Notes

[ Sunday 13 November 1983 - Saturday 19 November 1983 ]

[Creation - The Metaphysics of Peace = CMP I] = [DB20]

Sunday 13 November 1983
Monday 14 November 1983

[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.

...

Tuesday 15 November 1983

[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.

Wednesday 16 November 1983
Thursday 17 November 1983
Friday 18 November 1983
Saturday 19 November 1983