Notes
[Sunday 18 May 2008 - Saturday 24 May 2008]
[Notebook: DB 62 Interpretation]
[page 10]
Sunday 18 May 2008
[page 11]
Omnium ignotum pro magnifico Anything little known is assumed to be wonderful. Deighton, Hook, page 246: Tacitus. Deighton
And so the Church hangs on to its mysteries.
The simple task before me is to read quantum field theory as a description of a transfinite layered network that is capable of explaining its own evolution. It is both agent and patient. A patient is a memory location, open to change. An agent is something that changes the content of a part of the universal memory.
As in the Trinity, the Universe grows by mapping onto itself, something we can describe with a recursive function. We can divide recursive functions into two categories: reversible, operating at constant entropy, like a unitary operator; and non-reversible, functions whose range and domain have different cardinalities, in other words functions that work between layers of the network.
GOD'S BODY = {MESSAGES}
It takes an act of humility to accept that we are divine. From the Church's point of view the world is a defective mess held together by the grace of the mysterious God it represents. It tries to tell us that as intelligent children of God in a wasteland, we are very special. They never stop talking about human dignity. To realize that we are personalities of God amidst countless other divine personalities is to take one step further on that road that began when we learnt that the Earth is not the centre of the Universe.
[page 12]
One would like to see the Australian Catholic University repudiate institutional control and become a real university built around scientific theology.
Deighton page 257: 'They gripped my passport in that proprietorial manner that all bureaucrats adopt toward identity papers. For me who man frontiers regard passports and manifests as communications to them from other bureaucrats in other lands. The bearers of such paper are no more than lowly messengers.'
page 264: 'After a lifetime in the service, you look back and see how much time you wasted chasing bizarre solutions while the true answer was banal, obvious and under your nose the whole time.'
Christianity is a bizarre solution, contorted by the need to keep power in the hands of the monarch and his bureaucracy and away from the people.
Emch page 296: The quantum mechanical prediction rule is the dot product, ie the sum of the products of corresponding elements of two vectors. What do we get if we permute the order of the elements in such a product? [the same answer because the addition / integral destroys the order] Emch
Unitary transformation can rearrange the order of eigenvectors.
Magus Butler ' . . . the majority of the miracles derive from the practical functions of the medicine man or wizard, whose paramount duty is has always consisted in ensuring the prosperity of the tribe, clan or society to which he belonged, or the patrons to whom he was attached.' page 6. Butler
[page 13]
Religion, fitness and flourishing
'. . . the main function of the king, priest or magician was to ensure the food supply of the tribe by promoting fertility in man, beasts and crops.' Butler page 6
page 66: 'Both as god-man and as hero of a mystery tale, Christ represented a limit beyond which human imagination could not go in developing the magus-legend.'
From a scientific point of view, the worst consequence of the Church's sequestration of God has been the death of theology. While all the other sciences have followed a general trajectory toward broader and deeper understanding of the human milieu, the last significant developments in theology occurred in the Middle Ages about the same time as the Church became a military and political power and began the process of freezing belief and burning people with alternative hypotheses as a lesson to the others.
Butler page 212 quoting Cooper-Oakley 'The Secret of Kings' summed up [Sty Germain] in the following words:
'Thus clearly stands out the character of one who by some is called a messenger from the spiritual Hierarchy by whom the world's evolution is guided; such is the moral worth of the man whom the shallow critics of the world call adventurer.'
'This is a striking reminder of the autonomous nature of the mythopoetic force. The conscientious biographer who had unearthed some damaging documents about Saint-Germain from the record
[page 14]
offices and had had the honesty to publish them was as impervious to the hard facts she had discovered about her hero as if they had never entered her consciousness. '
Butler page 214: 'A senile old lady (Madame de Gergy) made a queer mistake in 1760 or thereabouts. A legend was set in circulation. It inspired a work of fiction. Another old lady took the fiction for reality. From such slight and apparently unrelated causes mythologies are religion spring.'
