Notes
[Notebook: DB 59 Draughts]
[Sunday 10 September 2006 - Saturday 16 September 2006]
[page 152]
Sunday 10 September 2006
Quantum mechanics is one dimensional field theory, ie a function of time alone. The interior of a computer is also one dimensional and all its states are a function of the clock. Clock pulses are long enough so that the travel times of signals from the memory etc are hidden and everything works in a 'formal' deterministic way.
So a small enough (spatially) or slow enough (so that its spatial size is irrelevant) has a 'light cone' consisting of a time line alone.
[page 153]
Photon = text no rest mass.
Massive particle = moving texts = internal process = computer = rest mass. Quantum mechanics and computers give no meaning to velocity. Velocity enters when we have space and time, v = dx/dt.
In physical terms, the only boundary condition is consistency.
The inconsistency of the Catholic system put me under great pressure to devise a consistent system. The greater the pressure on a network (ie my central nervous system) the faster it all works (stress energy tensor <==>
Every particle carries its own rest frame except the photon, which has no rest frame and so is outside dynamics just as formalism is essentially non-dynamic.
Control in a Turing Machine is subject to Shannon [Information theory] and [the Shannon-Nyquist sampling theorem], which control the effective cardinality or machine infinity. Shannon,
The level of control decreases as 1/x because the round trip increases with x, as does the time between observations and corrections. We must sample and correct at twice the frequency of change.
Error correcting power grows exponentially with processing time, so the tradeoff between frequency and freedom from error favours
[page 154]
taking one's time to avoid error. This is like Shannon type making the packets bigger.
Why do symmetries break, that is networks grow?
General covariance (action alone) breaks to give us 2D spacetime (spin 1/2)
In our attempts to make all permutations equiprobable in a given peer group, the permutations involved inevitably contain symmetries. No cardinality without symmetry, ie 2 digits allows us to construct all countable numbers.
Once we divide things into past and future we have a constraint. The only constraint on the future is past + consistency.
INTERFERENCE = COMMUNICATION = INTERRUPTION
Lorentz (Minkowski) - fixed metric (tensor eta(ij))
Monday 11 September 2006
Correspondence principle between symmetric Universe and harmonic Universe says two converge when Turing machines are simply adders and number of elements added is large.
Misner on geodesic deviation page 218: Observer measuring geodesic deviation is limited by quantum mechanics of measurement (uncertainty principle) in the precision of
[page 155]
measurement and therefore in the precision he can calculate the curvature of the space in which he moves. As he increases precision , he increases 4-momentum of measuring process, and so introduces perturbation which will ultimately exceed precision of measurement. Misner, Thorne and Wheeler
page 220 Route dependence = algorithm dependence.
What we do here is rather like Kirchoff, showing the existence of functions without completely defining them. This is a task for variation of software engineering.
The variational principle applies to software is non-linear in the resources required, particularly when someone discovers an exponential speedup of a process.
Einstein on Riemann: 'Only the genius of Riemann, solitary and uncomprehended, had already won its way by the middle of the last century to a new conception of space, in which space was deprived of its rigidity, and in which its power to take part in physical events was recognized as possible. 1934 Essays in Science, Philosophical Library, NY page 68
Bianchi identities: differential symmetries of Riemann tensor
Contractions of Riemann tensor: 'Ricci curvature tensor', 'scalar curvature' and 'Einstein curvature tensor.
PEER = MUTUALLY COUNTABLE [OBSERVABLE]
A water molecule has as much personality as I
[page 156]
do
Age is the affine parameter of life, ie elapsed time since birth.
Exponential growth in error correcting power enables exponentially growing number of unique identifiable messages. So we expect alphabets to grow like 2n, 0, 1, 2, 4, 16, 64k etc.
A function is a static mapping,but we can render its range dynamic (ie moving) if we introduce motion into its [domain]. As we move along the function, the variations in the domain drive variations in the range. The relationship between the two sets of values is the 'differential' of the function.
Cantor was interested in big numbers because in those days continuity was defined by proximity and it seemed logical that the more points we force into a given interval, the closer together they must be.
In general relativistic space, every point is unique. There are no laws of physics when we look at the whole. But there are local laws. We cannot discuss the whole structure of the symmetric Universe. This, like the set of all sets, as a self contradictory (non) entity.
The observable Universe is a set of events (symbols) which obeys the rules of set theory, predicate
[page 157]
calculus and all theorems of mathematics, each of which is a Turing machine that communicates between two points in the Universe, a function.
