VII Notes
2010
Notes
[Sunday 28 February 2010 - Saturday 6 March 2010]
[Notebook: DB 68: Salalah]
[page 237]
Sunday 28 February 2010
Time is not a degree of freedom in the same sense as the spatial degrees of freedom, since we cannot in fat choose to change our position in time even thought physicists (relativists) like to think that space and time are no longer distinct entities but one space-time (Minkowski Minkowski space - Wikipedia). This fact points us to the inherent dynamism of the Universe, iondicating that we are always moving from past to future and cannot turn back. There seems to be more to this than the thermodynamic 'time's arrow' which physicists use to discuss the direction of time. Entropy (arrow of time) - Wikipedia We can, however, imagine that in the beginning before the evolution of space, the direction of time could not be discerned, even though the existence of energy meant that time also existed in a sequence of (possibly identical) actions, although without memory, this characterization has no meaning since past actions could not be compared to present actions.
[page 238]
On reflection (ie looking into memory) we see that the passage of time is one of the primary characteristics of the world and the one people of mystical turn of mind deny first, attributing eternity to spiritual beings and counting space and time as among the defects of the world, to be denied of God. (Aquinas Aquinas 20)
All of this stuff is a search for my own origins and place in the world which is pretty clear, really, given the theory of evolution and all the science surrounding it. So what am I looking for? Something I have not yet found perhaps, and which cannot be found: why is it all here in the first place? This question was answered in my youth by God, the answer to all questions (and none) since we can then ask where did God come from and the historical logical answer is that God has always existed outside time, so don't ask. What I seem to be looking for (at this point) is some sort of logical argument that shows how the Universe has come to be what it is from the past time when it was almost nothing, and the analogous progression in my own life.
The key to survival in human society is one's relationshjip with other people, andwealth and honours come to whose who can most effectively manipulate these relationships to their own benefit by whatever means, honest or deceitful. Archer, 4th Estate Archer
Control: doing the dishes. Parititining the set of dirty dishes into clean dishes and dirty warer, allegedly increasing the entropy of the Universe while decreasing the entropy of the dishes. Then gardening,
[page 239]
turn the 'weeds' to mulch, encourage the 'vegetables' all the while trying to discern an abstract pattern in my activity which will feed my theological ambition.
Logical action at a distance vs physical action at a distance.
It is something like 25 years since I did the 2BOB lectures and in the light of subsequent developments they still seem pretty sound. A theory of peace
The establishment of heaven [and peace] is a matter of management and control something rich people and rulers can do for themselves usually at the expense of others who are consigned to hell for the benefit of their masters. Like Nazism, Catholicism and Monarchism, these operations and attitudes fall within our definition of religion : here the technology of peace (which includes violence) is applied for the benefit of a minority. We wish to show that a stable system can be constructed out of a set of willing workers who all enjoy equal wealth, the concentrations of wealth and power being held by public corporations rather than private hands.
Corporate and constitutional law are the foundation of religion, vide The Code of Canon Law. Holy See
The dishwater then goes into the ground where billions of organisms process it for its food value, finally leaving a collection of zero energy elements and compounds which plants, with the help of solar energym make back into food which may eventually dirty more dishes.
Quantum mechanics allows us to view all the processes as rotations of vectors (or operators) in Hilbert space.
[page 240]
A Hilbert space realization. We can map the progress of a Turing machine by rotation of vectors in a sate space, where each dimension of a vector corresponds to a bit.
What happesn between messafges. No matter how frequent the messages, there is no limit on the import of a single message Mum died vs nothing happened.
CONTINUITY = NOTHING HAPPENING= NO STEP / NOP
All that we see is the world communicating with itself. It is all language, and the languages are always evolving
A set of tools may be said to be complete with respect to a given task when it is adequate to perform that task effectively (efficiently?) (as efficiently as possible).
OPERATION = TOOL (NOP, GRIPNUT, etc)
Information: a is b, ie a sentence, a coupling of two symbols.
Monday 1 March 2010
We use invariance with respect to complexity to carry us from one end of the Universe (timewise) to the other, from initial singualrity to god. It is energy that is invriant with respect to complexity, so the energy of the Universe (as an
[page 241]
integral) does not vary with time, although the disposition of the energy does [and total kinetic + potential may remain 0].
