Notes
[Sunday 5 July 2009 - Saturday 11 July 2009]
[Notebook: DB 67: jciii]
Sunday 5 July 2009
[page 31]
Monday 6 July 2009
Probability of error in a symbol in a string varies as the length of the string, given that the probability of error per symbol is constant. On the other hand the distance between strings varies (on the average, given random sequences of symbols) exponentially with string length, so the probability of confusing strings drops exponentially with string length. [not if we mean Hamming distance].
We say that entropy always increases and power engineers and physicists have sort of convinced us that this is a bad thing and they predict the heat death of the Universe when the whole thing is at thermal equilibrium and no Carnot engine stirs. Heat death of the Universe - Wikipedia Carnot heat engine - Wikipedia This point of view, coupled with the wondrous dynamic complexity of our planet and its universal environment suggest that somewhere there is an Über Maxwell's Demon that sorts out low entropy systems from high entropy and so makes complex structure possible. Not possible, it turns out. All information (and entropy) is represented physically, and we learn that Maxwell's demon must generate as much entropy by tracking the fast molecule as it eliminates by its sorting operation. An impasse, which since the world works and we are here, needs some sort of explanation.
[page 32]
We begin with the tautology at the foundation of information theory, that the information carried by a point is equal to the entropy of the space in which the point is to be found. Shannon based the mathematical theory of communication on this connection.
We begin with a source . . . Summarize Khinchin Khinchin
Entropy is simply the logarithm of the cardinal of a set. The choice of logarithms turns multiplications into additions, simplifying the arithmetic which perhaps slightly defocussing the subject, since the power of multiplication is not so clear in addition. And the difference between the two is crucial, as Cantor showed, because multiplication (in the form of exponentiation) carries up the ladder of transfinite numbers.
Steinbeck, Thursday page 42 '[The Patron] knew that the only person you can trust is an absolutely selfish person. He always runs true to form.' Steinbeck
Direct selfishness (payment in the moment) vs enlightened selfishness (playing a longer game).
Set theory is built on correspondences which are realized in texts like this as strings of symbols made of ink and bound by paper, and at the most basic physical level by the simultaneous creation of the correspondence and the corresponding elements, ie fermions and bosons.
An electron is a system capable of occupying many states in the potential environment of a set
[page 33]
set of charged particles.
If religion is about symbolism, physical theology deals with the physical embodiment of those symbols. So we can see that the biblical statement the 'Word was made flesh' [corresponds to] Landauer's hypothesis, that all information is represented physically. This may seem a little blasphemous to traditional theologians, but insofar as we are speaking formally and hypothetically [it makes sense]. One may point to one underlying idea expressed in ancient times in terms of human love and reproduction, on modern times by a very plausible hypothesis linking the spiritual and physical world. Landauer's hypothesis is almost obvious. Every available religious symbol is realized in physical media, food, wine, music, silver, gold and jewels,marble and human movement.
Thinking along these lines, our question 'is the Universe divine' [is transformed to] 'is the physical Universe capable of representing the divinity.' We say yes, first on grounds of size and complexity and secondly on grounds of creative ability. Our physical Universe is an infinite self creating creator and as such qualifies as god. We make headway, we need to cast these arguments in formal mathematical forms. We shall approach the question of size from the point of view of Cantor's transfinite numbers and the question of creation using the mathematical theory of communication developed by Shannon. We imagine Shannon's strategy for error free communication being executed by the abstract mathematical computers known as Turing machines.
[page 34]
Theory of creation is the theory of the Trinity: three orthogonal persons in the one God.
We might see Augustine and Thomas' psychological model of the Trinity as a personified account of Hilbert spaces increasing their dimension by communication (observation and measurement).
I have some flu, but my mind seems to work just as well while the body is a bit weak.
Tuesday 7 July 2009
Wednesday 8 July 2009
Virus induced thoughts. Dramatically coded ideas: the agents are people; physically coded ideas: the agents are atoms, particles, etc. The network view can encompass both approaches, and we can use it to step between them using invariance with respect to complexity as the ladder. The underlying ideas are the same, we just seek to gain understanding by applying them in many situations and looking at them from many points of view, so this notebook records the same ideas again and again, but (hopefully) finding new ways to express them. One day, one of these expressions may catch the popular imagination and we will have a business.
Philokalia: Mysticism: these people really think they are getting closer to god by poverty, chastity, silence, self-abegnation, isolation and (self fulfilling prophecy) having visions and mystical experiences. This may be good for them, but it has the downside of suggesting to the
[page 35]
rest of us that they are better than us.Over the millennia people of this mind have developed a complex support network declaring certain members saints, writing books, begging money from the unholy, and so on. From the natural theology point of view this is nothing special. We are all in intimate contact with God all our lives, since we are personalities of God. Raising children, earning a living and all these other common worldly activities eschewed by the holy are much more actively divine than running away from it all.
