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VII Notes

2010

Notes

[Sunday 23 May 2010 - Saturday 29 May 2010]

[Notebook: DB 69: Creation]

[page 24]

Sunday 23 May 2010

Tymoczko Philosophy of Mathematics: Rene Thom. Tymoczko, Rene Thom - Wikipedia

My problem at the moment with Creation is the possession of a forest of ideas ranging from logical to theological which I am having trouble organizing into a coherent narrative.

Introduction: dynamics and fixed points.

Tymoczko page 72: 'There is no rigorous definition of rigour. We

[page 25]

will therefore assume that any proof is rigourous is it wins acceptance by all readers who are adequately educated and prepared to understand it. Furthermore, the evidence leading to persuasion results from having a sufficiently clear understanding of each of the symbols involved so that their combination convinces the reader. From this point of view rigour (or its contrary, imprecision) is essentially a local property of mathematical reasoning. No elaborate axiomatic structure or refined conceptual machine is needed to judge the validity of a line of reasoning. It suffices merely to have an understanding of each symbol involved and a clear idea of how to combine them.'

Actus purus = pure action. But fixed point theorem says pure action in a compact complex place leads to fixed points.

Quantum mechanics represents the fact that even from a formal point of view, multiple different outcomes are consistent with a given input situation.

Quantum mechanics may be seen as a linear algebra constrained only by orthonormality.

Quantum computation completely overlooks the dynamics of quantum processes (which depend heavily on timing) just as Turing machines overlook the dynamics of changes of machine state. In real physical computers, we use the clock to isolate the dynamic processes of change of state from the fixed states that succeed one another in an actual computation.

Our first step is to interpret the complex and rather unintuitive formalism of quantum mechanics in terms of networks, something we understand very well because we are inherently network communicators.

[page 26]

That is what I am doing here, trying to get a hearing on the network of professional philosophers.

Let us assume at the outset that quantum mechanics describes the real Universe perfectly as far as it goes. As far as I am aware., there is no empirical evidence against this proposal.

We must pass over much detail, but let us admit here that I find the mathematics of quantum mechanics fascinatingly beautiful. The core of this beauty for me lies in the many and varied amazing properties of the complex exponential. As I point out below, we may regard the quantum mechanical energy equation as isomorphic to the classical model of God expounded by Aquinas. On the other hand I have to admit that the mathematics of quantum mechanics is often beyond me and I rely more on general impressions that completed calculations.

Tymoczko page 126: '. . . the following essays argue the philosophical relevance of mathematical practice. the critical stem in approaching them is to conceive of mathematics as rational human activity.'

More generally, mathematics is a rational universal activity since in the network model human activity is a new layer in the network which obeys the same general [protocols].

The assumption behind philosophy is that every philosopher takes personal responsibility for her or his actual positions, and so is allowed to write in the first person rather that

[page 27]

the intransitive third person grammar which we were taught at school [for writing up our science].

The amazing thing about the continuous mathematics of quantum mechanics is that it naturally produces stationary states.

Three axioms and two rules: Very simple. Now to interpret them. 1. Hilbert space and unitary operations
2. Eigenvalues - the stationary points
3. P = |ψ|2

How did I get here? via Lonergan.

Lonergan's claim that there are meaningless data (empirical residue) is the Universe is tantamount to claiming that it is a puppet whose motions have no reason within itself but can only be understood when one includes the puppeteer. It is the puppeteer that is living, not the puppets. The alternative is that the real Universe is a living god, and that every event in God has a pedigree that extends back to the source of the Universe, call it God, the initial singularity, Shiva or a host of other names in different cultures.

Rawson page 102: 'II Sex and reality: Tantra's view of the final goal is shaped by a vision of cosmic sexuality. The male principle of Universal Creation is the seed of Being, which is at the same time infinitesimally small and all-embracing. It is often cal;led Shiva, and represented by an erect male organ or lingam. The female principle, projected from the male, is the Goddess or Shakti, who is the active partner, spreading out space, time and the Universe before each

[page 28]

individual. She is the nearer for worship that the male principle, in many guises, and under many names. Most important is the reverence pair to her female generative organs of the world, the yoni or vulva.' Rawson

'Sexual intercourse is thus taken as a paradigm or symbol of divine worship and bliss. Performed in special ways with appropriate rituals and mantra it can be the most powerful possible aid towards the goal of enlightenment. From ancient times specially endowed female initiators have been the partners in advance sexual rituals. In Tibetan Tantra there have been translated into the image of the dancing (often red) Dakini.' Dakini - Wikipedia

Contrast this with the Catholic attitude to sexuality and ask what is the more realistic religion?

What do we mean by enlightenment? More than pleasure? The ability to take pleasure in an situation, ie to deal courageously with the hardships of life. I have to get used to the idea that although I want a laptop, for winter, the market is going down and I do not want to touch my diminishing capital. Things will improve (I hope).

WORK = COMMUNICATION

Mathematical practice (Tymoczky page 127) is the physical embodiment of mathematics in mathematicians and their works (= all communications) COMMUNICATION = WORK (changing the state of the system).

[page 29]

. . .

Mathematics can describe mathematical practice through the transfinite symmetric neural network. Noetic network.

nice term NOETIC NETWORK

To simplify marketing the idea (increase its intelligibility? - no sex appeal) we might rebadge the transfinite symmetric network as te noetic network.

The eigenvalues of a network are the ideas that take hold, ie the software that reproduces itself the most (Google, Facebook etc).

