abstractly such is indeed a "recent evolutional
> developments in the biosphere", but that is not my point.


> [MP]
> > > 2. I only now realized that every infinite prime, whose inverse is
> > > infinitesimal is smaller than 1/0, the largest possible infinity.
> > >
> > > 3. The concept of lexicon is phantastic but I could not understand
> > > the notion of rational as novelty and subsequent claim that motion
> > > is illusion.
> [SPK]
> > Let us talk about it further... :-)
> >
> > [MP] I added to the original posting some additional comments about
> > lexicons, generalized reals and generalized rationals.
> Thanks, your ideas are very thought provoking! :-)
> [MP]
> > > 4. I realized a nice manner to represent surreals (or whatever TGD
> > > version about extension of reals is). Consider definition of a finite
> > > real as pinary expansion:
> > >
> > > x= SUM(n>n0) x(n)p^(-n)
> > >
> > > a) For ordinary reals all *finite* integers n
> > > are present in series
> >
> > [SPK] Can we encode a description of an arbitrary material system with
> > them?
> >
> > [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?
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?).

> > 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!

> > 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).

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.

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.

> [MP]
> > > b) For extened reals also infinite integers
> > > n are present. Certainly infinite values of n correspond to
> > infinitesimal
> > > contributions in the expansion of x in negative powers of p.
> > >
> > > c) How should one define the part of expansion for which the values of n
> > > are infinite? One can make the expansion unique by following trick: sum
> > > over all n expressible as products of finite and infinite primes!
> > > If one can construct *all* infinite primes (I have constructed quite
> > > many good candidates!) one can make sense of this expansion
> > > at least formally.
> [SPK]
> > How long does it take the Universe to "do" this summation
> > operation?! Consider the problem of deciding if a given number is prime.
> > Does the Universe have a look up table? If it does, "where" is it
> > "written" and how is it "accessed"?
> >
> > [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 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?

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?

> 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?

> > 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.
Havin 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

> The local evolution of matter is the dual to the local evolution of
> mind. The increase in the thermodynamic entropy of the Body "pays for"
> the increase in knowledge of the Mind, just remember that Body and Mind
> are local notions, not global primitives. Thus you and I have different
> bodies and thus different minds. This implies that if our bodies were
> "combined" into one, so would our individual minds. We would lose our
> respective individualities.

> [MP]
> > > 5. Riemann zeta function contains product over factors over
> > > all primes. An interesting question is whether one could understand
> > > something about zeta function by allowing
> > > also infinite primes in the product formula
> > >
> > > Z(s) = Prod(p prime) [1/(1-p^s)].
> >
> > Does this paper give you any ideas?
> > http://www.cs.auckland.ac.nz/CDMTCS//researchreports/032crisRR.pdf
> >
> >
> > I will look.
> It is strange, for me, that the "zeros" of the zeta function are
> asymptotically equal to 1/2. (?)
I looked the paper. It is too technical stuff. I have never really
studied this topic. Perhaps when I become retired: now I am busily


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