Aristotle: A little error in the beginning leads to a big error at the end (as with a ballistic missile, like an arrow). This is not so for guided missiles, which know where they are going and where they are, so that they can correct errors in their course. We capture this in differential equations, but implement it through digital processing - continuous - digital - continuous.
Butler page 218: 'In truth, the story of [Cagliostro] this world famous man might have been invented in the eighteenth century to illustrate the discovery that mystery and ritual are indispensable features in the contemporary fame and posthumous survival of wonder-workers of all kinds.'
page 219: 'It remains a fact that Cagliostro deliberately shaped the story of his life after a rediscovered model and that he has no need to rediscover the model himself. The secret societies had done that for him.'
I am a guided missile stabilized by my working in the building industry.
[page 15]
Monday 19 May 2008
On the origin of space and time.
Racecourses are for gambling and the foundation of the Papal visit must represent the longest odds ever quoted. The foundation of the Pope's position is the New Testament, a selection of writings made and edited by the Church itself to prove its own authenticity. Using these texts is declares itself infallible. If this is true, it is true. But if it is not the whole thing is a Castle in the Air.
Given the Church's way out beliefs: women are inferior; we don't really die; consecrated bread is really human flesh and blood, etc, I would guess that the chances of the Catholic picture coming out a real winner at the end of time are totally negligible, lets say a googol to one against.
OOST [On the Origin of Space and Time]: The concept of evolution has gradually been translated from biology to cosmology and physics. Critical examination of Einstein's picture of spacetime has shown that it predicts the observed expansion of the Universe, and can be extrapolated backwards to suggest that spacetime has a beginning. Mathematically this beginning is represented by geodesics (that is paths of free fall) that are incomplete. H&E p 256 sqq. Hawking & Ellis
[There is] a three parameter family of incomplete geodesics. This gives us grounds for postulating an initial singularity which in some way evolved into the Universe we see, including ourselves.
Now if we define the Universe as an isolated system, we conclude that this differentiation must have taken place 'inside' the
[page 16]
initial singularity.
One of the first physicists to have left an identifiable mark on our history was Parmenides. Parmenides - Wikipedia He has left us a fragment of poetry abut his model of the Cosmos or 'What is'. His argument appears to be epistemological: we cannot write down the truth about a moving system because truth means that writing and reality correspond, which they cannot do for more than a moment if writing is stationary and the world moving. Therefore, insofar as we can truly write down what we know about What is, What is must itself be eternal and motionless. In modern parlance, scientists who want to remain relevant forever must see that their writings correspond to invariant features of the world, that is fixed points. . . . Logos, Parmenides, invariant = formal.
Let us postulate that the evolution of the Universe takes place within the initial singularity by the initial singularity mapping onto itself. This is a modern mathematical expression of the process the ancients called the generation of the world. The question now becomes: how do we explain the origin of the family of incomplete geodesics that populate space-time.
Following ancient tradition, we need to generate a model. Hebrew tradition represented God as a complex often grumpy and vindictive old man with a taste for burnt offerings and enemy blood. This met the austere Greek theological models at the beginning of the current era and culminated in the doctrine of the Trinity. We go on (some might say blasphemously)
[page 17]
from there.
Google googol.
Our magic is work guided by knowledge.
The Church is a product of a magical era when people thought that the whole world could be made to respond to human language. They sound a bit like two-year-olds. Now we know that healing requires not just words but a deep understanding of human anatomy and physiology. The purpose of religion now is to to offer magic but to explain the necessity for work and show how to do it better, ie less environmental impact, less backbreaking toil, fairer distribution of the costs and benefits.
Tuesday 20 May 2008
The path integral method : every path is a route through network and the Universe operates to seek shorter paths, that is less action for every communication. Thus the paths tend to cluster around the optimum path and we call this clustering attraction be a stationary point.
Parmenides and his followers are inclined to think that the Universe is essentially static because the static elements of the Universe are speakable.
