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vol VII: Notes



[Notebook BOOK 4/5/94]

[Sunday 9 May 1999 - Saturday 15 May 1999]

Sunday 9 May 1999
Monday 10 May 1999
Tuesday 11 May 1999

[page 282]

We may look at transfinite numbers in terms of subsets (power sets) and permutations.

[Empirical residue] . . . The nature of insight, since it is relative to data and context, means that we cannot definitely assert that a set of facts do not have intelligibility. Lonergan In fact the whole art of Agatha Christie detective stories [and the like] is to bury the relevant evidence in the narrative so as not to call attention to it, so that the reader may be more surprised when the denouement comes.

Quantum Field Theory view of the world. Feynman diagrams = trees of relationships between events.

PATHS through the NETWORK

[page 283]

QFT gives us a glimpse of the transfinite structure of the Universe, in fact UNCERTAINTY does. Have to give this a lot of deep thought and get Lonergan, Weinberg, Dirac, Bell and other authors in harmony.

Model of insight - DECODE = MAP
Model of meaning - MAP = DECODE

This means that what?

Evolution- every little detail from the Planck scale up has been selected from a virtual infinity of possibilities, and so has deep meaning through rich relationships to the selective forces that shaped it.

Once we get the overall picture right, we can proceed brick by brick in full certainty, which is more certain than flimsy but virtuoso structures with little overall planning.

. . .

[page 284]

. . .

With enough observation we can sample almost all the states in a superposition.

Superposition is a parallel representation which can be read out serially (either at random or in an ordered manner (?). This is exciting, ie it allows a state to change to a state of lower energy, releasing that energy, which can move another state or set of states to a higher energy.

. . .

Love of god is love of the superposition of all states (which presumably cancels to the infinite nothing).

[page 285]


The full Cantor expansion of the real line is isomorphic to the exploding Universe, or less dramatically the growing Universe (an explosion being something that grows very fast).

This expansion is decreed by general relativity which must therefore be acting as a bound on the quantum behaviour of the Universe (causing the wave function of the Universe to evolve in a way that looks to its inhabitants (eg us) as though it is expanding.

Gradually the thought experiments cooked up by the patriarchs of quantum mechanics to give their fanciful equations some contact with reality are being performed in the laboratory, using exquisite control over quantum states to construct specific wave functions and watch them in action. cf QM Picture Book Brandt & Dahmen

Reading Evolution of Mind. Cummins


Modelling insight. To understand is to decode, that is to find the meaning of, that is to find the relationships

[page 286]

to. In this model we model meaning by the set theoretical operation of mapping.

The initial chapter [of MA] takes Lonergan's concepts and maps them onto the computational model.

By insight we see the relationships between the data. Let us look more closely at Lonergan's dramatic instance. Archimedes has a problem. What to do. He seeks a process to solve his problem, that is to make it go away. Such a process was an algorithm. What he needs is a procedure to test whether or not the crown is real gold. How to discriminate? Density. How to measure density? This is the procedure we want. For a start we need a bit of gold of guaranteed purity, a standard. How to compare the crown to the standard? Weight them in and out of water. Why? the denser object will have less volume per unit mass.

Our starting point is Insight.

Wednesday 12 May 1999

[page 287]

Thursday 13 May 1999

Check relationships between empirical residue and computability.

One has only to consider its attitudes to human equality to see that the RCC is too narrow a space to contain the modern human spirit (eg authoritarianism and sexism). Keep cool for the comprehensive demolition and reconstruction of all this.

. . . Consequences of this result for Lonergan's model of the world. It is too small. It sees intellect and intelligence as the outputs of uniprocesses, not parallel processes.

We have introduced elements of a model that can describe intelligence as a parallel process. The structure of this model is very simple but the beauty of it is that it is the natural habitat of computing machines.

The old hierarchy of input/decision/output is converted into a loop. Lonergan correctly perceived the recursive nature of intellect within itself

[page 288]

but failed to see that this recursion continues down into the quantum area at the moment of the big bang and up towards what Teillhard de Chardin called the Omega Point and we might call the aleph of time.

A space has entropy. A point in space carries information.

One space on a CD carries one bit of information. Much more information is carried by the location of that bit among all the other bits on the CD. It is one in an ordered sequence of 600M symbols.

