Matti Pitkanen (matpitka@pcu.helsinki.fi)
Mon, 13 Sep 1999 14:23:30 +0300 (EET DST)
On Sun, 12 Sep 1999, Stephen P. King wrote:
> Dear Matti,
>
> Matti Pitkanen wrote:
> >
> > Dear Matti,
> >
> > Matti Pitkanen wrote:
> > [SPK]
> > > John Baez explains well my problem with QFT and symmetries!
> > >
> > > In article <sNluueA1XM03Ewgw@upthorpe.demon.co.uk>,
> > > Oz <Oz@upthorpe.demon.co.uk> wrote:
> > > >In article <7qpnl4$78f@charity.ucr.edu>, John Baez
> > > ><baez@galaxy.ucr.edu> writes
> > >
> > > >>(Personally I suspect that the whole idea of spacetime as
> > > >>a manifold breaks down at this point, but we really know
> > > >>rather little about these things - though we calculate
> > > >>endlessly and publish lots of papers.)
> > >
> > > [MP] I express point of view immediately. What breaks down, according
> > > to my belief, is the approximate identity of psychological and
> > > geometric
> > > time in time scale of order 10^4 Planck lenghts. Psychological time
> > > is discrete (the center of mass temporal coordinate of cognitive
> > > spacetime sheet increases the average amount by about 10^4 Planck times
> > > in quantum jump). No revolutions in understanding of geometric time:
> > > Riemann did something rather final!
> >
> > [SPK]
> > I see that you could understand what I has thinking right away! :-) But, you
> > are a minority in not seeing a problem with the concept of "geometric
> > time"! One problem I have is how do you model the communication between
> > two observers, do you propose wormholes connecting their "cognitive
> > space-time sheets". I am having trouble translating your fixed geometry
> > ideas over to my "every thing is process" way of thinking...
> >
> > [MP] Spacetime is not fixed: every 10^4 Planck times it is
> > replaced with a quantum superposition of new ones!
>
> This, to me, implies the a priori existence of an equivalence class of
> space-times! This is conceptually equivalent to a spinoral configuration
> space if we assume a spinor type relation to exist between any pair of
> space-times in the equivalence class...
> My main thought is that while the "existence" of space-times is real,
> we are seriously mistaken when we assume that a "space-time" has any
> meaning outside of the realm of observation. We observe objects that
> have metrical relations with each other, but the particular metrical
> relations can not be said to be "objective" in that they would have
> particular meanings , they are only meaningful within to observers. They
> are an aspect of experience. Even Spinoza recognized this, but his
> theistic leanings lead him to assume that "God" was the observer that
> gave them meaning. We can not have such metaphysical "obscurum per
> occultum" notions at the foundations of a model that is supposed to be
> falsifiable!
[MP] I do not know what you mean 'outside the realm of observation':
in TGD quantum jump is quantum measurement and fixes
macroscopic aspects of spacetime.
In any case, for me the ultimate criterion is physics. The
great discovery of Galilei was objective reality. Gradually
this objective reality became more and more geometrical.
The present day physics relies on spaceetime concept 'outside the realm
of observation': quantum field theory is formulated
in fixed nondynamical spacetime and works excellently
if one forgets the failure to construct quantum gravity
and difficulties with color confinement.
Of course, approximation is in question and TGD is
the next step making spacetime genuinely dynamical.
Giving spacetime concept up would mean starting from scratch. Every
concept of physics relies on geometric spacetime: momentum, energy, force,
angular momentum relty on isometries of spacetime. For example,
hydrodynamics is just conservation laws for energy and momentum plus
structural equations! Schrodinger equation in wave mechanics follows
from Galilei symmetry realizes as isometries. Dirac equation
results from the concept of spinor structure which geometrizes
in natural manner spin.
One can give all this up but I really wonder how one could
reproduce present day physics without concept of spacetime.
I regard philosophical clarity and consistency as crucially important
but physical facts dictate my philosophy, rather than
some pregiven beliefs.
I do not understand what you mean by nonfalsifiability
of the hypothesis. Geometric framework leads to
extremely detailed predictions: consider only mass
spectrum which is universal. These predictions are
testable. Also the physics as infinite-dimensional geometry
hypothesis is testable: recall that the resulting geometry seems to
be more or less unique.
>
> > Information transfer occurs certainly via wormholes since
> > they mean physical contact. "Ontogeny recapitulates.." suggests
> > the following that the following rules are OK.
>
> But this is were I come to a grinding stop in my understanding of your
> thinking! If two observers that are communicating is modelable as a pair
> of space-time sheets that are connected by wormholes, there would be a
> certain cohomology algebra definable over the whole. This is talking
> about the algebraic properties of loops that can be shrunk to points on
> the surface of the sheet.
Topology is important, but it is only part
of the story.
