vol 7: Notes
2006
Sunday July
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... to restore theology to the mainstream of science
Notes
[Notebook: DB 59 Draughts]
[Sunday 9 July 2006 - Saturday 15 July 2006]
Sunday 9 July 2006
[page 60]
Monday 10 July 2006
Dirac Page 80: dynamical variables referring to different degrees of freedom commute' so that a message string that gives a sequence of values of independent degrees of freedom is an observable. Dirac
As in quantum mechanics, we can distinguish an abstract communication C from its representation (in Greek, English, mathematics, etc)
Can we say that communicating entities are entangled?
[page 61]
We may think of the difference between dictatorship and democracy in terms of specific heats, where dictatorship suppresses individual human degrees of freedom, giving low heat capacity, while democracy reveals individual degrees of freedom, leading to high specific hear, ie a small temperature change for a large input of energy (fluctuation, tsunami, etc). We can imagine almost all disasters as sudden releases of energy, bomb, earthquake, etc.
Since the two slit experiment works an electron at a time, we can say that the electron interferes with itself and say the same for the initial particle n the universe, whose self-interference (communication, consciousness) has given us what exists now.
Light cone: everything that we can see can influence our current state, which can be generalized to 'communication cone',
Conversation between independent entities (degrees of freedom) is observable [to them, but maybe to noone else - quantum cryptography]
Dirac writes: 'We assume on physical grounds hat the total energy of a system is always observable. For an isolated system, it is constant and may then be written H. Even when it is not a constant we shall often write it simply H, leaving its dependence on t understood. If the energy depends on t, it means the system is acted upon by external forces. An action of this kind is to be distinguished from a disturbance caused by a process of observation, as the former is compatible with causally and equations of motion, while the latter is not.' Dirac Principles, page 110
[page 66]
(from page 61)
Is this so? We assume that all forces are due to exchanges of particles, as are all measurements, so under the communication paradigm, 'force' and 'measurement' are the same.
Quantum field theory is stuck on the problem of singularity a a source which becomes more attractive as you get closer to it without limit. Quantum mechanics solved this problem in the case of the atom by postulating a ground state below which (in energy terms) the electron could not go. Why can we not do the same thing with the self energy of the electron? We might suspect that the ground state of the electron is split into two, spin +- 1/2.
My habitat has grown more complex over the years, so it is often hard to find things out of their 'proper place' and to estimate the shortest route between two points, given changes of level and a limited number of doors and corridors.
We cannot have movement without a space to move in. The moving object may possibly be found at any point in space (spans the entropy) but is only found at a given point at a given time, the rest of the space being filled with other things, so that all movements are closed or grouplike [permutationlike] in that a closed chain of things must move if one is to move, and the probability of this movement is related to the sequential occurrence of the circuit of moves. This sequence may be random (as in spacefilling Feynman integral) or in
[page 67]
some sense controlled.
If the medium is the message, vector algebra is what the world has to say for itself. We can find a matrix to transform any vector into any other. The rules of quantum mechanics place constraints on these matrices which hopefully make them resemble transformations which actually take place.
When we come to coding and information theory we note a similar phenomenon, since the vectors and matrices need to be spaced out as far as possible from one another to avoid confusion. This is akin to speciation in the living world.
Tuesday 11 July 2006
Transfinite algebra takes us around the transfinite network. Our first step is to show the effects of the implementation of Shannon's ideas in this system. The transformations of information theory are limited to those which can be implemented with strings of Turing machines, ie functions of functions, each one transforming the output of its predecessor. Such a string is the propagator of a calculation.
All things move by calculation = proof.
page 69]
(from page 67)
Wednesday 12 July 2006
...
This is a work about the idea of work. Our model should naturally fit the way things actually are, the interplay of the actions and interests of parts and wholes. And, then, hopefully tell us how to secure our interface with the natural world to avoid the fate of those populations that grow beyond the carrying capacity of their habitat.
The quantum loose rein.
Is god capable of intelligent design? Arguments both ways? Classical and incomplete. Goedel's theorem in the flesh. The Word made Flesh, ie expanded to a viable entity, as Bernoulli's theorem ==> aeroplane. The full technological development of an abstract idea.
...
Survival - decision = survival - modelling - decision.
At the physical layer the universe uses unary (Roman, Cuisenaire) notation so that wavefunctions are simply additive. Once meaning enters, we can begin to abbreviate.
Quantum mechanical formalism mimics the behaviour of the world, but what is the actual mechanism?
Two sources can communicate by sharing the same database, as do genetic and flu researchers etc. A photon travelling between two sources is in the nature of an element of a database.
The degree of cosmological redshift tells us how 'far' a photon has been.
The universe gains structure by division, like cell division, either symmetric or asymmetric. Morrison Nature 441:1068 Morrison
The genes are in effect the parts (the alphabet) from which we are constructed. Or, if proteins are the alphabet, the genes are an abstract representation of the alphabet, needing transformation by ribosomes, etc.
[page 71]
We can condense a lot of talk about the Cantor universe into probability spaces, which (Creutz page 8) have deep connections with statistical mechanics.
