Matti Pitkanen (matpitka@pcu.helsinki.fi)
Wed, 21 Apr 1999 08:33:37 +0300 (EET DST)
On Tue, 20 Apr 1999, Hitoshi Kitada wrote:
> Dear Stephen, Peter and Friends,
>
> > [SPK]
> > > > I am trying to think of this in terms of Peter's
> > > > Interactive Machine paradigm. If we could show that a LS is equivalent
> > > > to a finite IM, we could easily bring in the power of Peter's analysis
> > > > in to play. :) http://www.cs.brown.edu/~pw/papers/bcj1.pdf
> > [HK]
> > > I downloaded the paper, but I could not find time to see it.
> >
> > I will try hard to be patient. :)
>
> 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.
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.
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 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
assumptions.
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(;-).
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.
Matti Pitkanen
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