Notes
[Sunday 1 February 2009 - Saturday 7 February 2009]
[Notebook: DB 65 Symmetric U]
[page 93]
Sunday 1 February 2009
E = h f. Each cycle of the quantum wave represented an elementary computation operation. The duration of this operation is the inverse of the energy devoted to that operation. The simplest operation is NOT. A complex computation may be seen as a superposition of simpler operation occurring at different frequencies.
[page 94]
To get down to the nitty-gritty, we have to imagine exactly how an operation is represented in both classical and quantum terms. Nielsen & Chuang
INSIGHT - TEMPORAL UNCERTAINTY. When will I understand, ie when will I be able to see this as a communicable, repeatable and teachable process? I do not know. But when it does come it will be definite and will enter into the shared technology of life, just like the discovery of scrambled eggs or automotive transport.
The operation of intelligence is a matter of satisfying constraints imposed by data, the operation of life in fact, where one must continue, given the environment as it is, to find food and shelter and surplus energy and other resources needed to rest and reproduce.
Insight is the result of search, and it is believed that a quantum computer can search faster than a classical computer. Lov Grover arXiv quant-ph 9706033. Lov K Grover
Reality is in every case a message resulting from the satisfaction of the constraints imposed by the interaction of two entities which have a meeting and provide a communique which . . . existed only potentially in them before they met. [Maybe they were one particle bifurcating into two] How does this fir the notion of entanglement? How do we restate the idea of entanglement in human terms?
A singlet state is the set {p, not-p}, eg {male, female}.
These ideas are connected by Cantor symmetry.
Entanglement gives stronger correlations that we would classically
[page 95]
expect, meaning that there are fewer degrees of freedom that we imagine in entangled states.
Nielsen & Chuang page 113: The point is that it does not matter in which direction we measure the spins of the entangled particles in 3D space, there are always anti-correlated, suggesting that they in fact exist in a 1D space which is indifferent to the existence of 3 dimensions (?). In general there is minimal coupling between the Hilbert spaces of quantum mechanics and the 4-space of observation, as we should expect if there are 'identical particles' ie particles whose representation in Hilbert space is independent of their position in 4-space. Once again we get the feeling that quantum mechanics occupies a lower layer than spacetime, or at least space; it is completely concerned with time and energy, and its exploitation by space is 'emergent'.
From my own experience I know that the space of intelligence and communication is not 4-space, but rather the space brought into being when two entities enter into a relationship. How does 4-space arise from such relationships? As before we speculate that it is the smallest space in which any two entities can communicate without 'crossing wires'.
One might guess that spacetime is constructed of the trinity of 'nots C, P and T.
Tindall Intruder page 223: 'The same week the Russians entered Poland, forcing the Germans to retreat. This move meant little to Jane, but she was aware that it was being widely said that the Maquis was Communist-run. This made people, according to taste and disposition, either like of dislike the Communists more or the Maquis even less, and the rifts that already existed in St Laurent widened and deepened. ' Tindall
[page 96]
A la Zeeman effect, stress introduces differentiation. Zeeman effect - Wikipedia
What we are saying (hoping) is that a network of oracle-machines, viewed from the outside, looks like a quantum mechanical system. The states of the machines look like a superposition and, depending on the one we communicate with at any given moment the result is rather like we would expect from a measurement of a quantum system.
The government layer of law and formal bureaucracy binds each of us into the nation. From the government's point of view each of us is a rather random quantum system which nevertheless responds to government requests to identify ourselves, fill out forms and so on. Birth certificates, marriage certificates, title deeds, tax file numbers and all the rest.
From this point of view, each layer in a network sees the layers beneath it as quantum systems, sending them messages and getting replies from its peers in its own layer.
My message to you goes down through the layers ultimately to the initial singularity and then back up through the layers to you. At the lowest layers where error is impossible, such signals may propagate instantaneously corresponding to infinite frequency (countably infinite) and infinite energy, ie the energy of the whole Universe, ℵ0 h bar, . . . .
Salart et al, Nature 454:861: 'According to quantum theory, quantum correlations violating Bell inequalities simply happen, somehow from outside space-time, in the sense
[page 97]
that there is no space-time explanation for their occurrence: there is no event here than somehow influences a distant event there.' Salart et al
'We shall use this terminology ['the speed of quantum information'] but we emphasize that it is only the speed of a hypothetical influence and that our result casts very serious doubts on its existence. Garisto arXiv/abs/quant-ph/0212078 Robert Garisto
INDISTINGUISHABILITY --> INTERFERENCE
The particles are entangled but the spooky action at a distance is not carried by a particle, in other words we will find particles (ie information packets) restricted to c by coding delay but information not encoded in packets is not (maybe) so restricted. This suggests that the structure of spacetime is an artifact of encoding.
Inside the Universe our guiding principle is the Cantor symmetry which shows us how life at every layer of complexity is fundamentally the same -- that insight and quantum measurement follow the same paradigm of a neural network bringing clarity out of the mist.
