### Notes

[Notebook: DB 61 Warm]

[Sunday 22 April 2007 - Saturday 28 April 2007]

[page 4]

##### Sunday 22 April 2007

Our clues to the source of the line element are Minkowski space an the one hand and Newtonian gravitation on the other, united by the principle of equivalence.

Hobson page 157: 'We therefore need some means

[page 5]

of telling [observing in the symbols] whether a manifold is flat
directly from the metric g_{ab}, *independently of the
coordinate system being used. *Hobson

. . .

Hobson page 128: 'We can find a solution to the problem of measuring the curvature of a manifold at any point by considering changing the order of covariant differentiation.'

The (anti) commutator of this change of order is a measure of curvature.

page 159: '[the] curvature tensor . . . is defined in terms of the metric tensor and its first and second derivatives.'

'. . . vanishing of the curvature tensor is a necessary and sufficient condition for a region of a manifold to be flat.'

Physically speaking, 'line element' = interaction (of 'particles', ie 'definite and separate things'))

page 160: '. . . a general metric at any point P is characterized
by the N^{2}(N^{2}-1)/12 second derivatives that
cannot be made to vanish there.' In 4-space = 20 degrees of freedom
in the determination (specification) of 4-space.

PARTICLE = OBSERVED PARTICLE.

No cloning means that we can teleport state by annihilation

[page 6]

and creation, but we cannot duplicate them. This is a constraint on chaos that arises naturally in the definition of the symmetric Universe.

The transfinite network is a Platonic model waiting to become manifest. How does it achieve this? By using the power of 'error correction' to create and exploit structure to create more by creating structures that feed themselves effectively off their environment. This is just evolution by repeated reproduction and selection.

Evolution requires memory, and we do not think fundamental particles like photons, that are completely created and annihilated in their interactions can have any memory [but they serve as memory in a higher system]. These particles then have not evolved but owe their structure to some deterministic constraint in the system.

My proper time is the interval between my actions.

The squared length of the line element may bear some relationship to the probability calculated by quantum mechanics, since both are features of an 'event'. A point in spacetime is an event. A line is a history of events, an ordered sequence of messages whose causal relationships define spacetime structure.

CAUSALITY <--> SPACETIME

[page 7]

Hobson page 163: Curvature and parallel transport: in a curved space parallel transport is path dependent.

Does the world have a computer that works out gravitational
interactions or are they a determined consequence of some other
process, the simplest and most generic and universal process in the
Universe, the ur-process defined by e^{it}, going around and
around, being dynamic. To be dynamic one must have two states at
least, and so the qubit becomes our ur-model.

General relativity constrains the projection of quantum events on
the 4-D interface we all share. This constraint operates purely in
terms of the energy of the event and takes no account of its
complexity, ie gravitation is invariant with respect to complexity,
simply does not see it except insofar as it is coupled to energy
[which may in some way measure the *cardinal* of the
complexity].

All our windows on the nature of the Universe, all communications, are associated with an exchange between kinetic and potential energy.

GEOMETRY = ORDINAL NUMBERS

ARITHMETIC = CARDINAL NUMBERS

Hobson page 176: 'Einstein's equations are . . . a set of second
order partial differential equations , , , for the metric
coefficients g_{mn} of spacetime.

They map physical logic to spacetime (?).

[page 8]

Hobson page 184: 'Only in four dimensions or more that gravitational fields can exist in empty space.

Einstein: deterministic (computable) general covariance. We take general covariance into the transfinite realm where it becomes an incomputable network, built on computable foundations. Uncertainty in quantum mechanics seems to represent the incomputable side of things, ie interaction, communication and superposition of computable basis states. The computers in a computer network are the bases of that network, each one orthogonal to the others although sharing a common communication subspace. The network is indeterministic because the computers in the network can interrupt and redirect one another, leading to a non-linear potentially chaotic system. Chaos is avoided by the enforcement of communication protocols, of which, maybe, gravitation is the doyen.

Error proof communication protocols contribute to their own survival and the same is true for good software in general, both in the realm of commerce and in the broader realm of all existence, fitness and survival.

Hobson page 499 Gravitational waves travel at c (and therefore have no mass and cannot be their own source?).

