Stephen P. King (firstname.lastname@example.org)
Wed, 21 Apr 1999 11:57:04 -0400
Dear Matti and Friends,
Just a brief note. I am trying to catch up on my reading, I just got a
big batch of books in... ;)
Matti Pitkanen wrote:
> On Tue, 20 Apr 1999, Hitoshi Kitada wrote:
> > I have read Peter's paper bcj1.pdf. :)
> > It is an impressive paper in the point that it seems to describe one turning
> > point of science.
> I read also Peter's paper for some time ago. I found also the idea of
> coinduction very deep. I see the job of theoretical physicist mostly as
> coinduction in practice. There is guess for action principle, quite too
> complicated to be solved exactly (of course, even this does not help much
> in practice) and one tries to gradually understand what all is about.
> I would rather call this all pattern recognition, discovery of mutually
> consistent hypothesis consistent with the master equations.
Could we think of observation in general as pattern recognition? I am
stumbling over how to think of the action principle. :( Matti, could you
give us a undergrad explanation? Your idea of "master equations": how is
it considered ontologically?
> Or course, reductionism prevails in the sense that most colleagues
> believe that all physics is understood below intermediate boson mass
> scale or even Planck mass. I see this as a fatal belief and
> only due the interpolation of local physics to all length scales.
> There is long list of anomalies (neutrino physics
> being the most productive branch of physics in this respect) but
> people stubbornly refuse to consider the possibility that reductionism
> would fail. This is just what manysheeted spacetime concept predicts:
> there is infinite hierarchy of p-adic physics labelled by prime, the
> larger the prime, the larger the length scale. Each p brings in something
> new not reducible to previous levels.
We see this hierachical situation in theories when we consider their
Goedelian completeness. The one very interesting aspect of
non-well-founded set theory is how we can use the infinite regress as a
benefitial property. Since the Universe as a totality is Infinite and
Eternal we can see that streams as more expressive in modeling the
evolution of subsets that other models that require absolute unique
initiality/finality. We can see with streams that initial/final cutoffs
are relative to the finite observations and thus our model of time
achieved more coherence. :)
> Consinstency implies existence philosophy I found also especially close
> to my personal belief system. Most physicists would presumably represent
> objections here. If mere mathematical existence seems to be to etheric for
> physicist and clearly the physical world seems to be rather unique.
I think that we should be carefull with this thinking. The uniqueness
of the physical world can not be assumed to be independent of the
observations of it qua its finite properties! It is more consistent to
think of our common physical world as the construction of finite
observers engaged in co-inducive interaction. We need to look more
carefully at how common worlds are constructed via communication.
I see the way to model communications between LS is by using the
concepts of information flow (cf. Barwise & Seligman
http://www.phil.indiana.edu/~barwise/kjbbooks.html). Peter is
constructing a wonderfull piece of the puzzle!
> I would however go even further: 'Consistency implies physical
> existence=mathematical existence' hypothesis. Already in string
> models internal consistency requirements, in particular, cancellation
> of infinities, lead to highly unique theory. In TGD same occurs:
> now infinite-dimensional Kahler geometry endowed with spinor structure
> requires metric to have infinite-dimensional isometry group
> and seems to fix metric highly uniquely (configuration space of
> 3-surfaces is union of infinite-dimensional symmetric spaces). And most
> importantly, also the imbedding space itself is unique with very general
Matti, can you elaborate on the role of the embedding space from an
ontological perspective? It is clear from the conversations of the
experts (cf. Conceptual problems of quantum gravity : based on the
proceedings of the 1988 Osgood Hill Conference, North Andover,
Massachusetts, 15-19 May 1988, etc.) that spacetime is not as
ontologically primitive as Newton, Kant et al would claim. It might even
bear seriously contemplating that spacetimes are stream
> All this sums up to what might be called quantum platonism: physical
> states/quantum histories/ideas are the objective
> realities and quantum jumps between them represent moments of
> consciousness giving (very limited) information about these ideas.
> We learn by living. LOGOS=COSMOS/PHYSICS=MATHEMATICS identification would
> solve the basic counterarguments against Platonism represented by
> intuitionists (we learn mathematical skills in very mundane manner; no big
> revelations of mathematical truths in their full deepness).
> One could perhaps also understand our unability to make only discrete
> mathematics as a signature of our level of consciousness: perhaps
> some day new Homo Mathematicus will be born(;-) or perhaps it exists
> at the level of collective consciousness and uses us as
> intelligent printers(;-).
Perhaps the Intuitionist - Platonist dichotomy is related to the LS
inside - outside situation. The "Reality" inside is Platonic, it maybe
formally defined by some type of morphism between the Whole U and the
part LS, what is important is that is it unobservable "as a whole". On
the outside of the LS we have observations that are framed in the usual
situation as having spacetime framing, but there is a finite horizon to
the "window" as there is a finite restriction on the scale and on the
information content of an observation, thus the intuitionistic thinking
of a finite physical "reality"... ;)
> I had some problems with technicalities: what concepts likes co-algebra
> and signature meant (in practice) and did algebra have anything to do with
> rather restricted idea of physicist about it or was it defined only as a
> collection of symbols and symbol manipulation reules. This is of course
> due to my poor mathematical education.
I hope that we will continue to converse with Peter on this and gain an
understanding of each other's formalisms... :)
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