Conrad: 'A work that aspires, however humbly, to the condition of art should carry its justification in every line'. Conrad's Prefaces to His Works, Edward Garnett ed page 49. Preface to The Nigger of the Narcissus. Conrad
Real relationships: A point of view is a reality which guides our lives. The aim of religion is to develop a safe and fertile point of view.
[page 98]
Monday 2 February 2009
COMMUNICATION -- DIFFERENTIATION
vs
Indistinguishability - interference (= additivity, = cardinality)
ie communication ie associated with ordering, lack of ordering with cardinal number. But always in quantum mechanics, the ordering and additivity deal with two dimensional vectors, ie complex numbers.
Tuesday 3 February 2009
Wednesday 4 February 2009
Without doubt the most useful piece of mathematics for physicist has been differential and integral calculus. By differentiating, we discover the local behaviour of a system. By integrating we move from local behaviour to global. The most impressive example of this must be Einstein's derivation of the differential equations of gravitation and the integrations that have given us insight into the large scale structure of the space-time we inhabit and study with out astronomical and cosmological instruments and models. NASA
The mathematical analysis underlying calculus is built on the notion of a limit. When we differentiate, we seek a stable ratio of f (x + h) - f (x )/ h as h becomes smaller, and if we can find such a ratio we say the derivative exists. Similarly, when integrating, we seek a stable sum as we divide the function to be integrated into smaller and smaller slices of width h. In both cases
[page 99]
we are satisfied in the derivative or integral approaches a fixed value as h approaches zero.
The success of these methods could easily lead us to suspect that the Universe itself is continuous, a fact contradicted by observation. We are thus led to conclude that the calculus is not able to tell us the whole story.
The next most powerful weapon in the physical armory is group theory, and the wonderful success of calculus has led us to give continuous groups a leading role in our models.
As he made clear in his 'General Scholion', Isaac Newton depended on Divine intervention to give meaning to his System of the World.
['This most beautiful system of the sun, planets and comets could only proceed from the counsel and dominion of an intelligent and powerful being. . . . He is eternal and infinite, omnipotent and omniscient; . . . He endures forever and is everywhere present; and by existing always and everywhere he constitutes duration and space.'] Newton, Philosophiae Naturalis Principia Mathematica - Wikipedia
Things have changed very little since. Although quantum mechanics and general relativity give us formalisms which, carefully applied, closely match the observed phenomena, they do not explain how the world works and they are both internally inconsistent and in some cases inconsistent with the data. (Veltman Veltman, Weinberg, Weinberg)
Heisenberg cleared the field for quantum mechanics with a simple philosophical ansatz, [In this paper it will be attempted to secure foundations for a quantum theoretical mechanics which is exclusively based on relations between quantities which in principle are observable'. (Heisenberg Heisenberg)] Born Max Born, Pais (?) Pais Inward
Abstract
It is proposed that we model the Universe on finite computer networks such as the internet, extending this concept mathematically to a network with a countable infinity of fundamental processes corresponding to the countable infinity of computable functions each implemented by a Turing machine. It is argued that this discrete system is not only consistent with the observable Universe,
[page 100]
which physics sees as a system of observable events, but also has all the power and note of the pitfalls of the current crop of continuous models built on the classical mathematical notion of continuity. Mathematical continuity is replaced by the more powerful notion of logical continuity implemented formally by mathematical proof and practically by digital computing machines.
The organization of Normandy: Churchill History English . . . page 112 vol 1 Cassell 1956. Churchill
'In Normandy a class of knights and nobles arose who held their land in return for military service, and sublet to inferior tenants on the same basis.' Land division multiplexing. The initial singularity, source of action, sublets its action to the ever expanding Universe in the same way.
Noone but the Duke (god on earth) might build castles or fortify himself. The Court or "Curia" of the Duke consisted of his household officials, the dignitaries of the Church and of the more important tenants who owed him not only military service but also personal attendance at court. . . . [The Dukes of Normandy] welcomed the religious revival of the tenth century and secured the favour and support of its leaders. But they made sure that the bishops and abbots were ducal appointments.
Everybody must have an ecological niche which provides for material and spiritual needs, given the input of a little work.
Quantum mechanics such as Zurek see epistemology and ontology merged. It is a natural consequence of the divinity of the Universe. Lonergan has the right idea but he unnecessarily segregated God
[page 101]
and the world. Lonergan
History tends to be divided into discrete units by the succession of governments [and in fact all local time is punctuated by events].
The public service is the mechanism of government. The head of state in parliament is the director of this mechanism.
A bureaucracy is a network controlled by bureaucratic protocols.
Systems will cooperate if the benefit is seen to outweigh the cost.
Churchill page 122: 'To the full acceptance of the universal Christian Church was added the conception of a warrior aristocracy, animated by ideas of chivalry and knit together in system of military service based on the holding of land. This institution was accomplished by the rise of the mail clad cavalry to a dominant position in war, and new forces were created which could not only conquer but rule.'
page 125: '. . . the entire structure of the feudal world rested upon the sanctity of oaths. [now it rests on signed papers]
An oath established a true or reliable protocol for error free communication (until someone broke it).
page 131: Iraq: 'The very disunity which had made the assault successful made subjugation lengthy.