One big result we want is that parallel (network) processes have an intrinsic power beyond that the Turing Machines, so that a network can do creative things beyond the reach of determinism. Davis describes a Turing machine that can accept instructions from outside. Does this add to the universality of the universal computer?

. . .

[page 289]

Intro of the idea that [Lonergan's] idea of intellect and intelligence is too narrow and must be expanded into a network and hierarchical concept seems to be an excellent theme for the thesis.

Empirical Residue resembles the 'end of science' outlook, something that seems firmly rejected by the never ending complexity that each scientific observation yields. Horgan

The running engine is the superposition of all the states that its mechanical and other components can occupy.

Parallel processing is indicated in any situation where people work together to achieve more than they can alone.

Friday 14 May 1999

. . .

And what was it that I thought of on the way out the drive this morning? Each little entity is conscious to me for only a short

[page 290]

time and then flashes by, to be recovered at come indefinite time in the future.

Conscious awareness is a particular observation of the superposition we call mind.

integral superposition d index = personality of the thing.

So are all integrations with respect to a discrete variable, ie are all integrals sums of series (with n, aleph(0), aleph(1) etc terms)

Lesbegue integration only works in a Cantor space since measure(aleph(n)) = 0 in the set aleph(n+1)

In the end all communication must be digital (symbolic) because acts of communication are a) nested and b) of finite duration. See proof the binary is most error resistant in Gatlin(?), maybe Wiener. Gatlin, Wiener

Saturday 15 May 1999

Empirical residue corresponds to prime matter


nec quid nec quale nec quantum nec aliquid eorum quibus ens determinatur.

Corresponding to the numinous feeling I used to have about the Roman Catholic Church (which we now model as a very long established business deeply encrusted with tradition) is something special about the metaphysical concepts I learnt within the church such as being, act power, in fact the "transcendentals" ens res aliquid unum verum bonum, which now need to be seen naked as symbols in a model, to be manipulated according to the rules of the model. Such a model is the output of insight, which is seen in Lonergan Aristotle and Thomas as an abstraction process revealing the essence of the thing understood (eg that all points on the circumference of a wheel are equidistant from the centre of the axle etc.

Insight into the symbolic.


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Further reading


Click on the "Amazon" link below each book entry to see details of a book (and possibly buy it!)