General relativity makes every point unique, as does the symmetric Universe. Every pair of points of the same cardinality n can be transformed from one to another by an elements of the permutation group of n items,
So the set of transformations between aleph(n) unique points has aleph(n + 1) elements.
PEERWISE ISOMORPHIC
How do we model curvature in the symmetric network? Begin with the idea that it depends on the metric and that the unit (dimension) of the metric is action.
Special relativity defines spaces of possible causality and non-causality. Quantum mechanics determines 'degree of causality' by |overlap integral of amplitudes| 2 .
How do we model curvature in the symmetric network? FORCE is the product of INCONSISTENT contact [?]. There can be no inconsistency and therefore force in a matter free (flat) Universe, but the introduction of matter causes curvature, that is geodesic deviation. This too is force free except where the constraints of other forces prevent entities from following their geodesics (as the electromagnetic binding forces prevent me from following my geodesic to the centre of the earth by the g force on my bum.
[page 158]
Tuesday 12 September 2006
MATTER = {COMMUNICATIONS (MESSAGES, CONTACTS, PARTICLES)}
PARTICLE == MOTION (FORCE, ACCELERATION)
When we come to measuring geodesic deviation we find that the precision is limited by the uncertainty principle and the four-momentum density.
General covariance means every point has its own reference [rest, identity] frame which is tantamount to saying that the point 'is' in its own reference frame. This condition is fulfilled by the symmetric Universe.
I am a terrorist whose intention is to detonate an explosion under all those who deny general covariance by acting as though they have right (duty) to control the lives of others, particularly by killing, torturing or confining them.
Contact contradiction drives action = error correction
How do we make the covariant dust of action become symmetric? How does matter shape space? Communication shape space? This work is like climbing around on rocks, continually getting new views, gradually discerning the shape of the whole massif.
Each new view provides a new language, a new element of the descriptive alphabet that will eventually
[page 159]
enable us to construct an isomorph of the structure we are investigating.
In physics we are inclined to think that the reference frames are secondary to reality, an idea that seems to have motivated Einstein's difficulties with quantum mechanics. But in the symmetric model reference frame and reality have the same standing. Instead of asking how matter curves space, we ask how software influences software, ideas influence ideas, language influences language. Gravitation carries energy which is the source of gravitation and so the system here is, unlike quantum mechanics, non-linear. By devising the right language, like the coordinate version of the field equations, we can talk about things and calculate them without really understanding them. This is common. One needs very little knowledge of human physiology to have a baby!
Agatha Death Comes at the End: '"This is my life," she thought, "there is no escape . . . "' Christie
Evolution creates the 'tree of life'. The past controls the future insofar as it is controllable. If we wish to control a future, we perform actions in the corresponding past.
Eternity "tota simul". Aquinas 45 It is alright for mystics to talk about such things because they depend on others for their survival, but practical people need frames of reference in which to work, as in laying out a building or designing a water system. [How does this idea of eternity square with the divine life? Aquinas 113]
[page 160]
Physicists, following the path of Newton and thousands of years of theology, are trying to find the invariant structure of the Universe on the assumption that it is something fixed, put there by god, which could have been different. A fundamental tenet of Christianity is that it was different before the Fall and will be different again after the Apocalypse ['revelation']. Here we take the view that what invariants there are are features of the dynamics of a system that creates itself, subject to no external constraints.
The invariants are 'naturally selected' by the Lagrangian method.
Every measurement is a relationship between a 'reference frame' (the tape) and the thing measured (the object) which, when they are brought into contact yields a message ('the measurement')
Since god lives, we apply cybernetics, the study of control and communication in the animal (non-deterministic) and the machine (deterministic). Wiener
We assume that all structures are a consequence of natural selection under cybernetic constraints, ie requisite variety, error free communication, recursion, computability, [stability] etc,
The basic measurement is GO NO-Go, true/false or something else binary, as in digitizing sound at the Nyquist frequency.
[page 161]
In the spirit that the unfolding of the Universe is isomorphic to the evolution of mathematics, we can look at the history of mathematics for clues to the history of the Universe. This is in support of the idea that the Universe is divine, but does not prove it. Ultimately the decision whether to treat reality as (god + Universe) or simply god is a matter of taste or faith, although our model of god allows us to pick a peer group and call all large groups god and all smaller groups creation.
