natural theology

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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 R3, R is radius of Universe.

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.

Saturday 23 June 2012

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Further reading

Books

Click on the "Amazon" link below each book entry to see details of a book (and possibly buy it!)

Barnes, Peter, Capitalism 3.0: A Guide to Reclaiming the Commons, Berrett-Koehler Publishers 2006 Amazon Editorial Reviews Book Description 'In Capitalism 3.0, Peter Barnes redefines the debate about the costs and benefits of the operating system known as the free market. Despite clunky features, early versions of capitalism were somewhat successful. The current model, however, is packed with proprietary features that benefit a lucky few while threatening to crash the system for everyone else. Far from being "free," the market is accessible only to huge corporations that reap the benefits while passing the costs on to the consumer. Barnes maps out a better way. Drawn from his own career as a highly successful entrepreneur, the author's vision of capitalism includes alternatives to the current profit-driven corporate approach, new legal entities, and a more responsible use of markets and property rights. Capitalism 3.0 offers viable solutions to some of the country's most pressing economic, environmental, and social concerns.' 
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Cohan, William D, Money and Power: How Goldman Sachs Came to Rule the World672 pages Publisher: Anchor; Reprint edition (January 10, 2012) Language: English ISBN-10: 0767928261 ISBN-13: 978-0767928267, Anchor 2012 Amazon customer review: 'Every now and then, someone comes along and writes a book, and in the process lays out a new framework of understanding with such exquisite detail that the average reader's generalized understanding of how the world works is blown away, and a new understanding becomes the norm. This is EXACTLY what author William Cohan has achieved with "Money and Power: How Goldman Sachs Came to Rule the World."' Richard Stoyeck 
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Dawkins, Richard, The God Delusion, Houghton Mifflin 2006 Amazon Editorial Review From Publishers Weekly 'The antireligion wars started by Daniel Dennett and Sam Harris will heat up even more with this salvo from celebrated Oxford biologist Dawkins. For a scientist who criticizes religion for its intolerance, Dawkins has written a surprisingly intolerant book, full of scorn for religion and those who believe. But Dawkins, who gave us the selfish gene, anticipates this criticism. He says it's the scientist and humanist in him that makes him hostile to religions—fundamentalist Christianity and Islam come in for the most opprobrium—that close people's minds to scientific truth, oppress women and abuse children psychologically with the notion of eternal damnation. While Dawkins can be witty, even confirmed atheists who agree with his advocacy of science and vigorous rationalism may have trouble stomaching some of the rhetoric: the biblical Yahweh is "psychotic," Aquinas's proofs of God's existence are "fatuous" and religion generally is "nonsense." The most effective chapters are those in which Dawkins calms down, for instance, drawing on evolution to disprove the ideas behind intelligent design. In other chapters, he attempts to construct a scientific scaffolding for atheism, such as using evolution again to rebut the notion that without God there can be no morality. He insists that religion is a divisive and oppressive force, but he is less convincing in arguing that the world would be better and more peaceful without it.' Copyright © Reed Business Information, a division of Reed Elsevier Inc. All rights reserved. 
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Feynman, Richard, QED: The Strange Story of Light and Matter, Princeton UP 1988 Jacket: 'Quantum electrodynamics - or QED for short - is the 'strange theory' that explains how light and electrons interact. Thanks to Richard Feynmann and his colleagues, it is also one of the rare parts of physics that is known for sure, a theory that has stood the test of time. ... In this beautifully lucid set of lectures he provides a definitive introduction to QED.' 
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Fredriksen, Paula, From Jesus to Christ: The Origins of the New Testament Images of Jesus, Yale University Press 1988 Jacket: 'How did Jesus of Nazareth become the Christs of the Christian tradition? And why did the early Christian communities develop different theological images of Jesus? In this exciting book, PF answers these questions by placing he various canonical images of Jesus within their historical context.' 
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Fredriksen, Paula, From Jesus to Christ: The Origins of the New Testament Images of Jesus, Yale University Press 1988 Jacket: 'How did Jesus of Nazareth become the Christs of the Christian tradition? And why did the early Christian communities develop different theological images of Jesus? In this exciting book, PF answers these questions by placing he various canonical images of Jesus within their historical context.' 