Natural mysticism gives is a perspective of actions occurring at countably infinite frequencies at one end (minimal quanta of action) and zero frequency at the other, the life of the whole Universe which happens but once.
NATURAL MYSTICISM - HEAVEN
Rather than moderate our discussion, maybe the static approach is best and we create a body of text via the internet (and other media) and leave the reception of these views, their criticism and elaboration to the public domain. This will happen anyway, and [I] will get my work done more quickly without the distraction of interacting with other people until it is finished.
Thursday 9 July 2009
LAND (Australian Aboriginal) = UNIVERSE
Religions seem inclined to concern themselves with morals, but it seems to me the deeper questions concern meaning and morals. As in working with difficult people, life is so much easier if you love
[page 36]
it. The Christian ground for love is ultimately selfish. Love your neighbour in a practical way, like the good Samaritan, and you will enter the Kingdom of Heaven and like all who have one royal patronage, live a life of ease. Rest in peace. In other words, put up with this life for future reward. The foundation of investment (savings) and capitalism. Instead of profit and loss, one has entries in the book kept by the recording Angel (or Personnel Manager) which will be totted up in the end and the total set the course of the newly departed toward Heaven or Hell. This view is greatly abetted by the story of the Fall and Original Sin which establishes that we and the world are no good anyway and must grovel to the Almighty (and his self appointed servants) if we want to get paid.
From the natural religion point of view, this whole picture is totally wrong. Assuming (as we do) that the Universe is divine we are all children of God and so ourselves divine. Each of us has a biological and physical pedigree stretching unbroken to the initial singularity. If this line of descent is broken we are not here, like an aborted foetus or a possible species that either never evolved or became extinct. Rightly do the Christians fear the theory of evolution because it explains to us how god evolved and we evolved as parts of god. The cultural message of natural religion is the divinity of humanity, and not just humanity but the divinity of every personality in the Universe, every entity that can listen and speak, take in information and give it out.
PERSONALITY - PEER - NETWORK
The heart of natural morality is care and safety, and if morale is high in the community, we simplify these tasks by looking out for one
[page 37]
another, sharing experience and dealing communally with problems in life and the workplace, bringing our collective wisdom to bear From a formal point of view, we are talking about a network.
Theology deals with the theoretical side of religion.
CARE = ERROR REMOVAL {PREVENTION, DETECTION, CORRECTION}
If the Universe is divine, theology can be a proper science based on current experience, not old books.
PERSON = SOURCE
PERSONALITY = CODE (TEXT) DRIVING THE SOURCE, ie persistent elements in a named person, eg the personality of the writer, features of which are encoded in this text. Physiologically, my personality is coded in the states of neurons in my brain. These states have been moulded throughput my lifetime by my interactions with the rest of the Universe. This is not just a matter of looking at the stars, but all the physiological processes within me which are mediated by the electronic properties of atoms, for instance. I am a point of consciousness maintained by complex webs of signalling in a vastly complex structure of atoms. And remember that atoms are so small (or I am so big) that it takes a hundred million of them to stretch across my fingernail. Like me, atoms are persons with personalities. They speak an electromagnetic language with an infinite number of different words, that is distinct photon energies. Furthermore, they are not deterministic. The theory of atoms, quantum mechanics, cannot predict exactly what will happen, only the probabilities of different events. Just like human speech. You cannot predict what the baby is going to say next, even if you have a pretty good idea what it will sound like.
[page 38]
The world is not completely random, however. All personalities have certin fixed points and it is these fixed points that form the foundations of a durable structure. Nobody can build a skyscraper without connecting to solid rock underneath, by huge piles if necessary.
Slowly coming back to the plan for writing the development section of Natural Theology. Thousand word articles, exhaustively referenced making one point at a time to build up a coherent picture of the whole. The model gains more meaning as it is more widely applied, and with the meaning comes certainty. Since pure noise is statistically indistinguishable from perfect coding, the only way to distinguish signal from noise is to know how to decode the signal so that the noise makes sense, as the squeal of a modem becomes a picture on the screen, and so on.
From a practical point of view our response to the divinity of the Universe is to see that the Earth is our mother and we must take care of her. A tripod with a view. The personal motivation for a course of action.
How do we define acceptable profit? Profit made by trade within the law.
We do not have to create natural religion, it is among us already, at every level of complexity guiding what we are. It is simply the mathematical theory of communication, or rather the application or incarnation of the mathematical theory of communication / computation.
Christianity as a religion is badly distorted by political
[page 39]
considerations, particularly the fiction that it is rooted in an infallible monarch. Scientific investigation is impossible in such a regime if the monarch infallibly declares experience to be wrong.