Tymoczko page 127: '. . . mathematical practice is essentially the justification of mathematician's claim to knowledge.' [and sustenance]

'. . . it may well be that the verification of proofs is a public affair, an elaborate social process that proceeds by canons and paradigms of a particular community of experts.'

T page 128: 'So one can only reject the thesis that mathematical practice is a viable topic in the philosophy of mathematics by backing oneself into an exceedingly narrow philosophical corners. I can see no reason for doing this other than an antecedent commitment to foundationalism. Without the doctrine of foundationalism, the way is clear to a reexamination of mathematical practice.

[page 30]

Finding eigenvalues comes down to solving polynomials. [the characteristic polynomial]

Aristotle: 'Of course I love Plato, but I love truth more.' Nichomachean Ethics I:6. Aristotle

'. . . while both are dear, piety requires is to honour truth above our friends.' 1096a16. Piety - Wikipedia

Wang in Tymoczko pafe 131: Mathematics concerned with the formal skeletons of things.

'. . . calculation is not itself an experiment, since once the path is found . . .'

Does this follow? Calculation gives us instances of truth that may lead us to generalization.

Wang page 132: Proving Pythagoras theorem by finding the right diagram and seeing that c2 = a2 + b2 'fits' as a de Broglie wave fits a potential well or a potential gradient.

W page 136: ' . . . to call several pages of printed marks a proof presupposes a good deal of the sociological circumstances which made them a proof.'

The Universe creates its own resources for the physical representation of information.

'There is a great gap between what can be done in principle and what can be done in practice.' page 138. The Universe also feels this gap as it wends its way from omnino simplex to omnino complex.

[page 31]

A proof is a wormhole in a noetic network? Not so much a wormhole as business as usual.

All provable theorems are provable by propositional calculus. As the trick with quantum mechanics is to find s basis in which things appear simple, so in a proof the skill lies in finding and giving meaning to a set of terms to be filled into the proposition, like the cargo into a vehicle. So, in linear algebra we seem to have found a language to describe a significant foundational process in the universal process. It is linear, which means additive. All the inputs and outputs to quantum mechanics [have a definite form defined by a state vector]. What counts is what we are counting.

What we are looking for is a mathematical description of practical mathematics, this is an endlessly recursive process becasuse whenever we achieve it we have to start again because our achievement has added a new layer to the system which must now be described in a further layers, the transfinite Peano's axiom. Whereas adding 1 a la Peano is in a sense an arbitrary action, Cantor has proved that transfinite numbers are forced by consistency to increase. What we are thinking that every permutation of the alphabet of a source is possible, and at the lowest level of resolution all the possibilities are equiprobable, maximizing entropy. Then some of the possibilities turn out to be stationary states, points of accumulation or in some other way fixed that move probability distributions away from flat toward spectral.

Are proteins ordered? by descent, yes, nut their overall morphology must approach random,, whatever that may mean. Maybe not, certain substructures are preferred, an alphabet of building blocks.

[page 32]

Wang page 142: 'We understand arithmetic better than set theory, as evidenced by the highly informative consistency proofs for arithmetic. The foundation of arithmetic is more trustworthy than that of set theory -- what would be of greater interest is rather to found set theory on arithmetic, or an extension of arithmetic to infinite ordinals.

Wang page 143: '. . . the close connection to the physical world is an essential feature which separates mathematics from games with symbols. Mathematics coincides with all that is exact in science.

We cannot span the Cantor Universe with a Turing machine, we need a network of Turing machines [rather like the atlas of a manifold].

Wang page 145: '. . . . This suggests the possibility of a web of axiom systems such that each system determines an abstract structure [eg electron?] viz the class of all possible models of the system.'

W page 147: '3.5.8 It is not easy to understand why functions of complex variables turned out to be so elegant and useful. . . . Incidentally if we require the axioms of fields to be satisfied,, extensions of complex numbers are not possible.

Monday 24 May 2010

On doubt again, it being a bleak Monday morning.

One does not doubt the proposition the Universe is Divine, but the social problems of getting a hearing, making a living etc are inclined to make one look for another job. But

[page 33]

not really. it may take a century before this idea sweeps the world but the potential for human salvation is enormous.

The Titanic effect: '... the severity with which a system fails is directly proportional to the intensity of the designer's belief that it cannot fail. De Millo, Lipton and Perlis in Tymoczko page 279.

our system is built on Christianity which claims infallibility, whose failure promises quasi- extinction for humans. The most dangerous component of Xian belief is that the Universe was made just for is, and that God killed his Son for us so that everything would be allright on the end, at least for believers. Many Christians are emboldened by the fact that Unbelievers face an eternity of Hell.

Creation and resolution" I have glimpsed it (in an unresolved way).

Reliable never means perfect. De Millo, Lipton and Perlis in T page 282.

Gödel: either it is inconsistent or it is incomplete, ie any formal proof procedure = (?) any Turing Computable process.

Now Gödel's theorem itself is a fixed point in the dynamics of the Universe and is in a way the explanation of the dynamics. Gödel's theorem appears as a fixed point in the dialogue of mathematicians and we would like to apply it to the whole Universe by claiming that the dialogue of mathematicians is isomorphic to all other dialogues in the Universe.

[page 34]

Tymoczko page 289: 'Actually the moral [of Chaitin's work] is more general: insofar as we precisely and consistently specify the methods of reasoning permitted, we determine the upper bound to the complexity of our results. (This upper bound is the information theoretic limit imposed by Gödel's theorem).'

