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Notes

[Notebook: DB 58 Bringing god home]

[Sunday 21 May 2006 - Saturday 27 May 2006]

[page 132]

Sunday 21 May 2006

Experience is divine. Now we might divide experiences into two categories, painful and not painful. We are saying they both come from god. My pain is a response that tells me that something somewhere is not right and needs correction. I have suffered much pain from misaimed hammers and [other] faulty communications with my environment, both human and other.

Pain is an error signal. There are parts of my body that can be badly injured without pain, the outer layers of my teeth and my Achilles tendon, which broke recently. The ethically responsible way to respond to an error signal is to correct the error, and if thee is a disaster which does not emit an error signal, to instrument it so that it does, and so that enough information is gathered to understand and correct the error. In general this requires a thorough understanding the the normal functioning of the system at fault.

FAULT = OUT OF RANGE/DOMAIN FUNCTION. A case which the local system cannot successfully process. Better software can deal with more errors and so is less prone to fatal error. (The fatal error is an uncaught error)

if anything goes wrong, just start again. But I cannot start my life again, so we also need error recovery - surgery or its equivalent, disconnecting and connecting things, a network operation.

The aim of religion is to reduce human pain. It might be argued that some of the old religions seem bent on increasing the overall level of pain, but they mostly do it in the light of promised greater pleasures to follow. An ascetic hopes to be awarded with visions of god. We say you don't need to be an ascetic to see god, all experience is divine. Nevertheless, to play the game of life effectively one must sometimes exert painful levels of self control to save the money to buy a house, for instance, or to bring home a potential love.

[page 133]

The localization of control in an infinite medium. A control system must have requisite variety which in the classical world means a countable cardinal.

A new definition of infinity by permutation,which is consistent with the old: a set is infinite if it can be mapped onto a subset of itself. Whatever that means we can work it our in symbols.

NETWORK <--> FUNCTION (CORRESPONDENCE, MAPPING)

CAPITAL = f(CASHFLOW)

CAPITAL = POTENTIAL ENERGY (STRUCTURE)
CASHFLOW = KINETIC ENERGY (RATE OF CHANGE OF STRUCTURE)

See it all in the harmonic oscillator. The most magical little formula in the mathematical world: ei.T = cost T + i sin T.

Complex numbers are periodic because there is complex multiplication and division in their series representation.

PERIODIC = {INCREASING, DECREASING}

Bix page 312: 'The air power theories of the Italian Maj. Gen. Guilio Douhet were then in vogue among navalists, and the resulting contingency plan included a punitive air campaign against the civilian population of China's major cities as well as preparations for conducting a coastal blockade should one ever be needed.' Bix

Kokutai (national polity)

page 313: '"We loyal subjects differ completely in our nature from so called citizens of Western nations. We always seek in the emperor the source of our lives

[page 134]

and activities"'.

Bix page 314: 'The country had taken on the identity of a fascist state, and had even adopted the haunting rhetoric of fascism; its people laboured under the burdens of food rationing and total war economy; policies were in place to increase war production by lowering living standards; in the emperor's name, all open dissent had been squashed.'

page 315: '"Even in our private lives we always remember to unite with the emperor to serve the state.

page 342: 'American perceptions of Hirohito and the Japanese policy making process leading to the Pacific War were never rooted in reality.

page 372: 'Avowing "benevolent rule" and disallowing Machiavellianism, while simultaneously sanctioning the use of poison gas against the Chinese - these contradictory acts reveal Hirohito's divided nature. . . . Hirohito's action fit a pattern of exterminating people while enveloping oneself in moral humanitarian rhetoric that was just as much Western as Japanese.

page 374 July 17 1940 Matsuoka Yosuke: "In the battle between democracy and totalitarianism the latter adversary will without question win and control the world. The era of democracy is finished and the democratic system bankrupt. There is not room in the world for two different systems or two different economies. . . . Fascism will develop in Japan through the people's will. It will come out of love for the Emperor."