We want to describe the evolutionary paradigm in a transfinite network space which allows networks to reproduce themselves (like cells).
The initial singularity is the ur-stem cell of the universe. Muotri
Thursday 13 July 2006
Friday 14 July 2006
The engineering heat death of the universe approach sees entropy as a problem, a measure of disorder in the universe, while the information approach sees it as a resource, since the information carried by a point is equal to the entropy of the space carrying the point, and entropy can be exploited to achieve error free communication, the foundation of order.
The attitude that entropy is an 'evil' rather than a 'good' means that the question of generation of entropy (and information) in the universe tends to be overlooked. But we must ask, given the possible simplicity of the initial singularity, how does the universe complexify itself? ie create the structure (information + entropy) that we see and are?
Physics achieves this by filling the whole of space with a population of 'fields' corresponding to the various observed particles and postulating that wherever there is enough energy, different particles will materialize with probabilities and properties determined by the symmetries of the fields. But what does this ...
[page 72]
method of calculation point to in nature?
Ancient religions were ,marketed with miracles and wonders.
Christianity cracked onto the most miraculous and wonderful idea of
all, eternal bliss in heaven with god and all his mates. Natural
religion is the complete opposite, something very commonplace and
completely essential.
Here we define religion generally as a means of reaping the productivity gains that result from innovation and cooperation.
Religion is to the fore these days as he ancient rift between east and west projects itself globally.
What is the physics (mechanism) behind the mathematics of complex vector algebra? communication.
Saturday 15 July 2006
Quantum theory has long enjoyed a reputation for counterintuitive obscurity, but the advent of quantum information theory has set the coming out of quantum mechanics in motion by giving us an intuitively satisfactory [picture of what is happening]. We are born to communicate. The encoding and decoding of our interpersonal and intrapersonal communications occupies a good proportion of our central nervous system, a multiprocessor with some 1011 processors and 1015 interconnections. Muotri op cit page 1087 Quantum field theory is also a theory of communication. An abstract world of fields communicates with itself by the exchange of particles that is messages, which have a finite lifetime just like the sentences exchanged by people in
[page 73]
conversation. The following set of parallels between the quantum world and a communication network give some substance to this analogy between chat and particle physics. That it is more than a pretty picture can be shown by using it to pacify the problematic relationship between quantum theory and gravitation. I wish. But the payoff is so great that it is worth trying even though the chances of success are minuscule. So can be represented by a Dirac delta. We just have to hit the point x for which f(x) = 1 rather than zero.
We may consider the delta as a box 1/aleph(n) wide and aleph(n) high, whose area is therefore aleph(n)/aleph(n) = 1.
LOCAL = SIMPLE (since the addressable space is small)
ABSOLUTELY LOCAL = INITIAL SINGULARITY
The continuum version of quantum mechanics allows entropy and information to be packed o an infinite density, whereas there s a quantum limit in this too which describes the relationship between attract entropy and 4-space. Information packing density is a function of 4-momentum.
1, Soul and personality: the hidden soul [wave function] drives the observable personality.
2. Particulate communication : a consequence of Shannon.
3. Delay in communication : a consequence of processing needed for encoding and decoding.
4. Communication disturbance = uncertainty principle.
[page 74]
5. Superposition = states of soul = server
6. No cloning.
7. Teleportation (meaning) : a classical sentence transmits a quantum state.
We want to use communication to make space, and the resulting space to be the shape described by gravitation. What hope?
The source entropy (per person) of the human source is a large number, characteristic of the transfinite peer level of the same power as humanity.
In communication, 'distance' is something like 'Hamming distance', the number of letters that have to be changed to make two strings identical, regardless of meaning.
For strings, general covariance means that we are interested in the relative structure rather than the absolute values, so that we can replace all the letters in a string by their correspondents in some permutation, and the meaning would be the same, ie ab = ba when we substitute a for b and b for a. What matters is how these strings are encoded and decoded, and this depends on how the processor interprets the strings. So general covariance leads to the view that "I am hungry" has a meaning that can be encoded in an infinity of ways.
...
[page 75]
...
We might couple this idea of general covariance (something ordinal) with delay in communication (something cardinal) to get general relativity.
The soul controls the body because it is the 'disposition of the body' which leads it to process itself in a way that we can call soul.
Just as Boltzmann derived thermodynamics from hard sphere statistical mechanics, we want to derive the behaviour of the universe from the statistical mechanics of networks of Turing machines.
Every point in quantum mechanics is a variable orthogonal to all the others and so independent of them.