To physically represent formal logical computations we use the clock pulse to damp out the dynamics of the transition from state to state so that all the formal process sees are the kinematic sequence of logical state that are its stationary points but we have faith [that] the dynamics of the hardware will yield true representations of logical gates and so on.

The 'Gödel layers' in the Cantor Universe enjoy Cantor symmetry,

Mommsen in Pais Inward page 131: '"History distinguishes itself from its sister disciplines by its inability to bring its elements into a proper theoretical disposition."' Pais

the fixed points, like us, are fixed points in the global dynamics, just as we (considered as fixed points) are 'inside' god.

Pais 371: 'in his papers Planck alluded to the inspiration he has received from Boltzmann's statistical methods. But in Boltzmann's case the question was to determine the most probable way in which a fixed number of distinguishable gas molecules with fixed total energy and distributed over cell in phase space. The corresponding counting problem . . . has nothing to do with Planck's counting of partitions of indistinguishable objects., the energy elements. in fact this new way of counting,

[page 35]

which prefigures the Bose-Einstein counting of a quarter of a century later cannot be justified by any stretch of the classical imagination. Planck himself knew that and said so.

We may think of the Bible as a function and write it into a function space with as many dimensions as there are are letters in the bible, the value of each dimension being the corresponding letter.

Gödel: the past, no matter how complex, cannot possibly determine the future.

Atoms of action combine seamlessly to produce larger actions. The action is simple, although it has fixed points corresponding to all of its constituent actions: for every action (mapping of a compact convex set onto itself) there is a fixed point which amounts s[to an observable message.

The hippie ideal was free love. It has taken a bit of a battering over the years as the offspring go to school and we come into contact with the bureaucracy (ie the social set of algorithms) and are forced to adapt by the necessity to survive, but the dream remains. What do we mean by free love? Practically it means liberating lust from its ancient social constraints. The keys to this liberation are contraception and homosexuality, that is non reproductive sexuality and the associated love that arises from such intimacy.

Tuesday 25 May 2010

Why are there atoms of action: fixed point + Shannon.

[page 36]

'I love her' is a statement that has meaning at all levels of complexity. A necessary but not sufficient condition is that lovers be peers. What else? The indescribable?

'You belly kills me. I want to kiss you so much.' How do we see this in the light of Cantor symmetry?

Pornographic theology: easily the easiest to sell!

The scientific life is a subset of the real (full complexity, complete basis) life. [repression is to reduce the cardinal of the basis: carnal cardinals]

The real test of a philosophy is how it treats lust and love, the potentials of the human world.

The beauty of the Universe is to feel itself.

Cosmic eroticism: the pr department will love this.

Overall the portrayal of sexuality on the net is as sinful rather than joyful, and we probably owe this to the old religions where sexual activity was tightly bound to reproduction.

Although the fundamentalists are always seeking absolute certainty, the fact is that the future is a rather uncertain p[l;ace because there are so many possibilities [as a consequence of the rapid growth of transfinite numbers].

A romance is possibly a constructed thing [but its cardinal is greater than that of either participant, so requisite variety limits our control Ashby]

On the whole we might say that the Universe is

[page 37]

romantic and the odds of success in any venture are about 1 / e, favouring stability but allowing for jumps, ie, 'quantum leaps'.

Physics may lead us to believe that the Universe is a very high precision thing which it may be at the hardware layer, but it becomes vaguer as it becomes more complex because there are so many more possibilities.

Wednesday 26 May 2010

Tarski: 'Cardinal Algebras'. Tarski

The network of the Universe reflects both the vagueness and precision of my mind. Much of the vagueness lies in remembering where I have put one of the 500 or so tools, utensils, and books that i use. On the other hand, I am capable of the precision of these sentences which (at this time) appear to say exactly what I want to say.

Tarksi 1941b Fefferman page 409. Feferman & Feferman Tarski

Quantum mechanics tells us what we already know intuitively, that everything depends upon timing. This is how music works. It is all timing (or its inverse, frequency) [often subtley perturbed from predictability]

What we sek through this dust of words os some clarity of vision, a clear understanding of our predicament and how to deal with it.

The depressing and depressed view of the world characteristic

[page 38]

of most ancient religions is fate based: accept it, there is nothing you can do about your condition. A more modern view (and in many cases an ancient one too) is that we can do something about our condition, and we have a history of health care, improved nutrition and population growth to prove it. [In the days when lords lorded it over their subjects, the only way to improve things was to pray to the Lord. In most cases practical action outperforms prayer when it is possible.]

COMPUTER = SYNCHRONOUS (centrally controlled)
NETWORK. - LOCAL = ISOLATED = ADIABATIC

When we talk of the isomorphism of the traditional God with the isolated quantum system, it is necessary to abstract from the cultural embodiment of these models and consider them in themselves.

The axiom of God = World: not(p and not-p) This axiom is realized when p is well defined but not when it is infinite, as in a quantum mechanical superposition which is taken to mean the simultaneous mixture of many different states.

Thursday 27 May 2010

Logic deals with the relationships of hypothetical fixed points in the Universe whose relationships are fixed by the dynamics in which they are embedded.

Here we are taking a physical approach to mathematics: as long as we stick close to the data revealed by the world we cannot go too far wring because we assume the world to be consistent and so any mathematical model which is in

[page 39]

one-to-one correspondence with the world must also be consistent. This is the lesson of quantum theory, that in the continuous world there is no information so no inconsistency can arise as long as we limit our attempts at precision to the bounds defined by the uncertainty principle.