Monday 22 May 2006

THEOLOGY = HUMAN DYNAMICS

. . .

HUMAN DYNAMICS = {HUMAN STATES, HUMAN TRANSITIONS}

[page 135]

GEOMETRY From the beginning we have modelled states of the Universe with points and lines. From Descartes on, we have modelled our geometric models with arithmetic. This has made an issue of continuity. We have known for thousands of years that we cannot name every point on the geometric line using ratios of natural numbers, ie rational numbers. Continuity is also important in our understanding of motion. We believe that if something is to move along a line from A to B, it must go through every point on the line, and these points must be dense, so that at no time is a moving body 'nowhere' ie between points.

Classical geometry and its curved descendants have served us well in modelling the structure of the Universe at all scales from the Universe to quantum events.

Can we say every change of quantum state involves a countable number of quanta of action? Look it up. Eg spin flip electron, emit or absorb photon, anyon.

Communication theory is blind to the formal structure of messages, requiring only that the [messages] be placed at the maximum distance from one another possible in the space available (computable), ie invariant with respect to complexity?

Shannon's proofs operate across the boundary if two transfinite numbers, as do Cantor, Gödel and Turing's. The small number is countable (discrete) with respect to the larger. Ie the smaller number is resolved, the larger is continuous.

The transfinite network embodies an enlightened liberal agenda, showing how constructive sharing of the rewards of our labours can lead to increasing individual fitness broadly considered, ie beatitude. Beatitude comes as pleasurable (and unnoticed) passage of time. Pain makes us conscious of time because time becomes of the essence in pain relief.

[page 136]

We are going to explore the features of the Universe that make possible books, writing and knowledge in general.

Bix page 476: 'Confronted with certain defeat [Hirohito] dug in his heels and refused to accept it.

page 491: 'Yet until the very end, most Japanese people, whether living in the country or in large urban areas remained steadfast in their resolve to obey their leaders and to work and sacrifice for the victory that they were constantly told was coming.

page 496: 'American intelligence analysis meanwhile watched all these main island preparations. They saw how the Japanese had fought and died in Okinawa -- thousands almost daily for eighty -two days -- and how the whole nation had become enveloped in the imagery of national salvation through mass suicide. When political leaders in Washington said the Japanese were likely to fight to the death rather than surrender they were not exaggerating what the Japanese government and its mass media were saying.'

page 509: 'Unable to end the war unless the future of the throne and the all important prerogatives of its occupant were absolutely guaranteed, the Suzuki cabined and the Supreme War leadership Council never framed a peace maneuver from the viewpoint of saving the Japanese people from further destruction'.

Tuesday 23 May 2006

Bix page 516: 'At the meeting on August 9-10 it was Hiranuma, not Togo, who voiced the sense of the majority on the fundamental need, which was to view the theocratic view of the Kokutai [national polity] rather than Togo's secular cultural view. . . . Hirohito . . . believed himself to be a monarch by divine right. . . . '

page 517: 'In effect this amounted to an affirmation that the Emperor's right of sovereignty, including his all important right of supreme command, antedated the constitution and had been determined by the gods in antiquity

[page 137]

just as stated in the Preamble to the Meiji constitution.'

Bix page 517 '. . . continued subjecthood or shimmin status for the Japanese people. '

page 520: 'The wartime emperor ideology that sustained their morale made it almost impossibly difficult for them to perform the act of surrender.'

page 524: 'It is not known if Truman was troubled by the massive American conventional bombing of Japanese non-combatants - actions that qualified as atrocities.'

page 527: 'Hirohito's surrender rescript was the first text to redefine his new national image as a pacifist, anti-militarist and completely passive onlooker in the war -- none of which he had ever been.

page 528: 'In the weeks and months that followed vast amounts of secret materials pertaining to Japanese war crimes and the was responsibility of the nation's highest leaders went up in smoke -- in accordance with the August 14 decision of the Suzuki cabinet.

