Notes
[Notebook: DB 61 Warm]
[Sunday 26 August 2007 - Saturday 1 September 2007]
[page 162]
Sunday 26 August 2007
Aquinas first proof depends on the assumption that act and potency are causally ordered, act being able to realize potency but not vice versa.
Aquinas' work was comprehensively re-presented in the twentieth century by Bernard Lonergan, whose book Insight set me on the path described here. Lonergan rewrites the founding ideas of
[page 163]
Christian theology in a language drawn from Scholastic psychology and classical physics and mathematics. He has little to say about quantum mechanics.
I saw Insight as an information-theoretic proof for the existence of God, but I also saw that it failed. The argument begins with the experience of insight, the act of understanding epitomized by Archimedes vision of his principle in the baths of Syracuse.
POTENTIAL = algorithmic information THEORY
ACT = probabilistic information (need a better name) DATA
(it is probabilistic because it obeys no cloning and so every point is different.
POTENTIAL - THEORY - SYMMETRY - ALGORITHM
ACT - every detail and asymmetry
Although physics tells is that every atom on the planet has a particular placetime and a long history of how it got there, we can can still treat the world as 'Bulk matter', mass, ie see it in the same way gravitation sees it.
Theology is traditionally written in natural languages like Hebrew, Greek, Latin and German. In the last few millennia, all these languages have been augmented with mathematics, on algorithmic version of natural language.
Lonergan has got it exactly backwards, maybe, at least in terms of modern language;
POTENTIAL - ORDER
ACT - CHAOS
[page 164]
The corporate slippery slope : we all work weekends because we all do and not to would disadvantage oneself. But we would all agree to a level playing field with no non-essential weekend work and penalty rates.
Internets show us how to painlessly unite separate subnets. They are the opposite of Nazi symmetrization as practised by Herr Procrustes.
I like to sit here writing as the sun comes up.
What is the difference between a product space and an entangled space in network terms? First we model a network as a Hilbert space. At any moment a network is a superposition of states. Digitally we can assign an edge to each dimension in Hilbert space and the activity on the edge as the weight in that dimension. Total network activity normalized to 1.
The product network? The entangled network?
Entanglement arises when we transform to a new basis that has no vectors parallel to the bases of the states entangled; eg Bell states.
Looking for words - looking for basis vectors.
We generate transfinite numbers using POWER SETS and PERMUTATIONS. If we permute all the subsets and their contents e end up with the permutation of the whole set.
[page 166]
How do we rig this onto Hilbert space, their subspaces and tensor products> Would it help if I had done a bit more mathematics in my youth. Here at least I am being guided by some sort of intuition.
The world is a network of quantum gates.
So what happens is that god gets entangled with himself and next thing we know we have gone from a one state to a two state system, while remaining normalized. So we normalize the whole transfinite system and link it all together using logarithms and exponentials.
The world is more trustworthy than any institution.
Monday 27 August 2007
Map quantum circuits onto Hilbert spaces. Nielsen and Chuang
The data structure (event structure) used by physicists does not necessarily match than used by nature. We assume the natural data structure has evolved (unfolded) from one state and that initial unity is reflected ibn the Universe we have now. The network paradigm is an attempt to impose a data structure (configuration space) on the Universe that makes its functioning more intuitive and so more easily understood.
We may think of the configuration space as a differential equation which sets boundaries on the events that take place within. The Ultimate configuration space (the Cantor Universe) has
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in effect no boundaries, and so anything possible can happen within it.
The relativity of transfinity arises from the cardinal of the discrete set, the alphabet of everything. The empty set, cardinal 1, gives rise by Cantor's theorem to a string of 1s, since at this level ℵ0 = 1, so that ℵ0**ℵ0 = 1, and so on. As soon as ℵ0 > 1, the whole process takes off, growing a bit like e = (1 + 1/ℵ0 )**ℵ0.
The definition (cardinality) is bootstrapped by error resistant and corrective code and once the code gets going, can grow very fast (should learn to calculate this).
What we are saying when we say that ℵ0 is greater than 1 is that in ℵ0 instances of some system, the cardinal (definition) of one of them is 2, not 1, ie it is no longer an empty set.
The Trinity easily gets us going on this.