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Haight, Roger, Jesus Symbol of God, Orbis Books 1999 Jacket: 'This book is the flagship of the fleet of late twentieth century works that show American Catholic theology has indeed come of age. Deeply thoghtful in its exposition, lucid in its method, and by turns challenging and inspiring in its conclusions, this christology gives a new articulation of the saving "point" of it all. ... Highly recommended for all who think about and study theology.' Elizabeth Johnson CSJ, Fordham University. 
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Neuenschwander, Dwight E, Emmy Noether's Wonderful Theorem, Johns Hopkins University Press 2011 Jacket: A beautiful piece of mathematics, Noether's therem touches on every aspect of physics. Emmy Noether proved her theorem in 1915 and published it in 1918. This profound concept demonstrates the connection between conservation laws and symmetries. For instance, the theorem shows that a system invariant under translations of time, space or rotation will obey the laws of conservation of energy, linear momentum or angular momentum respectively. This exciting result offers a rich unifying principle for all of physics.' 
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Phillips, E G, A Course of Analysis, Cambridge University Press 1962 From the Preface to the first edition: 'The main purpose of this book is to give a logical connected account of the subject, by starting with the definition of 'Number' and proceeding in what appears to be a natural sequence of steps. Since modern Analysis requires great precision of statement and demands form the student a very clear understanding of its fundamental principles, I have aimed at presenting the subject in such a way as to make every important concept clearly understood. ...' 
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Thiering, Barbara, Jesus the Man: A new interpretation from the Dead Sea scrolls, Acacia Press 1993 'Some will see her as an anti-Christ, a mischievous scholar determined to destroy Christianity. To others she will be a source of comfort and peace, enabling them to live Christian lives without having to accept as fact Jesus's divinity, his miracles, the virgin birth and resurrection.' The Australian Magazine  
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Papers
Jones, Dan, "Moral psychology: The depths of disgust", Nature, 447, 7146, 13 June 2007, page 768-771. 'Is there wisdom to be found in repugnance? Or is disgust 'the nastiest of all emotions', offering nothing but support to prejudice? Dan Jones looks at the repellant side of human nature.'. back
Links
Born rule - Wikipedia Born rule - Wikipedia, the free encyclopedia 'The Born rule (also called the Born law, Born's rule, or Born's law) is a law of quantum mechanics which gives the probability that a measurement on a quantum system will yield a given result. It is named after its originator, the physicist Max Born. The Born rule is one of the key principles of the Copenhagen interpretation of quantum mechanics. There have been many attempts to derive the Born rule from the other assumptions of quantum mechanics, with inconclusive results. . . . The Born rule states that if an observable corresponding to a Hermitian operator A with discrete spectrum is measured in a system with normalized wave function (see Bra-ket notation), then the measured result will be one of the eigenvalues λ of A, and the probability of measuring a given eigenvalue λi will equal <psi,|Pi|psi> where Pi is the projection onto the eigenspace of A corresponding to λi'. back
Friedmann-Lemaitre-Robertson-Walker metric - Wikipedia Friedmann-Lemaitre-Robertson-Walker metric - Wikipedia, the free encyclopedia 'The Friedmann-Lemaître-Robertson-Walker (FLRW) metric is an exact solution of Einstein's field equations of general relativity; it describes a simply connected, homogeneous, isotropic expanding or contracting universe.' back
Gödel numbering - Wikipedia Gödel numbering - Wikipedia, the free encyclopedia 'In mathematical logic, a Gödel numbering is a function that assigns to each symbol and well-formed formula of some formal language a unique natural number, called its Gödel number. The concept was famously used by Kurt Gödel for the proof of his incompleteness theorems. (Gödel 1931) A Gödel numbering can be interpreted as an encoding in which a number is assigned to each symbol of a mathematical notation, after which a sequence of natural numbers can then represent a sequence of strings. These sequences of natural numbers can again be represented by single natural numbers, facilitating their manipulation in formal theories of arithmetic.' back