Above all we must avoid getting embroiled in the theocratic nightmare.

page 543: Henceforth, in the process of utilizing Hirohito's authority for their own respective purposes, MacArthur and the Japanese leadership would have to misrepresent a vital side of Hirohito's life and identity, jut as they had been misrepresented before the war.

page 548: 'Both Hirohito and MacArthur valued loyalty and cultivates remoteness. They regarded themselves as their nations leading asset and knew how to practice deception -- MacArthur of his superiors at every single stage of his career; Hirohito of the entire Japanese nation.

page 554: 'Even though the mystique of the throne has been punctured by defeat his subjects remained loyal, and many still regarded him as "sacred and inviolable".'

[page 138]

As we all are.

Theology studies stability in human dynamics. It studies this in the context of god, the environment for human activity.

Because theological beliefs are deeply ingrained from birth, you might find these words hard to interpret, but I request that you follow me, at least until you meet an insurmountable obstacle.

Bix page 577: '. . . the new constitution changed the Emperor from an absolute value to a relative one, from a "sacred and inviolable" divinity into a mere human being under the law. Henceforth it was the constitution, not the emperor, that articulated the highest ideals, aspirations and purposes of the Japanese people. And instead of Hirohito having enacted [emitted, communicated] the constitution, the Diet had enacted Hirohito.'

page 578: As with Christianity 'Powerful emotional barriers to questioning his conduct or criticizing his status continued throughout the occupation and for the rest of his life.

page 585: '. . . MacArthur's truly extraordinary measures to save Hirohito from trial as a war criminal has a lasting and profoundly distorting impact on Japanese understanding of the lost war.

page 593: '. . . distortions [of the war crimes trial process] stemmed from the subordination of international law to realpolitik by all the allied governments. These governments tended to rank national interests first, law and morality second. So did Hirohito and his advisors, working covertly behind the unfolding legal drama.

Wednesday 24 May 2006

Bix page 616: 'To this day it is unclear whether MacArthur or someone else high up in the army chain of command made the actual decision not to pursue the indictment of the Japanese army for its use of

[page 139]

chemical weapons. . . . President Truman, who lacked the imagination to see the implications of what was at stake, in affect allowed Roosevelt's wartime policy of condemning poison gas as an illegal inhumane method of warfare to be reversed..'

page 617: 'The widespread Japanese belief that was is a natural social phenomenon . . . '

We often use the prisoner's dilemma to explore the relationship of self interest to altruism and similar ideas. But the outcome of prisoner's dilemma simulations depend on the interaction rules and payoff structure within which the agents being studied are interacting. The setting of the parameters is the task for theology and religion.

THEOLOGY = HUMAN DYNAMICS
RELIGION = HUMAN ENGINEERING.

page 618: 'Protecting the emperor and remaking his image were complex political undertakings that could only be achieved by grossly exaggerating the threat of social upheaval in Japan, rigging testimony, destroying evidence, and distorting history.'

Progress: as the world becomes more conscious of religious problems, it is time to ask if science has any solutions to offer.,

Nothing like poverty for motivation: as the market goes down my enthusiasm for this goes up.

page 635: 'Early the next year [ie 1947] Detroit banker Joseph M Dodge arrived in Japan to implement a drastic deflationary fiscal policy projected to revive Japanese capitalism by generating massive unemployment.

And so rising profits? But contracted industry because the unemployed are not contributing to production except as consumers.

[page 140]

Emperor from God to Symbol of God. Jesus from God to Symbol of God. Haight

THE LEAP : An undertaking with a relatively uncertain (ballistic) outcome, vs STEERED undertaking. Nevertheless the quantum principle requires that even the best steered undertaking must proceed by quantum leaps, ie discrete processes.

Bix page 649: 'Hirohito's continuation on the throne after independence clearly inhibited popular exercise of the constitution's guarantee of freedom of thought and expression.'