[Hobson page 189 'The fact that the Einstein equations predict the
equation of motion is remarkable and should be contrasted with the
situation in electrodynamics. In the latter case, the Maxwell
equations for the electromagnetic field do *not* contain the
corresponding equation of motion for a charged particle, which has to
be postulated separately. The origin of this distinction between
gravity and electromagnetism lies in the non-linear nature of the
Einstein equations. The physical reason for this non-linearity is
that the gravitational field itself carries energy-momentum and can
therefore act as its own source, whereas electromagnetic field
carries no charge and so cannot act as its own source. ]

page 524: '. . . the variational approach that we shall outline is extremely powerful and provides the basis for much current research into the formulation of classical (and quantum( field theories, including general relativity and other candidate theories of gravitation.

Hamilton's principle: A mechanical system whose configuration can
be defined uniquely by a set of generalized coordinates q^{a}
together with time t and which experiences only forces derived from a
potential moves from one configuration to another in some a way as to
make the action S = integral (over time) of Lagrangian (
q^{a}, q^{a} dot, t) stationary.

Is this an example of evolutionary optimization?

Lagrangian L = T (kinetic energy) - V (potential energy, a
function of q^{a} and t)

Here we see an example of control.

Geodesic = path of uninterrupted computation = path of non-communication = path of no force [therefore an invisible path].

A theory of everything must do much more than explain a small set of cardinal numbers measured by physics. It must explain how everything works so that we can 'fit in' with it.

##### Monday 23 April 2007

Soames Churchill page 370 'Imagine what will happen to India

[page 10]

when sagacious, scientific and incorruptible direction is withdrawn.' Soames

DOUBT DESCARTES

page 391 (Soames) Churchill: 'If the Great War were resumed . . . it will be the end of the world. How I hope and pray we may be spared such senseless horrors.'

On the religion question: saving the world. How to write something publishable, ie which will attract enough readers to pay for itself? Getting closer to a story, but it takes so long. Fortunately my enthusiasm grows as the task also grows.

Soames page 401: 'We are getting into the most terrible position, involved definitely by honour and contract in almost every quarrel that can break out in Europe, our defences neglected and our government less capable a machine for conducting affairs that I have ever seen.

On avoiding impossible situations.,

page 433: 'A thousand years hence it will be incredible to historians that the victorious Allies delivered themselves over to the vengeance of the foe they had overcome.

page 444: 'It is quite astonishing to reach the end of life and feel just as you did fifty years before.' Happy but frustrated, wanting power to guide the world.

Molecular biology = 4D logic.

[page 11]

Hilbert oscillator differentiates and integrates itself up and down the transfinite tree whose lowest state is the quantum harmonic oscillator.

Transfinite network = materia prima

We might say that there are no things, only messages. The task of each scientist and every individual is to decode the messages it receives.

Yourgrau page 36: 'In all processes in which the principle of
conservation of energy holds, the forces can be derived from a
potential, that is there exists a function V of the coordinates such
that that work done on the system in changing from the configuration
q_{i} to q'_{i} is equal to V( q'_{i}) - V(
q_{i}).'

We can think of this in terms f two binary strings, the input and output of an entropy preserving Turing machine and the work done to make the change is the Hamming distance between the two strings. We would like to associate a different energy to every string. This is possible if the elements of the string form a position sensitive representation of the energy scale, a bit like Gödel numbering which encodes strings of symbols as cardinal numbers.

What are the appropriate generalized coordinates of the Universe? They are the particles (symbols) of the Universe and we say that the transformation of one fundamental symbol into another measures one quantum of action.

[page 12]

ALGEBRA = ABSTRACT ARITHMETIC

Hamilton's principle: 'a system moves from one form or configuration to another in such a way that the variation of integral Lagrangian dt between the path taken and a neighbouring virtual path coterminate in space and time with the actual path is zero.' Yourgrau page 47.

Page 49: 'One of the most salient characteristics of variational principles is . . . that they express the pertinent laws without involving coordinate system.

Hamilton's principle caries us from classical to quantum mechanics.

page 93: Whittaker on Hilbert's variation: 'gravitation simply represents a continual effort of the Universe to straighten itself out.

Quantum mechanics and general relativity are not 'what is' but what is communicated what we see.