How do we understand the algorithm for computing probability in quantum mechanics? ie p = | psi |2 or p = |< b | a>2, the probability of observing state b using the operator (decoder) a. We can understand the two state system in terms of a set of basis states for a and b which we cal |xi > where the basis [states] are orthogonal and normaized to p|<b|b>|2 = 1, p = |< xi | xj>2 = 0 (i ≠j), 1 i =j. The Kronecker delta xcontains both certainty and impossibility. From a ball and urn point of view, one can be certain of getting a black ball only if all the balls in the urn are black, and certain of not getting red if there are no reds in the urn. So we model basis states as urns of one colour only, and non-basis states as a matter of picking one urn at random.
. . .
The random choice between urns is described by the 'wave function which, squared, is a probability density function.
Feynman: Stern-Gerlach and the computation of spatial probabilities. Feynman
[Output of quantum mechanics:]
a) stationary state = eigenvalue
b) transition rate = overlap integral.
The essence of survival can be reduced to energy management / money management.
Merton calculates the returns on stocks treating them as random
[page 242]
walks with no fundamentals (field gradients). A living creature equipped with sensors can do better than this (a 'steered' walk) by adapting its behaviour to input from its environment. The initial singularity has no environment, and so no need of sense and can act in a fully unconstrained (random) way. [Every possibility has equal probability]
What are the chances that algorithm a can decode code b? If the algorithms are orthogonal, p = 0, if they are parallel p = 1, otherwise the result depends on the content of the messages, some being decoded correctly, some not. A correct decode means that the 'cybernetic condition' is fulfilled and the decoded message leads to fitness maintaining / increasing behaviour, or a false decode ('this means dive, not climb') can lead to increased error and death.
The quantum probability density function |phi|2 can be represented by an urn in which colours of balls (basis states) are present in the proportions indicated by |phi|2. This urn is a quantum source (with replacement) What we think is that the cause of this distribution is the rate of calling of various subroutines of a larger process similar to the rate of calling individual glyphs of the alphabet while writing English sentences such as this. An atom is such a larger process, receiving and emitting photons as a function of its internal state and its electromagnetic environment.
Back to Khinchin Mathematical Foundations of Information Theory
'Complete system of events" = One and only one occurs at each trial. Analogous to the basis states of an observable.
logaleph(n) (aleph(n)) = 1
[page 243]
Entropy of a certainty is 0. The past is a certainty so we may say that H (past) = 0. H (future) = f(t) where t is the distance in time from the present to the future moment t.
The entropy of independent schemes adds. That of dependent schemes is HAB) = H(A) + HA(B) where HA(B) means the entropy of B given that event A has happened.
Information is proportional to entropy.
'Crash Metrics' Wilmott 1988 Wilmott
Polanyi: The Tacit Dimension Polanyi : Because the tacit dimensions (ie religion, all unconscious experience) are tacit, it is very hard to identify and abstract from them, so that we are easily lead astray by tacit assumptions like the continuity of space and the irreducible complexity of the Universe.
Khinchin page 47: 'The fact that the entropy really exists for every stationary source of the first fundamental theorem of the general theory of discrete sources.'
We imagine strings ℵ0 symbols long drawn from an alphabet of ℵ0 symbols, giving us a set of all possible sequences AI. Each of these sequences has a probability mu(C) [= 1/ℵ1] and the entropy of the whole space of sequences Hℵ1 = -SUMC mu(C) log mu(C). The source entropy is then log (ℵ1) = ℵ0.
[page 244]
Tuesday 2 March 2010
We get from ordinal numbers to cardinal numbers via the theory of probability, particularly as applied to the mathematical theory of information.
Khinchin page 45: 'Let us consider a sequence of letters (3.1) x = (. . . , x-1, x0, x1, x2, . . .) which represents a "life history" of a given source.'
1. x is an ordinal number.
2. We can use x to represent the state of a Turing machine after each operation, so that for a given Turing machine it is a deterministic sequence, a fixed ordinal number. However, the probabilistic treatment considers each xi as a random event, so the random event x is an ordered set of subevents xi.
'We shall regard x as an elementary event in a certain (infinite) probability space, a space the specification of which characterizes the sequence (3.1) as a random process.'
