vol 7: Notes
2005
Sunday 26 June
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... to restore theology to the mainstream of science
Notes
[Notebook: DB 57 Language]
[Sunday 26 June 2005 - Saturday 2 July 2005]
[page 165]
Sunday 26 June 2005
Monday 27 June 2005
Tuesday 28 June 2005
Wednesday 29 June 2005
Science works because we can do the 'same things' over and over again. But every event in the universe is unique, up to a point. There are symmetries in the universe which give meaning to terms like same, similar, identical etc (even identical twins are unique, as is every particle interaction which ever has or ever will occur in the life of the
[page 166]
universe. A model of the universe (for natural theology a model of god) must be able to deal with this complexity. The structure we propose for the purpose is the Cantor universe (CU) which we construct from a set of natural numbers. For practical purposes we can represent the set of all natural numbers (to which Cantor assigned the first transfinite cardinal aleph(0)) by any set with two or more elements.
Each set of natural numbers has a cardinal number. Finite sets have cardinal numbers like 0 (the empty set), 5 (the set of fingers remaining on my right hand) or n. For the set of all natural numbers, n = aleph(0). Any set of natural numbers has a natural order starting with the smallest and growing toward the largest. Given any particular number from a set, we can, by examining the chosen number and all the other numbers, assign the chosen number to its proper place in the order. This property arises from our definition of cardinals by sets of objects.
From this basic order of a set of numbers, we can create permutations, that is reorderings of the numbers. We can achieve any possible reordering by swapping pairs of numbers. The number of permutations if n objects is n!, ie n x (n-1) x ... x2 x 1. The cardinal of the set of permutations of a set is generally greater than the permuted set (which we will call the alphabet of the permutation). The cardinal of the set if permutations of an alphabet whose cardinal is aleph(0) is the second transfinite cardinal, aleph(1). These permutations have a natural
[page 167]
(alphabetical) order and so themselves can become the alphabet of a set of permutations measured by the third transfinite cardinal, aleph(2), and so on without end, even unto transfinite subscripts on the transfinite symbols.
Alphabets make words, words sentences, sentences books and so on until we come to the level of complexity which we will label 'literature'. We may then thing of the CU as the space in which to define a literature.
Having defined a space that (we hypothesis) is large enough to address every event at every scale in the life of the universe, we must now see if we can understand if we can see how this addressing works by fitting it to the universe of experience. The proposed interface between the CU and everyday experience is the transfinite network.
It is customary to thing of abstract networks as two dimensional groups of nodes and edges joined in some subset of all possible ways. Real networks, however, are three dimensional structures because they are layered. At the bottom we have the physical layer, copper, silicon, photons, electrons and so on. On top of the physical layer network designers build layers of software that reach up to the user layers. An ISO standard, for instance, postulates seven layers of processing between physics and the user. Tanenbaum, USSG - Indiana University
[page 168]
First error correction, then transmission protocols etc. The user's input must bore down to the physical layer, travel whatever distance and then burrow back up to the user's output
Now we assume that all the in formation traded in the universe is encoded and transmitted in physical form. Landauer
Now let u equate the physical layer and the natural numbers. This is equation is made possible by the observation that every observable event in the universe involved at least one quantum of action. No smaller events are observed. Their discreteness renders the events of the universe countable and so we assume that they can be placed into correspondence with some set of natural numbers.
So let the alphabet of discrete events in the life of the universe has aleph(0) elements. The physical observation of discrete (quantum) events (particles) in the universe is supported by the mathematical theory of communication. The role of error correcting codes in communication theory is to make the distance between valid codewords so great that there is a suitable infinitesimal chance of confusion. If the role of the physical events in the world is communication, we would expect to find a fundamental alphabet of discrete events.
In the General Scholium of the Principia, Newton gave the role of designing and sustaining the physical universe he had revealed to God, conceived in the classical Christian model. The quantum
[page 169]
mechanical version of God is the wave function of the universe, an abstract piece of mathematical machinery that gives us a rather miraculously useful description of what selects the events we see from the ones we don't.
We get from the CU to quantum mechanics via the idea of function space realized as Hilbert space.
The Hamiltonian for a permutation, ie order 1 to order w. Hamiltonian matrix gives us all possible transitions. [matrix representation of the permutation or symmetric group Higman]
Thursday 30 June 2005
A mind is a superposition of all the things that it could say. So an atom is the superposition of an infinity of states which are revealed by the infinity of different photon frequencies that it can emit and absorb. Minds form the nodes of our network, and these nodes communicate by exchanging physical states, like this writing. The physical systems know nothing of the 'meaning' of the information they carry. The meaning is a property of the minds using certain algorithms to encode and decode the messages they exchange. A related set of communication algorithms may be understood as a language. The languages we see around us include the deterministic languages of conventional computers (ie assemblers, C, Perl etc) a the way to the rather indeterminate languages of music, love and so on.
Asking questions is a way of perturbing fixed energy states in order to increase the probability of transitions between them. Feynman ammonia maser. Feynman
[page 170]
Intuitive quantum mechanics - not Newtonian biffo, but the subtle interaction of complex processes.
Friday 1 July 2005
Saturday 2 July 2005
Further reading
Books
| Feynman, Richard P et al, and , 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 Amazon back |
| Higman, Bryan, Applied Group-Theoretic and Matrix Methods, Dover Publications Jacket: '... This work, a comprehensive, thoroughly reliable exposition of the basic ideas of group theory (realized through matrices) and its applications to various areas of physics and chemistry, systematically covers this important ground for the first time. ... Although [it] deals basiclaly with advanced level material, the unusually clear exposition provides much valuable insight and fruitful suggestion for student and specialist alike. Chemists, physicists, mathematicians, and others who would like an idea of the applications and methods of group and matrix theory in the physical sciences will profit greatly from this book. ...'back |
| Tanenbaum, Andrew S, Computer Networks, Prenctice Hall International 1996 Preface: 'The key to designing a computer network was first enunciated by Julius Caesar: Divide and Conquer. The idea is to design a network as a sequence of layers, or abstract machines, each one based upon the previous one. ... This book uses a model in which networks are divided into seven layers. The structure of the book follows the structure of the model to a considerable extent.' Amazon back |
Papers
| Landauer, Rolf, "Information is a physical entity", Physica A, 263, 1-4, 1 February 1999, page 63-7. This paper, associated with a broader conference talk on the fundamental physical limits of information handling, emphasizes the aspects still least appreciated. Information is not an abstract entity but exists only through a physical representation, thus tying it to all the restrictions and possibilities of our real physical universe. The mathematician's vision of an unlimited sequence of totally reliable operations is unlikely to be implementable in this real universe. Speculative remarks about the possible impact of that, on the ultimate nature of the laws of physics are included.. back |
Links
| Rolf Landauer Information is a Physical Entity 'Abstract: This paper, associated with a broader conference talk on the fundamental physical limits of information handling, emphasizes the aspects still least appreciated. Information is not an abstract entity but exists only through a physical representation, thus tying it to all the restrictions and possibilities of our real physical universe. The mathematician's vision of an unlimited sequence of totally reliable operations is unlikely to be implementable in this real universe. Speculative remarks about the possible impact of that, on the ultimate nature of the laws of physics are included.' back |
| USSG - Indiana University ISO/OSI Network Model 'The standard model for networking protocols and distributed applications is the International Standard Organization's Open System Interconnect (ISO/OSI) model. It defines seven network layers: Layer 1 - Physical ... Layer 2 - Data Link ... Layer 3 - Network ...Layer 4 - Transport ... :ayer 5 - Session ... Layer 6 - Presentation ... Layer 7 - Application back |
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