The length of every path (ie every transformation, every Turing machine) is one quantum of action, which quantum is nh, measured in units of the smallest unit of action, h.
[page 18]
Since c and h are the units of measurement in spacetime (in a sense, the units of construction) we can say nothing about their absolute size, only that every observer sees the same.
Noise in the cellular chemical network N453:150 Pearson
N rejected on gravitation. Science, and then Physical Review. Also [arXiv] arXiv - Wikipedia
It is one thing to have an idea, another to carry it through. What would Feynman have done with the network model? We want it to produce practical results, explaining and guiding work.
'. . . the impact of increased fossil fuel prices on technological change and on mitigation costs, or policies, cannot be analyzed in any meaningful way for policy-makes by assuming a 'frozen technology' scenario. Edenhofer at al, N 453:155 Edenhofer
One is always trying to program the dynamics of a process (like computer manufacture) to minimize costs, which are set externally by the environment in which the system lives. Increasing fuel costs will induce dynamic systems where intelligent processing replaces energy consumption by improving algorithms and changing the ration of modelling (thinking) to construction.
It might be nice to have a revolution, but there is an awful lot of sunk capital in the form of embodied information so that the system has a lot of momentum. Force is therefore required to change its direction. This force comes from two sources: the quality of the proposed new course, and the amount of effort put into developing
[page 19]
and promoting it. Are there any promoters out there who wand to fund a bit of blue sky theological research? By far the best (least action) course is to continue to develop the idea and continue to seek peer reviewed publication.
Any string of bits can be modelled with a suitable Fourier series? Phase information is important, ie the establishment of the relative phases of all the superposed periodic functions.
Nyquist. The harmonic oscillator gives us a set of evenly spaced frequencies which serve as an alphabet for communication. Nyquist-Shannon sampling theorem - Wikipedia
Wavelets.
The medium is the message. The message is the amount of traffic on each channel. Quantum mechanics tells us this without attributing any meaning to the traffic. The probability that a system prepared in |a > will be measured in |b > is |<b |a >| 2 and that is all it tells us. But what are things saying to each other when they actually communicate on the a - b channel? Meaningless communication can only be measured by its mass (or its energy), its cardinality. When we begin to consider meaning we must take note of the nature and order of the symbols rather than treating them simply as units.
In a one dimensional Universe a point can only communicate directly with its nearest neighbour on either side.
Pregeometry = arithmetic (Misner, Thorne and Wheeler) Misner, Thorne & Wheeler
I m outside and alone and (for security's sake) want to get
[page 20]
inside where there is company.
Maximum fitness = maximum (relevant) processing power. In society this means cooperative parallel processing, each of us carrying some of the load. This in turn points to universal education, human rights, distributive justice, democracy, reliable communication systems and so on.
Computational pipeline: a pipeline of Turing machines joined output to input.
Poverty and failure are the mothers of work and invention.
Wednesday 21 May 2008
The Myth of the Magus: we are very susceptible to dreams with happy endings, and we like people who can make them happen for us. The advertising industry is built on this feature of humanity: Smoke this and women will go for you; rub this on your skin and stay forever young. The adbusters of the world see this as a bad thing, but it is probably just another manifestation of the united we stand divided we fall principle that underlies the complexification of the world. Because we cannot unite without differentiating, that is assuming a role in the larger system. In armies and other emergency systems, these roles may be dealt out by a formal command structure, but in peaceful timers they evolve by communication. What is essential in both cases is a common language, common goals (ie survival), common methods and a common environment. Aristotle's four causes, formal, final, efficient and material. It simplifies communication to keep these common threads. The
[page 21]
leader of a cult weaves them together into an attractive package which brings in followers. Every community has a cult, that is an embodied subset of religion, the element unifying the community so that it may stand united.
Cooperation, of course, by lowering security barriers within a community makes possible the existence of cheats, those who benefit without contributing to the cost. These are to be controlled by an error correcting function which is essential to any complex system.
