Stephen P. King (email@example.com)
Wed, 18 Aug 1999 13:53:03 -0400
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?
> 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
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.
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!
> 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. :-)
> 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". 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. 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?
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!
> 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. :-( 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".
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
> 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!
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.
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!
> 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 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) 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.
> > 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.
> 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! :-)
> > 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
> 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 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?
> 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. :-)
> > b) For extened reals also infinite integers
> > n are present. Certainly infinite values of n correspond to
> > 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.
> 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?
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 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!)
> 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!
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
> > 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?
> I will look.
It is strange, for me, that the "zeros" of the zeta function are
asymptotically equal to 1/2. (?)
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