Quantum mechanics falls neatly into two halves, the invisible and the visible.[We postulate the invisible to explain the visible]

Having suggested that quantum mechanics can be imagined in terms of networks we can avoid some of the intricacies of the linear algebra that lies at the heart of quantum mechanics and talk about it in terms of communication, as is done by the quantum computation and quantum communication trade.

SCIENCE is a form of TRADE between individuals (the scientists) and the collective (taxpayers, shareholders, donors etc).

Our physiological paradigm is the sequence of processes through which the visual data passes on its way from eyes to consciousness, and of course hearing and all other complex natural processes.

In order to converse, I must convert the contents of my consciousness into streams of photons and phonons which you can decode in your own way and formulate a reply to my message.

Google exhibits the brute force approach to translation, correlating billions of words of text. This may be the only

[page 40]

way given the richness of natural language.

The iterative processes of conversation allow us to define precise points such as the time we have to leave home to get to the match on time.

Pontificia Universidad Católica de Chile. Pontifical Catholic University of Chile - Wikipedia

PEACE = FAIR TRADE
WAR = INJUSTICE (UNFAIR TRADE, RAPE & PILLAGE)

The question is: is the idea worth working for. And the answer is yes. The result of work is definition and clarification, and when the idea is fully clear we would expect it to sell itself. What is the fully clear idea? given the requisite conditions, the world creates itself (grows) and so what we need to do is establish those conditions and peace and creation will follow, like gardening (Peter Sellers [Being There Being There - Wikipedia] So we are looking for the necessary and sufficient conditions for creation, and thus a catalogue of the means that are used to suppress creation by dictatorships of various forms which fear an increase in the variety of their subjects. If the necessary conditions can be found and established the world will be a better place for my children, an instance of my biological role as father and grandfather.

Trying to work hard and intelligently and continue in the belief that completing an article on creation is a priority.

[page 41]

Each deterministic system has an ordered set of operations that can be mapped onto the natural numbers.

Nazism fails simply because it is inconsistent with human life, like Catholicism and all those other systems that claim to be complete.

Once we can establish the Universe as an organized and addressable flow of information driven by a hidden consistent process, we can begin applying the discoveries of logic (mutatis mutandis directly to the Universe, finding in the process that at every level there is an uncertainty principle there that is roughly the same size as the typical minimum action at that level. ,p. Quantum mechanics is about the fact that all information is encoded physically but that at the bottom layer, the isolated quantum system, there is no entropy and no information because this system is, for all we know, omnino simplex.

Pais [Subtle] page 30: Einstein: '"What I found in the quantum domain are only occasional insights or fragments which were produced in the course of fruitless struggles with the grant problem."' ,p> Events, like the second world war or the Darwin cyclone are no more sharp;ly defined than quantum wave-packets.

Clausius 'Entropy" 1865; Pais page 60. Rudolf Clausius - Wikipedia

Maxwell on atom: 'Though in the course of ages catastrophes have occurred and may yet occur in the heavens, through ancient systems may be dissolved and new systems evolved out of their

[page 42]

ruins, the molecules [ie atoms] out of which these systems are built -- the foundation stones [states] of the Universe remain unbroken and unworn. They continue this day, as they ere created, perfect in number and measure and weight. Pais page 82. Maxwell

Friday 28 May 2010

To be a centre of attraction / condensation is to become a 'star, gaining enough interaction from the attractive potential to initiate other processes (thermonuclear fusion, record production). One cannot have disproportionate influence without this phenomenon, that is without attracting many readers (hearers, etc).

Einstein on Brownian motion: Pais page 97: '[2> = RTt / 3πNaη} is the first instance of a fluctuation-dissipation relation: a mean square fluctuation is connected with a dissipative mechanism phenomenologically described by a viscosity parameter.' Fluctuation dissipation theorem - Wikipedia Nyquist Callen

Part of the more general mechanism independent motion (connected to a symmetry) changing to coupled motion by the 'discovery' of a stationary state corresponding to a sequence of actions. So we might see ir in the absorbtion of a random photon by an atom so moving an electron from an orbit that is maintened by a single action (anfular momentum 1) to one maintained by a sequence of n actions (n = principal quantum mumber). Dissipation may not be so necessary as the creation of the stationary state, that is a stable potential.

The theistic / deterministic view of the Universe is that everything is determined, it just looks random to us. One of the strongest outposts of this view is the belief in the power of quantum computing where people believe that continuous variables have

[page 43]

sufficient entropy to store an infinite amount of informatin and continuous operators can act on all this information simultaneously. But what if it is just not there and that the Universe is in fat a rather indeterminate system of symbols (at least that is what it communicates) that slowly defines itself as it becomes more complex. This is a tautology since definition (cardinality) is directly related to complexity. We measure complexity by counting definite (ie orthogonal, non-overlapping) states.

When we represent a book by a Hilbert function space we presuppose a definite order of the dimensions by mapping them to the natural numbers. An isolated function space does not have this order (the dimensions are symmetrical) so when we observe it we may see any one of its dimensions as picked out by our measurement operator.

