VII Notes
2010
Notes
[Sunday 14 February 2010 - Saturday 20 February 2010]
[Notebook: DB 68: Salalah]
[page 193]Sunday 14 February 2010
The network view of Dirac's equation.
Pais Inward page 244: 'The rejection of forces acting instantaneously at a distance in favour of forces transmitted from point to neighbouring point by continuous fields meant the
[page 194]
end of the purely mechanical picture of the physical world.' Pais
Hard to see - mechanical (engineering) systems always have a field (piece of matter) transmitting forces from A to B such as a pillar or connecting rod.
Einstein: 'Since Maxwell's time, Physical Reality has been thought of as represented by continuous fields . . . not capable of any mechanical interpretation. This change in the conception of reality is the most profound and most fruitful that physics has experienced since the time of Newton.'
Message = 'mechanical connection' = 'field'.
Field is not 'mechanical' (ie deterministic) insofar as it has its own degrees of freedom. Field is a thing with a personality whose communications are particles
Ladder of creation [stretching from the ultimate parent 'God' to all God's children, God + God's children = god]
QUANTUM MECHANICS - MUSIC (THE BEAT) - LANGUAGE (RHYTHM PLUS)Revolution = change of structure: Classical mechanics to quantum mechanics. From point to matrix, a step up in entropy. We can order layers by their entropy, but it is necessary to establish a scale of entropy which is represented by the hierarchy of transfinite numbers.
The layered network version of entropy.[page 195]
The purpose of a political revolution is (theoretically) the overthrow of a repressive regime by a more liberal one, and is a process fraught with error and expense, as we see in the world around us through the eyes of those reporting the war rather than those who are fighting it or are two busy with local problems to take a wider view. Like childbirth, all engrossing.
Build a religion = build a set of protocols fro maintain peae in human society. By verifying the network model at a sample of layers of sructure on the ladder of creation.
The world is not the puppet of an invisible higher being. The world is that higher being, and it is incumbent on us to learn its ways if we are to survive. This is the task undertaken by practitioners of science, the method of obtaining knowledge by watching what actually happens when we do something (like tease a sibling, or pour acid on a non-noble metal.
The lader of creation is the output of creation and annihilation operators working in the neighbourhood. From a physical point of view, the ancient's prime matter is energy, that is the flow of action through time. In physics, the more energy, the faster things happen.
Sex: a communication protocol implemented in the living body.
Pais 251: 'Six theoretical papers appeared during [the p[eriod of the old quantum theory} which are revolutionary . . . . If these papers have one thing in common it is that they contain at least one theoretical step which . . . could not be justified at the time of writing.'
[page 196]
Heisenberg (cannot say it too often): "'In this paper it will be attempted to secure foundations for quantum theoretical mechanics which is exclusively based on relations between quantities which are in principle observable.' With these words Heisenberg states specific desiderata for a new axiomatics. Pais page 251.
And have forgotten something it put on hold
OBSERVABLE == COUNTABLE
We express the world as a set of dyads message content / frequency (normalized to 1 across the whole message space) which comprises a set of discrete signals the coxe messages, and a continuum, corresponding to those which are represented only by themselves. Khinchin
Special relativity: everything is its own primary representation.
Ladder of creation : Harmonic oscillator --> black body radiation, the freest there is.
Every quantum is a message parametrized, in the case of photons by a real number, the frequency. The messages can be binned to give is the black body curve. The classical curve, on the other hand, tends to infinity with increasing frequency rather than tending to zero after a temperature dependent maximum. From the network point of view the black body curve approximates the energy distribution of messages in equilibrium with an environment at a certain temperature.
[page 197]
The frequency of events is controlled by the logical connections in the syste, ie the tuning of strings and cavities by the 'integral wavelength' criterion. Node in the free, antinode in the fixed.
One can perform a statistical analysis of the frequency of different notes in a song, giving us a distribution function on the alphabet of notes.