The ancients probably took a broader and more humane view of the world than we do because the complexity of our society is reflected by the complexity of our own lives, sustained by a large capital investment in housing (memory) and transport. In the spatial projection (Plato's shadows, with a huge increase in bandwidth) all things are achieved by moving things around in the presence of various conservative and dissipative fields, like the 'driving in a nail field' or the gravitational field.
FIELD = local formal expression of possible process, ie the field to create a photon or a house.
My task is to fit the proposition 'the Universe is divine' to the received body of science. This requires a reinterpretation of the terms Universe, divine and science, so that we can form the proposition 'our divine Universe evolves by the application of science'. In other words we sacrifice the supposed uniqueness of our scientific process of conjecture and refutation to the knowledge that all processes share the scientific symmetry because they are examples of a system looking at itself and exploring the possibilities it sees.
[page 22]
From a practical point of view we need a religion (to be locally inculturated) which recognizes the importance of our environment in our creation and survival and therefore declares it a 'mortal sin' to damage the environment. Cathnews This mentality will lead us to live off the sun and concentrate our activities so that 100% recycling of materials (memory) becomes possible. Such a global religious view might serve to unite local activities into a global whole.
Resolution: journalistic vs scientific, ie raw vs highly processed data.
So we see The Church that stole God is chapter 1 of a book that goes on to expose natural theology and natural religion. From magician to engineer.
The whole aim of science is to produce working models of the world which enable us to see the consequences of our actions: we plant a seed in the right conditions, it will probably grow.
Thursday 22 May 2008
We want to fly but we cannot do it without the necessary art, that is the structure that mediates between physical realities like energy, momentum, pressure and so on and the act of flying. A flying machine, in other words, A machine is a coupling between the physical world and a dream like flight or a continuous and abundant supply of food such as most people in this neighbourhood enjoy.
God is the whole world and every event in the world has roots reaching to the initial singularity and is just as
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meaningful as the Bible or the Catholic Church,
I am cranky with the Church, but insofar as it is past it cannot be otherwise and the only reason for attacking it is to gain resources for the evolution and propagation of an alternative, and maybe a touch of revenge, but one must assume that all the agents of the Church who influenced my life were sincere in their belief that they were doing what was best for me. I am a long way way now. Although it seems consistent with all the data, identifying God and the world is precisely what the Church cannot accept and remain unchanged.
Every communication transforms value.
Each new development is a critique of its own history made possible by reflecting on history, which is in turn made possible because the past is fixed and so can be written and compared to other writings in the search for a path ahead. No matter how long term our plans, there is always the present to deal with, the actual arena of action lying between the fixed past and the possible future.
The present is our proper time or inertial frame from which we see and are constrained by past and future. So I am a machine converting past into future and leaving a trace of my conversion in this squiggly (but meaningful) black line.
Self image, Narcissus and consciousness: Jaynes. Jaynes
The Church is thicker than a brick, absolutely fixed in its own
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belief in itself, so it is no use attacking it. Best to leave it to wither on the vine by attracting its constituency to an alternative, as Luther ended up doing, although he was trying to reform the Church, not replace it. But the Church is infallibly irreformable and so let it be.
Everybody is concentrated on immediate problems and it may seem unnecessarily abstract and physical to claim that our predicament requires a new view of the whole by which to navigate ourselves to safety. We can no longer rely on the dim light of a distant bible as the integrating factor for all the details which surround us.
Since I feel that a new theology is necessary, it is down to me to promote it, which I am trying to to at the same time as I try to develop the picture of God I prefer. The Universe of events us the screen upon which God is projected. The Bible is a pixel on this screen, with a certain position in spacetime and both an ingoing and outgoing information flow. The Bible is a potential that transforms pasts into futures.
A spacelike slice is a region of fixed memory.
From the point of view of an observer, a spacelike slice is contained in the incoming information cone, what I see at the moment. My spacelike slices succeed one another kinematically as time passes and I shift my gaze and the process of knowledge is a quest for the dynamics behind the kinematics, which we model as a succession of statics, like a string of wiring or DNA.
