vol VII: Notes
2012
Notes
[Sunday 17 June 2012 - Saturday 23 June 2012]
[Notebook: DB 72 Energaia]
ΔEΔt ≈ ΔxΔp ≈ h Jammer
As Heisenberg pointed out,w e only have to explain the observations, not the convoluted thought processes we have used so far to explain the observations.
2D space is conformally flat = Minkowski space up to the actual absolute value of the diagonal elements of the metric ημν.
[page 28]
The process. Notebooks blaze the trail. transcribing and referencing documents and tests the trail blazed. Essays try top put parts of it together and discern the overall picture. Development sets out to lay it down systematically, to produce an ordered set of words isomorphic to the divinity, ie revelation of god. Jammer psge 190: Bridgemann: 'the intellectual compulsion remains to give some instrumental meaning to the purported emptiness of space. The simplest way of meeting this compulsion is simply to say that the space is empty if no instrument gives any reading hen introduced into it.' ie no messages, no energy (Nature of some of our physical concepts).
Einstein 'the metric of space [-time] structure is function of the distribution of matter and energy.'
General relativity = structure of communication. Minkowski null vector ≡ contact ≡ sharing a fixed point ≡ sharing a language and a message.
We could say Gaussian coordinates are topological rather than metric and so the general theory represents network topology rather than spacetime. The invariant distance between two points is a quantum of action.
The impossible becomes possible when one invents a process, eg the steam engine (heat engine) the foundation of modern life.
Years of reading physics books with minimal understanding seem to be paying off.
[page 29]
Ie the network metric is determined by the rate of communication ds2 = 0 is maximum, ds2 = 1 minimum (horizon) (Normalized to R).
Padmanabhan: more energy, more communication, shorter distance - pair of wires, optic fibre. Thanu Padmanabhan: Thermodynamical aspects of gravity
Jammer page 191: Spherical space has finite volume 2π
What we can't observe we can't talk about. During the evolution of the Universe both methods of observation (languages, literatures)and the observations themselves have grown in parallel, the growth being measured by the cardinal of the Hilbert space representing the Universe.
How does the quantum mechanical R map to the cosmological R?
The Friedman-Robertson-Walker metric describes a space with no detailed structure, a perfect symmetry or continuum. Friedmann-Lemaitre-Robertson-Walker metric - Wikipedia
page 193: '. . . is the guiding field (the world metric) of general relativity exhaustively determinable by the energy=momentum tensor alone?'Two interpretations of the network : quantum mechanical (computational) and general relativity (communicational).
page 194: Einstein: '"I have chosen the name Mach's Principle because the Principle implies a generalization of Mach's requirement according to which inertia should be reduced to the interaction [or perhaps non=interaction] of bodies."'
page 195 Einstein: '"A space=time continuum, free of singularities,
[page 30]
with everywhere vanishing energy-momentum tensor seems to be predicted by the modified field equations."'
Jammer page 195: De Sitter: 'who showed that the ad hoc modified field equations admit of a space-time structure as a solution even in the absence of matter'. Energy-momentum = 0, space-time = 0.
The world is not a continuum, it is broken up by logical continua (Turing machines) that halt and emit a message which becomes the input to another Turing machine.
We ditch the anthropomorphic image of an 'observer' and consider all communication as observation.
page 198: Jammer on Einstein: 'Although matter may provide the epistemological basis for the metrical field, it does not necessarily have ontological priority of the field.' As ever we understand by duality, explaining one thing in terms of another locally better known model.
Observationally, gravitation is indistinguishable from acceleration, what stays constant as we transform between acceleration and gravitation is the metric, gμν.
What to do next, grind NN's exhaust or go on dreaming about the new apocalypse?
The human world appears to be deteriorating so it is time to get real and prophesy to the real nature of the world.
[page 31]
Logical continuity = logical contact
Special relativity 'mixes' space and time, general relativity 'mixes' acceleration and gravitation.