Network explanation of quantum mechanics: a) at a cardinal level, the distribution function of a set of events and b) at the ordinal level, where we define a process whose output is statistically indistinguishable from the chose distribution function.
TTC Our product: A theory of peace. We wish to ignite an open source development of a viable theory of peace modelled on the creative process of the Universe.
My task, as I see it, is to write a rudimentary kernel for the sort of system I envisage and hope that others will see its value and seek to improve it. If you find it to be of no value you can easily break your connection.
Heisenberg 28 July 1928 van der Waerden page 261; van der Waerden
WAVE - PERIOD - COMPUTATION PROCESS
Heisenberg: van der Waerden page 264: '[In quantum theory] frequencies are in general not commensurate with their harmonics'. Does this mean they are not harmonics.
[page 198]
FLOR of INFORMATION = FLOW OF PROBABILITY
Normalization SUM pi makes the flow conservative and the rate of flow in any channel is the energy (rate of action) in the channel.
At the heart of TTC is the creation theorem.
'Quantum-theoretical re-intepretation of kinematic and mechanical relations. Heisenberg: van der Waerden page 261.
EVENT == PARTICLE (doing something) which can be counted - car accidents.
Born: 'Themotion of particles follows probability laws but the probability itself propagates according to casuality.
This probability is a function of the code being transmitted.
Does the wve function guide particlesin the same way that our thoughjts guide our actions, as abstract models of reality guiding our interaction with reality? This is an example of form guiding action, as the mental picture of the ideal golf shot guides the execution of the actual shot.
Monday 15 February 2010
The weight of a spectral line measures the traffic on that channel.
[page 199]
Pais Inward page 262: 'Heisenberg's 'unknowability relations': the gap between digital measurements like 1.1, 1.2, where we have an uncertainty of the order of 0.1.
Pais page 266: Wigner: 'There exists a well developed mathematical theory which can be used [to deal with n identical particles] : the theory of transformation groups which are isomorphic to the symmetric group (the group of permutations).'
page 266: 'Quantum mechanically, a state is given by a vector in Hilbert space; symmetry operations are implemented by linear (more precisely unitary or anti-unitary) operations on that space. This linearity, the real novelty, iod directly related to the superposition principle: in quantum mechanics one can add two states. There is nothing like this in classical physics'.
Each quantum number corresponds to a degree of freedom of the electron.
The horizon of every particle corresponds in some way to the velocity of light and the interior of a particle is conscious only to the particle itself,not to an outside observer unless the particle transforms itself and emits a corresponding message. Pais 277, Uhlenbeck and Goudsmit Nature 13:953 1925.
Every little hunch adds hope to the hopeless task of redirecting planetary ideas about the source of reality, the tantra. Victor M Fic
'Einstein: "The electron in its rest frame sees a rotating electric field; hence by elementary relativity it sees a magnetic field. The net result is an effective spin-orbit
[page 200]
coupling." Bohr was at once convinced. When told of the factor of two he expressed confidence that this problem would find a natural resolution.' Pais page 278
We are beyond geometric into function space description of the Universe. The output of . . .
We have a template of sufficient complexity to encompass all the variable elements of the site in a way that can be processed into a page by a rendering engine that accepts values for all the variables and uses a find and replace mechanism to write particular configurations for rendering. The page cannot be rendered until every variable is fixed.
The basic process of life is a sort of find and replace, changing the way things are into the way things will be.There are two strands of coupling between the past and the future, formal, which constrains, and dynamic, which explores the space defined by the constraints.
A computer can only become formalized and deterministic if the whole machine moves to the same clock,moving states through the machine without conflict. Executable <--> execution.
Every degree of freedom must be maintained, and maintenance is facilitated by digitization, that is treelike structuring. Free Software FoundationA network is a superposition of trees, each of us at the root of our own tree, and the same the case for
every 'particle' in the Universe.
