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vol VII: Notes

1999

Notes

[Sunday 23 May 1999 - Saturday 29 May 1999]

[Notebook BOOK 4/5/94 DB 50]

[page 308]

Sunday 23 May 1999

Mob of x = set of x

I am a sinner => you are all sinners => we are all sinners. (but I thought of it first so you can all pay me to cure it).

TASTE <=> FITNESS

Insight, Inverse Insight, Being, Empirical Residue

Being is the object of the pure desire to know. Physics models desire as potential and the force impelling a particle toward the object of its desire as the gradient of the potential function.

Potential function --> field

Any function can describe a field, which is simply the function taken as a whole. The domain might be spacetime, the range might be electrical potential

[page 309]

So we construct the space of insight in the space of function. We have chosen permutation representation, but may also introduce combination representation = subsets, leading to set of all sets the power set.

The Cantor Universe is the home of insight

Being is the equilibrium at the base of the potential well, and we want it to turn out to be some sort of connection to the computable flow of action through the Universe. So we have a link between insight and quantum field theory.

So pure desire to know moves toward being as particle moves down a gradient of potential.

The fact that things exist and questions can be answered suggests that there are local minima in the field of knowledge.

The potential is generated by questions.

[page 310]

In general relativity we are not mapping from a space to a field in the space, but the structure of space is in some way the field itself. The starting 'points' are geodesics' inertial platforms observing one another through the medium of null geodesics.

*Transfinite version of general relativity shows us the general structure of noetic space.

Object of pure desire to know is a clear and distinct idea or model that serves as a starting point for the planning of action.

[eye] 1.4E8 receptors @ 500Hz - 7E10 bps = 70 Gbps.

Retinal insight yields 100:1 compression of data from primary receptors to be fed down the optic nerve.

Is there insight involved in an engine pulling a plane.

We keep coming back to the view that knowledge is the inverse of the Cantor expansion which

[page 311]

acts to keep the measure of action in the Universe constant at aleph(0).

A field becomes familiar when one learns the paths between the landmarks.

Tensor is a function on a manifold.

Can we use the mathematical theory of insight to unify QM and general relativity? This is what we want, the being toward which

Monday 24 May 1999

Insight is the mapping from world to mind. I say it is a function because the world is far more complex than any mind, so the world is many to one.

This job seems to be a constant battle to relieve

[page 312]

tension (assisted by what I take to be moderate and not life threatening drugs). Systems cannot move down a potential gradient without having a way to shed their energy eg atom.

MAPPING = meaning in general. Specific mappings = specific meanings

FUNCTION = INSIGHT = lens by which outside world is mapped onto the 'soul'

Tuesday 25 May 1999

RELIGION

The main yield from all this is mystical bliss. The one common thread of the 'professional' end of all religions (the region of popes, bishops, priests, ayatollahs and the rest) is the attainment of a mental state called heaven, bliss, nirvana, mystical union etc. The routes to this states (and hence opinions

[page 313]

about what and where they they are are [are varied].

The art forced by love

Wednesday 26 May 1999

The struggle is to get from the bright idea (principle of equivalence) to the calculation (solution of the differential equations of general relativity)

How do we model the beatific vision? The final insight, when the vision of god fully satisfies all questions. This is a static view. Thomas recognizes that we can see god but we cannot comprehend it.

"everything I have written seems like straw" apocryphal? Thos would surely have seen his writings as a realisation (incarnation) of the ladder (road, path etc) that carried him to his vision. Writing is a characterization of the geodesic. The Universe is continually rewriting itself according to the rules of a) mathematics and b) physics.

The pure desire to know has no inherent terminus (but at present death terminates us all. Later

[page 314]

we maybe reincarnated in silicon (neutrons?))

The proportionate beatific vision is an 'equivalent' (same cardinal) mate = peer.

PEER = EQUIVALENT

Or peer differs with relative difficulty of encoding and decoding. Limited memories (processes) can carry only a limited representation.