Bell, John S, Speakable and Unspeakable in Quantum Mechanics, Cambridge University Press 1987 Jacket: JB ... is particularly famous for his discovery of a crucial difference between the predictions of conventional quantum mechanics and the implications of local causality ... This work has played a major role in the development of our current understanding of the profound nature of quantum concepts and of the fundamental limitations they impose on the applicability of classical ideas of space, time and locality. 
Brandt, Siegmund, and Hans Dieter Dahmen, The Picture Book of Quantum Mechanics, Springer-Verlag 1995 Jacket: 'This book is an introduction to the basic concepts and phenomena of quantum mechanics. Computer-generated illustrations are used extensively throughout the text, helping to establish the relation between quantum mechanics on one side and classical physics ... on the other side. Even more by studying the pictures in parallel with the text, readers develop an intuition for notoriously abstract quantum phenomena ...' 
Churchill, Winston S, Arms and the Covenant: Speeches on Foreign Affairs andNational Defence, George G. Harrap And Co. Ltd 1938 ' The precursor to Churchill's great war speeches. A collection of speeches spanning the years 1928 to 1938 criticizing British foreign policy and warning prophetically of the coming danger. Churchill bibliographer Frederick Woods called this book "probably the most crucial volume of speeches that he ever published."' Churchill Book Collector 
Cummins, Denise Dellarosa, and Colin Allen (editors), The Evolution of Mind, Oxford University Press 1998 Introduction: 'This book is an interdisciplinary endeavour, a collection of essays by ethologists, psychologists, anthropologists and philosophers united in the common goal of explaining cognition. . . . the chief challenge is to make evolutionary psychology into an experimental science. Several of the chapters in this volume describe experimental techniques and results consistent with this aim; our hope and intention is that they lead by example in the development of evolutionary psychology from the realm of speculation to that of established research program' 
Feynman, Richard P, and Robert B Leighton, Matthew Sands, The Feynman Lectures on Physics (volume 3) : Quantum Mechanics, Addison Wesley 1970 Foreword: 'This set of lectures tries to elucidate from the beginning those features of quantum mechanics which are the most basic and the most general. ... In each instance the ideas are introduced together with a detailed discussion of some specific examples - to try to make the physical ideas as real as possible.' Matthew Sands 
Gatlin, Lila L, Information Theory and the Living System, Columbia University Press 1972 Chapter 1: 'Life may be defined operationally as an information processing system -- a structural hierarchy of functioning units -- that has acquired through evolution the ability to store and process the information necessary for its own accurate reproduction. The key word in the definition is information. This definition, like all definitions of life, is relative to the environment. My reference system is the natural environment we find on this planet. However, I do not think that life has ever been defined even operationally in terms of information. This entire book constitutes a first step towar dsuch a definition.' 
Horgan, John, The End of Science: Facing the Limits of Knowledge in the Twilight of the Scientific Age, Little Brown and Co 1996 Amazon Editorial Review From Publishers Weekly 'Scientific American columnist Horgan here interviews an impressive array of scientists and philosophers, who seem sharply divided over the prospects and possibilities of science. Among the pessimists, molecular biologist Gunther Stent suggests that science is reaching a point of incremental, diminishing returns as it comes up against the limits of knowledge; philosopher Thomas Kuhn sees science as a nonrational process that does not converge with truth; Vienna-born thinker Paul Feyerabend objects to science's pretensions to certainty and its potential to stamp out the diversity of human thought and culture. More optimistic are particle physicist Edward Witten, pioneer of superstring theory (which posits a universe of 10 dimensions); robotics engineer Hans Moravec, who envisions superintelligent creative robots; and physicist Roger Penrose, who theorizes that quantum effects percolating through the brain underlie consciousness. Other interviewees are Francis Crick, Noam Chomsky, David Bohm, Karl Popper, Murray Gell-Mann, Sheldon Glashow, Ilya Prigogine and Clifford Geertz. Despite the dominant doomsaying tone, this colloquium leaves much room for optimism.' Copyright 1996 Reed Business Information, Inc. 
Knightley, Phillip, Philby: KGB Master Spy, Pan Books 1989 Back Cover: 'The name Kim Philby has become synonymous with the most amazing exploits in the history of espionage.

Agent, double agent, traitor, enigma. Few knew the real man behind the impenetrable facade that for years fooled British Intelligence, the CIA and the FBI. After Philby defected to Russio in 1968 he maintained a code of silence for 25 years - until a few weeks before his death.

Then, in an unprecedented move, he invited journalist Phillip Knightley to his Moscow apartment, and in six days of conversation he bared his sour as never before. He told of his childhood, the influence of his extraordinary father and the events that lead him inexorably to turn traitor.

For the first time, Philby - KGB Masterspy tells the full story -- before and after defection. Through his views on everything from loyalty and patriotism to pop muic and Margaret Thatcher, revelation after revelation combine to build a unique picture of the most notorious spy of the 20th Century, a tale that rivals the best spy fiction.  

Liddell, and Scott, A Lexicon: Abridged from Liddell and Scott's Greek-English Lexicon, Clarendon Press 1963 Advertisement: 'The Abridgement of Liddell and Scott's Greek-English Lexicon is intended chiefly for use in Schools. It has been reduced to its present compass by the omission I. Of passages cited as authorities .. II. Of discussions upon the Derivation of words; III. Of words used only by authors not read in Schools ... ' 
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' 
Misner, Charles W, and Kip S Thorne, John Archibald Wheeler, Gravitation, Freeman 1973 Jacket: 'Einstein's description of gravitation as curvature of spacetime led directly to that greatest of all predictions of his theory, that the universe itself is dynamic. Physics still has far to go to come to terms with this amazing fact and what it means for man and his relation to the universe. John Archibald Wheeler. . . . this is a book on Einstein's theory of gravity. . . . ' 
Orwell, George, Homage to Catalonia, Mariner Books 1980 Review '"I wonder what is the appropriate first action when you come from a country at war and set foot on peaceful soil. Mine was to rush to the tobacco-kiosk and buy as many cigars and cigarettes as I could stuff into my pockets." Most war correspondents observe wars and then tell stories about the battles, the soldiers and the civilians. George Orwell--novelist, journalist, sometime socialist--actually traded his press pass for a uniform and fought against Franco's Fascists in the Spanish Civil War during 1936 and 1937. He put his politics and his formidable conscience to the toughest tests during those days in the trenches in the Catalan section of Spain. Then, after nearly getting killed, he went back to England and wrote a gripping account of his experiences, as well as a complex analysis of the political machinations that led to the defeat of the socialist Republicans and the victory of the Fascists.' 
Polya, George, and Gordon Latta, Complex Variables, John Wiley & Sons Inc 1974 Preface: 'After having lectured for several decades on complex variables to prospective engineers and physicists, I have definite and, I hope, not unrealistic ideas about their requirements and preferences. . . .