The ultimate Copernicanism: we are all particles. Size matters and it can be measured in different ways. By treating ourselves as completely symmetrical (ie pairwise equal) we maximize our entropy and stability.
Pais page 280: 'Since 1926 we have known that in quantum mechanics one does not need one but two new ways of counting, Bose_Einstein (BE) statistics and Fermi-Dirac (FD) statistics; and that permutations and symmetries of many particle wave functions are the key to their justification.'
Pais 283; Bose statistics: Einstein: '"the new ways of counting express indirectly a certaim hypothesis on the mutual influence of molecules which of quite mysterious nature." That influence is of course the particle correlations implied by the restriction to symmetric wave functions -- recall, however, that we are still years away from the discovery of wave mechanics.
Constraint by symmetry = simplicity
TTC - Religion for ever
Tuesday 16 February 2010
Natural religion for ever.
As wee see it, religion is both the cause and cure for war. Religion binds us into functioning organisms much greater than ourselves, but the rules of survival apply to religious groups as much as to
[page 202]
bacteria, birds or any other form of life. These rules are imposed by the spiritual propensity to grow forever and the material limits on the resources for growth, creating competition for living space. So we fight, one religious organism pitted against another, battles that began with the origin of the world.
How do we avoid such war? By multiplication of resources, but we are coming to the limits of population and planetary resources.
One planet, one religion, natural religion, founded in reality, not old men's fantasies of conquest and glory.
Natural religion: a manifesto: 'A public declaration, as of a sovereign or a government, or of any person or body of persons taking important action, making known intentions, objects, motives etc; a proclamation [Italian: manifest, noun} Macquarie. Compact Oxford 'ORIGIN Italian from Latin manifestus 'caught in the act, flagrant.'
. . .
Applescript, Mac Dev Center, Operator reference)
'An operator is a symbol, work or phrase that derives a value from another value or pair of values. An operation is the evaluation of an expression from
[page 203]
which an operator derives a value. Apple Inc. A Turing Machine with input and output, ie an o-machine. Alan Turing
'text: An ordered set of Unicode characters.' ibid
'The Advantage of Layers:' Mac OS Technology Overview
Another lost thought (while peeling the potatoes). I hope it comes around again. Maybe something to do with the relationship between formalism, differential equations and dynamics. The rules of a game like soccer are analogous to a differential equation, giving boundaries to the game which induce structure, strategy and tactics into it. Formalism (mathematics) - Wikipedia Differential equation - Wikipedia Dynamics (physics) - Wikipedia FIFA (Federation International de Football Association)
The Universe is generally covariant in the sense that there is no special coordinate system (like the outside God who guarantees the uniqueness of Newton's space). The Universe is its own coordinate system and we describe events purely by their relationships to one another and not to some coordinate system.
Wednesday 17 February 2010
The fact that quantum theory describes the flow of probability (which can be regarded as a flow of information) seems to clinch the network model.
While peace is our target, and we have good prospects and leads, the TTC is still an exploration company. What we hope to do is to develop our prospects to the point where they will attract
[page 204]
the capital for their further development. As far as prospects go, we appear to be almost alone (in the Christian world) in the space defined by the equation god = Universe.
Some leads:
1. The transfinite network model is big enough to describe God and it fits quantum mechanics and the rest of science, bolstering our faith in the propspect.
2. We have the roots of a mathematical theology, something which transcends natural language and national and cultural barriers, being applicable to all personalities from atoms to planets and beyond.
3. Our mathematical model underpins a theory of creation which justified the view that the Universe itself is divine and needs no outside divinity to [create or] run it.
The dimension of the relevant matrices is the 'cardinal signature' of a peer layer. Feynman, Lectures III page 11-1 sqq. Feynman
'to each quantity in classical physics there corresponds a matrix in quantum mechanics. It is really more correct to say that the Hamiltonian matrix corresponds to the energy and any quantity that can be defined by energy [ie the rate of communication between i and j] can be described by a Hamiltonian matrix.Feynman page 11-4.