Monday 18 June 2012
There can be no doubt that theology has had a major role in human affairs throughout thousands of years of recorded history and continues to do so in the modern world. . . . Since the time of Galilei, however, we have seen rapid growth in the influence of science and we attribute much of our power over the world to the scientific knowledge collected in the last four centuries.
The weak force of gravitation may arise from thje chance coincidence of certain events. Electrodynamics, however, depends upon memory to that coincidences are controlled and the force is 1040 times stronger. Rather like the force of universal intelligence which is weak when there is no memory (among humans no writing) and then grows exponentially as the network grows more memory (data warehouses)
Consider the tick which waits long periods in a state of near hibernation for the stimulus of a passing warm blooded animal upon which it can drop to get a feed. Tick - Wikipedia
We can see the creative process at work in the capitalist system where potentially profitable ideas attract the capital to make themselves come true. I have lost a fair bit of money on enterprises which are spinoffs from university research in immunology and drug development. There is no reason why
[page 32]
the theology company should not do so. We must begin a theological prospectus and place it with Goldman Sachs. This has been the idea all along of course, but now it is beginning to appear feasible (with a lot of work). Jesus apparently went around telling everyone his story and collecting 'followers', fans, who found his story good and worth propagating, like gardeners. Cohan
We wish to propagate on a global scale because we feel that natural theology would be good for the world and its people, showing us how to look after ourselves and our habitat. Jesus was no doubt motivated in a similar way, as a person who believes he sees a solution to a common problem and is motivated to promote her / his creation.
For Christians Jesus said the last word and we have been puzzling over its meaning ever since. There is never a last work in a living Universe, however, to we are taking up our relationship with God again.
At present the vast majority of academic departments of theology are Christian (data?) World Council of Churches
Christianity is founded on the notion that God and the Universe are different entities and that the only link between them is the Bible. The alternative view, proposes here, is that God and the Universe are identical, so all experience is experience of God and data for empirical theology.
The dichotomy between God and the Universe has deep roots. An early record are fragments of a text by Parmenides . . .
[page 33]
We learn by repetition since frequent events are more important to us that rare ones (although we also have to learn by tradition how to avoid rare fatal events.)Feeling inspired (deluded?) today. Natural theology is saved from delusion by the scientific method which leads us to explore the phenomena very carefully to see what they are trying to tell us. A feeling perhaps primarily associated with successful mating and reproduction. The Universe grows by copying - Trinity again.
Can we say: One can scour the God Delusion for any real understanding of the model of God developed by the scientists from Parmenides and Plato to Albert the great and Aquinas. To understand God, one must understand the problem that led to the invention of God, Creation and annihilation, birth and death. This question spans the whole gamut from quantum field theory through human birth and death to the births and deaths of planet, stars and galaxies. Dawkins
. . .
Birth and death are birth and death of observables. The heuristic principle is that it starts simple and complexifies by recursion. Somewhere deep in the complexity of a computer are 'atomic circuits' that execute logical functions not, ad, or, etc, and their operations are sequenced and connected to perform more and more complex operations.
Why does the Universe stop at 4 macroscopic dimensions = three macroscopic degrees of freedom. Basic network connectivity. We need a Lagrangian for this. What we are
[page 34]
looking at is a set of memory locations (addressed with transfinite and finite cardinal numbers) which can change one another's states by communication. The Universe is quantized. We see the memories as potential, sending the messages as kinetic. But we only see the messages, not necessarily the processing that generates them. These words represent my conscious state, but I do not really know why I am in this conscious state at this moment, except that it is explained by some unconscious neural process which can nevertheless be observed from 'outside' my brain with elecrtrodes, PET, etc. Positron emission tomography - Wikipedia
What do I want to do next? Avoid the chores, necessary communications with my environment, write business letter, do dishes, chop wood, clean, build, fix drive etc.
Message : signal; what's the difference?
. . .
Topologically different: no continuous rearrangement can bring identity.