Hillsong Church Hillsong Church 'WHAT WE BELIEVE We believe that the Bible is God's Word. It is accurate, authoritative and applicable to our every day lives. We believe in one eternal God who is the Creator of all things. He exists in three Persons: God the Father, God the Son and God the Holy Spirit. He is totally loving and completely holy. We believe that sin has separated each of us from God and His purpose for our lives. We believe that the Lord Jesus Christ as both God and man is the only One who can reconcile us to God. He lived a sinless and exemplary life, died on the cross in our place, and rose again to prove His victory and empower us for life. We believe that in order to receive forgiveness and the 'new birth' we must repent of our sins, believe in the Lord Jesus Christ, and submit to His will for our lives. We believe that in order to live the holy and fruitful lives that God intends for us, we need to be baptised in water and be filled with the power of the Holy Spirit. The Holy Spirit enables us to use spiritual gifts, including speaking in tongues. We believe that God has individually equipped us so that we can successfully achieve His purpose for our lives which is to worship God, fulfil our role in the Church and serve the community in which we live. We believe that God wants to heal and transform us so that we can live healthy and prosperous lives in order to help others more effectively. We believe that our eternal destination of either Heaven or hell is determined by our response to the Lord Jesus Christ. We believe that the Lord Jesus Christ is coming back again as He promised.' back
Laplace's demon - Wikipedia Laplace's demon - Wikipedia, the free encyclopedia We may regard the present state of the universe as the effect of its past and the cause of its future. An intellect which at a certain moment would know all forces that set nature in motion, and all positions of all items of which nature is composed, if this intellect were also vast enough to submit these data to analysis, it would embrace in a single formula the movements of the greatest bodies of the universe and those of the tiniest atom; for such an intellect nothing would be uncertain and the future just like the past would be present before its eyes. A Philosophical Essay on Probabilities' back
Led Zeppelin Stairway to Heaven back
Matthew 5:5 - Wikipedia Matthew 5:5 - Wikipedia, the free encyclopedia 'Matthew 5:5 is the fifth verse of the fifth chapter of the Gospel of Matthew in the New Testament. It is the third verse of the Sermon on the Mount, and also third of what are known as the Beatitudes. In the King James Version of the Bible the text reads: Blessed are the meek: for they shall inherit the earth. . . . This is a very well known verse, and perhaps the most famous of the Beatitudes.' back
Positron emission tomography - Wikipedia Positron emission tomography - Wikipedia, the free encyclopedia 'Positron emission tomography (PET) is a nuclear medicine imaging technique that produces a three-dimensional image or picture of functional processes in the body. The system detects pairs of gamma rays emitted indirectly by a positron-emitting radionuclide (tracer), which is introduced into the body on a biologically active molecule. Three-dimensional images of tracer concentration within the body are then constructed by computer analysis.' back
Sheffer stroke - Wikipedia Sheffer stroke - Wikipedia, the fre encyclopedia 'The Sheffer stroke, written "|" or "?", in the subject matter of boolean functions or propositional calculus, denotes a logical operation that is equivalent to the negation of the conjunction operation, expressed in ordinary language as "not both". It is also called the alternative denial, since it says in effect that at least one of its operands is false. In Boolean algebra and digital electronics it is known as the NAND operation ("not and").' back
Thanu Padmanabhan Thermodynamical Aspects of gravity: New Insights '(Submitted on 26 Nov 2009 (v1), last revised 19 Jan 2010 (this version, v2)) The fact that one can associate thermodynamic properties with horizons brings together principles of quantum theory, gravitation and thermodynamics and possibly offers a window to the nature of quantum geometry. This review discusses certain aspects of this topic concentrating on new insights gained from some recent work. After a brief introduction of the overall perspective, Sections 2 and 3 provide the pedagogical background on the geometrical features of bifurcation horizons, path integral derivation of horizon temperature, black hole evaporation, structure of Lanczos-Lovelock models, the concept of Noether charge and its relation to horizon entropy. Section 4 discusses several conceptual issues introduced by the existence of temperature and entropy of the horizons. In Section 5 we take up the connection between horizon thermodynamics and gravitational dynamics and describe several peculiar features which have no simple interpretation in the conventional approach. The next two sections describe the recent progress achieved in an alternative perspective of gravity. In Section 6 we provide a thermodynamic interpretation of the field equations of gravity in any diffeomorphism invariant theory and in Section 7 we obtain the field equations of gravity from an entropy maximization principle. The last section provides a summary.' back
Tick - Wikipedia Tick - Wikipedia, the free encyclopedia 'Ticks are small arachnids in the order Ixodida. Along with mites, they constitute the subclass Acarina. Ticks are ectoparasites (external parasites), living by hematophagy on the blood of mammals, birds, and sometimes reptiles and amphibians.' back
World Council of Churches International Directory of Theological schools 'International Directory of Theological Schools The data in this section is based on the electronic version of the book "An International Directory of Theological Colleges 1997" compiled by Alec Gilmore and published by WCC Ecumenical Theological Education (ETE).' back

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