A computer engineer (as I must be when I am publishing these pages) is concerned with a particular determined set of events, such as those generated by a process called render_page. In the theoretical realm we abstract from this detail and consider only the probability of various events, which gives us a broader view of what is going on at the expense of detailed resolution. AI = {x. 'Any subset of the set AI represents an event in our space and vice-versa', ie every event in our space is a Turing machine considered as a discrete
[page 245]
series of stationary states. The Markov transition matrix for this series is a function of the actual program being executed by the machine. It may be considered stationary insofar as the machine performs the same sequence of operations whenever it is executed. The minimal operations of this machine occur very frequently (eg [move]R, L) while the maximal operation (the whole machine process) occurs only once per execution. We assume that the machine represents a computable function [and so halts].
The letters of the Turing alphabet can be reduced to 0 and 1. These exist as a symmetry in any string 011011100 . . . represnting a Turing machine. Within this string we will find substrings which are also symmetrical, each representing the execution of a [particular] subroutine.
CALLING a SUBROUTINE = handing over execution (and a set of parameters) to a specific routine.
DO x = DO a then DO b (buid the foundations / build the house.)
Mapping the network to building - a concrete introduction Chapter 1 of GN III
Khinchin page 45: 'Generally, if t1, t2, . . . tn are any integers and alpha1, alpha2, . . . alphan are any letters of the alphabet A, then the event "the source emits the letter alphai at time ti (1 =<i =<n) is the set of all x for which
xti = alphai.
'. . . we shall call such a set of elementary events x a cylinder set or briefly a cylinder' By analogy with ordinary sound recorders?
[page 246]
'As is well known, it is sufficient to know the probability mu (Z) of all cylinders Z to define the sequence (3.1) as a random process.'
COMPUTER is a NETWORK
The Hebrew God was a fighting man, tough, vindictive, unforgiving but a deep lover of the people he was fighting for.' Miles
One can name symmetries in the code string with grep (regular) expressions. This This name selects the set that conforms to it according to the rules of grep.
Money is the dual of debt in the same way as kinetic energy is the dual of potential energy. A debt creates a coupling in a way not done by a payment. I can take the money and run, but the people who lent it to me need to know where to find me.
Vectors can be added (superposed) and multiplied by a number (scaled) to form a new vector.
Griffel page 85 'Rough definition 4.1 : A real vector space is a set of objects which can be added and multiplied by real numbers, giving in each case another member of the set. [so a vector space, like the Universe is closed, at least at one end of the entropy scale] Griffel
Insofar as the vector concept fits the world (relativity, quantum mechanics), what does it mean?
Linearity, which means that it is meaningless, a self realizing formalism in effect. The world is a vector space at all scales.
[page 247]
Vector space - the hardware of the Universe ie Hilbert space, [with] its vectors and operators is an 'engine' a self propelling (frictionless) machine realized as a purely formal description rather than embodied in material. These ideas, despite their formality, are physically embodied in this writing, it is simply that the code that couples the disposition of ink with meaning is quite complex.
Linearity - pure self with no reflection.
Gravitation is the most primitive application of quantum mechanics.
Manage anything using scale invariant control thewory.
God is the root of the tree, the mother of the children of god. To be interpreted in the language of object oriented programming.
On constructing big things from little things:
1. Just make a heap,like sand
2. Make a space filling structure, like the Eiffel tower
3. A big process out of little processes, a living system.
The network is the way we couple small processes to make large ones by communication between processes. How do we make a computer network in fuinction space? Quantum mechanics?
Communication theory ⊃ statistical mechanics ⊃ thermodynamics.
The Universe is structures by containment and the initial singularity contains all. One container explains
[page 248]
the consistency of the Universe structured buy eigenfunctions (modes) of the container.
Duals: energy - time / entropy - information / kinetic energy - potential energy (2 state systems)
One stationary state can be changed into another with a different alphabet of the same length by a rotation.
Where are we going to here? Trying to make the network into a vector space to prove its isomorphism to quantum mechanics. What are the eigenfunctions of a network? The Turing machines at the nodes of the network. And the eigenvalues? The rate of communication between these computers. Explicate this in a two state system. Sleep on it.
On the object oriented model, the root contains the branches, the parent contains the children.