. . .
Definition of momentum: frequency of impulse x strength of impulse.Perhaps gravitation is an exceedingly powerful but even rarer impulse.
[page 35] Make myself do it. . . . But (wriggle wriggle) I now can think of the theology as the real job and and do not have to [do the other] until I go to town tomorrow.General relativity sees space as a field of tensors whose inputs are vectors and whose works are differentials which operate to keep ds2 invariant as the reference system changes. From a mathematical modelling point of view this would seem to involve a large amount of computation and we wonder how the world itself does these computations. Whatever the process is, we should expect it to be described by quantum mechanics and we hope that the network model can help us understand this, the tensor fields taking care of the message transport (and the physical vehicles of this transport) while quantum theory takes care of what goes in in the nodes which we may conceive as single quantum events or the birth, lofe abnd death of a star. The events of general relativity are all the things we see around us.
Action and reaction are equal and opposite tells us something about the duality of covariant and contravariant tensors moving around the metric as a fixed point.
In formal calculus ds, dx, dt etc are defined by a limiting process to be infinitesimal, but this infinitesimal may nevertheless be seen as being big enough to have a definite size measured by a real number, so it can be seen as a real signal of indeterminate size but definite meaning.
Must improve my intuition for tensors to map them onto networks which have their metrics built in and spatial extension is unimportant
[page 36]
is unimportant at light speed, as we learn from the internet.
The alternative to the intense calculations we do to numerically impement the action of tensors is some sort of 'natural' process that makes all this happen 'automatically'. What can that be? It just needs to be a simple system which produces the statistical distribution of events observed by astronomers and cosmologists.
Noether's theorem links continuity, symmetry and conservation. Neuenschwander
All of our physics is a representation of the fixed points of the divine dynamics. But what is the dynamics that generates these fixed points?
FIXED POINT = NOTHING HAPPENS = SYMMETRY
There are no 'pure spirits'. All structures (like angels) are represented by an ordered set of physical symbols which may be photons, atoms or people. My 'spiritual soul' is represented by my phenotype which is a symmetry common to my species broken by my individual DNA string and other breaks in perfect human symmetry induced by the details of my development and education.
Neuenschwander again page 4: 'Noether's theorem relates conservation to invariance, and thus to symmetry.'
Functional boils a function down to a real number: 'As a mathematica machine a functional J takes a function as input and produces a real number as output. A real number is a mathematical representation of a symbol or signal,
[page 37]
which may be encoded and decoded using Gödel numbering. Gödel numbering - Wikipedia
Neuenschwander page 5: 'Because of the central role of the conservation laws, Noether's theorem may be one of the most strategic programs of deductive reasoning in all of physics.'
How do we calculate the Lagrangian and the action of a computing process? [action is count of operations, Lagrangian is time derivative of action]
The Universe is created out of nothing = symmetry by symmetry breaking.
Intelligence : encoding and decoding messages by knowing or discovering the code : learning the language.
page 20: 'A functional J is a mapping from a set of functions to the real numbers. The domain of the mapping is the set of twice differentiable functions x(t) on the closed interval [a, b].
Closed interval = execution of a computation from start to finish. The lifetime of a computation. Functional is minimized (maximized?) when the computation is most efficient. Why does space-time maximize?
page 20: Time is the universal independent variable.
I feel that after all these years (about 40) I am finally happy and relaxed about the idea that the Universe is divine and so have overcome my childhod indoctrination about the total otherness of god and the total hopelessness of humanity without redemption.[page 38]
We need to reconcile network structure with Hamilton's principle of extremal action, some sort of balance between processing power and memory, the balance between lookup tables and computation on the fly.
Logical confinement : what does not make sense cannot exist, a lead zeppelin, for instance. Led Zeppelin
Neuenschwander page 200: 'Physics is the art of creating, testing and improving a network of concepts [operations] in terms of which the physical Universe becomes comprehensible.'