The transfinite oscillator describes the dynamics of the transfinite network. A network is a set of memories and a set of computers. Both can be represented by sets of ordered sets. A stack is a memory with a definite first element but no definite last element. Nevertheless it is addressed relative to the current last element when something is pushed or popped.
One must have faith in one's work and keep on with it even though things may not tell out as well as hoped and / or planned. From a practical point of view work is not completely deterministic because it is influenced by events outside the planner's light cone. Although they do not happen in the planner's past they may occur in the past of the execution because execution occurs later in time so that the base of its light cone at a given epoch is wider.
So network structure harmonizes deterministic computing machines and indeterminate outcomes of events, ie determined only up to a statistic.
Science: We concentrate on two aspects of god, infinity and creativity. Following the scientific method, first we construct a mathematical model and then we test this model against observation. The more tests is passes the more our confidence in it grows. One clear failure, on the other hand, sends us back to the drawing board. We model the infinity of God using Cantor's theory of transfinite numbers and its descendants. To model creativity we imagine a transfinite network of memory powered by Turing machines
[page 40]
The creativity theorem then asserts that given a dynamic realization (ie a physical realization) the transfinite network is capable of creating itself from nothing. This idea first emerged thousands of years ago as a theory of knowledge. The Christian theologians who developed the psychological model of the Trinity raised it to the level of an ontological rather than a psychological condition. In God relationships create real distinctions and vice versa. Since this statement is invariant with respect to time, it true at all times, it is the formal foundation of the Universe. We do not say how things are created, but that the gain in error correcting power that comes with increased complexity can often pay the cost of the complexity, and in fact generate, (asymptotically) an infinite rate of return. What we wish to show is that the odds are in favour of a certain maximum ion complexity, of which we, homo sapiens appear to have become and example.
Your basic protein is about 200 amino acids and the mass of 20 000 (?) hydrogen atoms (100 per amino acid?) Protein - Wikipedia Amino acid - Wikipedia
Imaginative conjecture and refutation by reality are the foundations of science, basically the rules of scientific evidence: measurements repeatable by anyone, given the necessary equipment. Naturally there is a bit of fraud, but not enough to seriously hamper the overall effort. The first audience for natural theology is scientists, since they understand the method. So concentrate on 'Could theology be a science' (Science).
The Theology Company 'good news' is the creativity theorem, 'TCT'. Good news (Christianity) - Wikipedia Like the ownership of gold or oil, the ownership of these ideas ought to lead to economic benefit (after, perhaps,
[page 41]
considerable investment.
Friday 10 July 2009
Saturday 11 July 2009
Peano's axioms, bolstered by Cantor's theorem, describe the kinematics of creation and show how to construct a transfinite address space, assigning a unique number to each of a transfinite number of possible states. Peano axioms - Wikipedia, Cantor's theorem - Wikipedia These axioms and theorem say nothing about what is stored in these locations. We render the system dynamic by introducing Turing machines which store and retrieve data at specific addresses.
Error: a toddler in the kitchen, altering the structures constructed by the cook in such a way that the cook has to search for the vegetable peeler, instead of being able to go straight to it, since it has been relocated by the toddler. The function of a search engine is to index the locations of all the elements of space, so that one can go straight to them rather than search. In general this reduces the amount of work needed to obtain a specific element x (= vege peeler) from a space of n objects from n/2 to log n. In a typical kitchen containing a thousand objects, n = 1000, this reduced the search from 500 operations to 3. This is the foundation of Google's fortune and is an example of the power of order. Google search - Wikipedia
Now the logarithm (and its inverse, the exponential) are the foundations of discrimination in the Universe, and 'explain' Cantor's theorem. In the infinite limit, n and en are related, from a cardinal point of view, as 0 and 1. That is, as n approaches infinity, if card(en) = 1, n = 0, ie n can be understood as an empty set, with no interior to be investigated or concerned with. In communication terms, all that matters about an alphabet is that it comprises distinct symbols
[page 42]
that can be combined into strings in various ways, ie permuted. Strings are connected by computers which are capable of converting one string into another. The simplest computer is a look-up table, which gives a one to one correspondence between the alphabets of one string and the alphabet of another.
For all formalism is the manipulation of strings according to a set of rules. These sets of rules are realized in Turing Machines.
As I write these notes I feel that I am getting closer to the piece of good news I am after. I am also transcribing them onto the internet ('open notebook' and so reliving a past segment of the path that led me here. Open Notebook Science - Wikipedia
The Dirac delta 1 x 0 = 1, ie aleph(n) x 1/aleph(n) = 1.
The delta is a statement about cardinal numbers which we can understand by looking at the statistical mechanics of the ordinals which is described by the permutation group and its properties (ie theorems proved on it).
. . .
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