Wednesday 3 March 2010
Khinchin page 49: The 'message Universe' AI is invariant under the shift operator. Does this imply that for a Universe of finite messages each message is an element of a cyclic group whose order is the number of operations a particular computer takes to achieve a certain task, and the ordering of the operations in the group is the sequence of events needed to get from a starting (halted) position to an ended (halted) position which (apart from the data given to the machine and the corresponding input) are from the machine's point of
[page 249]
view identical. Everything is built out of the '1 op' machine which we see as simply a clock ticking a quantum of action at a time, from an actual position (start) to a possible position (end), given that start and end are identical.
House --> home (set of cyclic processes constrained by four walls)
Where there is no constraint all possibilities have equal probability? This does not seem to be so with stationary Markov processes that divide into the high probability and low probability sets. Needs to understand this via Khinchin. [The fact that the letters of the alphabet are not equiprobable points to some constraint (meaning) in the source].
Genesis is a creation story, the simplest; somebody (call him Yahweh) made it all. Christianity has the same idea. Here we go a bit deeper, identifying God and the Universe and seeking to explain how gods make themselves.
We might like to identify the high probability group of Markov processes with the string of operations executes by a halting Turing machine and so see them as cyclic. [probability density functions abstract from the order in which events are given and represent only their frequencies. Nevertheless, in the world, order is important and non-commutative multiplication in quantum mechanics shows]
Khinchin page 54: 'The E-property McMillan's theorem'.
The E-property arises when the entropy per letter of the output of a given source is less than the maximum ie the letters of the alphabet are not equiprobable. The high probability set contains the sequences in which the entropy of the letters is close to the source entropy, and the low probability group contains the rest of the [sequences]. The total number of sequences pf length n that can be made with an alphabet of a letters is an = 2n log a
[page 250]
The probability of the high probability sequences is approximately 2- nH where H is the entropy per letter, so that the number of these sequences (total probability 1) is 2nH. Except in the case where H = log a, ie the letters are equiprobable, for large n the high probability group contains only a negligibly small share of the n-term sequences from the source.
Khinchin page 57; 'For sources such that each letter is statistically independent of all previous letters, the E-property is an almost immediate consequence of the law of large numbers and always holds. . . . In 1953 McMillan succeeded in proving that any ergodic source possesses the E-property.'
The devil is in the details. When things are on the brink (unstable) a small change can make a big difference.
A big event is the sudden release of potetnial (stored) enegy in the form of kinetic energy: explosion, earthquake, etc. Technologically, it is prefereable to release potential energy in a manner which yields the maximum of useful processing per unit of energy.
Network = memory + processor to change the memory.
Thursday 4 March 2010
We can draw a Venn diagram of more complex objects inside simpler ones, as the Universe contains atoms and atoms (in a logical sense) contain us. Physically, the bricks are in the house; logically, the house is in the bricks.
[page 251]
A major defect with most of the traditional religions is that they encourage politics to outweigh reality by denying the data, natural religion's equivalent of the sin against the holy spirit.
Money as a public network, S 327:951. Christian Thiemann and Daniel Grady
Like Agatha, we are trying to find a picture that fits the facts, assemble the jigsaw. A theory of everything must, by definition, fit every fact. This, we claim, the transfinite computer network does. When a physicist talks about a theory of everything, he is basically talking about a theory that unifies the four fundamental forces of nature as revealed by careful and expensive (up to $10 billion) experiments in laboratories around the world. Such a theory has little to say about the enormous amount of data being generated by the rest of the world. Quantum electrodynamics provides a foundation for most of what we see, hear, feel, smell and taste, but it does not explain how or why these senses came into being any more than the Standard Model explains how the world came to be in way it is. It simply fits the world quite well when all the adjustable parameters have been set by observation. Obviously a theory of everything must be a theory of creation and annihilation rather than simply a formalism that describes the rate of creation and annihilation of various particles under various conditions.
Traditionally, we think that the world is the way it is because that is the way God made it, with the idea unspoken that he could have made it very different and most likely better. This is consistent with the idea that the world is
[page 252] not our real home but a testing ground to see who will be admitted to heaven, often consigning the failures to a hell of eternal torture, the sort of vindictive idea that seemed typical of the ancient creators of fictional Gods.
Vindictivity seems to be a human trait, perhaps evolved with the evolution of tribes and leadership: you hurt me, I hurt you and yours seven times as much, or, in recent Israelite practice, one hundred times as much, something of which Yahweh might be proud.