I hope that this book is useful not only to future engineers and physicists, but also to future mathematicians. Mathematical concepts and facts gain in vividness and clarity if they are well connected with the world around us and with general ideas, and if we obtain them by our own work through successive stages instead of in one lump.' 

von Neumann, John, and Robert T Beyer (translator), Mathematical Foundations of Quantum Mechanics, Princeton University Press 1983 Jacket: '. . . a revolutionary book that caused a sea change in theoretical physics. . . . JvN begins by presenting the theory of Hermitean operators and Hilbert spaces. These provide the framework for transformation theory, which JvN regards as the definitive form of quantum mechanics. . . . Regarded as a tour de force at the time of its publication, this book is still indispensable for those interested in the fundamental issues of quantum mechanics.' 
Wiener, Norbert, Cybernetics or control and communication in the animal and the machine, MIT Press 1996 The classic founding text of cybernetics. 
Zee, Anthony, Quantum Field Theory in a Nutshell, Princeton University Press 2003 Amazon book description: 'An esteemed researcher and acclaimed popular author takes up the challenge of providing a clear, relatively brief, and fully up-to-date introduction to one of the most vital but notoriously difficult subjects in theoretical physics. A quantum field theory text for the twenty-first century, this book makes the essential tool of modern theoretical physics available to any student who has completed a course on quantum mechanics and is eager to go on. Quantum field theory was invented to deal simultaneously with special relativity and quantum mechanics, the two greatest discoveries of early twentieth-century physics, but it has become increasingly important to many areas of physics. These days, physicists turn to quantum field theory to describe a multitude of phenomena. Stressing critical ideas and insights, Zee uses numerous examples to lead students to a true conceptual understanding of quantum field theory--what it means and what it can do. He covers an unusually diverse range of topics, including various contemporary developments,while guiding readers through thoughtfully designed problems. In contrast to previous texts, Zee incorporates gravity from the outset and discusses the innovative use of quantum field theory in modern condensed matter theory. Without a solid understanding of quantum field theory, no student can claim to have mastered contemporary theoretical physics. Offering a remarkably accessible conceptual introduction, this text will be widely welcomed and used.  
Shannon, Claude E, "Communication in the Presence of Noise", Proceedings of the IEEE, 86, 2, February 1998, page 447-457. Reprint of Shannon, Claude E. "Communication in the Presence of Noise." Proceedings of the IEEE, 37 (January 1949) : 10-21. 'A method is developed for representing any communication system geometrically. Messages and the corresponding signals are points in two function spaces, and the modulation process is a mapping of one space into the other. Using this representation, a number of results in communication theory are deduced concerning expansion and compression of bandwidth and the threshold effect. Formulas are found for the maximum rate of transmission of binary digits over a system when the signal is perturbed by various types of noise. Some of the properties of "ideal" systems which transmit this maximum rate are discussed. The equivalent number of binary digits per second of certain information sources is calculated.' . back
Alfred Tarski - Wikipedia, Alfred Tarski - Wikipedia, the free encyclopedia, 'Alfred Tarski (January 14, 1901, Warsaw, Russian-ruled Poland – October 26, 1983, Berkeley, California) was a Polish logician and mathematician. . . .