'[Hirohito had no sense of moral accountability to any but his ancestors,and when under pressure to abdicate, he sometimes intimated to aides that he continued to think of himself as a monarch by divine right.'

page 650 '"The Meiji emperor said that unlike ministers who can resign emperors can't abdicate because they must carry out the divine order as written in the dynastic histories. . . . My duty is to bequeath this country, which I received from my ancestors, to my descendants.

page 652: 'double standard' -- superposition.

The Emperor, instigator of all, was forgiven by his judges for reasons of the future rather than the past.

page 653: sacrifice : 'For the next quarter of a century, all conservative governments would make repeated and powerful use of the word "sacrifice".'

. . .

[page 141]

Bix page 657: 'kill all, burn all, steal all.

. . .

page 669: 'Above all, postwar Japan was politically dedicated to supporting big business, big manufacturing and big trade, no matter what the human and environmental costs. '

Without doubt the key to the explosive growth of human fitness since the discovery of fossil fuels has been our ability to work together, in large numbers. Undoubtedly the key to this has been the 'gauge principle' ' a fair day's pay for a fair day's work' [and vice-versa]

page 677 (1975) 'The work of unmasking the emperor had begun.'

. . .

The emperor system has no error correction, but relies on the loyalty and service of each of its subjects to function. The democratic (parallel processing) system can have error correction and can achieve its ends with almost zero reliance on the integrity of its alphabet [citizens].

In the physical world, a unit is endowed with energy which is modelled as a normalized vector rotating in a plane at a frequency identical to its energy. Furthermore, these arrows form an arithmetic and an algebra.

CARDINAL = FREQUENCY

. . .

[page 142]

The classical communication that goes with teleportation merely serves to select among the 4 possible states transmitted quantum mechanically.

Thursday 25 May 2006

Each particle is a space of cooperation.

The fundamental task of human dynamics is to partition the space of human action into events leading to war (annihilation) and events leading (contributing) to peace.

Virgil:' I sing of arms and the man fated to be an exile.' West

Christianity built on the 'classical' foundation since its first scholars were formed in the classical milieu. Like the Aeneid, the New testament is built around a central figure cast as the founder of a great human corporation (nation, empire, church, business, charity etc, and mixtures (superpositions) of these).

. . .

The importance of ancestors in the mythological phase of theology has been replaced in biology by the importance of genes. The human side of genetics is irrelevant to biology, but relevant to theology, in that the current theology is a product of all the theologies that have fed into it (its inward message cone) and out of it (its outward message cone).

Religion is a natural phenomenon and quantum mechanics is big enough to deal with it, as with other natural phenomena.

[page 143]

The Christian theoreticians had to fit new data into the classical (predominantly Platonic) worldview they inherited. The divine personality revealed in the Old testament was gradually refined by the modelling of Parmenides, the Pythagoreans and Plato to an abstract, eternal, immutable and incomprehensible being. Now a new personality, Jesus of Nazareth, enters the scene and is believed to be god himself, a person comprising both divine and human nature,

A further complication was the transformation of strict monotheism into the trinitarian concept of god generally accepted within Christianity. Thousands of people worked on these ideas, leading to a general consensus preserved for us in the work of Augustine of Hippo, who envisaged a City of God modelled on the Roman Empire as the ideal human state. Unfortunately Augustine also witnessed the fall of the Roman Empire, and the centre of gravity of scientific speculation about the world moved East and toward Plato's student Aristotle, who had taken a more 'naturalistic' view of the world.

. . .

Our understanding of religion has been very much compressed by interests of the incumbent crop of 'professionals', ie professed members of religious institutions.

In the mythical era, was was divine. So it was in Imperial Japan.

There are many on the planet who act as though empowered by divine right, even though they shrink from admitting that they have perverted the aims of democratic government.

We can characterize a network with four sets of values ie message string, time sent, source, destination.

OPEN MESSAGE = POTENTIAL
CLOSED MESSAGE =message plus reply = EVENT

[page 144]

Potentials are open messages waiting to be closed.