'opportunistic refilling of vacated ecospace' S 327:990 Friedman
Gödel: the world is incomplete, so I can go on writing new things forever (and the rest of the Universe too). But how long till the last star dies?
Axiom: Every particle has a heritage which both distinguishes it from every other particle and connects it to every other particle = message. The world [observable] is a network of interacting messages.
Fixed point theorems show us how the omnino simplex is consistent with the omnino complex
The previous three paragraphs are the result of my decision to have another been and another joint - or at least they came since that decision.
My confidence has increased immensely in the last ten years since I met my first 'fan'. Before that I was struggling in the darkness caused by a
[page 253]
fatal error in my religion. Since then I have come up again with a new religion, branded good news 3, good 3 news, gn3g.
gn3g registered - gn3g.net registered - spread the world, a new religion is coming.
. . .
Doctrine Policy: Energy / Footprint / Food
Stars could not exist without the isolation of space.
A galaxy is an island of complexity ultimately
[page 254]
the result of gravity. By their fruits you shall know them. We understand gravity when we map the network onto spacetime and find entropic forces between nodes appearing in spacetime as curvature / dynamism.
The pages are self-contained and can be read in any order. As they become more numerous we will assemble them into groups for easier browsing, and all are subject to continual revision until they reach a state sufficiently developed to be thrown open for comment.
By being a religious tycoon instead of a not for profit, my motives are clear and intelligible to all. In one way or another, we all want to be wealthy, and, as we shall preach, a sure way to wealth is commonwealth. And both the enemy and the friend of commonwealth is greed, bad greed and good greed (for every vice is a perverted virtue).
So I drug myself. There is a war on, religious as ever, and I want to propose a settlement. The settlement is quite abstract as settlements must be f they are to please everyone. The mathematical foundtaion of the settlement is the transfinite computer network. From it we can gain guidance in our everyday affairs at all scales.
BOSE behaviour / FERMI behaviour.
Individuals are motivated to prophesy [become entrepreneurs] by vision (imagination) is a picture of what might be, given certain assumptions (such as our God is all Powerful and he is on Our Side. Natural religion says this (without capitals) for the Universe in which we find ourselves.
Putting us outside rather than inside God has been a big blue, politically (if unconsciously) motivated (The forces of evolution are rarely conscious, but we certainly feel them, particularly in the reproductive domain (which include all the developments of reproductive behaviour since the days when sex was strongly coupled to reproduction)).
We can model the whole of computation into the transformation of one string of symbols into another which may be longer or shorter [ie encoding, decoding].
How do we think: imagination (gossip); testing (horses mouth).
Physics is obsessed with continuous and differentiable functions which are a tiny subset of all possible functions. All these 'random' functions (No correlation from point to point) can be represented by probability density functions which are themselves continuous though they use the law of large numbers that tells us that if we include enough points the thing is as good as continuous and enough may be as little as 2 or 3.
To be a programmer you need to get an idea of what you want to do (systems analysis) and then code it in whatever language seems easiest. [Computer code is something that a machine can read and act on]
[page 256]
The think is not impossible because it can easily be expressed in simple texts and multiplied without limit.
So actual quantum event are random delta functions in spacetime which nevertheless obey a certain probability density function, as we see by watching long enough. This is really no different from bird watching, working out their haunts and habits.
Friday 5 March 2010
gn3g Synopsis: Introduction
Christianity can abstract itself ont s simple 5 word spogan'love god, love your neighbour'. Jesus gives a clear defintion of neighbour, but god is a more nebulous concept. Here we think of god as a set of neighbours, so the Christian slogan can be summarised as 'love your peers, love your peer metalayer.'
Layering is a local phenomenon, where by local we mean a network with a certain minimal cohesiveness vis a vis its neighbouring networks. S 327:951 Christian Thiemann and Daniel Grady
Split development into religion and theology: religion to TNRP, theology to ANT. GN3G uses no technical terminology, but can refer to TNRP and ANT. AT links us to the past. TTC management and funding.
As a private Company, TTC is not for profit, but as its size and income increase, it must become public and a taxpayer. NT [here] is the personal story.