Toward calculation - explaining the maxims of religion

ie WISDOM the test of antiquity? the test of error probability.

A scientific measurement carries with it an 'uncertainty space' with a certain structure. The entropy of this space grows with the precision of the measurement.

Get people out of numbers into language.

The purpose of coding is to deny insight.

I want to express the nature of insight in a model based on computation of functions with

[page 315]

(possibly) transfinite domains and ranges ? The range of all observable functions is countable. This is the basic physical hypothesis.

. . .

The aim of religion is the beatific vision (peace, heaven etc). The classical theologian Thomas Aquinas tells us this.

. . .

Beatific vision. A phase change in the world. To be a nucleus of crystallization is to find and create what maybe a somewhat unstable structure. Growing crystal

Perhaps by the end of this year the main struggle will be over and the armature finished, to be fleshed out in the PhD years (as the online ? grows, so the PhD will become succinct.

So conceive of on line as supplementary

[page 316]

material, providing a cell into which the new genes/memes can be expressed

DECODING DNA into LIFE. A mere 10 000 protein x 1000 base pairs each = 200Mbits = 25MBytes defines how to make me out of my food.

The endpoint of the Catholic Religion, the beatific vision, is the starting point here.

Thomas has at his command a quite concise theory of knowledge and reality which he built himself upon the work of the Greek philosophers and the Fathers of the Church.

Hopefully this section will grow and be revised quite energetically, so that it will converge quickly to a clear representation of the picture I have in mind.

. . .

Notebooks (edited) (History)

Let the world crystallize back into peace and

[page 317]

harmony (where information but not so much ? ) move. Atoms hop around, exchanging photons and phonons. May also be free electrons. Not a too bad model for society given enough degrees of freedom.

The important feature of a crystal is LATTICE = NETWORK.

This all makes me so happy, but is there a word of truth in it?

. . .

[page 318]

Going into competition with all the other weird and wonderful religious offerings on the net. I only hope that in the long run the toward natural religion project reveals the most weird and wonderful of them all.

Toward natural religion project (tnrp), an activity of Dodgy Theological p/l

cool and loving

annual report

dodgy.com

Thursday 27 May 1999

. . .

Friday 28 May 1999
Saturday 29 May 1999

. . .

The 'denumenization' continues apace. Clearly the religion debate has to be opened up, but I must go into it with plenty of capital. Step 1 seems to be to keep silent until I have [developed my position] and then go

[page 320]

on the campaign trail to get people thinking about the true nature and purpose of religion and how quality control should operate in religious matters. Obviously we must stick to scientific truth, just as is done by the other reasonable (as opposed to adversarial) professions. So the tiger must come out of the lamb and the scientist turn political.

BUSINESS = publicity+income

Reading Nixon's memoirs brings these thoughts to mind. Nixon The global burden of political corruption is enormous, and it should be the duty of theology and . , ,

A business gains income by appropriating some of the benefits flowing from its chosen product/s.

So we can take part in advertising campaigns pushing our name over the others by a) emphasizing our advantage b) emphasizing their deficiencies

Religion is not above politics. All beings act through a superposition of possibilities

[page 321]

of which one set are political, ie relate to the psychological networks of a set of people.

So stress my rights as an animal as well as my aspirations as an angel.

POLITICS - the feeling of the group (dictator -> democracy)

To live, ideas must be embodied, and so some sort of procreative activity is required.

Nixon page 312 'collapse of the wave function' '. . . like most important decisions, this one would not be final until it was announced.'

Politics (democratic) depends on numbers.

CARDINAL = POWER (just as Cantor said)

What we have to do is translate the principle of extremal action into religion, culture, politics, economics, design and work. Through the Cantor symmetry.

[page 322]

The basic epistemological foundation is honest appraisal of one's self. This is because one's self is, through the power of evolution and survival

The theory of evolution is the root of epistemology, in that survival is the filter than we have come through to be here. Whatever we may turn out to be, we know that we have good credentials as an evolved being.