Stationary (minimum) action suggests equipartition of KE and PE, suggesting that they are two halves of a broken symmetry of zero energy.
Say that again: metric converts from coordinate differences to lengths.
The curvature tensor tells us the rate of flow of action between the different dimensions of spacetime. (?) Something like this.
Tuesday 19 June 2012
Continuous mathematics can deal with the concatenation of isomorphic discrete intervals, but if the concatenated intervals are discrete identifiable operations (eg break egg) the continuous model can give at best a very abstract view of the total process resulting from the concatenation of discrete processes (mix, cook, eat). Continuity is in effect
[page 39]
another name for invariance.
The model of continuity is the 'unobservable' clock, NOP, NOP, NOP, . . .
All physical observations are encoded as 'real' numbers (of limited real precision) and the game is to guess the process that is producing these numbers. Our best guess is quantum mechanics that sees a world of adding and subtracting complex phases, that is two dimensional vectors, rotating and interacting in their rotations to form standing waves (constant ratios) that are represented mathematically by eigenfunctions and eigenvalues of an infinite dimensional wave space where each dimension represents a discrete frequency and the wave equation maps the boundary condition (input) to the standing wave structure that we can reconstruct through repeated observations. (2-slit). All I see is a structure of standing waves made visible by the emission of particles corresponding to their maximum amplitude. Waves (ie periodic functions).
Should I be comfortable? Should I be tense? What are the traditional boundaries of human feeling, maybe sleeping out on a frosty night? Ie what proportion of their time did our ancestors feel stressed?
STRESS-ENERGY : the greater the stress the more energy needed to deal with it, maximizing in mortal combat.
What do all these equations and numbers mean? They are the 'data wormhole' through which we see our world.
Continuity : in reality the basic infinitesimal operation is
[page 40]
measured by h, but what it does depends on its 'form', ie the algorithm that specifies what the operation does. [complexification = increasing the palette of actions]
POTENTIAL = BOUNDARY CONDITION (input)
HALT = STANDING WAVE. We can imagine a superposition of standing waves of which one is choses to be 'created' (endowed with energy, phosphorylated, bankrolled) while other are annihilated (energy removed, written off).
All we have to show is that the Universe is creative, and we get out clues from evolution, which is driven by the interplay of an unconstrained imagination (the genome, which may be anything that can be written with the four letter A, T, G, C) coupled to a constrained testing system (the phenotype) which has to survive in the real world.
Survival and habitat modification. The Christian religion has defined an unrealistic view of the human habitat.
Theology, like gravitation, embraces all things, that is all entities that can send and receive massages
Form : an ordered set of elements, eg house = {brick}.
Neuenschwander page 63: 'We call the infinitesimal ε [its real value is h] and call the coefficients of ε to the first power the generators of the transformation.'
In the computer network all transformations can be generated by the Sheffer stroke, NAND. Sheffer stroke - Wikipedia
[page 41]
Calculus is very much a matter of gearing d(ω engine) d(ω wheels) is a gear ratio, which we require to be rational so that the gears can be manufactured.
The amount of information in a transformation cannot exceed that of the generators of the transformation.
The infinitesimal approach : '. . . any transformation that requires the strict definition J' - J = 0 exactly would be included in a less rigid definition of invariance for which the difference between J and J' is merely too small to detect.'
Smaller than h does not exist? Cannot be observed and so exists in imagination as a model that may or may not be right.
Neuenschwander page 64: 'because a set of such transformations has an identity element and each transformation has an inverse, the transformations form a group. . . . "Lie groups" . . . Sophus Lie (1842-1899) who pioneered their study. Emmy Noether ws an expert on Lie groups; hence Noether's theorem was, to her, an application of Lie group thoery.'
Counting(what) -- what = sheep, electrols, quanta of action, (lifetimes), (virtual particles).
