vol 7: Notes
2005
Sunday 15 May
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... to restore theology to the mainstream of science
Notes
[Notebook: DB 57 Language]
[Sunday 15 May 2005 - Saturday 21 May 2005]
[page 141]
Sunday 15 May 2005
Life of Pi Martel
Martel page 49: The Bank of Karma
Turing page 248: Computing machines join seamlessly and give us a paradigm for understanding the unity of dynamic systems comprising a multiplicity of atomic acts of 'motions'. Turing
Martel Pi page 64: 'They didn't know I was a practicing Hindu, Christian and Muslim
page 77: 'people move n the hope of a better life'
Monday 16 May 2005
Cantor's continuum exists in a Euclidian (or locally analogous) metric space. We seek a logical continuum where distance is measured by the number of logical operations between one form (ordered set of symbols) and another (a 'Hamming distance'). This measure of distance depends to some extent on the algorithm used to make the
[page 142]
transformation whereby the distance is measured. The space in which we measure this is the ;transfinite network' which we might consider a noetic (computational) measure space. This space allows us to measure the distance between two minds, two religions and so on.
We've been through a few paradigm shifts since the first well documented paradigms in our history, the work of the ancient Greek scientists from Parmenides via Zeno, Pythagoras, Socrates, Plato, Aristotle through to the beginnings of Christianity. Then , of course, Christianity, founded in the authors of the Bible. Christianity became coterminous with the Roman Empire. Then Christianity went dark for a while and the Arabic world shone and began to nibble way at Christian territory in North Africa, Spain and the Middle East. Christianity made a comeback in the middle ages, fired by political and militant Popes and the rediscovery of Ancient Greece through Arabic tradition. Then Reformation, Renaissance, Enlightenment (secularism, human rights, rule of law, democracy)
Variable depth network: The boundary between transfinite numbers is a software thing. The higher number is created by permuting the lower. The observable world permutes within the bounds of countable unitarity - ie the total number of 'simultaneous' quantum events in the universe is countable, and in the local universe finite. Every level on the scale of complexity looks pretty much the same. What is important is their ordering - what sits on what. Object oriented programming.
[page 143]
We are looking for a structure which is large enough to capture the universal process, event by event, from the beginning and forever, and our candidate, as ever, is the transfinite network.
Theodosius Dobzhansky: 'Nothing in biology makes sense except in the light of evolution.' Dobzhansky
'The wave function of the universe' Everett
The transfinite network is a model of everything (theory)
Tuesday 17 May 2005
Meaning = 1/frequency.
FREQUENCY is not arbitrary but is determined by constraints on stationary states, as in the atom. These constraints are unitarity and computability = observability = halting = 'emission of a quantum = sending a message. Computability also corresponds to the 'collapse of the wave function' or the diagonalization of a matrix, ie the discovery of a set of eigenfunctions of the matrix and of their corresponding eigenvalues. So the frequency of impossible events is zero and the continued existence of the universe in some form we take to be 1. Intermediate forms (like me) have intermediate frequencies.
GENERAL RELATIVITY
General covariance : things that are true in a network regardless of the actual messages being transmitted.
[page 144]
Very rarely are our relationships with another person completely tranquil. There are disagreements at all scales from imperceptible to murderous at a range of frequencies from 1 to 1/aleph(0) (like earthquakes. Highly inconsistent (violent) (fatal) events are rarer. We have long felt that consistency and probability are related by whether waves are in or out of phase (corresponding to canceling one another). So the probability of an event is |phi| 2 .
The transfinite numbers give us a framework big enough to correspond to every event in the universe.
Cantor began geometrically wondering how many points can fit into the natural like, but he ended up algebraically and arithmetically in whole new world of numbers transcending aleph(1) = 2 aleph(0), the assumed cardinal of the line.
Despite their huge size, 'resolution' in the transfinite cardinals is the same as the naturals, insofar as they proceed by distinct steps from aleph(n) to aleph(n+1) with nothing in between, just like the naturals. They have a sort of rounding expressed by the equation 2aleph(0) - aleph(0) aleph(0) = aleph(1) > aleph(0). Only transfinite exponentiation can carry us from one transfinite number to another; all other arithmetic operations are 'nilpotent'
. Transfinite exponentiation is an infinite task, expressed by Cantor as 'covering' (Belegung).