Nodes need just one index, i, links between nodes i and j need two indices, ij or ji depending on the direction of communication. In general, in quantum mechanics, <i | j> = <j | i>*.
[page 205]
Law of motion of quantum mechanics: the rate of communication in a channel is equal to the energy in the channel, almost a tautology, where each act of communication has the cardinal measure h bar.
Hamiltonian os the 'traffic matrix' for a system.
open source [or maybe free] vs proprietary theology.
Thursday 18 February 2010
Empirical science in the first instance moves from the particular to the general, observing individuals and on the basis of the symmetries obeyed by the individuals arriving at more general propositions, such as a growling dog with its hair standing on end has a greater probability of biting that a sleeping dog. Greater experience also reveals to us the outliers in the probability distribution functions associated with any class of observed phenomena, so an experienced rider will be ready for almost anything a horse can do.
Dirac 1927 (n Schwinger ed) page 2: energy and phase can be treated as canonically conjugate variables. E = d(phase) / d(time). Schwinger
quantum of action = one cycle of phase (phase mod 2 pi) = 0. We guess that one cycle of phase is represented logically by one computation. The smallest computation is a bit flip[ (NOT) which, in the case of any two state system (like an electron) corresponds to one quantum of action. The path from p to not-p we call a computation.
PATH = set of logical choices (used by analogy to the unix, (or most other systems) file tree). We see the Universe as such a tree, creating and deleting files being the fundamental
[page 206]universal process.
Everything there is to say can be said with a sufficiently large network of two state machines (each represented by a binary string). The interest lies not so much in the two states, which are all described by the same set of differential equations. The Schrödinger equation is the fundamental fixed point in two state dynamics. Schrödinger equation - Wikipedia [The interest lies in how the two state processes are linked together, as in an ordinary binary digital computer.]
Natural religion should be sexy insofar as creation outweighs annihilation so sex should outweigh violence, ie birthing should outweigh killing.
The survival of a machine depends on memory protection, which means making one's memory invisible to other processes, is local to myself. So most of my physical memories are stored in my head where they are not so accessible to other people.Christianity should be able to tolerate ideas that contain Christianity, so we will make a religious container which will hold all religions.
There is no God and Dirac is his prophet means [to me] that the old Judaeo-Christian God is obsolete and effectively non-existence except in the minds of certain believers and that the fundamental nature of the new Go, the Universe, is realized in Dirac's Principles of Quantum mechanics. Dirac
Dirac (Principles) page 3-4 expresses quantum uncertainty is terms of the disturbance to an isolated deterministic system
[page 207]
in the process of measurement, whose minimum interaction is a quantum of action, h bar.
page 4: 'A consequence of [the disturbance caused by observation] is that we must revise our ideas of causality. Causality applies only to a system which is left undisturbed. If a system is small we cannot observe it without causing a serious disturbance and hence we cannot expect to find any causal connection between the results of our observations. . . . There is an unavoidable indeterminacy in the calculation of observational results, the theory enabling us to calculate in general only the probability of obtaining a particular result when we make an observation.'
The emphasis on disturbance is disturbing. On the communication analogy (cf Zurek), communication can only occur when the two communicants agree on a protocol, ie both learn to operate in the same basis. Since the same abstract Hilbert space can be described in terms of an infinity of basis sets (which can all be transformed into one another by unitary (entropy / probability preserving) transformations, there is no particular preferred basis for communication but a distribution of probabilities depending on the distance (relative phase) between two the two states wishing to communicate. If they are 'parallel' the probability of communication is 1, if orthogonal, 0. In other words we are not so much concerned with disturbance as with the probability of various harmonics. Wojciech Hubert Zurek
One is imprisoned by a problem (like a flat tyre) insofar as one cannot go forward until the problem is solved.
Polarization of photons: Tourmaline is transparent only to photons plane polarized perpendicular to its optic axis.
