Notes
[Sunday 18 January 2009 - Saturday 24 January 2009]
[Notebook: DB 65 Symmetric U]
[page 62]
Sunday 18 January 2009
We explain the fact that P = |phi |2 = phi.phi* by the requirement that a message be sent and acknowledged before it can be considered certain. This is suggested by the fact that if
[page 63]
phi = <a |b >, then phi* = <b |a >, and this is a consequence of the need to preserve normalization. So why is a one way message a complex number (ie a vector) when the probability of a two-way message is a real number? In other words, what does the mathematics mean? [maybe complex numbers, representing periodic functions, point to a work in progress, whereas reals are the finished product?].
The speed of a quantum process is a function of its energy. We consider that (apart from scale) a quantum event is equivalent to an act of human insight, by which eigenvectors are picked from the set of all possible vectors and act as a basis for communication between two previously independent systems., the 'observer' and the 'observed', although in reality there may be no such ordering (at least at the quantum level) and to observe is to be observed.
'Bonum ex integro', like the halting of a Turing machine, only happens if everything goes right. On the other hand continued life (Archer, First page 93) is possible if there are no fatal errors and the process continues. Death is a consequence of fatal error, most probable near the beginning and end of the normal lifespan.
Computable functions are in effect the countably infinite set of eigenfunctions of the set of all possible functions, the majority of which are not computable. Information cannot be communicated unless it can be computed, that is encoded.
Let us imagine that a complex vector with a certain amount of energy represents a computation in progress. The product of such a vector with its complex conjugate represents the halting of a computation. Each sentence I write is the output of a network process in my reach[ing] a conclusion, ie coming to a halt or fixed point that can be recorded in an eternal formal medium, a fixed point in my dynamics.
[page 64]
EIGENFUNCTION = COMPUTABLE FUNCTION
The 'spiritual' world is structured by mapping logical addresses to physical addresses, so that my spirit is mapped onto all the articles, cells, tissues etc that keep me going, keep me thinking, and whose welfare I must attend to by finding food and shelter and correcting error by going to the dentist, the optometrist, and the doctor.
CONTINUOUS = MEANINGLESS
Evolution (eg thinking) is the process by which systems gradually extract definition from the continuum thereby acquiring increased cardinality and meaning. So we see the Universe developing from a one state initial singularity to a transfinity of states and beyond.
Q. 'Quid est hoc quod est esse ?' A. To be in touch. Which is exactly what the Catholic Church wanted me not to be, but sensuality won in the end, god bless her.
The waves represent the computation, the particle the conclusion.
Why do we observe a quantized Universe? Because it is.
An open letter to the Pope
[page 65]
Only the supremely deluded could possibly believe that a few thousand words of politically motivated plagiarism compiled three thousand years ago can adequately describe or define the nature and fate of the Universe in which we find ourselves.
Benjamin Disraeli: 'Today's extremist is tomorrow's moderate'. (?)
Mein Kampf: Explain what you want to do and then do it.
The year we started on the Pope. Like the bomb. Have been waiting for it for years and this year we will have a test.
Monday 19 January 2009
Numerical results: All the computations of quantum mechanics have as their inputs and outputs observed values which are ultimately ratios with respect to various standards of mass, length and time. The actual computations leading from input to output are ordered arrays of additions and multiplications encoded as complex numbers, vectors, matrices and Feynman diagrams guided by various symmetries.
The computations may be assumed to follow algorithms which in some way reflect the algorithms used in nature to achieve the same observed transformations. Our methods of 'preparing' and observing the world have led us, in accelerator physics, to concentrate on the S matrix which transforms the input parameters into the output parameters. S Matrix - Wikipedia
One of the most important symmetries in nature is represented by special relativity, which is a direct consequence of the time delay in
[page 66]
communication. My input as a transformer, was the need for an evidence based theology based on the notion that the traditional god and the observed Universe (sometimes represented by physical results but also including all other scientific observations and the general observations and feelings [of all personalities]) [are the same thing]. My output is network theory.