Cercignani, Boltzmann; 'This assumption, according to which the coordinate and velocities of molecules take on, in an equilibrium state, all values compatible with the assigned total energy of the gas, later became familiar as the ergodic hypotheses, the name given to it by Paul and Tatiana Ehrenfest. page 86-87 Cercignani

Friday 26 May 2006

Identical hard sphere network is the simplest. - DEMOCRITUS

COLLISION = COMMUNICATION

STATE OF MOTION = CHANGE OF STATE

There is n limit on the complexity of the states exchanged, only that they should be peers, ie equinumerous.

From the mythical age, we enter a period which we recognize as more scientific. This speculation was partly based on mathematical ideas like lines, circles and the regular geometric shapes in two and three dimensions. Here we find the scientific process well developed, with imaginative model making and critique by others. Aristotle recounts his view of this history, and it is clear that he has a strong sense of empirical justification for his ideas.

Aristotle hardly entered the first draft of Christianity, but his works were preserved in the Arabic world and reentered the west via translations of those of William of Moerbeke. Wikipedia Aquinas began his career by writing commentaries on many of these translations . . .

Behind the notion of 'pure act' is the logical idea of greatest set, which does not exist (mathematically).

[page 145]

The safe way in mathematics is to confine oneself to defined subsets of a larger world whose properties are recorded in a consistent set of statements or axioms.

The foundation of all this is the 'propositional calculus' which Gödel showed to be complete, ie it will never leave us in the lurch of uncertainty. Gödel

Aquinas recoded by Lonergan, and thee I saw my answer. The acts of insight, inverse insight and so on proposed by Lonergan were equivalent to the transformations of messages (encoding and decoding) envisaged in Shannon's theory of communication.

From there it has been a long chain of insights recorded (scrappily) here , searching for a clear expression condensed into an . . . article.

The ancients skirted the Scylla of idealism (Plato) and the Charybdis of indifference to causes as we do, pitting reasonable science against economic potentials.

Lonergan described insight as a rather rare and exciting feature of the Universe confined only to specially created spiritual souls of human being. I now see it every where in every 'functional' transformation of the universal communication network.

My progress has been a slow hobble toward more general (mathematical) expressions of the belief that if we look at our world through the right eyes, we will see heaven and hell subtly intermingled. The business of survival then amounts to staying on the heaven side of the tracks. The practical challenge is to find where the tracks are, somewhere between total anarchy and absolute monarchy. Between these extremes is the de Maupertuis extremum, which seems to be the operating

[page 146]

of the physical Universe. Yourgrau and Mandelstam Is this when all messages in the Universe are true? True at a peer level. Even though a message is transmitted without error at some level of a network [that] does not preclude it from being deceptive at another level.

The competitive evolution of networks will be governed (we suspect) by network efficiency which will be a network tuned to deal with all the messages it may receive from its environment, ie be able to deal with them (at least up to the level of a hyperspace freeway!). Adams

To injure (kill) a network is to cut it (in half).

Network model is a 'conceptualization'. We come to understand it through our local position in it.

Identical particle = identical messages [but maybe different sources [= sources and sinks].

Saturday 27 May 2006

Explanation: of parts in terms of the whole: of the whole in terms of the arts.

. . .

differentiation increases entropy, integration reduces it [?]

Integration <==> 'collapse of wave function' [Dirac 'When we measure a real dynamical variable x, the disturbance involved in the act of measurement causes a jump in the state of the dynamical system. Dirac page 36

Phase space addresses every particle, so the Cantor Universe is a a phase space for the physical Universe.

Work is a pain if the drudgery exceeds the excitement. Making a floor. Hundreds of pieces, thousands of fastenings.

The well known mood of hopeless hope, ie we still have not found a path to the goal but we are still convinced that the goal is there, ie hopeful as opposed to hopeless search,

The 10100 discrepancy between the observed Universe and the predictions of quantum field theory suggest that there is something wrong with the QFT picture. Bennett, Carroll

We want to draw a picture of god, and the Cantor Universe is our canvas.

