vol VII: Notes
2012
Notes
[Sunday 3 June 2012 - Saturday 9 June 2012]
[Notebook: DB 71 Israel]
[page 189]
Sunday 3 June 2012
I have been circling something for millions of words, trying to reverse engineer my life back to the sources from which it flowed, and the target seems to keep getting closer, suggesting that the journey is not endless. A clear target is the crisis in physics based around the inability to unify gravitation and the other forces using continuous mathematics and the associated mathematical definition of continuity. Instead we substitute logical continuity and make a bootstrap between logic and dynamics with the fixed point theorem.
Survival depends upon politics, which in turn depends on
[page 190]
common understanding of the nature of the world. So we can understand the political motivation of the dichotomy between God and the world.
Eureka Street -- why do we differentiate God and the world?
Feynman I 20-6: 'We may bow claim to understand the precession of gyroscopes and indeed we do, mathematically. However, this is a mathematical thing which, in a sense, appears as a "miracle". It will turn out, as we go to more and more advanced physics, that many simple things can be deduced mathematically more rapidly than they can be really understood in a fundamental of simple sense. . . . An example is the Dirac equation, which appears in a very simple and beautiful form, but whose consequences are hard to understand.'
We understand transformations in the world by calculus, differential and integral equations. How are these represented by the network? Answer that and the network picture of the world will be on its way.
A key move would be to translate logical continuity and network continuity into Einstein's equation and vice versa, ie to show that they are equivalent. General covariance is automatic if all the quanta of flow are identical, because their mappings are indistinguishable, ie symmetrical. What flows in the Universe are quanta of action, and the rate of flow is the energy of a connection.
Gravitation: the medium is the message (not the meaning conveyed by the messages which is a breaking of the symmetry of the medium. We do not ask the nature of the quanta of action,
[pages 191-194 not used]
[page 195]
merely their cardinal. So we might say that gravitation is the cardinal foundation of the ordinal Universe. When these quanta of action are ordered to for computers new structure is born, and self sustaining structure become more common than those that do not sustain themselves (open ended, non-halting)
We imagine spacetime pixellated by quanta of 4-momentum which transform as volumes in spacetime.
Gödel numbering: a cardinal representation of order derived by an algorithm rather than a dictionary. Ordinal representation of the cardinals so derived is used to represent them in writing.
The symmetry of cardinal units allows the exploration of the space of permutations that can by created by different orderings of distinguishable symbols (since what is indistinguishable cannot have order).
There are no true 'identical' particles in the Universe because to be identical is to be one, not two or more. Although we may say all a;s are the same letter, every a in the world has a unique physical realization in type, in print or in some other medium.
I imagine the system that made me from nothing, Insofar as it can be communicated and works logically = digitally it must be made of distinct interacting elements. Bandwidth = entropy flow, = information flow = energy.
Theology must be cleared of its unsavoury political associations - particularly monarchic repression.
The Lord holds his power by humiliating his underlings, cf Syria.
[page 196]
EXPERIENCE - INFORMATION
Monday 4 June 2012
Principle of least time ==> time is of the essence.
Feynman I 26-3 Fermat's principle of least time.
'Now in the development of science we want more than just a formula. First we have an observation and then we have numbers that we measure, then we have a law which summarizes all the numbers. But the real glory of science is that we can find a way of thinking such that the law is evident. Feynman
So the question raised by Parmenides in 2500 bp, how can we write true static text about a dynamic world? was ultimately answered by Einstein. The Universe has invariants which remain the same for all time and so can be represented by the invariant texts which constitute the scientific literature. John Palmer - Parmenides
Now I am right back where i started from trying to make a logical explanation, an algorithm for the two slit demonstration. We have that algorithm in the addition of phases seen as a field over the space of interest. How does this work with computers?
Event, reception of a message and a reply, one act of communication.
Space is a system which can transform things from one address to another.
Standard expositions of relativity put time on a par with
[page 197]
spatial distance, but there is the fundamental difference that time drive on inexorably whereas given enough energy to deal with the potentials we met, we can go almost anywhere in space.