[page 257]
A New Theology needs a history of theology,as The Natural Religion Project needs a history of religion. [the past is the problem and the opportunity]
Gn3g is the gospel: Good News: The Third Generation [The Gospel according to the World, no longer a cult of personality but of reality = {personality}]
Theology = model of god = model of love = bonding and differentiation.
Biology: the message is in the electron. Electron donors and electron accepters. [The behaviour of electrons is determined by their communications of their environment.] S 327:793 Newman
Jesus said look at the plants and animals. They do not work, but they do, of course, and we must take this into account. Luke 12:22-31Jesus did not seem to approve of too much prudence in the management of one's financial affairs; sell everything and give it to the poor and follow me could easily end in tears. Gospel of Luke
Griffel page 120: 'Solutions to the equation x = Tx are called fixed points of the transformation T; they are the elements of the space which are unchanged by the action of t. There is a large body of mathematics dealing with the existence of fixed points and how to find them.'
The root of hope in natural religion lies in the fact that there are certain fixed points in the personality of the divine Universe which we can exploit to ensure our survival and even happiness, not least being the fixed point expressed by this sentence.
Probability: The casting of lots revealed God's will. Shiloh The Book of Joshua
[page 258]
Jesus explains his mission in terms of the social, political and religious conditions of his day. Later theologians broadened this message to a cosmic history which was intended to embrace everybody, not just the locals who met Jesus and heard him talk. Here we have in mind a much more abstract network of communication which serves as a theory of everything which is instantiated by every event in the world. Every event is a result of a set of messages (a Feynman diagram) and it is also the source of a set of messages. Feynman diagram - Wikipedia We may think of this in terms of incoming and outgoing communication cones analogous to the physicists' light cones. Light cone - Wikipedia
Saturday 6 March 2010
The principal aim of gn3G is to lighten the enormous spiritual burden imposed by the Christian belief that we are inherently evil and the Universe we inhabit is fundamentally flawed, original sin. The Christian good news, that the murder of Jesus cured all this is no more credible that the doctrine of original sin itself. The sin and guilt based model of the human condition must be replaced by the nation that we an look after ourselves if we play our cards right in a universal game which is fair and reasonable if we understand it correctly.
Science 327:806 'Rat fatalism" Dennis Normile Normile
Food and energy Science 327:809 Science editorial
[page 259]
Perverse subsidy Science 327:811 Stokstad
Review: Food Security Science 327:812 Godfray et al Godfray
'A three fold challence now faces the [human?] world: Match the rapidly changing demand for food from a large and more affluent population to its supply; do so in ways that are environmentally and socially sustainable; and ensure that the worlds poorest people are no longer hungry.
The details of the food security problem are just technical problems which can be solved and the solutions disseminated and implemented provided only that there is full and free interpersonal communication, something which is currently hindered by religions and belief systems, national and tribal borders and inward looking cultures in general. We must remake the Catholic Church as a communication organism, keeping the communication channels but throwing away the doctrinal narrowness currently disseminated through these channels.
The Natural Religion Project will eventually morph into a think tank with a website for input and output, ie another node in the network. Given adequate security, the interiors of the nodes are invisible to the network. The same goes for our bodies, which has an immune system which makes them invisible to those who wish to eat us or enslave us.
We proceed by confronting the restrictive forces head on with a demonstrably better alternative. The fundamentalist Christians do well to combat evolution, because it exposes the errors in their world view.
[page 261]
We allow for creationism: the world creates itself by a process of evolution.
Our grail:" a consistent theory of creation.
1. Randomness: Cantor, Gödel and Turing : SPACE
2. Control: Shannon. TIME
Anais Nin: We are attracted by self exposure. Nin
Breaking the grip of all those forces which enslave us by telling us that life was not meant to be easy.
Our basic task is to control events in space so that we survive through time.
The wave function of the human community is the (nonlinear) superposition of the wave functions of all its people. What we seek to do is to make this superposition linear so that we all carry equal weight in the affairs of the world.
Sugarcane biomass productivity 2% Science 327:815 (Godfray op cit)
Godfray page 817: 'Together, these challenges amount to a perfect storm.
'Navigating the storm will require a revolution in the social and natural sciences concerned with food production as well as the breaking down of barriers between fields. the goal is no longer simply to maximise productivity, but to optimize across a far more complex landscape of production, environmental and social justice outcomes.
People will only bother to do something if there is
hope of a profitable outcome.