[page 208]
This transparency arises because the crystal does not interact with and annihilate the photon. Contrariwise, all photons polarized parallel to the optic axis are interacted with and annihilated.
Annihilation in one layer does not necessarily involve annihilation in another layer, as when I die (am annihilated) many of my subsystems and supersystems (eg atoms and family) live on.
A question arises for photons polarized in directions immendiate between parallel and perpendicular.
I tend to get cranky when I do too much building to the exclusion of writing, editing and publishing.
Comment box: to prevent overload (and to comply with reading habits) comments are presented batchwise based on time ordering.
One ad panel each side of page, different providers chosen at random. Does Google allow random rather than targeted ad serving? I want to display your ads with a frequency distribution isomorphic to the historical rate of clicks per presentation.
The result of an experiment (with 45 degree photons) is not determined, as it would be according to classical ideas, buy the conditions under the control of the experiments. The most that can be predicted is a set of possible
[page 209]
results, with a probability of occurrence for each.
Explained by saying 45 degree photons is a superpositon of 0 degree and 90 degree states. The formalism does not have the variety requisite to completely determine the motion of the photon.
Interferometer: each photon only interferes with itself (in the amplitude domain). Interference between two different photons never occurs.
WAVE = RECURSIVE COMPUTATION
Dirac page 10: Picture: 'any way of looking at the fundamental laws which makes their self-consistency obvious.'
So a tree is a picture giving an obvious and globally (vis a vist the tree) consistent address to every leaf relative to the root.
Dirac page 11: 'The limitation of the power of observation puts a limitation on the number of data that may be assigned to a state. Thus a state of an atomic systems must be specified by fewer and more indefinite data than a complete set of numerical values for all the coordinates and velocities at some instant of time.' Ie the Universe is pixellated and the size of the pixel is h bar
'A state of a system may be defined as an undisturbed motion that is restriced by as many conditions or data as are theoretically possible without mutual interference or contradiction.'
page 12: 'Any state may be considered as a result of a superposition of two or more other states, and indeed in an infinite number of ways.
[page 210]
Dirac page 17: All the states of a dynamic systems are in one to one correspondence with all possible directions for a ket vector, no distinction being made betwen the directions of ket vectors |A> and -|A>.
Concerte determinism may lead to abstract indeterminism, since there is less data in the abstract that the concrete, as there is less data in the fixed points than the total dynamics.
naturaltheology = the personal saga
physicaltheology = the corporate wrapper
tnrp = the application of theology to human affairs
atheology = a constrastive commentary on Aquinas
anewtheology = an exposition of the principles of mathematical theology a la Dirac.
. . .
Dirac page viii: 'With regard to the mathematical form in which the theory can be presented, an author mist decide at the outset between two methods. There is the symbolic method which deals directly in an abstract ay with the quantities of fundamental importance (the invariants etc of the transformations) and there is the method of coordinates or representations which deals with sets of numbers corresponding to these quantities. The second . . .
[page 211]
is known under one or other of the two names 'Wave Mechanics' and 'Matrix Mechanics' . . . .
The symbolic method, however, seems to go more deeply into the nature of things. It enables one to express the physical laws in a neat and concise way . . . . For this reason, I have chosen the symbolic method, introducing the representatives later merely as an aid to practical calculation.
Friday 19 February 2010
. . .
Dirac page 24: '[In the algebra of linear operators] the commutative axiom of multiplication does not hold, and also the product of two linear operators may vanish without either factor vanishing.'
Let us define 'God' as the entity studied by those theologies that hold that the observed Universe and the system that creates and controls the Universe are distinct entities. Contrariwise, 'god' is the entity studied by those theologies that make no such distinction, we have but one Universe and it is its won source. We reject the ld hypothesis that God is the source of the Universe and replace it with the hypothesis that the Universe is its own source. May sound counter-intuitive, but God theology effectively defines God as its own source. The Theology Company believes in god, ie that is our working hypothesis.