Tuesday 5 June 2012
What am I trying to do? To create a new theology based on the notion that the Universe is divine and to understand the unity of the Universe through logical rather than 'mathematical' continuity. Feynman presents a brilliant elementary exposition of the behaviour of the Universe using logical arguments which amount to mathematical proofs. These proofs depend ultimately upon mappings between various sets of symbols, either observed phenomena of symbols created by the axiomatic rules applied to various spaces. Most of this work is performed by differentiating and integrating in continuous spaces, that is sets of definite, separate and identified points which are nevertheless so close together that we ay call them 'continuous. From a logical point of view (information theory) a continuum carries no information and only the particles count, but we use the continuum (in the form of a field) to communicate between particles, so the influence of one particle on another is mediated by the continuum [boson]. This is satisfying, and since the continuum carries no information of its own, it serves as a bringing symmetry for the whole Universe. My difficulty is seeing this in logical terms. The answer, as in quantum mechnics, appears to be that the mathematical continuum is a smoothed (probabilistic) picture of the myriad detailed logical operations that make the Universe.
CONTINUITY - SYMMETRY - IDENTITY - COMMUNICATION
God is the Source of everything.
[page 198]
Einstein's idea, emphasized by MTW is that we understand the Universe by working from local to global. In a Universe that grows by the algorithm COPY ≡ DIFFERENTIATE, we may guess that every identity is isomorphic to the initial singularity.
To understand the world we must understand the logical structure of the mathematics that fits the world so well, calculus and the theory of computation.
Numerical solutions are demanded by the variety of locality. Analytic solutions are only possible when the different elements are in some way identical (symmetrical).
It has long been a philosophical belief that we can understand reality through an understanding of language. Further many have felt that the most fruitful language to study is mathematics because of its universality and transparency. Any language barriers in mathematics can be overcome by concentrating on the detailed logic of the mathematics itself until we come to a common understanding of the strings of symbols we use to represent the mathematical world.
The reformers strove against the 'scientification' of theology which has taken a big step forward in the work of Albert the great and Thomas Aquinas. Although we like to make a dichotomy between medieval and modern knowledge our knowledge is in fact built on theirs and we still accept many of their ideas , being at pains to differentiate ourselves from their text based rather than experience based approach to truth. In this way the Reformers are very similar to those who would revert to what they believe to be a better practice of Islam. Protestant Reformation - Wikipedia
A computer is a dynamic system whose invariants are is physical structure
[page 199]
and its code. Sine structure can be coded , we can say that the whole invariant element of a computer is code, that is an ordered set of symbols which defines the way these symbols, or subsets of symbols are to be manipulated. Such a machine can achieve all possible manipulations of a given ordered set, that is all permutations. We may thing of some areas of the space of symbols as protected from change, and this area encodes the fixed points of the dynamic system. Electronic Frontier Foundation A halting computer, one which outputs a result, proceeds deterministically from its initial to its final state along a 'logical continuum'.God is big, and the Universe is big. So big that nobody could oppose its divinity on grounds of size. We measure size here not just in terms of light years but also by the relationship of cosmological times and distances to the quantum of action, an exceedingly small quantity, meaning that the Universe despite its size is also very fine grained.
Wednesday 6 June 2012
All the physical quantities that we measure are ultimately scalars, that is sets of units like atoms, quanta of action or repetitions of a given event (scalar time).
Since time is an ever increasing positive real scalar, we suspect that the correct metric for flat space s 1, -1, -1, -1. This makes space in a sense 'imaginary', that is periodic, the venue for computations which are in effect a set of 'clock' pulses each coupled to an operation corresponding to a value of the program counter. Movement in space is a sequence of quanta of action stepping an object (like a photon) from memory address A to memory address B.
In the Universe the contents of memory are the things and processes we see all around us, including our own bodies which are predominantly 'outside' our consciousness. Don't see people thinking like this, but may not read and talk widely enough in books, periodicals and internet.
Feynman I 39 The Kinetic Theory of Gases
page 39-1: '. . . matter is made out of a great many atoms which interact electricity and obey the laws of mechanics.'