MOTIVATION
Science is a struggle against anthropocentrism. The nineteenth century hoped to totally abandon it, so giving us the killing event known as the first and second world wars. Quantum mechanics and relativity abandoned the absolute world and introduced relativity through Einstein and the interpretative hypothesis of quantum mechanics : what we see depends on how we looked. Relationship and transformation became constituent features of the Universe rather than artifacts of our observations. Aristotle saw relationship as an accidental feature of an entity, saying in effect that physical environment did not matter. This is because he and his contemporaries believed that the world was motivated by invisible forces known generally as gods. This view is reflected in the Iliad. Homer Aquinas hypothesized that although relationship is indeed accidental in the created world, it is real in god. Aquinas 165 Slowly this and [our] consideration of the Universe as god, diversified by real relations into not the three persons of the traditional trinity, but to the countable infinity of personalities around us, ranging from people up to global organizations an from people down to fundamental particles. I slowly began to see that this could all be modelled by a formal network of the type we call the [computer] network. Such a
[page 67]
network is controlled by layers of software stretching from the physical embodiment of the network in copper, gold, silicon etc to us the users. The basic mathematical theories of networks represented by the theorems of Shannon, Turing, Gödel and the whole edifice of mathematics, all based on Cantor's transfinite set theory begin to appear as a formalism quite large enough to model a divine network. By a divine network we mean an isolated network, one constrained by no external inputs or outputs. This view was promoted by the realization that from an observational point of view, quantum mechanics is a digital process and our continuous mathematical formalism a simplifying and abstracting artifact, all nevertheless processible by Turing machines. So we liberate the Universe of continuous functions into the far larger world of 'network computable; functions. (Ross Ashby Ashby). The struggle against anthropomorphism thus reveals a symmetry which makes us one with the atoms and all the other independent entities jostling for life in this world. It also shows us how communication complexifies, that is creates, the Universe. Further maximal communication (maximal entropy) corresponds to equilibrium (in human terms, peace). Nuclear weapons and exploding hatreds have a lot in common. Reality calls. I have to go to work to pay for my self indulgent dreams. A chain reacting nuclear weapon and an exploding hatred have similar features and work done on one may lead to understanding of the other.
Einstein founded modern theology by making relationships substantial rather than accidental. Euclid rightly abstracted the idea of Euclidian space which is potential free, but real spaces are full of potentials. We achieve big things (be they explosions or structures) by talking one another into things,
[page 68]
ie marketing and politics. This talk is 'force' and it may come from someone's mouth, or the barrel of a gun.
. . .
It seems probable that the intersection of the sets of readers of the above journals is almost empty. My reason for seeking joint publication is to create a communication protocol that will bring them together for our salvations. Physics has given us weapons strong enough to sear the earth. Religion in its current fractured form gives us the motivation to use them
In a network computation all machines are what Turing called o (for oracle) machines that could stop and ask their environment a question before proceeding. Turing All practical machines [except god] are in effect o-machines, receiving and giving information from and to users. Every machine represents a set of transformations in the universal network.
Spirit influences the material and vice versa which is why I have to go and do other work until I can make this stuff pay.
Tuesday 20 October 2009
My story is lovely to me, its my baby, I designed it etc (Yellowbeard Damski) But what are its weak spots? In particular does it show any promise of delivering better computational results or better explaining the world that the standard model and all the other intellectual products that
[page 69]
underlie our individual and corporate behaviour? Once quantum mechanics was developed in principle, the next task was to apply it to real problems.
What we would like to do is describe and compute some of the constants that must be input to the standard model to get it to work. Since all these constant are numbers, ie ratios of one sort or another, our first problem is to seek the basic denominators of the Universe, the units in terms of which all measurements are expressed.
The basic unit is the unit, and the basic ratio is a count. So the unit of sheep is one sheep and when I count my sheep I arrive at the ratio of my mob of sheep to one sheep. Such counting requires classification, since I would be misspeaking if I counted my dogs and a few stray wallabies as part of my mob. The most basic count is a count of thing which are so little defined that they cannot be misclassified, that is what we might call identical universal particles. Here the universal is an act or event, and since events are discrete, our count is the number of quanta of action.