Cybernetics: expanding on the nature of evolution. What you see is the result of a long path of evolutionary time meandering hither and thither as it makes its way from the big bang to the human race.

I need to truly fall in love with myself overcoming those barriers which were downloaded into me in the first 24 years.

This is the point of writing. To observe as carefully as possible and record mental

[page 323]

states. This sentence is such a record. Each sentence is the 'collapse of a wavefunction', that is an event selecting one of a superposition of states to interact with the outside world.

HEAVEN: to be at home with oneself. That is the closes point on god and the window to the beatific vision.

The fact that mathematicians can write books and communicate ideas to one another about infinite and transfinite spaces must mean something. Language is a symmetry. We talk in symmetries, using a finite number of symbols to dissect an infinite space.

Work brings order out of chaos, minimizing the action needed for survival, that is communication from generation to generation.

Symbolic (ie communicable) representations of the world have an inherent duality, since it takes two static symbols to represent an event, one before and one after It is they [sic] physicists desire to fill in the contents

[page 324]

of the black box, giving us eg field theory.

The ends of the duality, the change wrought by AB followed by BA is measured by the uncertainty in the closure of this commutator, ie the fundamental point of QM is that certain operations are non-commutative, ie they have the characteristics of rotations in a certain space, ie they are complex quantities = ordered sets.

See nature:

The dualities of energy-time, position-momentum and spin-number must be ordered (?) and naturally we opt for spin. The world is a superposition of all three.

SPIN - NUMBER Arithmetic/Set Theory Pauli principle
ENERGY - TIME Rate of execution of numbers
MOMENTUM - POSITION Geometry=cantor symmetry.

All objects no matter how complex move in space the same way = gravitation.

Work brings order out of chaos. Maximized entropy subject to the constraint on representation which requires duality. As chaos increases in the yin it decreases in the yang and vice versa, so that the value of the commutator is normalized by one unit (independently of the complexity of the operations? No Action of total operation = sum action of sub operations.

The unit of uncertainty. The unit of distance, one action has the measure h or h bar, amounting to the the same thing in h bar omega = h nu.

The unit is measured when we close the loop by doing BA - AB or AB - BA in each case coming back to the starting point A or B. The [ ] difference in action between the two operations is ih bar. The energy associated with an action depends upon the actual states involved, some (like isomorphisms in the nucleus) separated by 100's of MeV and other, like Fermi gas, almost non-existent.

This is the thing I am reaching for, the optimization theorem in Cantor space that corresponds to the Lagrangian approach to finding the actual relationships in

[page 326]

How do we get the Lagrangian into the study of Insight. Via Cantor symmetry. Action integral = integral pdx = integral Edt = integral jdn.

How do we get this bright idea (= Cantor symmetry) from physics into world government? How, in other words, do we learn to calculate with this symmetry. A symmetry is a wormhole in noetic space.

MIND CYBERSPACE vs NOETIC SPACE

The first thing we learn when we apply the Trnsfinite Network to the study of mind is the distinction between cyberspace and noetic space.

CYBERSPACE = physical, countable, communicable
NOETIC SPACE = metaphysical, transfinite, not directly observable (requires decoding)

Signals at the physical level require no decoding. All the electronic equipment simply obeys the laws of physics within certain bounds and

[page 327]

has no interest in the actual sequence of states that it goes through. Quantum system has no memory. True. And false, since exact values of states are remembered through time and space as eigenvalues of certain operators.

Eigenvalues are communicable. Off-eigenvalues are not.

Action of one is the move form one eigenvalue to another.

The minimal action is the shortest route between the two states (or was it the longest, cf path integral method)

PHASE = measure(CONSISTENCY) = proportion of identical steps in the proof/algorithm,

Shortest route is deterministic (error free) using optimum algorithm. Finding optimum algorithm requires noetic invention, since space of possible cyberspaces is transfinite.