The personal struggle is to feel authentic.Although I like to shrug off my expulsion from the Dominicans and concentrate on the manyy benefits it has brought me (how nightmarish to be in there still), to be rejected by such a major organization in my social world is to be in a large degree rejected from society, which is probably why I am still sitting here in the country trying to build up my case until it is strong enough to be vindicated in a proper hearing. (Wrote to the Pope on these lines last Friday 22/5.) My mental state is a superposition of varying potentials, hunger, thirst, the need to finish a plumbing job, the need to wait for some phone calls, the possibility of getting stuck if I go to work because the track us muddy and it is raining . . . etc etc. I can only respond to them one at a time, and the probability of

[page 44]

my response is a function of the strength of the potential. The outcome, of course, is that I am writing this paragraph, the desire to write has won, but the writing (interrupted by the phone call) has dissipated the potential, visitors are on the way and the dominant urge now is to light the fire.

Why is the velocity of light the same for all observers, regardless of their relative velocities? It is a symmetry, and like other symmetries, things are the same because there is no reason for difference. What is constant is not the velocity of light but the velocity of light as measured by an observer (in a vacuum, et). We have become accustomed to saying that the finite velocity of light is the result of communication delay caused by error resistant encoding. The is goodish in principle, but it will need some sort of mechanism to explain how it works.

Michelson & Morley Pais Subtle page 112.

Since the locomotion of inertial frames is irrelevant to the velocity of light, we are led to suspect that it is a feature of a layer deeper ('more physical') than space, and is in some way related to the fixed value of the quantum of action, which itself has something to do with communication. At this level space (memory) has yet to come to be and all we have are time, [action] and frequency. Time of itself is not a degree of freedom (since we cannot in any way change it locally) but rather a manifestation of the pure action of the Universe.

Michelson in Pais page 115: '" . . . without a medium, how can the propagation of light be explained? . . . How explain

[page 45]

the constancy of propagation, the fundamental assumption (at least of the restricted theory) is there be no medium?"'

The Universe does not exist in a medium. it is its own medium, ie its own hardware and we assume that the hardest hardware is the initial singularity, pure action, which appears in spacetime a stationary point, the velocity of light. This velocity is a result of an initial mapping of the Universe onto itself, perhaps the mapping (layer) subsequent to the ayer whose stationary point is the quantum of action. All these mappings (in their proper layer) are identical, but appear in more and more concrete instances as the Universe complexifies, ie its dynamics grows more stationary points.

For a photon (and all bosons) space does not exist and so everywhere is local for them. SPACE - MEMORY - POTENTIAL vs TIME - TRANSFORMATION - KINETIC.

Time comes first its stationary point being the conservation of energy. So which layer is defined by E = hf? Higher of lower than the energy equation (Schrödinger dψ/dt = Eψ), ψ = exp(i/h E), so frequency of ψ = E/h, or its period is h/E.

The aim of theoretical physics is to dream up a calculation (algorithm or set of algorithms) that agrees with observation and to both use and find the calculation from wondering how something (like the propagation of light) might work.

[page 46]

Poincaré 1898: Pais page 126: 'We have no direct intuition about the equality of two time intervals. People who believe they have this intuition are dupes of an illusion.'

Poincaré 1900: Pais 127: 'One knows where our belief in the aether stems from. When light is in its way to us from a far star . . . it is no longer on the star and not yet on earth. it is necessary that it is somewhere, sustained, so to say, by some material support.'

We cannot observe a photon 'on the way' without destroying it. From the photon's point of view, its space-time path is a null geodesic, so we can say that it is nowhere - photons do not exist in space although they can be emitted and absorbed by sources in space [ie they are a component of a layer below space].

Einstein: Pais 132: 'It is never easy to talk about how I got the theory of relativity because there would be various concealed complexities to motivate human thinking and because they worked with different weights.' (like eigenfunctions of an operator).

Light cannot be transformed to rest, ie it is purely kinetic, a stat than antedates potential?

Pais page 138: 'Special relativity represents the abandonment of mechanical pictures as an aid to the interpretation of electromagnetism.'

Einstein: Pais page 139: 'My solution[to the problem of special relativity] was really for the very concept of time, that is that time is not absolutely defined but there is a inseparable connection between time

[page 47]

and signal velocity.'

Pais page 141: 'There are as many times as there are inertial frames'. ie each inertial frame is synchronous within itself but distinct inertial frames are asynchronous. The invention of space out of inertial frames is relatively simultaneous - ie a symmetry breaking. The breaking of symmetries does not destroy the symmetry. it simply means that elements which are symmetrical in layer n can be treated differently from one another (symmetry broken) in layer n + 1.

The interaction of light and matter is to be explained by the interaction of two layers, the matter layer (space-time) being built out of the light layer (pure time ticking by 'acts').

Saturday 29 May 2010

Formalism may be seen as a concomitant of a monkish way of life motivated by the feeling that there is something wrong with the world [and] this becomes a self fulfilling prophecy the monks seek to justify their ways by finding errors in the world.

I want to go and plumb, but it is just too wet so home and write, which may have better long term prospects but it is hard for me to se it as real profitable work. I guess this view will remain until someone pays me for some writing, at least takes notice.

Fowles Collector page 144: 'I don't think the Campaign for Nuclear Disarmament has much change of affecting the government. it is one of the first things y9u have to face up to. But we do it to keep our self-respect, to show ourselves, each one to himself or herself,

[page 48]

that we care. . . . the only thing that really matters is feeling and living what you believe -- so long as it is something more than belief in your own comfort.'

But comfort comes from 'feeling and living what you believe' because that is to reflect oneself and be normalized. My 'complex conjugate' is my mirror image in the real axis. Analyze that! We multiply by reflection: The Father and the Son (Word).

TRINITY -- QUANTUM FIELD THEORY

Major reorganization of Creation.

