Mathscape and Logical Fields

From: scerir (
Date: Sat Jan 13 2001 - 16:57:28 MST

Geometrodynamics, quantum fields, symmetry,
supersymmetry, topological quantum fields,
strings, superstrings, branes.
And now also: pre-geometry, ge-bits, topoi,
algorithmic-informational ontologies,
categorifications, logical fields.
Physical things become more and more abstract.
The mathscape. Or Plato's revenge?

But Aristotle already said that all things
go from material [hylê] to form [eidos].

And Heisenberg wrote: "The underlying structure
of phenomena is not given by material objects,
as are Democritus' atoma, but by the form
determining the objects. Ideas are more essential
than objects".

But Einstein noticed: ³As far as the laws of
mathematics refer to reality, they are not certain;
as far as they are certain, they do not refer to

David Mermin now says: ³Fields in empty space have
physical reality, the medium that supports them
does not. Quantum correlations have physical reality,
that which they correlate does not².

And John Baez writes: ³Can philosophers really
contribute to the project of reconciling general
relativity and quantum field theory? Or is this a
technical business best left to the experts? I would
argue for the former. General relativity and quantum
field theory are based on some profound insights about
the nature of reality. These insights are crystallized
in the form of mathematics, but there is a limit to
how much progress we can make by just playing around
with this mathematics. We need to go back to the
insights behind general relativity and quantum field
theory, learn to hold them together in our minds,
and dare to imagine a world more strange, more
beautiful, but ultimately more reasonable than our
current theories of it. For this daunting task,
philosophical reflection is bound to be of help².

Von Weizsaecker said that "Nature is earlier than
man, but man is earlier than natural science".
Suggesting some morphism between neural nets and
logical fields?

For now: correlations, just correlations.
At the most: some morphism between mathematical
and logical objects and ontologies.

Like these...

Christof Schmidhuber
³Strings from Logic²
What are strings made of? The possibility is
discussed that strings are purely mathematical
objects, made of logical axioms. More precisely,
proofs in simple logical calculi are represented
by graphs that can be interpreted as the Feynman
diagrams of certain large-N field theories.
Each vertex represents an axiom. Strings arise,
because these large-N theories are dual to string
theories. These "logical quantum field theories"
map theorems into the space of functions of two
parameters: N and the coupling constant.
Undecidable theorems might be related to
nonperturbative field theory effects.

Jurgen Schmidhuber
³A Computer Scientist's View of Life,
the Universe, and Everything²
Is the universe computable? If so, it may be much
cheaper in terms of information requirements to
compute all computable universes instead of just ours.
I apply basic concepts of Kolmogorov complexity
theory to the set of possible universes, and chat
about perceived and true randomness, life,
generalization, and learning in a given universe.

Max Tegmark
³Is the theory of everything merely the ultimate
ensemble theory?²
We discuss some physical consequences of what might
be called "the ultimate ensemble theory", where
not only worlds corresponding to say different
 sets of initial data or different physical
constants are considered equally real, but also
worlds ruled by altogether different equations.
The only postulate in this theory is that all
structures that exist mathematically exist also
physically, by which we mean that in those complex
enough to contain self-aware substructures (SASs),
these SASs will subjectively perceive themselves as
existing in a physically "real" world.
We find that it is far from clear that this simple
theory, which has no free parameters whatsoever,
is observationally ruled out.
The predictions of the theory take the form of
probability distributions for the outcome of
experiments, which makes it testable. In addition,
it may be possible to rule it out by comparing
its a priori predictions for the observable
attributes of nature (the particle masses,
the dimensionality of spacetime, etc) with
what is observed.

Max Tegmark
³Does the universe in fact contain almost
no information?²
At first sight, an accurate description of the state
of the universe appears to require a mind-bogglingly
large and perhaps even infinite amount of information,
even if we restrict our attention to a small subsystem
such as a rabbit. In this paper, it is suggested that
most of this information is merely apparent, as seen
from our subjective viewpoints, and that the algorithmic
information content of the universe as a whole is close
to zero. It is argued that if the Schroedinger equation
is universally valid, then decoherence together with
the standard chaotic behavior of certain non-linear
systems will make the universe appear extremely complex
to any self-aware subsets that happen to inhabit it now,
even if it was in a quite simple state shortly after
the big bang. For instance, gravitational instability
would amplify the microscopic primordial density
fluctuations that are required by the Heisenberg uncertainty
principle into quite macroscopic inhomogeneities, forcing
the current wavefunction of the universe to contain
such Byzantine superpositions as our planet being in many
macroscopically different places at once. Since decoherence
bars us from experiencing more than one macroscopic reality,
we would see seemingly complex constellations of stars etc,
even if the initial wavefunction of the universe was
perfectly homogeneous and isotropic.

Reginald T. Cahill, Christopher M. Klinger
³Self-Referential Noise as a Fundamental Aspect
of Reality²
Noise is often used in the study of open systems,
such as in classical Brownian motion and in Quantum
Dynamics, to model the influence of the environment.
However generalising results from Goedel and Chaitin
in mathematics suggests that systems that are sufficiently
rich that self-referencing is possible contain intrinsic
randomness. We argue that this is relevant to modelling
the universe, even though it is by definition a closed
system. We show how a three-dimensional process-space
may arise, as a Prigogine dissipative structure, from a
non-geometric order-disorder model driven by, what is
termed, self-referential noise.

Reginald T. Cahill, Christopher M. Klinger, Kirsty Kitto
³Process Physics: Modelling Reality as Self-Organising
The new Process Physics models reality as self-organising
relational information and takes account of the limitations
of logic, discovered by Goedel and extended by Chaitin,
by using the concept of self-referential noise.
Space and quantum physics are emergent and unified,
and described by a Quantum Homotopic Field Theory of
fractal topological defects embedded in a three dimensional
fractal process-space.


³Gravitation is not responsible for
people falling in love² (A.E.)

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