The notebooks are sketches of bits and pieces of the beast as it slowly emerges from invisibility.

[page 328]

Social and political minimum action

a) implement policy at minimum cost by 1. good and effective policy 2. efficient management of implementation

POLICY = DESIGN
IMPLEMENTATION = CONSTRUCTION

Cost, ease and utility of the actual implementation depends heavily on the design.

SOFTWARE DESIGN = a) enumerating degrees of freedom b) discovering optimal boundaries between black boxes ie defining nodes and links = objects.

Spirit designs matter for its own convenience. What about black holes, animals etc.

Start straight in with the Lagrangian and speculate about its application to all levels of being through the

[page 329]

Cantor symmetry,

Lagrangian in evolution, cybernetics, mind and theology -> go for the spirit.

STABILITY

What does extremalizing action do in a communication network ie what doe it correspond to? OPTIMAL CODES(?)

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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!)

Aristotle, and H Rackham (translator), Aristotle, XIX, Nichomachean Ethics, Loeb Classical Library 1934 ' . . . This book opened my eyes to the true meaning of "Philosophy". The translation is in modern English, free from the back-to-front syntax of the Ancient Greek text (which makes it impossible to understand the meaning of a sentence until you reach the end of it!). The subject matter is "Ethics". However, a modern author may have called it something more akin to "The Meaning of Life" or "The Art of Living". Aristotle proceeds with simple and clear logic, to reveal the objective of human struggle in this life. He demonstrates a deep understanding of the Human Being, what we are and what we are not, what makes us act in one way or another and what makes us feel joy or distress. He addresses anxienties of the modern human, such as the question of nature or nurture, the moral action versus the practical, violence versus non-violence. His recommendations for living this life in a manner that is meaningfull and rewarding are profound yet simple.. . . ' Agis Liberakis 
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Ashby, W Ross, An Introduction to Cybernetics, Methuen 1964 'This book is intended to provide [an introduction to cybernetics]. It starts from common-place and well understood concepts, and proceeds step by step to show how these concepts can be made exact, and how they can be developed until they lead into such subjects as feedback, stability, regulation, ultrastability, information, coding, noise and other cybernetic topics' 
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Feferman, Anita Burdman, and Solomon Feferman, Alfred Tarski: Life and Logic, Cambridge University Press 2004 Review "A chain smoker, a heavy drinker, a frequent user of 'speed', a relentless womaniser, and a man of Napoleonic self-regard and worldly ambition. This is not how one pictures an eminent Professor of Logic. And yet, this is how the great logician, Alfred Tarski, emerges from this marvellous biography. The Fefermans, of course, are uniquely qualified to lead the reader through the intricacies of Tarski's work, which they do very engagingly and with great expository skill. Tarski's colourful personality is conveyed with prose that is economical, superbly readable and extremely vivid, and the whole book is a joy to read." Ray Monk, Professor of Philosophy, University of Southampton 
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Feynman, Richard P, and Albert P Hibbs, Quantum Mechanics and Path Integrals, McGraw Hill 1965 Preface: 'The fundamental physical and mathematical concepts which underlie the path integral approach were first developed by R P Feynman in the course of his graduate studies at Princeton, ... . These early inquiries were involved with the problem of the infinte self-energy of the electron. In working on that problem, a "least action" principle was discovered [which] could deal succesfully with the infinity arising in the application of classical electrodynamics.' As described in this book. Feynam, inspired by Dirac, went on the develop this insight into a fruitful source of solutions to many quantum mechanical problems.  
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Fowles, John, The Collector, Back Bay Books 1997 Amazon Product Description 'The Collector (1963) is disturbing, engrossing, unforgettable -- the story of an obsessive young man and the girl he kidnaps and holds prisoner in his cellar.' 
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Kolmogorov, A N , and Nathan Morrison (Translator) (With an added bibliography by A T Bharucha-Reid), Foundations of the Theory of Probability, Chelsea 1956 Preface: 'The purpose of this monograph is to give an axiomatic foundation for the theory of probability. . . . This task would have been a rather hopeless one before the introduction of Lebesgue's theories of measure and integration. However, after Lebesgue's publication of his investigations, the analogies between measure of a set and mathematical expectation of a random variable became apparent. These analogies allowed of further extensions; thus, for example, various properties of independent random variables were seen to be incomplete analogy with the corresponding properties of orthogonal functions ... ' 
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Lonergan, Bernard J F, Insight : A Study of Human Understanding (Collected Works of Bernard Lonergan : Volume 3), University of Toronto Press 1992 '... Bernard Lonergan's masterwork. Its aim is nothing less than insight into insight itself, an understanding of understanding' 
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Maxwell, James Clerk, The Scientific Papers of JamesClerk Maxwell Volume 2, Dover Phoenix Editions 2003 Amazon Product Description 'One of the greatest theoretical physicists of the 19th century, James Clerk Maxwell is best known for his studies of the electromagnetic field. These 101 scientific papers, arranged chronologically in two volumes, testify to Maxwell's scientific legacy and offer modern students of mathematics and physics stimulating reading. 197 figures. 39 tables. 1890 edition.'