The choice of title arises because I like to set myself goal that i do not really understand and them try to work my way toward them, like shapes dimly perceived in the mist. This, I imagine, is a model of the way the Universe itself (being god looking at itself) [comes to be]. The procession of the
[page 167]
Son encapsulates the idea of recursion. Although moderns may find Aquinas' model of the Trinity [dates] it is built on concepts whose earliest record is to be found in Heracleitus. The act of looking (reflection) creates more thing to look at and so on. This idea is captures by the idea that the Son is a real image of the Father.
Aristotelian psychology mistakenly attributes mental processes to spiritual substances ad hold that in created being mental images are accidental rather than substantial features of the spirit. We oppose this hypothesis with the Landauer hypothesis, that all information is embodies, ie physically represented. All these ideas are represented in me by a vast array of chemical states i my brain. My mental images are just as real as God the Son.
We proceed by differing from the establishment [with] new ideas. Lonergan made a small step recognizing that the world is a symbolic system decoded by insight. Lonergan
INSIGHT is an OPERATOR (Agent intellect = Hamiltonian, which specifies the pairwise interaction of the components of two vectors).
A manifold is a mapping between numbers and a geometric object.
GEOMETRY is the study of MEMORY, ie how we store data. Quantum mechanics is how we transform it.
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Energy is eternal delight but effort is a pain. I go to make a water network for the day, a sort of laboratory experiment to see if all this works. Strings of insight like this make me tense across the back. Is the back a thermodynamic cold source which makes it possible to distill zero entropy algorithms out of a hot source>
DIFFERENTIAL EQUATION == ALGORITHM
Each differential equation has to be confined by an adequate set of initial conditions if it is to give definite answers ie have definite solutions. So it is like a rigid system mapping definite inputs into definite outputs, a function in other words.
The solution is a function. The differential equation is something vaguer, ie less well defined. The formalism of quantum mechanics is considered to be deterministic, but since it is written in itself there is a limit to determinism set by the finite quantum of action.
DETERMINISTIC = INFINITESIMAL = infinite resolution = digital.
Landauer: a bit is a thing, eg 0 (10 micrograms of ink, 10 square millimetres, 1 micrometre thick)
This is another point about science. In the first instance, you do not preach it but publish it so that the peers can have a look and if it is found to be
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good the implications passed onto to anyone who has an interest in that particular piece of information about the world.
Chapter 2: Logic. The first requirement of a scientific model is self-consistency. Given self consistency, it becomes reasonable to test [for] consistency with the world.
Deighton Line: 'Did you see that item in the newspaper about the residents of Gator taking their complaints about the British army to the High Court in London? Apparently the British army commander in Berlin told the court that since he was the legitimate successor to Hitler he could do anything he wanted. page 8. Deighton
A text is like a differential equation, constraining the action but leaving out the details. 'Werner Volkman came down the staircase and slid into the room in that demonstratively apologetic way he always assumed when I was keeping him up too late.'
Tuesday 28 August 2007
Each string of words in this book represents the fact that somewhere in my neural maze an observation has been made, ie a basis has been discovered (insight) that simplifies a vast superposition of chemically coed states into a sentence like this. Accomplishing this is an emotional situation (pioneered by Archimedes) which cuts through the sometimes desperate feeling that I am lost with the joy and energy that motivates me to pass my insight on to somebody else by writing it down.
[page 170]
Corporate management motivates with money and status, ie by exchanging value for value. Profits and losses arise when the values are unequal. They cannot be measured until they are expressed in the same basis. Humans ultimately operate in a two state emotional basis which ultimately decides 'do x' or not-do x. Prior to the decision may be a lot of debate if the choice is not clear.
Deighton Line page 142: 'Life in Eastern Europe was like that nowadays. Belief was gone. Communication had failed but capitalism had not arrived; every one muddled along, complying without believing.' It seems that believers win, even if the unobservable (and so effectively irrelevant) portion of the beliefs are incredible, like the Christian History of Salvation. They are saved by being mysterious, that is unobservable. From a strictly logical point of view quantum mechanics is just as bad. The wave function is invisible, and 'collapses' to become real. A decision.
SUPERPOSITION - TRINITY
'when a farmer's life was punctuated with the role f warrior.'
Deighton: Sampson meets his wife: lover split by hostile institutions. Romeo and Juliet etc. The root of such pain is ultimately the coupling between love, reproduction and economics.
Order has given us phone books ad the population explosion.
Deighton page 150: We were us, discussing technique, man to man. A product state on unentangled basis.