N page 72: Einstein: 'Pure mathematics is in its way, the poetry of logical ideas. One seeks the most general ideas of operation which will bring together in simple, logical and unified form the largest possible circle of formal relationships. In this effort toward logical beauty spiritual formulas are discovered necessary for the deeper penetration of the laws of nature.' [NAND = 'most general idea of operation?]
[page 42]Cantor's theorem: the only constraint of God is consistency.
Wednesday 20 June 2012
Jesus taught mainly by assertion, gathering together 'words of wisdom' from the 'Old Testament' and tradition: 'Love your God . . . ', 'Blessed are the meek, for they shall inherit the earth', etc. Now we are more interested in evidence based wisdom: blessed are the communicators, for they shall bind the community into a coherent whole, etc. Matthew 5:5 - Wikipedia
Fields are in effect the modern version of the ether tweaked to take care of relativity and linear so that we van accommodate the superposition of an infinity of different fields (e, γ, n, p, . . . ) in one place. Like the ether, fields are a device to prevent us having to get our heads around action at a distance. The network model deals with this by the assumption that there is no distance at the lowest hardware layer and all communications go through this layer so there is no problem. See 'spooky action at a distance' and related issues. Salart et al
In general continuous mathematical models do not tell us what actually happens but rather define a distribution which as attained in the limit of large numbers. The network model, on the other hand, can deal with exact details and by assuming certain symmetries we can arrive abstractly at the distributions computed by continuous mathematics. The logic of continua works because it is based on the symmetry that all continua are built of identical discreta.
[age 43]
network = {memory, computer} ≈ {essence, existence}
In God, = initial singularity, essence = existence, memory = computer.
Computer has to observable actions, read and write. Normal office computer reads through the keyboard and writes through the screen.
dx, dy etc are not magic (an idea that has for a long time been an element of my calculus block) but just numbers representing magnitudes that can be geared together, ie non-slipping motion. We imagine continuous changes of ratio but in reality we have to change gears, moving from one rational ratio to another.
The simplest gear has one tooth and it changes the direction of rotation if placed between any two other gears. A shockingly simple idea related to the wheel. Real wheels move in discrete steps, -½ ==> +½, 0. ==> 1 etc. Represented by quantized complex exponential, h = 1, 2, etc = nh.
Neuenschwander page 102: 'Logical conservation implies an equation of continuity.
Fixed point theorem is the bootstrap which enables logic to be brought into the world so as to logically prove its own existence.
We cannot read process, we can only read memory and imagine the process that connects the readings. We do this at all scales from the Large Hadron Collider to our personal relationships. As the prophets say, by their fruits you shall know them, the fundamental axiom of science.
Human knowledge, Universal knowledge.
[page 44]
The application of network theory at the human level is pretty obvious, and is the subject of psychology which has a hard scientific wing and a more artistic wing we might call literary criticism or theology. We can also briefly outline how the network theory applies at the extremes quantum theory and general relativity.
The mouse I am watching is dying. I poisoned it. They were just beginning to enter an exponential mode of reproduction after the arrival of the original pair. Sad, but I feel necessary. Alternative is to trap them, alive and relocate them somewhere else.
Mouse can move as a unit through space. We might guess that inertial motion is a symmetry, a nothing in itself which, by being a boundary, induced structure elsewhere, in this instance the locally constant velocity of light.
At its simplest, a photon is just a quantum of action. The on, with no prefix. Θεοσß = το ον
Neuenschwander page 103: 'Now we turn to Noether's theorem as it applies to a field theory, where the spacetime coordinates and the field itself undergo infinitesimal transformations.'
page 104: 'G denotes the Jacobian of a transformation, the determinant of the matrix of coordinate transformation coefficients G = |∂xμ' / ∂xν|
page 101: Equations of continuity, the heart of physics, the plumbing, which deals with vast numbers of identical operations (processes) eg water molecules.
[page 45]
Summation convention : what does this multiplication and addition (dot production) mean? Depends on the quantities, which are the coefficients of components of a vector which sometimes represents an observable force or gradient.