>I think of the sheet as an n-genus manifold,
> like a torus with n-handles. Your q-jump idea seems to imply that we can
> jump from a n-tourus to a m-torus n=/=m. This is very controversial! I
> would recommend that you read: Quantum Norm theory and the quantisation
> of metric topology, by Isham, Kubyshin & Renteln, Class. Quant. Grav. 7
> (1990) 1053-1074. I'll send you a copy if you would like.
>
Topology change occurs in two manners in TGD.
a) Topology change can occur classically, via
cobordism: the topology of 3-surface can changed during
its time development. For instance, 3-surface can decompose
to two. Elemantary particle reactions correspond to
this kind of cobordisms. There is actually only single
conservation law involved: one can assign to boundary
components of 3-surface holomology charge
telling its homology equivalence class. If
spacetime surfaces are orientable this charge
is conserved, if they are nonorientable this charge
is conserved only modulo 2.
[In GRT the requirement of global time orientation
defined in terms of everywhere vanishing timelike
vector field makes topology changes impossible. In
TGD there is no reason to apply this constraint.
Global time orientation is defined by the arrow
of the imbedding space time (lightcone proper time): again imbedding
space saves the situation. Imbedding space
time orientation makes it also possible to define
the concept of positive and negative frequencies
which is problem in GRT.]
b) Topology change can occur purely quantum mechanically.
Configuration space spinor field disperses from 3-topology
to a new one. In this case no spacetime surface interpolating
between initial and final topologies need exist. Also
the past changes topologically.
I remember that I read Isham's work at 1990:s or so: we
still had then preprint room serving as coffee room and there was
communication between people: now there is only competition! p-Adic
topology means that effective topology becomes dynamical. I believe that
the success of p-adic topology is basically related to the fact
it allows to regard coordinates as elements of
number field. This makes it possible to formulate
basic variational principles, differential equations, etc..
If one allows completely general topologies one 'loses physics':
it is difficult to know what physics one could assign to
the definition of what open set means.
> > a) Cognitive spacetime sheetsglued to material spacetime sheet
> > or larger cognitive spacetime sheet by *wormhole contacts*
> > is the geometric counter part for subself of self: my mental image
> > psychologically. Ideas in my head are cognitive spacetime sheets
> > and ideas might float around everywhere as Sheldrake and
> > meme theoreticians suggest. Very good ideas (from my
> > point of view) might be enlightened Buddhas providing good vibes
> > for a patient thinker.
>
> I don't understand how you justify the concept of "cognitive space-time
> sheets" :-( It looks like you are identifying an information structure
> with a space-time sheet. To me this is overkill! The "mind" is defined
> in terms of the information structure dual to a particular space-time
> sheet. We do not need to posit a separate "sheet" for mind!
Cognitive spacetime sheet is *purely* geometric concepts.
I want to emphasize this since there seems to be misunderstanding
here. The motivation for attribute 'cognitive' is that it
makes possible cognitive representations in terms
of spacetime geometry. It has nothing to do with
consciousness: cognitive spacetime sheets
are not conscious, they only determine partially the contents
of consciousness.
This is simply pure geometry but in much more general sense than one is
accustomed in GRT framework. And behind the concept is nondeterminism of
Kaehler action impying vacuum absolute minima. Cognitive spacetime sheet
is unavoidable prediction of TGD, which also distinguishess between TGD
and other theories. No cognitive spacetime sheets in GRT.
>
> > b) Cognitive spacetime sheets can also get glued to other
> > cognitive spacetime sheets by join along boundaries contacts.
> > Join along boundaries contacts make possible *entanglement*: formation
> > of larger wholes, associations.
>
> Would the idea that "the boundary of a boundary is zero" apply here?
>
Take two disjoint disks and glue them by ribbon. Ribbon makes
interactions between disks possible: ribbon is the bridge
along which interactions can propagate. Join along boundaries
bond is bridge along which interactions propagate. It means
simply that 3-surfaces touch each other via the bond.
> > Formation of JABs is topological synonym for direct touch. Join along
> > boundariers contacts can also be long: the axons from sensory organ to
> > brain could give rise to occasional formation of join along boundaries
> > contacts between cognitive spacetime sheets in sensory organ and brain
> > representing objects of perceptive field.
> >
> > I am now working with the model of brain. The strategy has been
> > to invent all possible objections against *sensory organs as primary
> > sensory experiencers* hypothesis. The strategy has been very successful.
> > It has led to understanding of how TGD:eish brain computes part of
> > sensory experiences and provided connection with hologram brain idea,
> > which reduces to its bare essentials in TGD: neurons have neuronal windows
> > to external world provided by axons where microtubules serve
> > as wave guides making coherent light from sensory organs to propage
> > to brain. Small piece of hologram <---> small window.