Books
| Aristotle, and (translated by P H Wickstead and F M Cornford), Physics books I-IV, Harvard University Press, William Heinemann 1980 Introduction: 'The title "Physics" is misleading. .. "Lectures on Nature" the alternative title found in editions of the Greek text, is more enlightening. ... The realm of Nature, for Aristotle, includes all things that move and change ... . Thus the ultimate "matter" which, according to Aristotle, underlies all the elementary substances must be studied, in its changes at least, by the Natural Philosopher. And so must the eternal heavenly spheres of the Aristotelean philosophy, insofar as they themselves move of are the cause of motion in the sublunary world.' Amazon back |
| 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 ...' Amazon back |
| Cohen, Paul J, Set Theory and the Continuum Hypothesis, Benjamin/Cummings 1966-1980 Preface: 'The notes that follow are based on a course given at Harvard University, Spring 1965. The main objective was to give the proof of the independence of the continuum hypothesis [from the Zermelo-Fraenkel axioms for set theory with the axiom of choice included]. To keep the course as self contained as possible we included background materials in logic and axiomatic set theory as well as an account of Goedel's proof of the consistency of the continuum hypothesis. ..' (i) Amazon back |
| Creutz, Michael , Quarks Gluons and Lattices, Cambridge UP 1983 Jacket: 'This book introduces the lattice approach to quantum field theory. The spectacular successes of this technique include compelling evidence that exchange of gauge gluons can confine the quarks within subnuclear matter. The treatment begins with the lattice definition of the path integral method and ends on Monte Carlo simulation methods.' Amazon back |
| 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) Amazon back |
| 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. Amazon back |
| Feynman, Richard, QED: The Strange Story of Light and Matter, Princeton UP 1988 Jacket: 'Qunatum electrodynamics - or QED for short - is the 'strange theory' that explains how light and electrons interact. Thanks to Richard Feynmann and his colleagues, it is also one of the rare parts of physics that is known for sure, a theory that has stood the test of time. ... In this beautifully lucid set of lectures he provides a definitive introduction to QED.' Amazon back |
| Goddard, Peter (editor), and Abraham Pais, Maurice Jacob, David Olive, Michael Atiyah and Stephen Hawking, Paul Dirac, The Man and His work, Cambridge University Press 1998 Amazon back |
| 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' Amazon back |
| Siegel, Warren, Introduction to String Field Theory, World Scientific 1988 Introduction: 'The experiments that gave us quantum theory and general relativity are now quite old, but a satisfactory theory which is consistent with both of them has yet to be found. ... Strings ... offer a possibility of consistently describing all of nature. However, even if strings eventually turn out to disagree with nature, or to be too intractable to be useful for phenomenological applications, they are still the only consistent toy models of quantum gravity ... so their study willbe useful for discovering new properties of quantum gravity.' page 1. Amazon back |
| Tomonaga, Sin-itiro, The Story of Spin, University of Chicago Press 1997 Jacket: 'The Story of Spin, as told by Sin-itiro Tomonaga and lovingly translated by Takeshi Oka, is a brilliant and witty account of the development of modern quantum theory, which takes electron spin as a pivotal concept. Reading these twelve lectures on the fundamental aspects of physics is a joyful experience that is rare indeed.' Laurie Brown, Northwestern University. Amazon back |
| Veltman, Martinus, Diagrammatica: The Path to the Feynman Rules, Cambridge University Press 1994 Jacket: 'This book provides an easily accessible introduction to quantum field theory via Feynman rules and calculations in particle physics. The aim is to make clear what the physical foundations of present-day field theory are, to clarify the physical content of Feynman rules, and to outline their domain of applicability. ... The book includes valuable appendices that review some essential mathematics, including complex spaces, matrices, the CBH equation, traces and dimensional regularization. ...' Amazon back |
| Wannenburg, Alf, and Peter Johnson and Anthony Bannister (photography), The Bushmen, Chartwell Books Inc 1979 'Even as this book goes to press, the last of the Kalahari Bushmen are being drawn into the vortex of our civilisation. Aware of the urgency of the task, the author and photographers searched deep into the Kalahari thirstlands to find those few remaining Bushmen who still live as their forefathers have done for the last 20 000 years' Amazon back |
Papers
| Morrison, Sean J, Judith Kimble, "Asymmetric and symmetric stem-cell divsions in development and cancer", , 441, 7097, 29 June 2006, page 1068-1074. 'Much has been made of the idea that asymmetric cell division is a defining characteristic of stem cells that enables them to simultaneously perpetuate themselves (self-renew) and generate differentiated progeny. Yet many stem cells can divide symmetrically, particularly when they are expanding in number during development or after injury. Thus, asymmetric division is not necessary for stem-cell identity but rather is a tool that stem cells can use to maintain appropriate numbers of progeny. The facultative use of symmetric or asymmetric divisions by stem cells may be a key adaptation that is crucial for adult regenerative capacity.'. back |
| Muotri, Alysson R, Fred H. Gage, "Generation of neuronal variability and complexity", Nature, 441, 7097, 29 June 2006, page 1087-1093. 'The production of specialized differentiated neurons derived from stem cells has been proposed as a revolutionary technology for regenerative medicine. However, few examples of specific neuronal cell differentiation have been described so far. Although stem-cell tissue replacement might be seemingly straightforward in other cases, the high degree of complexity of the nervous system raises the challenge of tissue replacement substantially. Understanding mechanisms of neuronal diversification will not only be relevant for therapeutic purposes but might also shed light on the differences in cognitive abilities, personality traits and psychiatric conditions observed in humans.' . back |
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