[page 171]
The process of knowledge (and so differentiation) is to distill independent (product) states out of entanglements. [find the alphabet generating the entanglement] The world began as one, totally entangled, one might say, and gradually (or explosively) differentiated itself into independent entities.
Deighton page 151: 'London Central had sent Fiona to be a field agent in the East and decided not to confide in me.'
page 153: 'Trent was killed'. Religion is a mater of life and death for some. It is good that one man dies for the good of the people. 'It was Caiaphas who suggested to the Jews, 'It is better for one man to die for the people'.' John 18:14 John 'Crucifige, crucifige eum.' Luke 23:21 Luke The scapegoat.
We feel good when we have something to do which we know we can do, though very little in the way of human action goes exactly as planned.
One chess set can realize a large superposition of chess games which can be transformed into one another one move at a time [via the initial positions if necessary] Such games are reversible because the number of pieces and the arrangement of the board are fixed. Do some chess pieces have more entropy than others? Queen near the centre of the board has the choice of about 30 squares, knight 8, pawn two maximum.
We have to play the hand that is dealt is. It would have been nice to avoid the Nazi thing, but it happened and we can examine what historical data we have and try to estimate why this happened and devise ways to prevent a repetition.
FEDERATION: the formation of a political unity, with a central government out of a number of separate states etc each of which retains control of its internal affairs.
I am a federation of cells.
Every entity (event) has its own basis in which it can control itself and maintain its existence.
The Trinity: mathematically it is but a short distance (algorithmically) from 3 to transfinity and beyond (Toy Story) Toy Story - Wikipedia
The new realism. A movement. Natural religion sounds a bit tame but carries the right idea like natural theology and natural science.
A movement is the propagation of a message which might be like a phase change. Greater and lesser movements (fashions, music, ideologies etc) are continually propagating (superposed) through society and we may think of an individual as the superposition of all the movements in his history.
In a divine Universe we can bring evil on our own heads or avoid is to some extent not by begging or praying to him, but by acting in a divine way.
Plumbing: a network between roof and drain.
Deighton page 194: 'but it was difficult to imagine Mauser acquiring sozialistiches Staatsbewusstsein, that unquestioning enthusiasm for the regime that the DDR expects of its
[page 173]
citizens.'
Wednesday 29 August 2007
Deighton Winter 3: 'Fiction had unity and styles, fiction has a beginning and a proper end, fiction showed evidence of planning and research and usually attempted to impose an orderly pattern upon the chaos of reality. Deighton
Maxwell's demon, with the help of algorithmic information which must (?) eventually be erased can temporarily reduce the entropy of its surroundings. This is the information theoretic view of the Carnot Cycle. Bennet et al. Reversible computing - Wikipedia
Gaia, Lovelock. Lovelock
A novel is a local view of the human world, seen through the eyes of human characters, a human history, as opposed to the global histories of historians.
We express the Trinity in quantum mechanical terms, and then quantum mechanics and then both as a network, a complete network with both quantum and classical features (like the world) quanta on the links, continua in the nodes. Although it is called quantum mechanics, the mathematics of physics is the epitome of complex [continuous] analysis.
To those who might feel such a mathematical approach to theology is blasphemous, we emphasize the dichotomy between symbol and meaning: a rose by any other name would smell as sweet.
[page 174]
In the physical (complete) network all communication is teleportation.
Has the rug under my feet been teleported from a sheep's back to its present condition? Fortune favours the prepared mind.
Deighton Winter page 9: 'His Apostolic Majesty, our most gracious Emperor and Lord, Franz Joseph I.'
In practice the only qubits we actually meet are solutions to some wave equation and so from an algorithmic point of view their entropy does not exceed that of the equation and its initial conditions.
A message is a set of initial conditions impressed by one entity on another.
The Christian story is the jealously guarded intellectual property of the Roman Catholic Church, which propagates its story vigorously (for free) and makes a living from its application.
US has a kind of socialist capitalism in that the public purse is very kind to private interests (considering a public company here as private in the context of the state)
Trinity and 3-space suggest the fundamental Hilbert space of the Universe is 3-D? And that all the rest is derived by 'tensor production'.
Father; Son; Spirit: creator; communicator; motivator.