Omnes: Quantum Philosophy Omnes (digital philosophy?)
Net work is the work of communication
COMMUNICATION = WORK
Drama : bringing the formal text to life
Science : reducing life to the formal text
[page 70]
I am excited but nothing is happening. I am hoping for more insight, new halts to the ceaseless web of communication I call my mind, waiting for something to be deemed sufficiently complete to enter my consciousness.
Mathematics, as practised by mathematicians, is computable just like mechanics as practised by mechanics, juggling definite and separate parts to construct (eg) a running engine or a running computer.
Each layer of the Universe is an understanding of its past which it uses to constrain its future.
The network version of Landauer's hypothesis: everything communicates through the physical layer. Landauer Logical communication requires as a minimum two symbols, but cardinal communication requires only lots of units which are considered to be all the same, differentiated only by their addresses.
Omnes page xxii 'There appears to be a gap, a chasm, between the world of thought , the theoretical world, and physical reality. It is as though the power of logic and mathematics, after accounting for the minutest details of reality, were unable to penetrate to its essence.'
The essence is that networks can be constructed from networks and the meaning lies in this construction, not in the symbols we use to represent information in our networks.
DARK MATTER = PURE CARDINALITY (undifferentiated units). This is why general covariance works, it treats every message in exactly the same way, merely counting (or weighing) it.
[page 71]
All begins as mist and increases cardinality toward clarity.
FORM (Plato) = ALGORITHM (Turing, Gödel, [Chaitin]) Chaitin
MATERIAL - CARDINAL - PHYSICAL
FORMAL - ORDINAL - SPIRITUAL
'The more you realize that war criminals might be ordinary people the more afraid you become' Slavenka Drakulic quoted by Adam Kirsch, Beware of Pity, New Yorker 12/1/2009 page 62. Kirsch
Hannah Arendt: The Origins of Totalitarianism Arendt
Kirsch page 66: 'To live fully and securely every human being needs what Arendt calls 'specificity', the social and political status that comes with full membership in a community.'
Wednesday 21 January 2009
Omnes page 51: 'There are cases while solving a cubic . . . equation . . . one needs to introduce in the solution process imaginary numbers which act as a kind of intermediaries (but do not appear in the original equation or its final solution).
This appears to be the role of complex numbers in quantum mechanics, appearing only in the computations leading from the initial to the final states represented by real numbers or integers.
page 55: Karl Weierstrass (1815-1897) Karl Weierstrass - Wikipedia
page 56: 'Thanks to W and to some others, analysis finally rests on a solid basis and it
[page 72]
becomes possible to verify the scope of its theorems.
Creation by resolution.
Omnes page 57: 'In mathematics what matters is not the nature of things but the relationships that exist among them.'
We represent relationships by the transformations necessary to convert one into another, and we equate transformation and communication.
Omnes page 63:
'One of my most precious dreams -- partly responsible for this book -- is to see one day scientific knowledge so clearly established as to allow a return of philosophy to its pre-Socratic sources, finding in science its own foundations or its most fitting mold.'
The network communication model may do this by replacing out geometric intuition by our intuitive understanding of communication and gossip.
page 64: Descartes and Reason: Survival (natural selection) guaranties the parallelism between the human (and every other) mind and 'reality'/
The probabilities computed by quantum mechanics are analogues of the 'synaptic weights' of a neural network. Beale & Jackson All technology comes down to modifying the probabilities of events. The internal combustion engine, for instance, increases the probability that energy released by burning fuel will appear as mechanical work. The second law
[page 73]
of thermodynamics places an upper bound on this probability. Second law of thermodynamics - Wikipedia
COMPUTER = CHANNEL
COMPUTER = {COMPUTER}
All the basis vectors in quantum mechanics are normalized so that |<a |a >| 2 = 1. So in the path integral method all the paths contribute an equal amplitude. It is only at the superposition stage that the independent paths interfere (add) and give a sum which depends on the relative phase of the paths at the point of measurement. The relative phase, in the computational model, is the relative time of halting, which in a parallel real time network system may be imagined to give the same results as the path integral.