Logic is scale free, like arithmetic, so applies in all situations involving 'atoms'.
ATOM ≡ ALGORITHM (invariant set of responses to inputs).
Coming down after six months of panic, trying to get something done. inspired perhaps by the Israeli mess and the serious need for a new religious and theological foundation on which to build a solution, the software of peace.
Matter and form : energy and momentum.
To DB 72, ENERGAIA
[page 1]
Feyman I 39-2: '. . . we all know that equal volumes of gases at the same pressure and temperature contain the same number of molecules. . . . Can we deduce from Newton;s laws that the number of atoms should be equal?
What am I doing? Living, driven by the energy of the Sun.
Many atoms are subject to the same laws, each an instance of some algorithm.
Algorithmic information theory sees no information in a continuum. The continuum is the symmetry of different instances of the same algorithm. Nor is [there] information in a perfect symmetry. Chaitin: Algorithmic Information Theory
The world is at all times fully concrete ad all symmetries are actually broken but they nevertheless exist, enabling us to take an abstract view of the concrete world as an end to navigation and pleasurable understanding.
All these insights seem to be worth the physiological stress (and consequent strain) of a single joint, so I have decided to have another.
In the abstract context, 'atom' can mean any [discrete] system or organism.
The Universe is organic. Organon = Organon- Wikipedia
The liberation of science came with its depoliticisation, no longer the will of the King (or Pope) but the Will of God (or World). [Science lets the world speak for itself]
[page 2]
Kinetic theory describes pure democracy, every atom contributing equally to the overall effect,. Elastic interaction.
Conservation of action / momentum / energy: we al share a big fixed pool. What I gain, you lose, enforced by some accounting system, built into the Universe. This system is the 'tree of action' which can enforce the symmetry (or is the symmetry) because all messages go through the physical layer, the initial singularity.
Each atom has momentum but the total momentum of a stationary body of gas is zero. This is possible because momentum is vectorial, it has direction in space, since it is associated with motion.
COLLISION - TRANSFORMATION - COMPUTATION - COMMUNICATION
Sitting in my cave with a hot water bottle becoming prophetic, ie artistic, broadcasting part of myself.
A gas is in perpetual motion and does not wear out: Maxwell (ref?) James Clerk Maxwell: Molecules
Natural religion slogan: cool it.
How do we measure an elastic collision? Energy and momentum in and out, as in a particle accelerator. No other details? Direction of motion before and after? A symmetry since all directions are equal in an inertial frame. [gravity and acceleration break this symmetry]
Molecules deliver momentum to the walls which feel the
[page 3]
pressure even though they do not move and momentum is conserved (always 0 in the CM (local) system),
How do we think of a network in terms of action, energy and momentum? A gas in a box is a bounded network with n! states, where n is the number of particles in the box. Boltzmann Ludwig Boltzmann - Wikipedia, Cercignani: Ludwig Boltzmann
A Church is a survival oriented community. The broadest Church is that of Adam Smith, who felt that an invisible hand formed 'everyone for themselves' to 'we're all in it together'. This invisible hand is the power of cooperation, conscious or unconscious. Adam Smith - Wikipedia
Watching the game = recording the memory represented by photons.
Feynman 39-3: Compressibility of radiation.
Universe may begin as a box of radiation.
39-7: 'What we mean by temperature is just that -- the final condition when things have been sitting around interacting with one another for long enough.'
Social thermodynamics, developed from a network model of thermodynamics, which is statistical mechanics.
My personal communication network (nerve system) contains representations of all my experience and every now and then confronts me with the desire to write down a sentence like this.
[page 4]
I am putting my words into your mouth Jeremiah 1:9. The Book of Jeremiah
Jerusalem Bible pp 1116-7: 'It is important to notice that the prophet, like the mystic, is raised to a 'supranormal' psychological state by this divine intervention. To deny this would be to reduce the prophet to the rank of a poet or to credit him with the illusions of misguided visionaries. Jones: The Jeruslalem Bible
Natural theology disagrees.: all experience, no matter how trivial, is experience of God.