Our picture of god is kinematic, because we are modelling a living god and it has multiple personalities because we are modelling a divine collective (traditionally, the trinity)

Sounds good, has to be said, but not orgasmic. We make the system dynamic by instituting communication whose effect is to substitute one letter of the universal alphabet for another, ie one message for another.

Finally we introduce a shaping force which changes the a priori equiprobability of all the symbols in the Cantor Universe (our state space) into something that resembles our Universe.

1. Everything is done by Turing machines that take time (relativity)

2. Everything is a 'writable computation' = vector algebra, quantum mechanics.

DISTANCE = 1/OVERLAP.

Like the nuclear weapon, there is time pressure in developing the 'peace weapon', ie a useful model of god -- what religion needs. Because we are involve din the search for fitness too.

Our god is a lot more complex, but a lot easier to see.

Let us say that error free communication best serves the maintenance of the structure of the Universe.

Communication shapes the village (Mrs Marple)

'A coded ensemble of particles;

Clock: All change; all hold.

Related sites

Concordat Watch

Revealing Vatican attempts to propagate its religion by international treaty


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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!)

Adams, Douglas, The Ultimate Hitchhiker's Guide, Random House 1996 Jacket: 'Finally, here they are in one outrageous volume - all six bestslling Hitchhiker stories by Douglas Adams, including his latest addition to the collection, Mostly Harmless. Plus you'll find a perplexingly frank introduction by the author himself, giving a behind-the-scenes look at the books and the zany radio series that inspired them' 
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Bix, Herbert P, Hirohito and the Making of Modern Japan, HarperCollins Publishers 2000 Introduction: 'One of the most fascinating and complex figures in twentieth-century Japanese hitory, Hirohito began his reign in late 1926, on the eve of renewed conflict in Japan's relations with China. It continued for sixty two years of war, defeat, American occupation, and Cold War peace and prosperity. During the first twenty years he was at the centre of the nation's political, military and spiritual life in the broadest and deepest sense, exerting authority in ways that proved disastrous for his people and for those countries they invaded. Though the time span of his great Asian empire was brief, its potential was enormous. He had presided over its expansion and had led his nation in a war that cost (according to the official estimates published by governments after 1945) nearly 20 million Asian lives, more that 3.1 million Japanese lives, and more than 60 000 Western Alllied lives.' Events nad not turned out as he had anticipated and hoped. Yet when his turn came to provide explanations of the role he had played in those events, and so set the record straight, he and his aides were far from candid. They skillfully crafted a text deseigned to lead to the conclusion that he had always been a British-style constitutional monarch and a pacifist. ... ' 
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Cercignani, Carlo, Ludwig Boltzmann: The Man Who Trusted Atoms, Oxford University Press, USA 2006 'Cercignani provides a stimulating biography of a great scientist. Boltzmann's greatness is difficult to state, but the fact that the author is still actively engaged in research into some of the finer, as yet unresolved issues provoked by Boltzmann's work is a measure of just how far ahead of his time Boltzmann was. It is also tragic to read of Boltzmann's persecution by his contemporaries, the energeticists, who regarded atoms as a convenient hypothesis, but not as having a definite existence. Boltzmann felt that atoms were real and this motivated much of his research. How Boltzmann would have laughed if he could have seen present-day scanning tunnelling microscopy images, which resolve the atomic structure at surfaces! If only all scientists would learn from Boltzmann's life story that it is bad for science to persecute someone whose views you do not share but cannot disprove. One surprising fact I learned from this book was how research into thermodynamics and statistical mechanics led to the beginnings of quantum theory (such as Planck's distribution law, and Einstein's theory of specific heat). Lecture notes by Boltzmann also seem to have influenced Einstein's construction of special relativity. Cercignani's familiarity with Boltzmann's work at the research level will probably set this above other biographies of Boltzmann for a very long time to come.' Dr David J Bottomley  