Now the symmetric Universe seems very large, but when we examine the Universe, we find some very simple things. How can this be? The answer seems to be the relativity of transfinity. This feature of transfinity is encoded in cardinal arithmetic in the equation 2 exp (aleph(n) = aleph(n) exp (aleph(n) = aleph(n+1). What we are saying is that the world is fundamentally quantized into different degrees of transfinity, but for simplicity (and without loss of generality) , we can imagine each transfinite number as an element of a binary number of a higher power. Their essential quality is that one is not the other, like spin up and spin down. We are talking about machine infinity. Turing discussed the question of how many distinct symbols a machine could read and print. Turing page 250
What we are saying is that each increase in definition moving from binary to human and beyond. We see a number of binary distinctions around the place, spin up, spin down, space, time, alive, dead and so on. This is the first break in the symmetry of the eternal, immutable, invisible, extraspatial, omnipotent etc etc god of the ancients, the initial singularity from which all else springs.
[page 163]
Making structure is controlling possibilities. Today I made trusses, that is physical triangles of steel connected together so as to carry a load over a wide span of open space, ie the roof. The thing cannot fail as long as the sides of the triangles do not change their lengths, a condition enforced by the strength of the steel beams and the bolts. Engineers analyze things like this to convince themselves that the thing will stand up. Insofar as they are very conservative, they are mostly right. Another level of engineering examines the failures of engineered structures to see here they went wrong. At the computable level, things can be controlled, but once they become incomputable, we must take our chances. But we can continue to improve our chances by expanding our ability to compute the Universe in which we find ourselves. The earth is a system closed to almost everything apart from a negative flow of entropy from the sun. If we are to last, we must fit in with the environment in which we find ourselves. Fit in means basically to close the cycles of all the flows we induce in the environment, billions of tons of coal and oil ad steel and groceries.
Machine infinity = 1/machine resolution + 1.
Evolution by variation and selection.
We are to interpret the minimum action with maximum fitness. Many, even all, maybe at the maximum of fitness (like the sides of a die) and then outcomes are equiprobable. . . .
[page 163]
Relative phase measures logical consistency = overlap = how much I understand your conversation.
How long can a loop of error free communication be. Each entity has a generation time until it evolves to a fixed state, after which all generations are the same, as for electrons. The electron structure only has meaning in the context of the rest of the elements of the Universe.
FITNESS = MINIMUM ACTION = MINIMUM ERROR
So what corresponds to amplitude, the quantum way of calculating probabilities? The overlap is a function of the 'angle' between the states in an infinite dimensional space, calculated by the inner product.
The key to peace: swap rigid human space for flexible and general human covariance, ie we are all to be measured by our own coordinates, ie null or no measurement. I am what I am, ie moving inertially through life. This is gravitation, which would never have been noticed unless thee were non-gravitational structures in the Universe to provide contrast, as it were.
We implement general human covariance by everyone treating everyone with equal respect.
Why differentiate? Does Cantor say it is inevitable?
Why is the structure of the Universe 'legolike'.
[page 164]
ie quantized, one photon, one book, all sorts of distinct unities.
The first constraint: not all possibilities can be realized. This is because realization of possibilities feeds upon itself, by creating even more possibilities that each demand realization in their own way. In business, for instance, there are a spectrum of ways to fleece the punters, each appropriate to a given situation. Deighton Only When I Larff. Deighton
NYQUIST on SURVIVAL
a) error free
b) timely, ie responding with sufficient bandwidth to control a
situation
In order to avoid error by using integration alone we must use very redundant physical systems (eg lots of electrons, troops, workers) to get secure communication.
Using transfinite arithmetic, we may equate the cardinal ℵ0 different events (Turing machines) in the Universe with the cardinal ℵ0 of events that have occurred (at the quantum or any other level) in the Universe since it began, or in fact throughout the life of the Universe. This is the physical layer.
[page 165]
To go there means to be observed there. So, the path integral is not telling us the probability of a particle going from a to b. It is telling us [the probability] of a particle being created at a and annihilated at b. Quantum field theory is the statistics of birth and death. No one observes Feynman's little arrows rotating their way along all the alternative paths from a to b. Feynman It is only when an observation is made that the phases of all the arrows are added to give the final arrow which squared gives the probability of the event born at a, died at b.
Quantum mechanics does not know what all the little arrows mean and does not ask. It just knows that the arrow game, played according to the rules, gives credible results.