[page 25]
We are seeing that DNA is not just a string of genes for proteins that once formed carry out the roles in the cell, but also contains code to determine which genes should be turned on and off in response to signals from the environment: when there is a shortage of engineers, we train more engineers because the shortage makes each one worth more.
We might say the cell has a labour market.
Solar electric: we are electric Bartleby.com
Solar thermodynamic: and also thermodynamic, ie statistical but controlled.
The special thing about quantum mechanics is the use of complex amplitudes to compute real probabilities. We can approach this through the theory of real measurable probabilities. What does it mean? It tells us something about the fundamental physical encoding of the Universe. Real numbers, for us real information, comes as the absolute square of a complex number.
A state is represented by a vector which may be expressed in terms of an orthonormal basis and a set of coefficients normalized so the sum of the probabilities of the basis states is 1. Quantum mechanics defines possibilities and probabilities 'simultaneously'. The size of the basis space and the corresponding operators measures the complexity of the process (to which there is no limit) and the entries in the operator correspond to the probabilities of the possible events so defined.
[page 26]
which still does not explain the utility of complex numbers. My guess is that an amplitude and its complex conjugate represent two halves of a complete cycle of communication, you call, I answer, the call is 'complete'. The probability of completion is represented as the product of the amplitudes representing the calling and answering. Why is answering the complex conjugate of calling? Mathematically, it is a way (the only simple way) to get a real answer out of an operation on complex numbers. And physically? We may think of a complex number as a vector in the complex plane. It is defined by two real numbers on the orthogonal real and imaginary axes. The tricky bit in complex numbers is the i = sqrt(-1), i2 = -1, an object that clearly violates the requirement that all probabilities are positive numbers. So we might imagine (in probability terms) that the imaginary part of a complex number is the antagonist of the real part, this making possible complex exponents which are periodic. So the use of complex numbers makes possible a model of dynamics which is both periodic and normalized. The periodicity is a product of recursive function theory, the normalization comes from the quantization of physical events that makes it possible to implement recursive function theory. From the point of view of this fantasy, complex numbers represent the two coupled and antagonistic degrees of freedom from which the Universe is built.
Why must I try to understand physics to do theology? Because physics is the foundation (protocol) of my communication interface with God.
Hypocrisy: proclaiming one thing and doing another, as the US rejects torture but sends it offshore.
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Our range of interaction runs from reproduction to killing, from tenderest love to lethal hatred. The foundation of both these extremes is the selective competition for limited resources driven by the will to live.
The foundation of peace on earth is fair trade in the earth's resources, everyone getting a reasonable quota within reasonable limits.
The quantum no cloning theorem excludes the possibility of empirical residue? Lonergan No two states are the same? Something differentiates them or (tautologically) if things are not differentiated in some way they are the same. Empirical residue implies the existence of meaningless or unintelligible data, but all data are differentiated and so may have meaning. We remember again that the more densely coded a data stream, the more it looks like noise (Shannon?).
Agatha Moving Finger page 45: 'Quite absurd, because Caleb has absolutely no taste for fornication. He never has had. So lucky, being a clergyman.' Christie
Thought, presumably, is a response to stress, so that we might expect wars, famines, disasters and diseases to provoke a lot of creative thought. Much science is a response to pathology and the promise to cure some ill or another encourages funding.
We cannot know our future very clearly, but we can know where we came from, insofar s vestiges of our past exist in the present, like photons travelling through the expanding Universe to the present from the distant past.
[page 27a]
Kinetic energy is always positive because time moves only in one direction. Potential energy is outside time, ie time is not relevant to it, it is static of itself and can only change by the emission or absorption of kinetic energy,
Friday 23 May 2008
Coupling constant - probability that a 'conversation' will be initiated, ie a question and answer. For gravitation, this [probability] is very small, whereas in a well programmed and error free computer it is very close to 1. It might be considered as the ratio of meaningful to meaningless messages, things worth listening to to noise.