The whole of mathematics (insofar as it can be discovered) can be embodied in a network of Turing machines each of which represents a theorem and which all working together can permute all the theorems of mathematics in any consistent order. These machines (formally represented by algorithms) are the stationary points in the Universe which are the subjects of science and, because they are stationary, can be represented by stationary text such as this.
Algorithm = function. So the set of eigenfunctions of the Universe has the same elements as the set of Turing machines.
Omnes page 117: 'It is true that for diehard formalists mathematics is entirely reducible to symbol manipulation and in this sense it coincides with nominalism. However, few
[page 74]
mathematicians are prepared to go that far.'
Omnes page 122: 'Present day physics is based on objects that cannot be conceived as elements of a set from which subsets can be formed.'
Do we believe this? Accelerator physics spends a lot of time designing instruments that follow the spacetime paths and identities of particles with considerable precision, dividing them into bins whose statistics are compared with theory.
page 123: 'There is nowhere in physical reality an anchorage for mathematics that imposes itself as initial evidence' (:)
Does counting count?
For the path integral method all information is carried by phase since amplitude is normalized.
Thursday 22 January 2009
Turning from Bierce to Omnes provides a flash of deja vu. Bierce
Omnes page 121: 'There exist come 'ultrafinitists', mostly physicists or computer scientists, who refuse to see in mathematics anything but a finite process executed by a computer, or directly in nature by the objects themselves. It is an extreme position which we shall not elaborate on.'
But maybe right? Maybe a Universe that starts as an initial singularity and then differentiates into a duality ('Father, Son'), then a trinity (Father, Son, Spirit) and
[page 75]
so on to a countable infinity is built on very simple finite computable foundations.
Omnes page 149: 'The purpose of interpretation is to reconcile these extremes [wave and particle models of the world]; to show if possible that they are coherent; to establish modes of thought capable of bringing them together without deforming them. It is hard to imagine a more philosophical enterprise, for it boils down to knowing how to think about the world.'
In a word, the world is gossip.
page 149: fact = message, requiring interpretation, best achieved by sharing the language of the sender [ie the same set of eigenfunctions].
Seeing the effect before the cause: if the ship carrying the legislation arrives before the one carrying the parliamentary debates that formed the legislation one sees, in a relativistic way, the effect before the cause and may speculate from the wording of the law the issues that were canvassed in framing it.
page 150: 'In a nutshell, everything in classical physics is determined, and the use of probabilities is only a substitute for the exact knowledge of the acting causes.'
'Things are very different in quantum mechanics, for in it events really occur at random. No cause is at work to make an excited atom decay at some specific moment. There are of course laws governing the whole process, but they only express the probability of the event taking place at one time rather than another. Quantum probabilities are not a substitute for a
[page 76]
detailed knowledge of hidden relevant details; there are no relevant details, but pure chance?' [ie symmetry]
How can we be so sure of this?
First, the process of decay is something definite with a limited range of predictable outcomes, like emit alpha particle, electron, neutrino etc.
What is indefinite in embodied in the symmetries of space and time - when will the atom decay? Where and in which direction will the decay products go? The actual probabilities of space and time are indifferent to the location in space and time, which is the essence of symmetry.
On the other hand, quantum events can be caused, the whole justification for spending billions of accelerators and detectors.
The network interpretation of this symmetry is embodied in the sentence 'the alphabet cannot determine the sentence'. Nor the alphabet, the lexicon and the grammar. It is for the speaker to select from the possibilities of a language the actual sequence of words used to convey a meaning, as here. So physics does not determine the spirit, but presents it with an array of possibilities.