The physical Universe is god's body.
Dirac page 29: 'We must make a further development of the theory of linear operators, consisting in studying the equation
[page 212]
Α|P> = a |P>
where Α is a linear operator and a is a number.
Devotion vs mathematical theology. The implementation of mathematical theology will have no more effect on human devotion that the invention of quantum mechanics had on football. Almost none. Only a small fraction of the population views football through the lens of quantum mechanics. The same goes for the community of scholars who study their experiences of the world through the lens shaped by the dogmatic pronouncements of the Roman Catholic Church, our rival organization in the religion business.
. . .
The god hypothesis contains the God hypothesis as a special case where we set part of god aside and treat the set aside part as an independent entity which we may call God. In this way god can accommodate an infinity of Gods which appear in our treatment as independent personalities or sources that fall under the general heading 'particles' [little parts] of the Universe.
Quantum mechanics can no more predict the outcome of a football match that you or I. Like bookmakers, the best we can do is define a 2 point distribution by some 'odds' although the Universe, unlike the bookmaker, does not adjust the odds to make a
[page 213]
by setting the payout ratio less than one.
We have enough evidence for the existence and value of our product to introduce it into the market in its embryonic form with a view to gaining the resources to bring it to term, not the least the personal morale resulting from successfully deploying some websites.
As things stand, we have four sources of uncertainty in the Universe, incompleteness, incomputability, network interrupts and the finite amount of data in a finite digital string. So life is uncertain at all scales. I have a few plans for today but all sorts of things can happen to affect their execution.
We tend to pick non-commutative multiplication and the uncertainty principle as the principal novelties in quantum mechanics, but I prefer to concentrate on the absolute simplicity (linearity) of the mathematical model that seems to fit perfectly with what we observe. Quantum mechanics describes the source of the world as far as it can be described. Given a two state system all we can predict is the existence of two stationary states of different energy and the rate of transition between them.
Dirac, Fock and Podolsky in Schwinger page 31: 'This obvious relativistic invariance is achieved by the introduction of a sepaprate time scale for each particle.' is frames moving at different velocities are relatively asynchronous and communication between them requires a store and forward algorithm which is exactly what the finite velocity of communication achieves, since the message is stored by the messenger during
its passage from source to sink.
Source creates / sink annihilates / particle [message] stores (symbol).
Saturday 20 February 2010
In the network model the Turing machines correspond to the field (with their independent internal degree of freedom) and the particles correspond to the messages transmitted between the machines on a network.
. . .
It is easy to write a Hamiltonian for a network. The dimension of the matrix is equal to the number of nodes and the individual entries Hij correspond to the rate of communication between node i and node j. Beale and Jackson. Beale & Jackson
GROWTH = CREATION = COPYING + DIFFERENTIATING
Classical equations of motion have the variety necessary to constrain their solutions to specific real values once all the initial conditions are satisfied. Quantum equations on the other hand, have less than the variety requisite for complete constraint and instead leave their solutions free to explore all the space between the constraints.
. . .
Potential energy is the same as kinetic energy, only of opposite sign. Perhaps we can think that the Universe needs energy to represent itself, but every representation
[page 215]
requires a duality centered around some invariant (as covariant and contravariant tensors meet in the metric), so the representative duality in the Universe is potential and kinetic energy and the unifying invariant is action. I write the wors without knowing what they mean, just as I live my life without really knowing my meaning (ie all my links) in the global system.
Aquinas uses this duality to model God by the via negative, not telling us what God is (which is considered unspeakable) but what God is not, which is considered speakable and is in fact (in the Thomistic view) the created world, including me but not God. Aquinas sees that in the end we will achieve bliss through the vision of God, which (on his theory of knowledge) means that the elect carry within themselves a mental word isomorphic to God, and so may be said to have changed their status from not-God to God. In natural religion we say god contains both Gd and not-God, that we are all divine and that everything we experience is an experience of God.