Feynman, Gravitation page 11: 'there is apparently no hope of our ever observing a graviton.
Gravitation not quantized? Feynman page 12: '. . . the postulate that defines quantum mechanical behaviour is that there is an amplitude for different processes. It cannot then be that a particle which is described by an amplitude, such as an electron, has an interaction which is not described by an amplitude but by a probability.
Amplitudes describe possibilities. Amplitude (cat) = 1/ sqrt(2) (psi(alive) + psi(dead))
At any time, cat is realizing one of the possibilities.
Me must distinguish between possibility and actuality and potential and motion (in some way)
[page 27b]
We might say that for each one of us consciousness (knowledge) is the screen upon which God is projected, and by comparing these projections between ourselves, we arrive at the data for theology, which includes all the sciences.
So we repeat our claim: If the Universe and God are one, theology is the theory of everything.
The standard theological model for the last 2000 years has been God >< Universe. Here we examine the alternative. Theological Studies.
Amplitudes interfered (because they are complex). Classical probabilities do not.
Although some might be inclined to reject this hypothesis outright on some a priori ground, let us at least examine the hypothesis enough to arrive at our conclusion: that there is no observational test that can distinguish between the two hypotheses, so both are equally tenable. Occam's Razor, however, suggests that we should concentrate on the simple hypothesis, since there is no need to postulate two entities, God and the Universe where one will do, and all doubts about reliable communication between God and the Universe are removed at a stroke.
Parmenides: we can only have certain knowledge of certain things. He interpreted certain to mean outside time of eternal and concluded that reality was eternal, full, spherical etc. Parmenides
It seems natural that the ruling class (eg Plato) should be concerned with stability in the Universe because their lives were made unstable by the need to tax unwilling populations.
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Symmetries are the vacuum from which reality (= complexity, broken symmetry) is constructed.
Saturday 24 May 2008
Propagator = amplitude to go from one point in spacetime to another. Coupling constant = probability that something will happen when it gets there. Propagator - Wikipedia, Coupling constant - Wikipedia
Nature: What does quantum mechanics mean?
To give meaning to two points we map them to one another. So we map quantum field theory onto a communication network. This brings our intuitions about communication to bear, which are just as important to us as our spacetime intuitions. The latter are the sorts of things we use in sport, or any form of construction. The former cover gossip, music, and all the other interactions in the human and spatial sphere. It is clear that the network model contains the spacetime model.
To make a network we need memory and processes that change the states of units of memory. An abstract network is a set of nodes and edges that may be assembled in different ways. Edges cannot join to edges nor nodes to nodes, but nodes are connected through edges and edges through [nodes]
Quantum mechanics and communication theory both work in function space. Shannon Communication theory uses a real space, quantum mechanics a complex one: quantum states are represented
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by vectors or strings of complex numbers. Messages in communication theory are represented by strings of real symbols which may be read by a suitable operator. What the message string means is a function of both the string and the algorithms used to decode it. These algorithms may be as complex as ourselves, encoding and decoding ideas through the medium of writing. The writing is static, whereas the encoding and decoding are dynamic, seeking to compare the new input to existing knowledge to connect it to our tree of knowledge and so give it meaning to ourselves, meaning that we can share. So we can see for instance, the historical event known as the development of quantum theory. The network model is not just a theory, but a theory that explains how we put theories together by thinking and talking to one another. From an abstract point of view, the same way as we gossip together, using on the whole a looser epistemological foundation than science. Epistemological quality may run from 1 (definitely seen) to 0 (pure fantasy).
The financial markets are an epistemological problem.
The recent common mode failure in the mortgage market arose from the fiction that statistical averaging could make bad loans good.
In the ideal case there is a deterministic encoding and decoding at each end of the channel so that me might say that the users of the channel understand eachother perfectly. This is the case in transparent trade, but may become more difficult when the interests of the communicants conflict.