The transfinite tree has its leaves in the present and gives us a way to represent the pedigree of every event back to the initial singularity.
[page 145]
While 4-space is adequate to map the events a the physical level, transfinite dimensional function space is necessary to express the meaning of the events.
In the transfinite network, all communications come down to the countable physical layer (what about quantum teleportation?), which acts as a bottleneck, so that no matter how transcendent and complex my mind may be, you can only see it through the finite means of these words.
Unitarity = conservation of probability tells us that the universe is 'full' from physical point of view (pleroma, pure act) - as much is happening as can possibly happen, and if one thing happens it excludes their possible outcomes.
The human social network runs on language, human language, spoken, written, the language of love, body language, and all the languages that belong to more general animal biological and physical layers. As we move from society to society we encounter a large set of human languages, although the gradual coalescence of small human groups into large ones has led to the fading and death of many small languages. Collectively, all the protocols of the human social network are here known as religion [culture?]
Many levels of complexity flow through me, the molecules I breath, eat, drink and secrete through many different channels.
Agatha Zero page 130: Truth easier than lies, more efficient, more stable, more conducive to fitness. Christie But one can always defect to advantage on an efficient system, put less in, take
[page 145]
more out.
Wednesday 18 May 2005
Thursday 19 May 2005
Friday 20 May 2005
The critical prerequisite for efficient management is global perspective. This is the role of the directors who for that reason do not involve themselves in the day to day detail, but try to simplify things down to the big picture.
Mathematical induction is a symmetry with respect to complexity.
CARDINAL = SIZE
ORDINAL = COMPLEXITY
We learn the cardinal number of a set (and its minimum ordinal number) by compressing it until it can be compressed no more (Chaitin, Shannon). The difference between the transfinite cardinals is that while aleph(n) is the alphabet for aleph(n+1), all the information in aleph(n+1) cannot be compressed down to aleph(n)
Is the space of mathematics one or many? It is one insofar as any structure can be transformed into any other (vie for instance arithmetic (Goedel) or a computing machine (Turing)
Abstraction - renormalization group - reducing complexity while retaining meaning - translation of mind to language. Wilson
Infinity means without a boundary, but does not say anything about size, only no boundary (open)
[page 147]
Although a consensus takes time to evolve, the evolution does not even start until someone comes up with a nucleus around which consensus can accrete; in other words, something that everyone can recognize as honestly capturing their point of view.
Dauben/Cantor: 'Russell ... affirmed the ultimate reduction of all mathematics to purely logical principles. ... Mathematics for the logician, concerned only the proper use of symbols'. [ie communicating according to established protocols.
Catholicism is noetically normative, as the old dictionaries used to be lexicographically normative. No more. Science must now follow reality, not direct it. This is the role of technology.
Saturday 21 May 2005
Further reading
Books
| Christie, Agatha, Toward Zero, Berkley Publishing Group 1998 Jacket: '"I like a good detective story, but they begin in the wrong place! They begin with the murder. But the murder is the end. The story begins long before that." So remarks esteemed criminologist Mr Treves. Truer words have never been spoken, for a psychopathic killer has insinuated himself, with cunning manipulation, into a quiet village on the river Tern. But who is his intended victim? What are his unfathomable motives? And how and when will he reach the point of murder ... the zero point? In this ingenious and noteworthy departure for Agatha Christie, it is the intricate workings of a pathological mind that become the stuff of startling mystery as a group of friends at a seaside resort remain blithely unaware that their weekend will be the death of them all ...' Amazon back |
| Everett, Hugh, and Bryce S Dewitt, Neill Graham (editors), The Many Worlds Interpretation of Quantum Mechanics, Princeton University Press 1973 Jacket: 'A novel interpretation of quantum mechanics, first proposed in brief form by Hugh Everett in 1957, forms the nucleus around which this book has developed. The volume contains Dr Everett's short paper from 1957, "'Relativge State' formulation of quantum mechanics" and a far longer exposition of his interpretation entitled "The Theory of the Universal Wave Function" never before published. In addition other papers by Wheeler, DeWitt, Graham, Cooper and van Vechten provide further discussion of the same theme. Together they constitute virtually the entire world output of scholarly commentary on the Everett interpretation.' Amazon back |