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Dirac, P A M, The Principles of Quantum Mechanics (4th ed), Oxford UP/Clarendon 1983 Jacket: '[this] is the standard work in the fundamental principles of quantum mechaincs, indispensible both to the advanced student and the mature research worker, who will always find it a fresh source of knowledge and stimulation.' (Nature)  
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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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West, David, Virgil: The Aeneid, Pengui Books 2001 Introduction: 'A poem for our time: The Aeneid is the story of a man who lived three thousand years ago in the city of Troy in the north-west tip of Asia Minor. What has that to do with us? Troy was besieged and sacked by the Greeks. After a series of disasters, Aeneas met and loved a woman, Dido, Queen of Carthage, but obeyed the call of duty to his people and his gods and left her to her death. Then, after long years of wandering, he reached italy, fought a bitter war against the people of Latium and in the end formed an alliance wth them which enabled him to found his city of Lavinium. From these beginnings, in 333 years, in 753 B.C., the city of Rome was to be founded. The Romans had arrived in italy. ... The Aeneid presents a heroic view of the life of man in all its splendour and anguish, but it is full of just observation and of details of individual behaviour. It is not yet out of sate.' 
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Yourgrau, Wolfgang, and Stanley Mandelstam, Variational Principles in Dynamics and Quantum Theory, Dover 1979 Variational principles serve as filters for parititioning the set of dynamic possibilities of a system into a high probability and a low probability set. The method derives from De Maupertuis (1698-1759) who formulated the principle of least action, which states that physical laws include a rule of economy, the principle of least action. This principle states that in a mathematically described dynamic system will move so as to minimise action. Yourgrau and andelstam explains the application of this principle to a variety of physical systems.  
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Papers
Bennett, Charles L, "Cosmology from start to finish", Nature, 440, 7088, 27 April 2006, page 1126-1131. Cosmology is undergoing a revolution. With recent precise measurements of the cosmic microwave background radiation, large galaxy redshift surveys, better measurements of the expansion rate of the Universe and a host of other astrophysical observations, there is now a standard highly constrained cosmological model.It is not a cosmology that was predicted. Unidentified dark particles dominate the matter content of our Universe, and mysteries surround the processes respnsible for the accelerated expansion at its earliest moments (inflation?) and for its recent acceleration (dark energy?). New measurements must address the fundamental questions: what happened at the birth of the Universe, and what is its utimate fate?. back
Carroll, Sean M, "Is our Universe natural", Nature, 440, 7088, 27 April 2006, page 1132-1136. 'It goes without saying that we are stuck with the Universe we have. Nevertheless, we would like to go beyond simply describing our observed Universe, and try to understand why it is that way rather than some other way. When considering both the state in which we find our current Universe, and the laws of physics it obeys, we discover features that seem remarkably unnatural to us. Physicists and cosmologists have been exploring increasingly ambitious ideas in an attempt to explain how surprising aspects of our Universe can arise from simple dynamical principles.'. back
Gödel, Kurt, "On the completeness of the calculus of logic", in Solomon Fefferman et al (eds), Kurt Gödel: Collected Works Volume 1 Publications 1929-1936, New York, OUP 1986, , , , , page 61-101. '1. Introduction The main object of the following is the proof of the completeness of the axiom system for what is clled the restricted funcitonal calculus, namely the system given in Whitehead and Russel 1910 part 1 *1 ns *10 ... Here 'completeness' is to mean that every valid formula expressible in the restricted functional calculus ... can be derived from the axioms by means of a finite sequence of formal inferences. ...'. back
Links
Wikipedia William of Moerbeke 'Willem van Moerbeke, known in the English speaking world as William of Moerbeke (ca 1215 -1286) was a figure of great culture, in touch with many of the first minds of his day. He was the most prolific medieval translator of philosophical, medical and scientific texts from Greek into Latin. His translations were influential in his day, when few competing translations were available, and, more to the point, are still respected by modern scholars.' back

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