There is no 'objectivity' in a communication network. What you see is what you get, and what you see depends on how you look, with what apparatus, eye, ear, nose, skin, tongue, etc.
UNMEASURABLE = INCOMMUNICABLE
Some interpretations of quantum mechanics have understood 'observer' to mean human observer and so implicated human consciousness in our understanding of the world. We think that anything can be an observer and there is no real difference (apart from complexity) between an atom decoding the motion of a photon and one human person decoding the motion of another.
Friday 23 January 2009
Omnes page 162: 'For coherence is a circle without a prescribed beginning or end.'
page 164: 'There lies the originality of our approach: to deduce the common sense from the quantum premises, including its limits -- that is to demonstrate also under which conditions common sense is valid and what is the margin of error.'
Common sense is the protocol of all human communication, a protocol whose physical layer is described by quantum mechanical communication.
page 168: 'Classical determinism is the logical equivalence of two propositions of Newtonian dynamics with respect to two different instants of time.'
A Turing machine parametrized by a clock can imitate such classical determinism since its state at time t2 is determined by its state at t1 and the algorithm it is executing.
[page 78]
Omnes page 285: 'In quantum mechanics, the role of a physical quantity is played by an operator . . . which is called an observable. This is one of the theory's most formal aspects.'
'Operator -- in mathematics and quantum mechanics [Universe of discourse] an operator A is a mathematical operation which, acting on a given function u (usually a wave function) generates another function Au. Linear operators, by far the most important ones, are those that preserve the sum of two functions and the product of a function and a constant.'
Eigenvalue equation Au = au, A operator, a scalar.
The point is that observation corresponds to operation which we model by a Turing machine (or network of same) which in communication theory would be called a channel, something that transforms a message from source to source, transmitter to receiver. Further, the interpretative protocol for quantum mechanics, P = |phi |2 = phi.phi* suggests that a two way process is required to establish a real message.
page 287 Projector P2u = Pu, ie P = {0, 1}.
page 287: 'Property -- in quantum mechanics a property means that a certain physical quantity (an observable) falls within an interval of possible values at a given instant. Properties are the basic elements of any description of physics.'
page 172: 'The essential thing to remember is that each property has a corresponding [projection] operator whose only possible values are 0 or 1.
[page 79]
Religion is business too. We've got a superior product, we take over the market.
Saturday 24 January 2009
Griffiths - history of a physical system, (Omnes page 177) a sequence of properties. Griffiths
Omnes page 186: 'microlocal analysis or pseudodifferential calculus'
We can look at the symmetric Universe is two ways - as a set of memories and as a set of processes modifying memories.
page 199: 'The decoherence effect'
page 207 'Decoherence fully saves the appearances of ordinary reality.'
page 283: 'Decoherence -- in quantum mechanics decoherence is a physical effect due to which quantum interference effects between states that are distinct at the microscopic level disappear very quickly.'
page 211: 'Nothing in our theory offers a mechanism, a cause from which the virgin present, the immutable and pure uniqueness of Reality would result.'
I offer the halting of a Turing machine, the completion of a process.
[page 80]
Omnes says (page 241) '. . . science's inability to account for the uniqueness of facts us not a flaw in some provisional theory; it is on the contrary the glaring mark of an unprecedented triumph. Never before has humanity gone so far in the conquest of principles reaching into the heart and essence of things, but that are not the things themselves.
Symmetric Universe offers a model of uniqueness and 'no-cloning'. No cloning theorem - Wikipedia
Omnes page 215: 'How is a unique datum produced when an atom or particle interacts with some measuring device? As a matter of fact there is no language endowed with logic in which the question makes sense. Just like the famous question 'Through which hole did the particle go?' this illusory problem is only a treachery of our classical mind: the mirage of common sense creating visions where there is really nothing sensible.'
Weird. I am certainly capable of producing unique data like this book, and its output is explained by my input and the way I process it to transform it into this. Why can the Universe not do the same?
Quantum mechanics is the mechanism proposed hypothetically (and quite successfully) to explain our 'classical observations'.
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