>
> I like this spirit of this idea! I too am very interested in the
> hologram paradigm! I am more focused on the Fourier symmetry and the
> relationships between the generators of the reference beam and the
> "reflecting object". I am interested in general principles not
> particular examples...
>
I am interested in both: I have found that healthy interest
in particulars makes it possible to avoid at least the
worst blunders in General-Principle'ing(;-). The simplest
manner to kill Great Generalization is to look special case.
> snip
> > > [MP] Why not try something more simpler and less radical: already
> > > Riemann tried this but too early when he proposed that 3-space
> > > is curved surface in 4-space. Start from the
> > > age old problem of General Relativity. How to define energy and momentum
> > > when spacetime is not curved anymore and does not possess Poincare group
> > > as its isometries? What about spacetime as surface in M^4_+xS?
> > > You get Poincare! Plus isometries of S, color group perhaps! And You
> > > get generalization of string model too! This should make bell ringing
> > > in every head thinking about theoretical physics! But it does
> > > not. I am frustrated(;-).
>
> It is one of the properties of Riemannian geometry, as I understand it,
> that an "embedding" space is not necessary!
Certainly not if one regards spacetime as abstract metric space. This is
basic departure between TGD and GRT. Imbedding is only necessary to
realized Poincare symmetry and GCI simultaneously.
And imbedding leads to the geometrization of classical
gauge fields: submanifold geometry is considerably richer
tha abstract metric geometry.
> I tentatively think of
> energy and momentum as given by the degree of difference between a pair
> of space-time framings that a given observer can have, e.g. when we
> compare two observations of a given observer with the scale and clock of
> that observer as its standard of "straightness" and minimal "duration",
> the deviation of the two gives the energy. The way that an analog clock
> is defined by the "face", the "hands" and an observer's comparison of
> the two, follow this notion well!
> I need to explain this in more detail!
[MP] Your idea reminds about how various conserved currents
are defined in field theories. They are nothing but variational
derivatives of action with respect to the parameter
of symmetry transformation. One can associated currents
also with non-symmetries but these currents are not conserved
and do not define any charged.
>
> > [SPK] I really would like to see this mental picture you have. I am just
> > not bisimulating your thinking at all, I see too many contradictions, but
> > that is, more than likely, due to my way of thinking... :-)
> >
> > [MP] I see also contradictions and this is why I am updating all the time.
> > This is the only way to keep this big thing in control. I however dare
> > say that contradictions are at the level of models and of
> > interpretation now.
> >
> > I want to emphasize one important thing. My approach have been
> > problem motivated: not an attempt to explain universe starting from some
> > existing philosophical or mathematical paradigm: the
> > mathematics and philosophy around TGD has developed painfully
> > during 20 years.
>
> You are not alone in this! My own naive thinking has been evolving for
> 15 years, ever since I first read books on GR and QM. We must be careful
> not to become attached to any assumptions that, although beautiful,
> ultimately are trivial. My dualism hypothesis is something that I am
> very willing to dismiss, if it fails to be tenable. I feel that one of
> the most important aspect of a theory is that it can, will due
> diligence, be understood by anyone. I do not expect common sense to
> reign! It is usually what gets us into trouble in the first place!
>
Not by anyone: we must be realists. To become scientist requires
the lifetime. I just read a good article relating to the
fashionable idea about educating people which can in five minutes
transform from biologist to physicists to a nurse to a
physician. This is not possible. One can of course learn to behave
like physicist or biologist but to really think like physicists
or biologist requires whole lifetime.
This does not mean that one could not move between sciences:
one must however known the limitations.
> > The difficulties related to time concept are numerous and TGD solves
> > them.
> >
> > a) The existence of reversible and irreversible worlds.
>
> Show me a "real" "reversible world"!
>
I am generous and can show much more than single reversible world.
10^40 real reversible worlds went by during the second
when I wrote this.
The point is that reversibility is necesary for variational
principles. Irreversible worlds do not allow variational principles
and one loses practically everything what Newton and followers
have painfully achieved. Irreversibely can be brought
in only by adding phenomenological dissipative terms to
reversible equations: as small perturbations of them.
> > b) Nondeterminism of quantum jump contra determinism of Schrodinger
> > equation.
>
> How is it that we are so sure that the q-jump is "nondeterministic"? I
> am very interested in how you define this notion.
>
> > c) Loss of time in General Relativity
> > d) The difficulties related to the definition of energy concept in General
> > Relativity
> > e) Difficulties in understanding the irreversibility of psychological
> > time contra reversibility of geometric time of physicists: why
> > we remember only past experiences.
>
> It is astounding to me that the notion of "reversible geometric time",
> idealistic as it is, carries more weight that the fact of experience!
The point is that all predictions of physical theories are
based on the following steps.
a) S-matrix elements are calculated in reversible world
b) Probabilities are used to derive the parameters
of kinetic equations etc.. and one obtains the
irreversible everyday world.