Thursday 5 February 2009
Introduction
All paradigm changes in physics seem to involve a
[page 102]
change in our understanding of space. Aristotle and his contemporaries lived on a ball of earth, air, fire and water sitting in the middle of a system of concentric spheres carrying the heavenly bodies around the earth. These heavens were composed of a fifth element of a much higher grade than the Earthly elements.
The motions of the heavens controlled motions on earth and the whole was kept in motion by the first unmoved mover, since it was seen as impossible that something should move itself.
This model could not be reconciled with the rather unspherical motions of the heavenly bodies revealed by careful observation and measurement.
Macquarie Group: 'Lessons learned from the current downturn: . . . until July 2007 -- prior to the credit crunch -- the assumption was that wholesale short term money markets (commercial paper) would remain open at some level even in stressed times. It became obvious in the course of 2008 that this was not valid. Operational Briefing 5/February/2009. Macquarie Group
Euclid produced an abstract model of the three dimensional space which we experience on earth which had nothing to say about spheres or elements and stuck simply to the results of measurements of distance and angle in the ordinary space of surveyors and travellers. Newton used this space, fixed by god, as a divine reference frame to plot the courses of the heavenly and earthly bodies and work out the dynamic relations between them mediated by gravitation and collision.
[page 103]
The next developments, both due to Einstein, were the introduction of 4 dimensional space time with a Minkowski metric, and then the generalization of these local frames of reference to a system brought to life by the presence of energy whose presence was detected by curvature of a 4-dimensional gaussian space.
Cantor, Hilbert, Heisenberg, Dirac and von Neumann led to the next development, the conceptualization of quantum mechanics in the infinite dimensional function spaces that sprang from Cantor's ultimately doomed effort to measure the cardinal of the continuum. Cohen
Cantor's ideas not only fuelled an attack on the continuum, but forced (like Newton's calculus) a critical review of the logical foundations of mathematics. This line of development also starts with Hilbert and leads to the world of Gödel, Turing and Shannon. Here the emphasis shifted from physics to logic. Logic fills the whole of Cantor's transfinite space. All possible functions are open to study, not merely the continuous and differentiable, an infinitesimal subset of all possible function. (Ashby Ashby)
It is in this new space that we take our stand here, guided by the mathematics of classical and quantum computation and communication.
While the mathematical world is absolute and infinitely resolved [at least in our minds], the physical world has an uncertainty principle related to the 'size' of the quantum of action.
[page 104]
Churchill page 154 '[Henry Plantagenet] embodied all [the Plantagenet] ability, all their energy, and not a little of that passionate ferocity which, it was whispered, came to the house of Anjou from no mortal source, but from a union with Satan himself.'
Chesterton Wisdom Father Brown, Purple Wig page 118:
Brown: 'And I say to you, whenever you find men ruled merely by mystery, it is the mystery of iniquity. If the devil tells you something is too fearful to look at, look at it. If he says something is too terrible to hear, hear it. If you think some truth is unbearable, bear it.' Chesterton
Friday 6 February 2009
Aristotle's space was endowed with a potential that expressed the natural places of the elements, earth in the middle, then water, air, fire and quintessence. This space is in a sense curved, that is, dynamic. Euclid, abstracting from all potentials, gave us a model of flat space in which nothing has a tendency to move and parallel lines do not meet. Newton linked Euclid's space with gravitational potential. Einstein produced a new version of flat space, Minkowski space, and used it as the infinitesimal element in an integration which yielded the present understanding of the large scale structure of the Universe.
Continuity by proximity: insofar as points are distinct, their closeness has no meaning; insofar as they are not distinct, we cannot frame logical arguments about them.
[page 105]
Churchill page 209: 'The whole moral scheme of the Western world was based, albeit precariously, upon Original Sin, Redemption by Grace and a Hell of infinite torment and duration, which could only be avoided through the ministrations of the clergy.
1209 Crusade against the Albigenses. Albigensian Crusade - Wikipedia
Evolution and the Lagrangian.
Zero point energy and multiple counting.
Churchill page 224: Edward I page 225: Edward: 'To each his own. . . . We must find out what is ours and due to us, and others what is theirs and due to them.'
page 230 Peckham, Archbishop of Canterbury to Edward: 'By no human constitution, not even by oath, can we be bound to ignore laws which rest undoubtedly on divine authority.'
'Divine authority' has been a good and profitable scam for a long time.
Page 235: Armour piercing archery. English longbow - Wikipedia
So we come to see logic not just as a tool for studying physics, but in some way embodied in physics.
EMBODIMENT, INCARNATION
Physicists are basically interested in calculating cardinal numbers that can be measured. Of these the foremost is energy, since,
[page 106]
the equation E = hf and our ability to measure [frequencies] with exquisite precision makes it an easy target. On the other hand, the detailed quantum theoretical calculation of energies is an exquisitely complex business, requiring us to investigate networks of thousands, millions or billions of inputs into the measurable parameter which we wish to compute. Grozin