Fowles 1521: '. . . I want to make beauty.'

FORMALISM (COLD) vs RHETORIC (HOT)

We think of the Spirit as the stationary point (the love) between Father and Son. Love exists in the product space, analogous to entanglement.

Fowles page 169: 'They're teaching you to express personality at the Slade -- personality in general. But however good you get at translating personality into line or paint its no go if your personality isn't worth translating. Its all luck. Pure hazard.'

We might assume that because the ancient theologians were pretty much on the right track (attested by the survival of their doctrine by people being ready to fight for it) so that any new theology will be a development of the old, contradicting

[page 49]

dead ends and building on the sound parts.

We are our best friends.

The essence of the model is that the initial singularity grows within itself so it is a mapping onto itself and so 'generating' fixed points, each corresponding to one of the mappings. The Word is a map of God. Jesus is a map of God. We all are.

The writers of the New Testament invented the Trinity and the Incarnation in a vague (undefined) literary form which led the theologians to generate models of the Trinity and the Incarnation that eventually hardened into creeds and dogmas that still motivate the faithful seeking understanding.

The act of intelligence is to generate a fixed point. So the interaction of two quantum systems is to generate a particle, a message between them. So the electronic stationary states of an atom are represented by an orthonormal basis in some Hilbert space and photons serve as the messengers between these states, being emitted or absorbed as the need to increase or decrease angular momentum requires. The stationary states are fixed but invisible. What we observe are the transitions between them. All transitions in the Universe are physically represented by sets of quantum transitions.

Fowles page 210: 'I suddenly felt I didn't want to paint, painting is just showing off, the thing was to experience and to experience for ever more' But experience motivates some of us to act, write.

[page 50]

How can God be the fullness of being and yet create another being the World) separate from itself? Not possible therefore God = World, or at least God ⊃ World, World ∈ {God}. The Church weasels its way out of inconsistencies like this by claiming that everything to do with God is a mystery.

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Books

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Aristotle, and H Rackham (translator), Aristotle, XIX, Nichomachean Ethics, Loeb Classical Library 1934 ' . . . This book opened my eyes to the true meaning of "Philosophy". The translation is in modern English, free from the back-to-front syntax of the Ancient Greek text (which makes it impossible to understand the meaning of a sentence until you reach the end of it!). The subject matter is "Ethics". However, a modern author may have called it something more akin to "The Meaning of Life" or "The Art of Living". Aristotle proceeds with simple and clear logic, to reveal the objective of human struggle in this life. He demonstrates a deep understanding of the Human Being, what we are and what we are not, what makes us act in one way or another and what makes us feel joy or distress. He addresses anxienties of the modern human, such as the question of nature or nurture, the moral action versus the practical, violence versus non-violence. His recommendations for living this life in a manner that is meaningfull and rewarding are profound yet simple.. . . ' Agis Liberakis 
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Ashby, W Ross, An Introduction to Cybernetics, Methuen 1964 'This book is intended to provide [an introduction to cybernetics]. It starts from common-place and well understood concepts, and proceeds step by step to show how these concepts can be made exact, and how they can be developed until they lead into such subjects as feedback, stability, regulation, ultrastability, information, coding, noise and other cybernetic topics' 
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Feferman, Anita Burdman, and Solomon Feferman, Alfred Tarski: Life and Logic, Cambridge University Press 2004 Review "A chain smoker, a heavy drinker, a frequent user of 'speed', a relentless womaniser, and a man of Napoleonic self-regard and worldly ambition. This is not how one pictures an eminent Professor of Logic. And yet, this is how the great logician, Alfred Tarski, emerges from this marvellous biography. The Fefermans, of course, are uniquely qualified to lead the reader through the intricacies of Tarski's work, which they do very engagingly and with great expository skill. Tarski's colourful personality is conveyed with prose that is economical, superbly readable and extremely vivid, and the whole book is a joy to read." Ray Monk, Professor of Philosophy, University of Southampton 
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Feynman, Richard P, and Albert P Hibbs, Quantum Mechanics and Path Integrals, McGraw Hill 1965 Preface: 'The fundamental physical and mathematical concepts which underlie the path integral approach were first developed by R P Feynman in the course of his graduate studies at Princeton, ... . These early inquiries were involved with the problem of the infinte self-energy of the electron. In working on that problem, a "least action" principle was discovered [which] could deal succesfully with the infinity arising in the application of classical electrodynamics.' As described in this book. Feynam, inspired by Dirac, went on the develop this insight into a fruitful source of solutions to many quantum mechanical problems.  
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Fowles, John, The Collector, Back Bay Books 1997 Amazon Product Description 'The Collector (1963) is disturbing, engrossing, unforgettable -- the story of an obsessive young man and the girl he kidnaps and holds prisoner in his cellar.' 
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Kolmogorov, A N , and Nathan Morrison (Translator) (With an added bibliography by A T Bharucha-Reid), Foundations of the Theory of Probability, Chelsea 1956 Preface: 'The purpose of this monograph is to give an axiomatic foundation for the theory of probability. . . . This task would have been a rather hopeless one before the introduction of Lebesgue's theories of measure and integration. However, after Lebesgue's publication of his investigations, the analogies between measure of a set and mathematical expectation of a random variable became apparent. These analogies allowed of further extensions; thus, for example, various properties of independent random variables were seen to be incomplete analogy with the corresponding properties of orthogonal functions ... ' 
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Lonergan, Bernard J F, Insight : A Study of Human Understanding (Collected Works of Bernard Lonergan : Volume 3), University of Toronto Press 1992 '... Bernard Lonergan's masterwork. Its aim is nothing less than insight into insight itself, an understanding of understanding' 
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Maxwell, James Clerk, The Scientific Papers of JamesClerk Maxwell Volume 2, Dover Phoenix Editions 2003 Amazon Product Description 'One of the greatest theoretical physicists of the 19th century, James Clerk Maxwell is best known for his studies of the electromagnetic field. These 101 scientific papers, arranged chronologically in two volumes, testify to Maxwell's scientific legacy and offer modern students of mathematics and physics stimulating reading. 197 figures. 39 tables. 1890 edition.'