Greene page 129: [As we magnify spacetime] 'The notion of smooth spatial geometry, the central principle of general relativity, is destroyed by the violent fluctuations of the quantum world on short distance scales.' Greene

The whole idea of 'quantum foam' is contradicted by cosmological observations. Just because delta p.delta x = h bar does not mean that if we observe delta x, we see momentum delta p, rather delta p is the

[page 13]

uncertainty in any attempt to measure motion.

We like the permutation approach to generating transfinite numbers to the subset approach by writing permutations in the form of cycles and see each cycle as a subset of the whole permutation. Different permutations range from that that can be completely expressed in one cycle to those whose 'atomic' cycles are just one letter, ie the n cycles of the identity permutation of set of cardinal n.

DEGENERATE = NOT RESOLVED

The relativity of transfinity. In the Platonic world we talk about
the countably infinite set of natural numbers and there transfinite
permutation,. but all the theorems remain true if the cardinal of the
natural numbers is two or greater. If card (**N**) = 2, then three
is a transfinite number and so on. As the Universe evolves, it slowly
resolves itself by improving its defences against error so that the
cardinal of the resolved set gradually increases toward its Platonic
maximum.

Greene, Elegant Universe: String theory sounds like a desperate dream on a par with Christianity in the realm of credibility. Greene

FRUSTRATION: Bursting with energy but unable to couple to anything (eg physical or theological establishment) to use it.

##### Tuesday 24 April 2007

Huge capital, nothing to invest in.
Buddhist patience is called for: '*In patientia vestra possidebitis
animas vestras* ' ['Your endurance will win you your lives'] (Luke
21:19, Luke).

[page 14]

Greene page 153: 'Particle accelerators . . . hurl bits of matter such as electrons and protons at eachother . . . and elaborate detectors analyze the resulting pray of debris to determine the architecture of the the objects involved.

The whole problem seems to be in the interpretation of the
uncertainty principle. Quantum field theory assumes that the numbers
delta E, delta p, delta x and delta t in the equation (eg) delta E
delta t >+ h are real numbers. What if we go all the way to
quantization and assume that they are naturals, the delta p delta x
>= h becomes a Diophantine equation and all our problems with the
vacuum go away because all the deltas come from the set **N** =
{1, 2, 3, . . .}.

From Newton's time until the end of the nineteenth century mathematicians spent much energy expanding calculus and making it logically sound so that we have definitions of differentiability, continuity etc which make the massage to the continuous limit plausible. The logical definition of continuity developed in this period was founded on the notion of continuity by cardinals, so it seemed natural for Cantor to seek the cardinal of the continuum and he set about doing this using logic to study sets of symbols, ie doing mathematics.

The results of this mathematical work are everywhere to see, not least in quantum theory and relativity. In other words, we can make a consistent theory if we say that continuity means putting so many points into a fixed interval that there are no gaps between them. So even though a point has no magnitude we can imagine putting so many of them in a box that they all touch, ie

[page 15]

the gaps between them may be ignored and the theory works out.

But is this really continuity. Aristotle and overlap. ['. . . things are called continuous when the touching limits of each become one and the same, and as the word implies, are contained in one another. Aristotle, Physics V:3 226b10 ]

The metaphors of atom smashing lead us away from the truth, a legacy of our nuclear weapon days.

A fighter. One who will suffer pain to achieve a goal.

Greene page 152: 'Recall that the problem in merging general relativity and quantum mechanics turn up when the central tenet of the former - =that space and time constitute a smoothly curving geometrical structure -- confronts the essential feature of the latter -- that everything in the Universe, including the fabric of space and time, undergoes quantum fluctuations that become increasingly turbulent when probed at smaller and smaller distance scales.'

How you look influences what you see.

##### Wednesday 25 April 2007

Greene page 156: 'In a Universe governed by the laws of string theory, the conventional notion that we can always dissect nature on ever smaller distances, without limit, is not true.'

And this is how it solves all our infinity problems!

page 157: '. . . the supposedly problematic sub-Planck_length spatial fluctuations are an artifact of formulating

[page 16]

general relativity and quantum mechanics in a point-particle framework.'

String is an extended object. In what? Can we interpret a string logically as a proof?

Torture the body to release the soul. Is this a real feature of our system, or something developed by the ruling classes to placate the suffering masses. Certainly, poverty brings one closer to the realities of life and survival.

SUPERPOSITIONED = DYNAMIC

The transfinite network is complex enough to represent a superposition of all possible states.