The basic religious threat is Isaiah 1:19-20: 'If you are willing to obey, you shall eat the good things of the earth, but if you persist in rebellion, the sword shall eat you instead.' As Assad would say. Isaiah
Quote 1:21=28 in manifesto.
Feynman 39-9: 'The mean molecular kinetic energy is a property only of the "temperature" . . . and not of the gas.'
Particle carries 1.3 x 10-23 J K-1. Why does Boltzmann's constant have this value? Because of our choice of units?
So to Brillouin. Brillouin: Science and Information Theory
Feynman: '40-2 The Boltzmann law: n = (constant) e-PE/kT, . . . known as Boltzmann's law, is another of the principles of statistical mechanics: that the probability of finding molecules in a given spatial arrangement varies exponentially with the negative of the potential energy of that
[page 5]
arrangement, divided by kT."
The isothermal atmosphere, n = n0 e-mgh/kT, n0 at h = 0
These equations are the logical consequences of a certain set of assumptions )Newtonian mechanics), and the path of the logic is set out in a derivation like that given by Feynman for the equation above. Given a certain constraint, we can expect certain behaviour [defined by a Turing machine].
logical consequence = mathematical consequence (in a certain axiom system).
The structure of divinity : self-consistency -- conservation. Yet we have motion which means annihilation and creation. A 'continuous' process = 'transparent' process, from the users point of view nothing is happening (even though a vast number of ells and molecules are cooperating to write this).
Kinetic theory of gases: the pool table entrypoint into the theory of networks. A defined structure in reality can be mapped onto a defined structure in the literature, eg electron.
We understand motion by a duality, A moving, B still, or B moving, A still. These are the extremes of relativity.
Einstein Relativity page 78: '[The principle of relativity asserts that] If we formulate the general laws of nature as they are obtained from experience, by making use of [different reference bodies] then these general laws of nature (eg the laws of mechanics or the laws of propagation of light in vacuo have exactly the same form in both cases.' Einstein
[page 6]
Einstein page 85: 'The gravitational> mass of a body is equal to is inertial mass. . . . The
How does the quantum of action relate to the quantum of spacetime [the graviton?].
In the network we take two communicating nodes as defining a point and name the point (the message) by the names of the bodes. The point only lasts as long as its constituents are bonded.
Einstein page 125: 'In gravitational fields there are no such things as rigid bodies with Euclidean properties; thus the fictitious rigid body of reference is of no avail in the general theory of relativity.
'For this reason non=rigid reference bodies are used which as a whole are not only moving in any way whatsoever but which suffer alterations of form ad lib during their motion.'
"reference mollusc"
page 126: 'The general principle of relativity requires that all these molluscs can be used as reference bodies with equal right.
Thursday 7 June 2012
Struggling for a point of view but beginning to settle for time / phase as the first emergent 'fixed point', ie fixed entity, and see natural selection in path integral terms. The effectively random phases cancel and only those with a certain state persist, defining in the large scale the classical path through space-time, although we have not[page 7]
got space yet!
Pure act, pure rotation, the ancients thought the circle was perfect. The fixed points in such a system are the boundaries of the vibrating source and the standing waves (orbits) induced by these boundaries which in an atom are defined by a potential≥ Harmonic motion is an interplay between two forms of energy which is self sustaining and (as quantum mechanics shows) can go on forever reversibly and losslessly. The path integral method picks out harmonics in this random mix of phases,. From a computing point of view, phase is the measure of progress (like the ubiquitous 'worms').
Is gravitation the first and weakest potential or are there others too weak to detect? We work on the assumption that it is first and wish to see how it explains the 'big bang'. Why does the Universe expand and differentiate, or as the ancients might ask, why does the Universe emanate from the divinity? The answer to this question, insofar as it can be written down, is the fixed points of this process [an 'equation of state'].
AND = POSITIVE 'INTERFERENCE' (something appears)
NAND = NEGATIVE " (nothing appears)
Events and harmonies -- everything fits together space-time harmony. The 'music of the spheres' is represented in both space and time. The cratering of the spheres shows how they have interacted over the years.