'Though in the course of ages catastrophes have occurred and may yet occur in the heavens, through ancient systems may be dissolved and new systems evolved out of their ruins, the molecules out of which these systems are built -- the foundation stones [states] of the universe remain unbroken and unworn. They continue this day, as they ere created, perfect in number and measure and weight.' pp 376-77 
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McKeon, Richard, and (editor), The Basic Works of Aristotle, Random 1941 Introduction: 'The influence of Aristotle, in the ... sense of initiating a tradition, has been continuous from his day to the present, for his philosophy contains the first statement, explicit or by opposition, of many of the technical distinctions, definitions, and convictions on which later science and philosophy have been based...' (xi) 
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Nixon, Richard Milhous, The Memoirs of Richard Nixon, Buccaneer Books 1994 Amazon editorial review: 'Former President Richard Nixon's bestselling autobiography is an intensely personal examination of his life, public career, and White House years. With startling candor, Nixon reveals his beliefs, doubts, and behind-the-scenes decisions, and sheds new light on his landmark diplomatic initiatives, political campaigns, and historic decision to resign from the presidency. Throughout his career, Richard Nixon made extensive notes about his ideas, conversations, activities, and meetings. During his presidency, from November 1971 until April 1973, and again in June and July 1974, he kept an almost daily diary of reflections, analyses, and perceptions. These notes and diary dictations, which are quoted throughout this book, provide a unique insight into the complexities of the modern presidency and the great issues of American policy and politics.' 
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Pais, Abraham, 'Subtle is the Lord...': The Science and Life of Albert Einstein, Oxford UP 1982 Jacket: In this ... major work Abraham Pais, himself an eminent physicist who worked alongside Einstein in the post-war years, traces the development of Einstein's entire ouvre. ... Running through the book is a completely non-scientific biography ... including many letters which appear in English for the first time, as well as other information not published before.' 
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Pais, Abraham, Inward Bound: Of Matter and Forces in the Physical World, Clarendon Press, Oxford University Press 1986 Preface: 'I will attempt to describe what has been discovered and understood about the constituents of matter, the laws to which they are subject and the forces that act on them [in the period 1895-1983]. . . . I will attempt to convey that these have been times of progress and stagnation, of order and chaos, of belief and incredulity, of the conventional and the bizarre; also of revolutionaries and conservatives, of science by individuals and by consortia, of little gadgets and big machines, and of modest funds and big moneys.' AP 
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Rawson, Philip, Tantra: Indian Cult of Ecstasy, Crescent 1988 Jacket: 'Suggesting as its final goal a vision of cosmic sexuality, Tantra embodies fundamental patterns of symbolic expression in a view of life which offers a uniquely successful antidote to the anxieties of our time. The act of creation is continuous: therefore sexual intercourse between human beings can be a microcosmic representation of the creative process -- a symbolic tribute to the great Goddess from whose womb, and through whose wisdom, all things in the Universe are manifested in Time.' 
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Tarski, Alfred, Cardinal Algebras, Oxford University Press 1949 'This book is an axiomatic investigation of the novel types of algebraic systems which arise from three sources: the arithmetic of cardinal numbers; the formal properties of the direct product decompositions of algebraic systems; the algebraic aspects of invariant measures, regarded as functions on a field of sets. ... The book is replete with novel algebraic notions; it is written in logical style; all theorems (important and unimportant) are explicitly stated, and the proofs are carefully cross-referenced.' Saunders MacLane 
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Tymoczko, Thomas, New Directions in the Philosophy of Mathematics: An Anthology, Princeton University Press 1998 Jacket: 'The traditional debate among philosophers of mathematics is whether there is an external mathematical reality, something out there to be discovered, or whether mathematics is the product of the human mind. ... By bringing together essays of leading philosophers, mathematicians, logicians and computer scientists, TT reveals an evolving effort to account for the nature of mathematics in relation to other human activities.' 
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van der Waerden, B L, Sources of Quantum Mechanics, Dover Publications 1968 Amazon Book Description: 'Seventeen seminal papers, dating from the years 1917-26, in which the quantum theory as wenow know it was developed and formulated. Among the scientists represented: Einstein,Ehrenfest, Bohr, Born, Van Vleck, Heisenberg, Dirac, Pauli and Jordan. All 17 papers translatedinto English.' 
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Papers
Born, Max, Werner Heisenberg and Paul Jordan, "Zur Quantenmechanik II (On quantum mechanics II)", Zeitschrift fur Physiks, 35, , received November 16, 1925, page 557 - . Translation available in van der Waerden, B L, Sources of Quantum Mechanics, Dover Publications 1968 . back
Callen, Herbert B, Tjheodore A Welton, "Irreversibility and generalized noise", Physical Review, 83, 1, 1951, page 34-40. 'A relation is obtained between the generalized resistance and the fluctuations of the generalized forces in linear dissipative systems. This relation forms the extension of the Nyquist relation for the voltage fluctuations in electrical impedances. The general formalism is illustrated by applications to several particular types of systems, including Brownian motion, electric field fluctuations in the vacuum, and pressure fluctuations in a gas.'. back
Nyquist, Harry, "Thermal Agitation of Electric Charge in Conductors", Physical Review, 32, 1, 1928, page 110-113. 'The electromotive force due to thermal agitation in conductors is calculated by means of principles in thermodynamics and statistical mechanics. The results obtained agree with results obtained experimentally.'. back
Links
The Internet Classics Archive | On Generation and Corruption by Aristotle 'Written 350 B.C.E , Translated by H. H. Joachim. ... 'Our next task is to study coming-to-be and passing-away. We are to distinguish the causes, and to state thedefinitions, of these processes considered in general-as changes predicable uniformly of all the things that come-to-be and pass-away by nature. Further, we are to study growth and 'alteration'. We must inquire what each of them is; and whether 'alteration' is to be identified with coming-to-be, or whether to these different names there correspond two separate processes with distinct natures.'' back
Being There - Wikipedia Being There - Wikipedia, the free encyclopedia 'Being There is a 1979 American comedy-drama film directed by Hal Ashby, adapted from the 1971 novella written by Jerzy Kosiński. The film stars Peter Sellers, Shirley MacLaine, Melvyn Douglas, Jack Warden, Richard A. Dysart, and Richard Basehart. Douglas won the Academy Award for Best Actor in a Supporting Role and Sellers was nominated for Best Actor in a Leading Role. This was the last Peter Sellers film to be released while he was alive.' back
Dakini - Wikipedia Dakini - Wikipedia, the free encyclopedia 'A dakini (Sanskrit: डाकिनी ḍākinī; Tibetan: མཁའ་འགྲོ་མ་ khandroma, Wylie: mkha' 'gro ma, TP: kandroma; Chinese: 空行女) is a tantric deity described as a female embodiment of enlightened energy. In the Tibetan language, dakini is rendered khandroma which means 'she who traverses the sky' or 'she who moves in space'. Sometimes the term is translated poetically as 'sky dancer' or 'sky walker'.' back
Fluctuation dissipation theorem - Wikipedia Fluctuation dissipation theorem - Wikipedia, the free encyclopedia 'In statistical physics, the fluctuation dissipation theorem is a powerful tool for predicting the non-equilibrium behavior of a system — such as the irreversible dissipation of energy into heat — from its reversible fluctuations in thermal equilibrium. The fluctuation dissipation theorem applies both to classical and quantum mechanical systems. Although formulated originally by Nyquist in 1928, the fluctuation-dissipation theorem was first proved by Herbert B. Callen and Theodore A. Welton in 1951.