This is internally inconsistent description but it works: *experience*
demonstrates it.
The problem is to understand why it works and how one must
generalize time concept so that everything is consistent.
Quantum jump between quantum histories concept does this
and not only this: it also leads to a theory of consciousness.
> In
> trying to get some verification of M. C. Mackey's work on
> thermodynamics, I found that there is a fierce and even irrational
> reaction to his "proof" that irreversible behaviors can not be gotten
> from strictly reversible physical laws! That experience, combined with
> the, at best, neglect fullness that has been shown to Hitoshi's work
> makes me think that humans really do not wish to give up their
> anthropocentrist stance!
>
The reaction is understandable: the reversible-irreversible
contradiction is extremely unpleasant fact. Physicists
do not want to talk about it and are ready to believe
all kinds of magic tricks making reversible to look
irreversible. The ability of bright mindedd super brains
to cheat themselves when it comes to questions which
threat their basic beliefs is amazing: they are little
childs after all.
> > Typically colleagues do not start from these problems but see
> > the problem as a highly technical one, which can be circumvented
> > if sufficiently clever formalism is invented. Smolin's approach is
> > typical example of this. He suggests a flaw on arguments showing
> > that time is lost in GRT rather than starting from these big problems
> > obvious to every graduate year student in theoretical physics.
> > In string models situation is degenerated also to this kind of
> > game.
>
> This reaction to difficulties is typical; actually it is expected if we
> consider that any given observer can only recognize patterns that are
> similar to those that are within the set of their experiences! This
> suggest a set of algebraic rules, like closure under unions, complements
> and intersections, but I am not in a state of mind/body to figure out
> the details right now... :-(
>
> snip
> > {SPK] The way that Pratt discusses how CABAs "collapse the whole algebra
> > into a singlet" when a "new equation" is added, seems to me to relate to
> > what you are saying! The difficulty that I see is that the "classification
> > of 3-surfaces" is NP-Complete computationally! We can not just assume
> > non-constructive arguments! I am thinking that each particular
> > "experience" is a particular "classification" (a morphism from a subset
> > of MEM to a subset of InfDimGeo, see below...) of a 3-surface. We can
> > just assume that the 3-surfaces are "out there" already sorted for us.
> > This thought is equivalent to the idea that there exist a single
> > absolute space-time and all events are like bubbles frozen in the 4-cube
> > and the subjective flow of time is an illusion! (See [time 623])
> >
> > [MP] I cannot say anything about about classification of
> > 3-surfaces. What is however clear that NP completeness is based
> > on a model of mind which relies on classical computationalism.
> > And I am sceptic about this model of mind.
>
> Have you looked up the definitions and applications of the NP-Complete
> problem? Would it help if I wrote a post about it? Why do you consider
> that NP-Completeness is "based on a model of mind which relies on
> classical computationalism"?
If computing is involved and if the model of computer used is Turing
machine then I think that this is precisely the case.
>
> > TGD mind corresponds to infinite quantum computer perfoming quantum
> > computation of infinite duration during every 10^4 Planck times. The
> > entire universe has infinitely long memory about its
> > experiences: the number of quantum jumps occurred can quite well
> > have cardinality much larger than that of integers of reals.
> > Consider what this means when one introduces lexicons and generalizations
> > of them! We should not assume that we are the master minds of the universe
> > when trying to understand universe(;-)!
>
> I need to better understand the specifics on how this idea of yours
> works. I need explanations not declarations... For example: how do you
> propose that the computation itself could be modeled? How do you take
> into account Bremermann's limit?
> (http://pespmc1.vub.ac.be/ASC/Bremer_limit.html) How is the information
> encoded? How is the "infinitely long memory" accesses by the subsets of
> the Universe?
>
I see classical computation as emergent feature of consciousness, not
basic stuff of the universe. Of course, TGD universe
is quantum computer in the sense described but the
'computation' that we do involves the concept of self and
is macroscopic thing: 10^40 quantum computations per
second typically and selves waking-up and falling asleep.
We are selves who have just started to perform
actions which resemble classical computation.
As far as our own thoughts are considered are
computational in the sense that they are
hierarchical structures: self decomposes into subselves
decomposes into ... Main program calls module calls....
The contents of consciousness form hierarchy of
abstractions analogous to hierarchy of computer languages
giving increasingly grainy picture about entire program.
There is of course no program code anywhere: program
and its subprograms (self and its subselves) are created
when program runs. Self cascades representing
various skills are typical examples of this
kind of self organizing programs. For instance, playing
piano from notes is program like in over all aspects
but the details of performance contains the nonpredictability
which makes it art.
There is section about computational
aspects of TGD inspired theory of cs in
http://www.physics.helsinki.fi/~matpitka/selfbind.html.
> Onward,
>
> Stephen
>
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