Greene page 183: 'A physical dream is that the search for the ultimate answers will lead to a single, unique, absolutely inevitable conclusion. ideally, the final theory . . . should be the way it is because there is simply no other possibility. If we were to discover that there is only one logically sound theory incorporating the basic ingredients of relativity and quantum mechanics, many feel that we would have reached the deepest [or perhaps broadest] understanding of thy the Universe has the properties it does. In short, this would be unified theory paradise.'

But how does it explain the beg bang, the origin of life and this exported interior monologue? Only a communication/computation model is rich enough to do

[page 17]

it, but how does this relate to particle physics as we know it?

How come thee are so many protons (electrons . . . )? The software explanation says that they are all children of the original proton process that were born as necessary to serve different more complex processes.

Explain the inevitable passage of time? We are on a 3-line through 4-space.

##### Thursday 26 April 2007

Physics in action provides us with a set of symbols and techniques for their manipulation which have enabled us to build our world. We are not alone in this. In fact the world has built itself, including us, al by itself. It is this process of creation that we have to understand if we are to fit in. Traditional religions have closed the creation question, telling us that it is the work of an invisible and omnipotent God, and that is that. People living on the understanding that the Universe is divine and we are divine persons need to face this question, however, in order to be familiar with and sure of our foundations.

New Yorker: It is time for reform in the religion industry. And earn two fares to the US. New Yorker

Mathematically, energy behaves like an incompressible fluid. Even though it may be really particulate the continuous model is sufficient for many purposes but not unification.

[page 18]

String theory introduces new letters into the alphabet of physics, but it remains to be seen whether these new letters correspond to anything in reality.

LETTER = EVENT

Can we say that the local quantum processes are deterministic but that the selection of which of a superposition of exclusive processes to execute at a given moment is outside the determinism. A turing machine is a link in a chain (a channel) from input to output, but something outside sets it in motion and reads its results.

##### Friday 27 April 2007

Life is a balance between searching and knowing. Both have their costs, and so there might be an optimum level of investment in each, given the technology available.

The invention of writing increases the availability and decreased the price of memory in human affairs, and printing established symmetries of shared memories which led ultimately to the creation of a global culture overlaying the nation states created by the invention of bureaucracy = paper based computation.,

The purpose of religion is to create a community of interest.

SPIN = WEIGHTING EVENTS - which is what

[page 19]

quantum field theories do by applying quantum theory to certain Lagrangians (eg 'Standard Model')and trying to find models that fit the observations.

What we are weighing is the probability of the occurrence of a certain deterministic process.

SPIN, in the more political sphere is a made possible by the new degrees of freedom opened up when the system begins to give meaning to physical events. The physical layer is bound by local logical consistency n as are the layers of meaning, provided that by 'local' we mean 'in communication with'. Hence the desire of dictators for secrecy - where there is no communication and so they can continue to profit by the control they can exercise over an unwitting population.

Veltman page 249: 'The Lagrangian of the Standard Model is quite voluminous and it is already a problem by itself to get all the Feynman rules correct. Veltman

'The ghost fields must be included for internal lines, but they should not occur as external lines. They do not correspond to physical particles, but they occur in diagrams to correct violations of unitarity that would otherwise arise due to the form of the vector boson propagators chosen here. The proof of that fact is

[page 20]

really the central part of gauge field theory'. Veltman page 249.

All the vast complexity seems to contradict the idea that we are trying to describe the simplest level of the Universe. it would be nice to see it replaced by the basic software of a network, which may e conceived as a set of Turing machines. The simplest such set, containing the simplest machine, is the empty set, no operation. Followed by the set NOP, NOT and so on up the scale each of these sets requiring more memory for its implementation.

Pervert the course of justice.

JUSTICE - EQUALITY - MAXIMUM ENTROPY - STABILITY - PEACE

Quantum mechanics - probability plumbing.

PLUMBING = VOLUME (MASS) CONSERVATION

Standard model: although the processes are each considered to be continuous, the actual number of discrete processes is discrete and countable.

Our paths crossed and another person appeared, just like the standard model.

Quantum mechanics attributes a dimension in Hilbert space to every point in the continuum, thus

[page 21]

transforming the points in the continuum to variables, that is memory locations with addresses in the continuum.