The fluctuation dissipation theorem relies on the assumption that the response of a system in thermodynamic equilibrium to a small applied force is the same as its response to a spontaneous fluctuation. Therefore, there is a direct relation between the fluctuation properties of the thermodynamic system and its linear response properties. Often the linear response takes the form of one or more exponential decays.' back

Piety - Wikipedia Piety - Wikipedia, the free encyclopedia 'The word piety comes from the Latin word pietas, the noun form of the adjective pius (which means "devout" or "good"). Pietas in traditional Latin usage expressed a complex, highly valued Roman virtue; a man with pietas respected his responsibilities to other people, gods and entities (such as the state), and understood his place in society with respect to others.' back
Pontifical Catholic University of Chile - Wikipedia Pontifical Catholic University of Chile - Wikipedia,.the free encyclopedia 'The Pontifical Catholic University of Chile (UC or PUC) (Spanish: Pontificia Universidad Católica de Chile) is one of the six Catholic Universities existing in the Chilean university system and one of the two Pontifical Universities in the country, along with the Pontifical Catholic University of Valparaíso. It is also one of Chile's oldest universities and one of the most recognized educational institutions in Latin America. Since it is a Pontifical University, it has always had a strong and very close relationship with the Vatican. It was founded on June 21, 1888 through a decree issued by the Santiago Archbishop. Its first chancellor was Monsignor Joaquín Larraín Gandarillas, and at the very beginning, the university only taught two subjects, law and mathematics. It is part of the Universities of the Rectors' Council of Chilean Universities, and although it is not state-owned, a substantial part of its budget is given by state transferences under different concepts.' back
René Thom - Wikipedia Rene Thom - Wikipedia, the free encyclopedia René Frédéric Thom (September 2, 1923 – October 25, 2002) was a French mathematician. He made his reputation as a topologist, moving on to aspects of what would be called singularity theory; he became world-famous among the wider academic community and the educated general public for one aspect of this latter interest, his work as founder of catastrophe theory (later developed by Erik Christopher Zeeman). He received the Fields Medal in 1958.' back
Rudolf Clausius - Wikipedia Rudolf Clausius - Wikipedia, the free encyclopedia 'Rudolf Julius Emanuel Clausius (Born Rudolf Gottlieb,[1] January 2, 1822 – August 24, 1888), was a German physicist and mathematician and is considered one of the central founders of the science of thermodynamics.[2] By his restatement of Sadi Carnot's principle known as the Carnot cycle, he put the theory of heat on a truer and sounder basis. His most important paper, On the mechanical theory of heat, published in 1850, first stated the basic ideas of the second law of thermodynamics. In 1865 he introduced the concept of entropy.' back

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