'Though in the course of ages catastrophes have occurred and may yet occur in the heavens, through ancient systems may be dissolved and new systems evolved out of their ruins, the molecules out of which these systems are built -- the foundation stones [states] of the universe remain unbroken and unworn. They continue this day, as they ere created, perfect in number and measure and weight.' pp 376-77 
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McKeon, Richard, and (editor), The Basic Works of Aristotle, Random 1941 Introduction: 'The influence of Aristotle, in the ... sense of initiating a tradition, has been continuous from his day to the present, for his philosophy contains the first statement, explicit or by opposition, of many of the technical distinctions, definitions, and convictions on which later science and philosophy have been based...' (xi) 
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Nixon, Richard Milhous, The Memoirs of Richard Nixon, Buccaneer Books 1994 Amazon editorial review: 'Former President Richard Nixon's bestselling autobiography is an intensely personal examination of his life, public career, and White House years. With startling candor, Nixon reveals his beliefs, doubts, and behind-the-scenes decisions, and sheds new light on his landmark diplomatic initiatives, political campaigns, and historic decision to resign from the presidency. Throughout his career, Richard Nixon made extensive notes about his ideas, conversations, activities, and meetings. During his presidency, from November 1971 until April 1973, and again in June and July 1974, he kept an almost daily diary of reflections, analyses, and perceptions. These notes and diary dictations, which are quoted throughout this book, provide a unique insight into the complexities of the modern presidency and the great issues of American policy and politics.' 
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Pais, Abraham, 'Subtle is the Lord...': The Science and Life of Albert Einstein, Oxford UP 1982 Jacket: In this ... major work Abraham Pais, himself an eminent physicist who worked alongside Einstein in the post-war years, traces the development of Einstein's entire ouvre. ... Running through the book is a completely non-scientific biography ... including many letters which appear in English for the first time, as well as other information not published before.' 
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Pais, Abraham, Inward Bound: Of Matter and Forces in the Physical World, Clarendon Press, Oxford University Press 1986 Preface: 'I will attempt to describe what has been discovered and understood about the constituents of matter, the laws to which they are subject and the forces that act on them [in the period 1895-1983]. . . . I will attempt to convey that these have been times of progress and stagnation, of order and chaos, of belief and incredulity, of the conventional and the bizarre; also of revolutionaries and conservatives, of science by individuals and by consortia, of little gadgets and big machines, and of modest funds and big moneys.' AP 
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Rawson, Philip, Tantra: Indian Cult of Ecstasy, Crescent 1988 Jacket: 'Suggesting as its final goal a vision of cosmic sexuality, Tantra embodies fundamental patterns of symbolic expression in a view of life which offers a uniquely successful antidote to the anxieties of our time. The act of creation is continuous: therefore sexual intercourse between human beings can be a microcosmic representation of the creative process -- a symbolic tribute to the great Goddess from whose womb, and through whose wisdom, all things in the Universe are manifested in Time.' 
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Tarski, Alfred, Cardinal Algebras, Oxford University Press 1949 'This book is an axiomatic investigation of the novel types of algebraic systems which arise from three sources: the arithmetic of cardinal numbers; the formal properties of the direct product decompositions of algebraic systems; the algebraic aspects of invariant measures, regarded as functions on a field of sets. ... The book is replete with novel algebraic notions; it is written in logical style; all theorems (important and unimportant) are explicitly stated, and the proofs are carefully cross-referenced.' Saunders MacLane 