Why did geenral relativity take so long?
[page 8]
'Now it came to me . . . the independence of the gravitational acceleration from the nature of the falling substance may be expressed as follows: In a gravitational field (of small spatial extension) things behave as they do on a space free of gravitation. . . . This happened in 1908. Why then were another seven years required for the construction of the general theory of relativity? The main reason lies in the fact that it is not so easy to free oneself from the idea that coordinates must have an immediate metrical meaning.' MTW page 5. Misner, Thorne and Wheeler: Gravitation
Since all Gaussian coordinate systems are equivalent (no permutation of action is superior to any other) we may say that gravitation deals with meaningless (continuous) systems, or rather the meaningless continuous (classically divine) predecessor of all systems.
My insight came in about 1964. Why have I not constructed a new theology 48 years later? Perhaps because the otherness of God was drilled into me much more deeply that the notion that coordinates must have immediate metrical meaning was part of Einstein's education.
All our physics is a representation of the fixed points of the divine dynamics. But what is the dynamics that generates these fixed points? Our understanding of this is our vision of God. Here the hypothesis is that God is best understood as a unbounded communication network which we model on finite practical networks.
Quantum mechanics lies at the interface between
[page 9]
continuity and information.
All that we see is messages, like this sentence or that leaf outside the window.
Quantum mechanics tells us that zero does not exist, and so it cannot be the denominator of any fraction or function.Do fixed point theorems apply to the Universe? Looks like it. The Universe is dynamic, so we have mapping. It is all that there is, so that it is mapping onto itself. It is convex, because at least at the beginning is not not have enough structure to have holes in it.
ds2 = dt2 - dx2
dp2 = dE2 - p2
Hobson et al: Special relativity is kinematic and can be developed using the right diagrams, Euclidean geometry and calculus. Hobson, Efstathiou and Lasenby
Special relativity defined the 'message space' in an inertial frame, and so establishes the phase relationships between various points in the pace depending on their position.
Layer n-1 provides tools for layer n and so on.
Friday 8 June 2012
MUNDANE = DIVINE
The human pecking order is poorly constructed,
[page 10]
wealth and the violence that wealth can buy.
Each religion locates its people in a story. The idea of natural (scientific) religion is to be situated in the true story.
The metric is the link between the reciprocal (dual) vectors that we use to describe a differentiable manifold. The One space compensates the other to yield an invariant interval.
The observer is the reference frame. Dual reference frames observe one another through the lens of the metric.
Spatial degrees of freedom are so symmetrical that we cannot distinguish different instances of them even though they are present in every structure, a few layers above the initial singularity.
So we look at the observable Universe as a data structure and everything we see in in memory, or [is] memory simpliciter. Wrestling women is my favourite image of a dual mollusc like space.
As I get older I have to move energy from creation to documentation, so any progress that has been made will not be lost.
Saturday 9 June 2012
Communication is the metric that binds the dual spaces[page 11]
(reciprocal spaces, isomorphisms) of mind and reality.
Degrees of freedom are continuous (aleph(>0)) because their very freedom is the denial of the existence of discrete structure.
Spacetime is the layer from which all other structures are constructed, and it seems that the first generation of these might be the photon, electron, neutrino, quark etc. So we assemble the Universe out of instances of spacetime which appear in more complex form as Hilbert spaces. What is the difference between Hilbert and Minkowski? What about in 1D, 2D . . .
Perverse incentives: Science 336:795 18 May 12 Mara Hvistendahl
Space is a dynamic element of the structure of the world rather than just the stage, as we see from the parallel transformations of space-time and momentum-energy. Since spacetime operates in a digital manner we might do away with all the renormalization problems. Renormalization - Wikipedia
We build the Universe up the way recursive functions are built up, beginning with the archetypal recursive function, the complex numbers and complex exponentials.
The 4D instances of space-time that we use to build the Universe are transformed into one another by the Lorentz transformation of anfular relationship and relative velocity. By analogy with c, we see velocity as fundamental. c is a fixed point in the Universe, along with h and e and then the rest mass of various stable particles.