Function is a metric, flat space scaled by the Lagrangian.
Among our imagined coordinates for the description of the Universe we hope eventually to find the set that the Universe actually uses, which we imagine to be all possible coordinates pruned by selection.
Each differential is a degree f freedom, a dynamic ratio [function].
On any job we can ask are we making effectiuve progress or just spinning our wheels, toothless cogs, not getting a grip. A gear train is the simplest example of logical confinement.
Neuenschwander page 104: The linearizing (Taylor expansion) process eliminates off diagonal terms to give an 'unperturbed' picture of a situation.
Coordinates and reality are coupled through the metric which outputs the real observable quantity gμνxμxν etc.
page 110 'Complex variables offer convenience in acoustics, optics and electrical engineering. . . . But quantum mechanics finds complex numbers compelling
Flow of amplitude - a 'better idea' will attract the energy to implement itself over the 'worse idea'.
[page 46]
Neuenschwander page 113: 'An especially important transformation of the fields arises in so called gauge transformations, Here we transform the phase of a complex field leaving spacetime coordinates unchanged.
Physics tells us what is not, what is not different, that is what is the same, the symmetries that we all share.
So we think about how to extend Noether's ideas from physics to psychology and theology.
Thursday 21 June 2012
We work from local to global keeping scale invariance in mind as we seek to develop the principle of 'creative intelligence.
In physics, fields and continuous functions of the time and space coordinates which we develop by constructing a discrete local derivative, taking the continuous limit and then integrating. The connection of the resulting continuous functions to reality is via the theory of probability, the continuous functions representing probabilities of discrete events computer from the superposition of phases. Phase is a measure of the completeness of a computation, analogous to the worm used by many computer applications to show progress. The worm begins at φ = 0 and ends at φ = 2π.
N page 91: 'Most fields evolve according to second order partial differential equations, ie 'acceleration' or 'force' equations.
[page 47]
'Quantum mechanics depends crucially in the conservation of probability'. [Is probability conserved because all processes are time division multiplexed onto the initial singularity?] Given the probability that something (x) happens, we compute the probability of observing various values of x whose sum is 1. So a quantum mechanical source follows the same rule as a communication source emitting different values (letters) of x.
Neuenschwander page 92: 'Conservation laws for fields usually find expression in equations of continuity, . . . '
page 92: 'Elementary particles, [signals] which are detected as localized bits of mass energy can be conceptualized as discrete units of their respective fields. The photon as the quantum of the electromagnetic field offers the conceptual prototype. From this perspective of the ground state of the electromagnetic field contains no photons. The excited state of the field contains one or more photons.''. . . the continuous classical fields and their microscopic renditions in quantum theory are effectively developed in the language of Lagrangians.
And so a good target is to develop a netork explanation of why the Lagrangian method works and the basic answer seems to be that the Universe selects for algorithmic efficiency. We might guess that the most efficient algorithms are those that use the least energy to achieve the coincidences in time (phase) that complete computations and result in the emission of a signal (particle).
08.22 Sun hits N end of kitchen table - solstice day.Random drops falling off the roof as the first frost melts.
Management: getting the right things to happen at the right time
[page 48]
and place.
Feynman QED: when all the little arrows which represent fragments of a process line up head to tail along the extremal path we have a complete process. Feynman: QED
All conservation laws are localized by the fact that all communications flow through the fundamental hardware, the initial singularity = classical God.
We do nt need the - sign in time, which goes relentlessly forward, but each dimension of space is bi=directional so we need + and - and we can see the invention of space as coupled to the invention of negative numbers. (See also +ve kinetic and -ve potential energy.
Intelligence = code making and breaking.
A carnot engine conserves entropy (it is an example of the symmetry we call reversible) so, in order to give out zero entropy mechanical [energy] it has to park all the entropy of the hot source into the cold source in order to harvest the associated difference of energy. Insofar as quantum operations are both reversible and operate at constant with 100% efficiency, we must assume either that T1 is infinite and T2 finite or T2 is finite and T1 is zero.