[page 175]
We can see God as a superposition of these. When the superposition 'collapses', one of the personalities of god speaks.
capitalism - socialism - democracy
Two extremes of regime - kill [or eject] anybody who does not fit in (Roman Catholic Church, Hitler, Stalin etc) vs let everyone do as they wish. The later can lead to the former because it gives the advantage to violence. Better to structure society so that it gives the advantage to creation rather than destruction.
3 state system, spin 0 photon, the principal carrier of entropy in the Universe. Peacock page Peacock
A political platform may be phrased as a series of slogans, ie calls to action: save the X (possibly at the expense of the Y) tax the Y.
The basic personality of society is enshrined in its policies on taxing and sending. The administration of the common fund is the means of 'social entanglement'
Quantum information theory simplifies the Trinity to a Duality. A Bi lity .
Marketing (propagating) a religion by organic growth. IATA has reached 80% electronic ticketing in 4 years (?) A phase change, same information, different substrate, to connect a person, a payment and a service.
What is the service that natural religion renders?: harmonious
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action, ie a common basis built on the physical basis of our human spirit.
All this brainy stuff we are talking here is a product of the extraordinarily (or should I say normally) complex systems like ourselves and our environment.
Natural religion demolishes the arrogant position that we are the masters of the Universe which was created just for us by our best mate God.
Work: for me impressing my will on pieces of steel; for a bureaucrat: writing documents telling people what to do. Different layers in the communication network all operated by systems no more complex than Turing machines.
The nodes in the physical network are logically confined; the edges are 'algorithmically confined'. Logical confinement implies zero entropy? The Universe differentiates by classical communication.
We begin our theoretical journey by bringing the Trinity into contact with quantum mechanics.
Thursday 30 August 2007
Remove the economic incentive for war by distributive justice (including the planet in the calculations)
Discovering what you are.
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Infiltrate the organization with new ideas that will ultimately begin to have some control over it.
Love God, love the World. The world is not our slave but our peer [and master].
Deighton page 160: Kaiser Wilhelm . . . All-highest Warlord.
Freedom is to be measured by the entropy of the space in which one moves, and the meaning or information of each move has the same measure.
It may be that we are inclined to think that all the rather miraculous terrain that the study of formal systems has exposed to us is the product of our own minds, unique to us. It all rests on a couple of conditions that are fulfilled in the physical Universe: 1. no inconsistency and 2: a set of distinct and identifiable symbols. 3. a set of orderings and operations on those symbols which can be expressed (encoded) as a Turing machine.
MESSAGE = TEXT OF A TRUING MACHINE = OPERATOR
We use the well known and explored framework of quantum mechanics as a map to show us around network theory and vice versa.
REAL FORMALISM IS EMBODIES IN PHYSICAL SYMBOLS
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Kaiserzeit
Deighton page 210: '[Hitler's] a sort of romantic and he understands that blend of sentimentality and cruelty that us uniquely German.'
'But in Germany too many people are ready to believe in the quick and easy solution.
The fact that information is embodies in symbols of some fixed measure us why cardinal physics works and we can integrate and differentiate various counts.
Can you count the parts of an angel? Pure spirit arises from the reification of formalism (as opposed to embodiment).
INFORMATION = {MARK, SPACE}
Friday 31 August 2007
The political and economic fortunes of a nation are rather like Brownian motion on a larger scale.
ALGORITHMIC INFORMATION == ORDINAL NUMBER
'Everyone strives for expansion, [Hitler] told them, and every people strives for world domination.' [security] page 265]
'Secularism' is another religion.GOD = SECULUM.
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At its heart lies a) the rule of law; and b) the community determination of the law. What we also need is c) a trustworthy theology.
Politicians tell people what they want to hear otherwise they would be out of work. Theologians have to expose the true nature of the milieu in which we exist and the consequent limits to fitness enhancing activity,
Rule of law - power of text - DNA. Putting down text is like putting down bricks. The result is something built which constrains activity in its environment,
A despotic ruler must so tailor its environment that it can kill with impunity.
There is a lot of emotion in these words (for me). That is the continuum behind these digital (literal) strings, The process is a continuum because it is so complex it cannot be resolved by the messages it emits. Millions of synapses behind every word.
Al the Hitler stuff would have been prevented if 'do not kill' had been (magically?) in force. If the law ruled.
All killing people is murder, no excuses, no divine right.
BUREAUCRATIC MURDER vs PERSONAL (PASSIONATE) MURDER
'The final solution'
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Power (government) vs influence (religion).