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Tymoczko, Thomas, New Directions in the Philosophy of Mathematics: An Anthology, Princeton University Press 1998 Jacket: 'The traditional debate among philosophers of mathematics is whether there is an external mathematical reality, something out there to be discovered, or whether mathematics is the product of the human mind. ... By bringing together essays of leading philosophers, mathematicians, logicians and computer scientists, TT reveals an evolving effort to account for the nature of mathematics in relation to other human activities.' 
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van der Waerden, B L, Sources of Quantum Mechanics, Dover Publications 1968 Amazon Book Description: 'Seventeen seminal papers, dating from the years 1917-26, in which the quantum theory as wenow know it was developed and formulated. Among the scientists represented: Einstein,Ehrenfest, Bohr, Born, Van Vleck, Heisenberg, Dirac, Pauli and Jordan. All 17 papers translatedinto English.' 
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Papers
Born, Max, Werner Heisenberg and Paul Jordan, "Zur Quantenmechanik II (On quantum mechanics II)", Zeitschrift fur Physiks, 35, , received November 16, 1925, page 557 - . Translation available in van der Waerden, B L, Sources of Quantum Mechanics, Dover Publications 1968 . back
Callen, Herbert B, Tjheodore A Welton, "Irreversibility and generalized noise", Physical Review, 83, 1, 1951, page 34-40. 'A relation is obtained between the generalized resistance and the fluctuations of the generalized forces in linear dissipative systems. This relation forms the extension of the Nyquist relation for the voltage fluctuations in electrical impedances. The general formalism is illustrated by applications to several particular types of systems, including Brownian motion, electric field fluctuations in the vacuum, and pressure fluctuations in a gas.'. back
Nyquist, Harry, "Thermal Agitation of Electric Charge in Conductors", Physical Review, 32, 1, 1928, page 110-113. 'The electromotive force due to thermal agitation in conductors is calculated by means of principles in thermodynamics and statistical mechanics. The results obtained agree with results obtained experimentally.'. back
Links
Aristotle, , The Internet Classics Archive | On Generation and Corruption by Aristotle, 'Written 350 B.C.E , Translated by H. H. Joachim. ... 'Our next task is to study coming-to-be and passing-away. We are to distinguish the causes, and to state thedefinitions, of these processes considered in general-as changes predicable uniformly of all the things that come-to-be and pass-away by nature. Further, we are to study growth and 'alteration'. We must inquire what each of them is; and whether 'alteration' is to be identified with coming-to-be, or whether to these different names there correspond two separate processes with distinct natures.'' back
Being There - Wikipedia, Being There - Wikipedia, the free encyclopedia , 'Being There is a 1979 American comedy-drama film directed by Hal Ashby, adapted from the 1971 novella written by Jerzy Kosiński. The film stars Peter Sellers, Shirley MacLaine, Melvyn Douglas, Jack Warden, Richard A. Dysart, and Richard Basehart. Douglas won the Academy Award for Best Actor in a Supporting Role and Sellers was nominated for Best Actor in a Leading Role. This was the last Peter Sellers film to be released while he was alive.' back
Dakini - Wikipedia, Dakini - Wikipedia, the free encyclopedia, 'A dakini (Sanskrit: डाकिनी ḍākinī; Tibetan: མཁའ་འགྲོ་མ་ khandroma, Wylie: mkha' 'gro ma, TP: kandroma; Chinese: 空行女) is a tantric deity described as a female embodiment of enlightened energy. In the Tibetan language, dakini is rendered khandroma which means 'she who traverses the sky' or 'she who moves in space'. Sometimes the term is translated poetically as 'sky dancer' or 'sky walker'.' back
Fluctuation dissipation theorem - Wikipedia, Fluctuation dissipation theorem - Wikipedia, the free encyclopedia, 'In statistical physics, the fluctuation dissipation theorem is a powerful tool for predicting the non-equilibrium behavior of a system — such as the irreversible dissipation of energy into heat — from its reversible fluctuations in thermal equilibrium. The fluctuation dissipation theorem applies both to classical and quantum mechanical systems. Although formulated originally by Nyquist in 1928, the fluctuation-dissipation theorem was first proved by Herbert B. Callen and Theodore A. Welton in 1951.