Clearly all we have to do is translate a book like Neuenschwander into network language and do it very concisely (4000 words) which means we have
[page 49]
to use the sacred language of mathematics to compress it enough. So we need the 'network continuity equation' as a foundation and we already have it because every symbol requires a quantum of action and all computations are flows of symbols.
The continuous paradigm is closed insofar as it is a pattern of conserved flows which of themselves cannot create anything new because they are deterministic. We have learnt that quantum mechanics shows that Lagrange's (should be Laplace's) idea of being able to compute the whole of the future of the Universe from its present state does not fly. Nevertheless we still consider the evolution of the wave equation to be deterministic, that is computable. The disconnect comes with the mysterious 'collapse of the wave function' that, like the fall of a die, narrowed an infinite space of possibilities with a probability structure derived from the wave equation by Born's rule, down to one. Laplace's demon - Wikipedia, Born rule - Wikipedia
From this point of view various collapses of the wave function 'just happen' with a certain frequency that is the absolute square of an evolving complex amplitude.
Friday 22 June 2012
Duplex communication, ψ, ψ*
The whole mechanism of classical and quantum mechanics revolves around the extremalization of action and equations of continuity.
Eigenvalue equation reveals the communication codes used by quantum systems. NOP is unobservable and represents symmetry - the clock. Nothing happens art each clock pulse = continuum. [clock pulses are digital affine parameter?]
[page 50]
DUALITY = NOP ≡ CLOCK
1 + 1 = 2 is a basic continuity equation (logical).
Self reference does not imply infinity but uncertainty, since one cannot consciously map the whole of oneself.
Mathematical lines can do anything, but real lines must obey the laws of physics.
This is as good as it gets, or at least median, cruising along and being constantly excited by what I see, my input.
As we know, we can maintain couple bonding by intelligent contact and certainly do not have to be touching all the time. The same goes for other bonds, which are a sporadic 'exchange of quanta'.
Neuenschwander page 140: 'Tp sum up what we have learned so far: To have a local gauge invariance in the matter-photon system the matter field must be coupled to the photon field with a covariant derivative. The field Aμ that represents the photon compensates for local change of phase in the wave function of the electrically charged particles. The photon itself carried no electric charge, even though it interacts with particle that carry electric charge., To preserve local gauge invariance, the photon must be strictly massless.
'Gauge bosons (or vector bosons) are generic names for quanta that carry the force between charged particles. The photon is the gauge boson of electrodynamics, the spin one quantum of the
[page 51]
electromagnetic field Aμ.Physics defines the world in such a way that overall nothing happens - action and reaction are equal and opposite and cancel.
From a logical point of view a continuum is a not operation and so we could think of it rather like a null vector signifying contact, logical contact.
The action is at the ends of the continua, ie between the particles in contact. If they come to share a set of basis states they can communicate and so change one another's internal state.
A 'logical vector' is a machine state like the quadruple of a Turing machine (Davis) that carries all the information necessary to determine the next step of the machine, as imagined by Turing when he envisaged the computer writing out the state of his computation so he could leave it and come back and make the next step later. So a Turing machine is in effect a sequence of stationary points represented by vectors and a set of transformations (program steps) that make the transformation from stop to stop. In a differentiable continuous manifold the transformations at each point along the trajectory of a system are determined by the local metric and the transformations are required to be continuous and differentiable, a strong constraint [that deprives the transformation of any information carrying capacity!]. In a computer the full space of permutations is open to the transformation, the affine parameter being the program counter and the local metric being the line of code currently being executed.
These things look and feel so good when they are first
[page 52]
born and then gradually subside into the vast mass of insights that seem necessary to fully implement the proposition 'the Universe is divine'.
Once we have invoked logic and digitalism we can assume that mathematics takes over and theorems like Cantor's have their hypotheses fulfilled and so their conclusions are realized.