The first constraint on the symmetric Universe. Not all possibilities can be realized. The first to realize this was Heracleitus in 500 BC who saw that every time a scientific question was answered is spawned a forest of new questions. If we accept the symmetry that god lives and the Universe is an intelligent living thing like ourselves, we should expect what happens to us should happen everywhere and be everywhere visible in the tree of life, rooted in the big bang.
[page 166]
Applying invariance with respect to complexity, we expect to find intelligence as we attribute it to ourselves everywhere, and everywhere implemented by physical networks like the brain that processes our minds.
Possibilities 'compute' as in quantum mechanics and the fit ones (long arrows achieved by integrating harmony, tend to win out.
Burgess Here Comes Everybody page 49: 'The growth of the embryo and the growth of the soul mirrored eachother in Joyce's personal symbolism. In the "Oxen in the Sun" episode in Ulysses, a history of English literature -- which is a good enough record of the spiritual history of a nation -- is used to symbolize embryonic growth; in A Portrait of the Artist as a Young Man, embryonic growth to symbolize the spiritual history of a young poet.' Burgess
Eliminate violence and bullshit.
The best way I can repay them for deluding me is to debunk their delusion.
Creation. God created the Universe. If the Universe is god, the Universe creates itself. This is how it has seemed to be, from the big bang to now. We have a long history of creation. It will be valuable of we can understand it.
Wednesday 13 September 2006
Thursday 14 September 2006
[page 167]
We identify the initial singularity with the standard model of god, and on the assumption that the past controls the future (insofar as it can be controlled) it follows that god controls the evolution of the world.
All communication links lead from past to future [in 4-space, ie in the direction of increasing time].
Friday 15 September 2006
Saturday 15 September 2006
Insofar as space is not time, questions of precedence and causality do not arise within it, but it can be seen a[s] something in itself formally invariant. Our measure of distance in undifferentiated time is the quantum of action. Special relativity gives us the equation ds2 = dx2 - dt2 where the interval is zero if we measure dx in terms of light travel time, ie that we let c = 1.
Definition of space = simultaneous existence of distinct entities, or in terms of communication, simultaneous reception of distinct messages, as in the receptors of our eyes. But what of sound? Two ears, with much sharper phase (time) perceptions than our eyes serve to locate the sources of sound in space with considerable precision.
Feynman page 2-8: 'Unless a thing can be defined by measurement, it has no place in the theory' Feynman Ie only communicable things can be part of the theory. All measurements are cardinal. A measurement of an ordinal is a sequence or ensemble of measurements.
[page 168]
In an uncontrolled system error increases exponentially with time. Therefore stationary states, which are elements of space, are controlled. Control removes the effect of time, so that control at the Nyquist Frequency of the error can establish eternity.
. . .
PHASE <==> ACTION <==> COUNT.
Phase differences are the result of different processing times via the different possible routes (algorithms) available < x | i >s via algorithm i.
SPACE = MEMORY. Somebody's law: space stays the same unless somebody changes it. Dynamically space == momentum, time == energy.
We cannot measure phase without two scalars, ie enough pieces to make a complex number.
INDISTINGUISHABLE PATHS <=> INTERFERENCE
Tomonaga: 'As you know a physical quantity is expressed by a matrix in matrix mechanics and as a linear operator in wave mechanics' page 43. Tomonaga ie the physical quantity is not the state but the transition between states, and
[page 169]
not even this, but the absolute square of the amplitude to be in both states at once.
Boson vs Fermion / Past vs Future / Space vs Time.
Wave functions are function of degrees of freedom. The Trinity is three degrees of freedom. How do the persons interact?
ds2 = dx2 - dt2, |q> = a|0> + b|1>, |a|2 + |b|2 = 1.
Place value notation breaks the symmetry of the digits, since a digit in place n+1 is worth one tenth of the digit in place n [given decimal numerals]. This split in value arises from the meaning encoded in the process of encoding and decoding numerals.
The evolution of the Universe is the evolution of new degrees of freedom = new entropy = new error correction.
Boson = cardinal; fermion = ordinal. Death = bose, life = fermi.
Shelley Frankenstein [page 37; 'I was obliged to exchange chimeras of boundless grandeur for realities of little worth' (!) Shelley
page 44: 'I wished, as it were, to procrastinate all that related to my feelings of affection until the great object, which swallowed up every habit of my nature, should be completed.