| Martel, Yann, The Life of Pi, Harcourt 2002 Editorial Reviews Amazon.com: 'Yann Martel's imaginative and unforgettable Life of Pi is a magical reading experience, an endless blue expanse of storytelling about adventure, survival, and ultimately, faith. The precocious son of a zookeeper, tries on various faiths for size, attracting "religions the way a dog attracts fleas." Planning a move to Canada, his father packs up the family and their menagerie and they hitch a ride on an enormous freighter. After a harrowing shipwreck, Pi finds himself adrift in the Pacific Ocean, trapped on a 26-foot lifeboat with a wounded zebra, a spotted hyena, a seasick orangutan, and a 450-pound Bengal tiger named Richard Parker ("His head was the size and color of the lifebuoy, with teeth"). It sounds like a colorful setup, but these wild beasts don't burst into song as if co-starring in an anthropomorphized Disney feature. After much gore and infighting, Pi and Richard Parker remain the boat's sole passengers, drifting for 227 days through shark-infested waters while fighting hunger, the elements, and an overactive imagination. In rich, hallucinatory passages, Pi recounts the harrowing journey as the days blur together, elegantly cataloging the endless passage of time and his struggles to survive: "It is pointless to say that this or that night was the worst of my life. I have so many bad nights to choose from that I've made none the champion." Amazon back |
Papers
| Chaitin, Gregory J, "Randomness and Mathematical Proof", Scientific American, 232, 5, May 1975, page 47-52. 'Although randomness can be precisely defined and can even be measured, a given number cannot be proved random. This enigma establishes a limit in what is possible in mathematics'. back |
| Dobzhansky, Theodosius, "Nothing in Biology Makes Sense Except in the Light of Evolution", American Biology Teacher, 35, 3, 12 November 1937, page 125-129. Concluding paragraph: 'One of the great thinkers of our age, Pierre Teilhard de Chardin, wrote the following: "Is evolution a theory, a system, or a hypothesis? It is much more it is a general postulate to which all theories, all hypotheses, all systems much henceforward bow and which they must satisfy in order to be thinkable and true. Evolution is a light which illuminates all facts, a trajectory which all lines of though must follow this is what evolution is." Of course, some scientists, as well as some philosophers and theologians, disagree with some parts of Teilhard's teachings; the acceptance of his worldview falls short of universal. But there is no doubt at all that Teilhard was a truly and deeply religious man and that Christianity was the cornerstone of his worldview. Moreover, in his worldview science and faith were not segregated in watertight compartments, as they are with so many people. They were harmoniously fitting parts of his worldview. Teilhard was a creationist, but one who understood that the Creation is realized in this world by means of evolution.'. back |
| Goedel, Kurt, "On formally undecidable problems of Principia Mathematica and related systems I", Monatshefte fur Mathematik und Physic, 38, , 1931, page 173-198. Reprinted in Goedel, Kurt, Kurt Goedel: Collected Works Volume 1 Publications 1929-1936, Oxford UP 1986 pp 144-195. Amazon. back |
| Shannon, Claude E, "The mathematical theory of communication", Bell System Technical Journal, 27, , July and October, 1948, page 379-423, 623-656 . back |
| Turing, Alan, "On Computable Numbers, with an application to the Entscheidungsproblem", Proceedings of the London Mathematical Society, 2, 42, 12 November 1937, page 230-265. 'The "computable" numbers maybe described briefly as the real numbers whose expressions as a decimal are calculable by finite means. Although the subject of this paper is ostensibly the computable numbers, it is almost as easy to define and investigate computable functions of an integrable variable or a real or computable variable, computable predicates and so forth. The fundamental problems involved are, however, the same in each case, and I have chosen the computable numbers for explicit treatment as involving the least cumbrous technique. I hope shortly to give an account of the rewlations of the computable numbers, functions and so forth to one another. This will include a development of the theory of functions of a real variable expressed in terms of computable numbers. According to my definition, a number is computable if its decimal can be written down by a machine'. back |
| Wilson, Kenneth G, "The Renormalisation Group and Critical Phenomena", Reviews of Modern Physics, 55, , July 1983, page 583. back |
Links
| Kenneth G Wilson The Renormalisation Group and Critical Phenomena Nobel Prize Lecture, 8 December 1982 back |
Click on an "Amazon" link in the booklist at the foot of the page to buy the book, see more details or search for similar items
Related sites:
Concordat Watch
Revealing Vatican attempts to propagate its religion by international treaty