His biographers Anita and Solomon Feferman state that, "Along with his contemporary, Kurt Gödel, he changed the face of logic in the twentieth century, especially through his work on the concept of truth and the theory of models."' back

Brouwer fixed point theorem - Wikipedia, Brouwer fixed point theorem - Wikipedia, the free encyclopedia, 'Brouwer's fixed-point theorem is a fixed-point theorem in topology, named after Luitzen Brouwer. It states that for any continuous function f with certain properties there is a point x0 such that f(x0) = x0. The simplest form of Brouwer's theorem is for continuous functions f from a disk D to itself. A more general form is for continuous functions from a convex compact subset K of Euclidean space to itself. back
Catholic Church - Wikipedia, Dominican Order - Wikipedia, the free encyclopedia, 'The Order of Preachers (Latin: Ordo Praedicatorum), after the 15th century more commonly known as the Dominican Order or Dominicans, is a Catholic religious order founded by Saint Dominic and approved by Pope Honorius III (1216-27) on 22 December 1216 in France. Membership in the Order includes friars, congregations of active sisters, and lay persons affiliated with the order (formerly known as tertiaries, now Lay or Secular Dominicans).' back
Cauchy-Riemann equations - Wikipedia, Cauchy-Riemann equations - Wikipedia, the free encyclopedia, 'In mathematics, the Cauchy–Riemann differential equations in complex analysis, named after Augustin Cauchy and Bernhard Riemann, consist of a system of two partial differential equations that provides a necessary and sufficient condition for a differentiable function to be holomorphic in an open set. This system of equations first appeared in the work of Jean le Rond d'Alembert (d'Alembert 1752). Later, Leonhard Euler connected this system to the analytic functions (Euler 1777). Cauchy (1814) then used these equations to construct his theory of functions. Riemann's dissertation (Riemann 1851) on the theory of functions appeared in 1851.' back
Complex number - Wikipedia, Complex number - Wikipedia, the free encyclopedia, 'IA complex number is a number that can be expressed in the form a + bi, where a and b are real numbers and i is the imaginary unit, which satisfies the equation i2 = −1. In this expression, a is the real part and b is the imaginary part of the complex number. Complex numbers extend the concept of the one-dimensional number line to the two-dimensional complex plane (also called Argand plane) by using the horizontal axis for the real part and the vertical axis for the imaginary part.' back
Felix Klein - Wikipedia, Felix Klein - Wikipedia, the free encyclopedia, 'Felix Christian Klein (25 April 1849 – 22 June 1925) was a German mathematician, known for his work in group theory, function theory, non-Euclidean geometry, and on the connections between geometry and group theory. His 1872 Erlangen Program, classifying geometries by their underlying symmetry groups, was a hugely influential synthesis of much of the mathematics of the day.' back
Holy See, Congregation for the Evangelization of Peoples - Index, '1. Con la Bolla Inscrutabili Divinae, (22 giugno 1622) emanata da Papa Gregorio XV, ebbe inizio il periodo costitutivo della Congregazione, con il nome de Propaganda Fide, cui fecero seguito altri documenti pontifici fondamentali: Romanum decet (con la medesima data), Cum inter multiplices (14 dicembre 1622), Cum nuper (13 giugno 1623), ed infine Immortalis Dei (1° agosto 1627).' back
John Palmer - Parmenides, Parmenides (Stanford Encyclopedia of Philosophy), First published Fri Feb 8, 2008 'Parmenides of Elea, active in the earlier part of the 5th c. BCE., authored a difficult metaphysical poem that has earned him a reputation as early Greek philosophy's most profound and challenging thinker. His philosophical stance has typically been understood as at once extremely paradoxical and yet crucial for the broader development of Greek natural philosophy and metaphysics. He has been seen as a metaphysical monist (of one stripe or another) who so challenged the naïve cosmological theories of his predecessors that his major successors among the Presocratics were all driven to develop more sophisticated physical theories in response to his arguments.' back
MS-DOS - Wikipedia, MS-DOS - Wikipedia, the free encyclopedia, 'MS-DOS (pronounced . . . em-es-dos; short for MicroSoft Disk Operating System) is an operating system for x86-based personal computers, which was purchased by Microsoft. It was the most commonly used member of the DOS family of operating systems, and was the main operating system for personal computers during the 1980s up to mid 1990s.' back is maintained by The Theology Company Proprietary Limited ACN 097 887 075 ABN 74 097 887 075 Copyright 2000-2014 © Jeffrey Nicholls