[ Sunday 13 November 1983 - Saturday 19 November 1983 ]
[Creation - The Metaphysics of Peace = CMP I] = [DB20]
[page 128]
Bronowski: A sense of the future.
Bronowski.
"My ambition has been to create philosophy for the twentieth
century which shall be all of a piece. There cannot be a decent
philosophy, there cannot even be a decent science, without humanity.
For me, the understanding of nature has as its goal the understanding
of human nature, and the human condition within nature.
This volume: science as natural philosophy.
It would seem to me that my aim is the same, but I have not seen
the vision complete yet. It would be good, and is good, to
communicate my current thoughts to others as I go along but I do not
seem to get much of this done. We each seem to have to make our
breakthrough in life before we are respected, by both ourselves and
others, to go forth and preach the world. I know the breakthroughs I
want to make, I can delineate many of its characteristics, but I am
not there yet and must struggle on, somewhat unsure of whether I will
ever get anywhere or not; but confident that if I do it will be
worthwhile.
[page 129]
...
[Articles I DB 25]
[page 186]
Angular momentum seems to be of principle importance. 1: dimension
of planck's constant; 2: related to spatial structure; 3: a
determinant of energy.
[page 187]
Postulate: The energy (mass) associated with a structure is a
measure of the rate of communication needed to sustain it. This must
be a function of complexity; spatial resolution; temporal resolution.
Variational principle relate to most
efficient coding. Yourgrau and
Mandelstam.
A body remains at
rest etc: This is memory. Newton.
...
[page 188]
A programmer deals with different variables, e, B, m etc simply by
storing them in different locations and assigning different
subroutines to take care of their properties and interactions. This
is expressed in a functional relationship, ie by modelling.
...
[page 190]
Particle with free entropy (ability to know and communicate) can
bind without losing its life.
...
[page 191]
Hawking and Ellis: The large scale
structure of space-time. Hawking
and Ellis.
Hawking page 3: 'one can think of a singularity as a place where
our present laws of physics break down' or 'part of the edge of
space-time.' - black holes and initial singularity.
...
page 12: complete atlas of a manifold is the set of all possible
coordinate systems covering M.
...
All these definitions impose structure on the spaces, which can be
thought of as programming and an information structure can be
developed (in the appropriate linguistic context) to define these
properties.
...
page 15: A tensor field is equivalent to a tensor defined at each
point in a manifold.
page 59: ...
The only relations defined by a manifold structure are tensor
relations. The only connection defined so far is that defined by the
metric.
[page 192]
Hawking page 61: Light travels on null geodesics, a consequence of
the nature of light, not of general relativity.
...
page 71: it is not necessary to introduce an extra field to
describe gravitation. 'we adopt the view that the gravitational field
is represented by the space-time metric itself'.
[the] active gravitational mass of a body (producing field) is the
same as the passive (acted on by the field) - action and reaction
equal and opposite - all communication channels in the Universe full
duplex.
page 74: pressure contributes to total mass; it can assist, rather
than prevent, gravitational collapse.
page 75: all the differential equations in physics are of the
first or second order.
...
[page 196]
Kogut: Lattice gauge theory approach to
quantum chromodynamics. Kogut.
Kogut page 776: 'topological change is discussed in the context of
asymptotically free spin model in order to see when the continuum
idea of continuity is a good guide to lattice physics and vice versa'
'symmetry breaking is so mysterious in these theories and is
handled in such a contrived, artificial fashion in most models of
Grand Unification gauge theories.
This is where intelligence comes in, maybe by some sort of
spontaneous increase in complexity.
...
[Articles I DB 25]
[page 195]
U0 [initial state of Universe] is a 1 loop Turing
machine with a tape 2 bits long and a processor.
Energy, time and action exist and are related by energy = Planck's
constant of action times frequency. No space, no spatial
differentiation - zero spatial dimensions.
Then we get space, time, relativity, numerous particles,
communication.
This is a spontaneous symmetry breaking - energy [per particle]
decreases, particles created, new relationships established.
U0 mass scale arbitrary.
U1 ... Un in some way related to U0
by conservation of energy, number of particles, extent of symmetry
breaking, lifetime of particles and related variables.
New relationships, new particles, caused by identical; action.
Communication between particles must be maintained as the Universe
remains one particle differentiating within.
U0 provides the context of energy/time/action.
U1 adds numerous particles, space, momentum, photons
and communication, differentiation, particles and antiparticles.
...
[page 196]
Where there are two particles, thee can be internal and external
communication. But all communication is interior to the Universe and
within the context of U0 . A particle needs a memory for
each of its personal characteristics and each of its communication
channels.
The first few generations of particles may be confined because
they don't have enough togetherness for independent existence.
...
Kenneth G Wilson: Problems in physics
with many scales of length. Wilson.
Wilson page 140: 'The success of almost all practical theories in
physics depends on isolating some limited range of length scales.'
'Water near critical point, fluctuations exist at all length
scales'
'The renormalisation group is not a descriptive theory of nature
but rather a general method for constructing theories.'
...
[page 202]
Allan Calder, Constructive Mathematics.
Calder.
Calder page 134: 'It is commonly held that if human beings ever
encounter another intelligent form of life in the Universe, the two
civilisations will share a basic mathematics that might well serve as
a means of communication. In fact, since the time of Plato it has
been generally believed that mathematics exists independently of
man's knowledge of it and thus possess a kind of absolute truth.'
Is mathematicians job to discover mathematics or invent it?
Construction: it is not enough to prove its existence, one must
demonstrate how to make it.
135: Infinities in calculus: irritating grain brought forth a
pearl, set theory.
A binary computer, such as us, can talk about infinity without it
having to exist. - This is what set theory does - 'the set of all
real numbers' is an actual infinity, but we talk about it, we
do not talk it. Cantor devised ways of talking about different
degrees of infinity.
'Beginning with the countably infinite sets, a hierarchy of
infinities can be generated.'
[page 203]
A mathematical idea is a structure or particle which needs for its
existence a substrate of intelligent communicating abstract thinkers.
...
Cantor [used] the classical reductio ad absurdum - the proof of a
proposition is that its denial leads to contradiction - but doe the
argument exist in the first place?
Ideas exist in human minds, and suitable communication experiments
(collisions) can elicit the internal logical and ideological
structure of any mind, and its connections, so that to know the mind
is to know the whole thing.
The abstract formulation of this idea must be mathematical and
metaphysical and then have its physical exposition - creation must be
an integral part of it. The difficulties experienced so far come from
going in too low. We must treat it as Einstein treated his principles
of relativity, and go from the general to the particular.
Kroenecker believed in constructability, ie an algorithm
'pure existence theorem' contradictory not to exist (given the
axioms)
Hilbert's pure existence proof: Gordon's problem. "this is not
mathematics, its theology' (Gordon)
[page 204]
...
Existence proof says given A, B must follow (contradiction if not)
- let the Universe exist, them what? - each stage of creativity
brings its inevitable consequences, which may take a long time to nut
out.
Calder page 139: Goedel proved Hilbert's formalistic scheme
doomed.
...
page 143: 'The major problems that determine the development of
mathematics are usually highly intuitive ...'
'go on and faith will return' - Jean
d'Alembert. Davis and
Hersh.
[page 205]
[Creation - The Metaphysics of Peace II = CMP II] = [DB31]
...
let us begin in Cantor's paradise. Cantor,
Hallett, Jech.
Tuesday 15 November 1983
Wednesday 16 November 1983
Thursday 17 November 1983
Friday 18 November 1983
Saturday 19 November 1983