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The basic epistemological question (formal version): How is it possible for mathematicians to talk about infinite structures in very finite strings of symbols that fit into papers, letters and textbooks? The traditional answer is abstraction, that is establishing a correspondence between a simple symbols and an complex entity, as when we talk about N, the set of all natural numbers. We can speak of such sets if we can have an effective means of deciding whether something belongs in the set or not.
And the question that arises when we wish to map quantum mechanics onto network theory is, what is the meaning of all the mathematical complexity that lies behind the computation of the nature of events and their probabilities. By analogy with human communication, we are inclined to think of the quantum mechanism as the thought processes behind the utterances of the Universe, an infinitesimal fraction of which are received and analyzed by scientists.
A proof has direction, and is not necessarily reversible? Fan in; fan out.
Feynman Gravitation page 28: 'If we allow a new particle we can construct a perfectly good theory by assuming the existence of a spin-two particle of zero mass which couples linearly with matter.' : a message that is always decodable because it is trivial?
mass = potential; inertia = kinetic. Write these little things to see if they can be given an y meaning.
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And he writes: 'In the first place the fact that gravity is found to have a long range automatically means that the interaction energy depends on separation as 1/r .[
ie the frequency of the communication is the inverse of the distance.
'There is no other possibility in field theory.
All long range physical forces travel at the velocity of light.
Quantum mechanics is in some way the computation behind events, just as our thoughts are the computations behind what we say, so that we might ask : what was I thinking when I said that? One might object to this analogy in that it seems to ascribe intelligence to the Universe, but that is the point : a new definition of intelligence enabling it to be attributed to al process in the Universe.
We can say that the Universe, like God, is the essence of truth, seeing all the apparent contradictions as the convolutions of a mysterious plan.
The difference between classical and quantum mechanics is the difference between probabilities and amplitudes. Quantum mechanics shows us how to compute amplitudes. No matter how huge the computation, the absolute square of the amplitude is the answer in probability terms. So quantum mechanics gives a probability structure to events by the superposition of amplitudes arising from different sources. And an amplitude is a minimal vector, a two component quantity, a real part and an imaginary part, an exponential part and a periodic part.
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Orgasm: an exponentially growing periodicity leading to a completion. Orgasm - Wikipedia
He does not complete things. Everything is a work in progress. Not sufficient in the contractual world of performance and completion.
Computation via superposition vs computation by a string of operations woven through the structure to be transformed.
So we see the differential operator as a Turing machine, a node lying between two edges, transforming one into another.
In a sense there us no space between events, but events are distinguished by the spaces between them, So let us design an alphabet of n letters which are as far apart as possible in the human visual letter recognition space.
We may imagine quantum processing as them simplest possible, based on simple logic or arithmetic.
The details of an event, like a marriage, can be very complex, and yet we can assign a probability to marriage.
Heisenberg Physical . . . " A much more radical departure from the classical conception of the world was brought about by the general theory of relativity, in which only the concept of coincidence in space-time was accepted uncritically'. Heisenberg
A completely coordinate independent event and the
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foundation of network theory where we accept a duplex communication (message and reply) as the definition of an event involving the coincidence of two points. We coincided, we talked, we mated . . .
The basic algorithm of quantum mechanics is the dot product which requires pairwise multiplication of a complex number and its conjugate and addition. <a | b > = Sumi biai . This computation lies behind diffraction and interference.
Heisenberg page 10: 'The concept of stationary states . . . is the most direct expression of the discontinuity in all atomic processes.
'The solution to this difficulty [wave / particle] is that the two mental pictures which experiments lead us to form - the one of particles, the other of waves - are both incomplete and have only the value of analogies which are accurate only in limiting cases.'
Heisenberg page 57: '. . . the values of two dynamical quantities are causally related if, and only if, the tensors corresponding to them have parallel principal axes.' ie both quantities are expressed in the same code.
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