The fluctuation dissipation theorem relies on the assumption that the response of a system in thermodynamic equilibrium to a small applied force is the same as its response to a spontaneous fluctuation. Therefore, there is a direct relation between the fluctuation properties of the thermodynamic system and its linear response properties. Often the linear response takes the form of one or more exponential decays.' back

Piety - Wikipedia, Piety - Wikipedia, the free encyclopedia, 'The word piety comes from the Latin word pietas, the noun form of the adjective pius (which means "devout" or "good"). Pietas in traditional Latin usage expressed a complex, highly valued Roman virtue; a man with pietas respected his responsibilities to other people, gods and entities (such as the state), and understood his place in society with respect to others.' back
Pontifical Catholic University of Chile - Wikipedia, Pontifical Catholic University of Chile - Wikipedia,.the free encyclopedia, 'The Pontifical Catholic University of Chile (UC or PUC) (Spanish: Pontificia Universidad Católica de Chile) is one of the six Catholic Universities existing in the Chilean university system and one of the two Pontifical Universities in the country, along with the Pontifical Catholic University of Valparaíso. It is also one of Chile's oldest universities and one of the most recognized educational institutions in Latin America. Since it is a Pontifical University, it has always had a strong and very close relationship with the Vatican. It was founded on June 21, 1888 through a decree issued by the Santiago Archbishop. Its first chancellor was Monsignor Joaquín Larraín Gandarillas, and at the very beginning, the university only taught two subjects, law and mathematics. It is part of the Universities of the Rectors' Council of Chilean Universities, and although it is not state-owned, a substantial part of its budget is given by state transferences under different concepts.' back
René Thom - Wikipedia, Rene Thom - Wikipedia, the free encyclopedia, René Frédéric Thom (September 2, 1923 – October 25, 2002) was a French mathematician. He made his reputation as a topologist, moving on to aspects of what would be called singularity theory; he became world-famous among the wider academic community and the educated general public for one aspect of this latter interest, his work as founder of catastrophe theory (later developed by Erik Christopher Zeeman). He received the Fields Medal in 1958.' back
Rudolf Clausius - Wikipedia, Rudolf Clausius - Wikipedia, the free encyclopedia, 'Rudolf Julius Emanuel Clausius (Born Rudolf Gottlieb,[1] January 2, 1822 – August 24, 1888), was a German physicist and mathematician and is considered one of the central founders of the science of thermodynamics.[2] By his restatement of Sadi Carnot's principle known as the Carnot cycle, he put the theory of heat on a truer and sounder basis. His most important paper, On the mechanical theory of heat, published in 1850, first stated the basic ideas of the second law of thermodynamics. In 1865 he introduced the concept of entropy.' back

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