VII Notes
2010
Notes
[Sunday 21 February 2010 - Saturday 27 February 2010]
[Notebook: DB 68: Salalah]
[page 215]
Sunday 21 February 2010
. . .
We may see quantum mechanics as the shell of the Universe and as a primary description of creation which quantum mechanics call the collapse of the wave function. Once we have understood the quantum mechanics of two state systems we have learnt all quantum mechanics
[page 216]
has to say and the rest is application. Quantum mechanics has no memory, and is purely one dimensional, showing us how to computer temporal sequences at constant entropy. The principal applications of quantum mechanic are in non-relativistic electronics, where quantum mechanics is applied to the computation of an hypothetical structure such as a transistor.
The development of a relativistic quantum field theory, on the other hand, has been fraught with difficulty and the current model, although very efective given sufficient computing power, cannot really be called consistent or beautiful. (Streater and Wightmann, Veltmann) It seems that we must accept that the complexity represents the complexity of the Universe, but its endemic infinities and the means used to treast them are cumbersome. Veltman, Streater & Wightman
Streater & Wightman: 'In fact the Main Problem of quantum field theory turned out to be kill it or cure it: either show that the idealizations involved in the fundamental notions of the theory (relativistic, invariance, quantum mechanics, local fields etc) are incompatible in some physical sense, or to recast the theory in such a form that it provides a practical language for the description of elementary particle dynamics.'
The parental object of all particles in the initial singularity. We decribe the world in terms of object oriented programming.
Quantum mechanics describes the moment of creation, when the infinite (represented in the Hilbert space) becomes finite (represented by the 'reading' on a 'meter', eg a click on a Geiger counter), that is a message from the infinite.
[page 217]
The infinite and the finite are duals whose duality is exposed in the mathematical field of analysis.
S & W page 4: Heisenberg vs Schrödinger: different ways of looking at the same being vs same way of looking at different things.
Duality: the theory is a contracted dual of the reality.
Again quantum, mechanics describes the transition from past to future. The set {past, future} is a two state system.
The process of knowledge is to climb down the tree of creativity toward the root finding and exploring the symmetries that have generated the variety of the world to be seen in the leaves. The fundamental symmetry lies in the root of the tree.
S&W page 7: 'A symmetry operation (sometimes called an invariance principle or simply a symmetry) of a physical system is a correspondence which yields for each physically realizable state φ another &ph;i', such that all transition probabilities are preserved:
|(φ, ψ)|2 = |(φ', ψ')|2
ie the communication network is the same with the same traffic on every link when we change the representation. Since the network is itself a formal object it has its own native representation, and this is what is invariant under symmetry operations.
[page 218]
Spin is a characteristic of a memory cell. It is what is recorded in the cell (?)
Where is the data allegedly represented by the wave function stored? Hopfield network associative memory. Hopfield net - Wikipedia
Symmetries are all about putting the same thing in different contexts, so we can have no symmetries without different contexts, ie we can have no symmetry under Lorentz transformations until we have space-time and velocity.
Does the Lorentz transformation create the space-time, or vice versa, or do they both spring into existence simultaneously as duals of a prior symmetry.
COMPUTATION = {READING, WRITING}
Monday 22 February 2010
A continuous line as such cannot carry information because it has no marks. However, it may be made to do so by placing it in a context (ie in 2D space) where points of inflection and absolute values may be imposed and measured to give information carrying capacity.
One difficulty in understanding a layered world is separating one layer from another, since they are all transparent to the user (me or a physicist). One clue is that each layer is a symmetry which is broklen by the next so we may have a layer that processes all keystrokes identically whose symmetry is broken by the user pressing
[page 219]
different keys to enter a message meaningful to the user.
Your Platonic mathematicians assume that the whole mathematical world is already built with symbols defined with perfect sharpness (delta functions) and no possibility of confusion. This system, is then used to model the physical world which is assumed to exist in a similar degree of perfection (cf eg the [hopes of the] quantum computation people) so that the game is to match the perfect mathematics to the perfect world. When we are creating the world, however, we must learn to start with just one symbol with no context (no dual) and watch (and so model) the growth of symbols and dualities within it. These symbols watch one another, just as I am sitting here watching the world. From this point of view every particle is the same, since in an infinite system (eg ℵ0) every finite member (eg 2) has measure zero, we are all equally small before the whole. So begin theology with an article on the copernican principle and then move to evolution.
All these words (above) encapsulate one thought which came to me 'fully formed' in an 'instant' but took a minute of so to write our in the physical serial string of letters that you read.
We use topological spaces (like Venn diagrams) to [provide pictures of logical relationships]
Theology: Copernican principle / Evolution / Mathematics / Cantor's Theorem
Like a termite, I have performance anxiety until I find a starting point (in the termite's case, putting one blob of
[page 220]
carefully prepared mud on top of another) and then clarity and passion take over, the anxiety goes away and work proceeds unconsciously until next time the way forward is not clear. I seem to go through this process every morning, awakening confused and depressed and taking a cup of coffee to arrive at a clear starting point for the day's work, at which point energy takes over and I get on with it. Marais
Model
Epistemology (= f(model) or {f(model)}) / duality
physics (= f(epistemology) or {f([epistemology])}
Suzuki - unconscious processing prajna [conscious processing] paramita Suzuki
Model: invariance
ANT:Summary:creation
We spend the immediate future (2 years?) as a home made religion until we are ready to go public and start evolving towards industrial strength.
Given that in its growth the Universe passes from 0 states to n states, we can expect it to pass through all values of n and at each of these values have a description that can be represented by n symbols, each of which an instance of each of the states.
Our model of the Universe arises from software engineering. [object, tree]
[page 221]
We use God for the Roman Catholic Church private God and god for the Theology Company god, which includes all that exists, the Universe and God.
. . .
ANY: to a private goddess.
TTC: Bringing the [Catholic Church] [Religion] [God] down to Earth.
Streater & Wightman page 85: 'A Hilbert space is separable if it contains a denumerable complete orthonormal set; it is non-separable if complete orthonormal sets are non-denumerable.'
And we presume this relationbshiop holds all the way up the transfinite scale, so one layer's non-denumerable set is denumerable in the next layer.
'In von Neumann's original axiomatization the rquirement of separability was included as a defining property of Hilbert spaces.' von Neumann
S&W page 86: '. . . . All these arguments make it clear that there is no evidence that separable Hilbert spaces are not the natural state spaces for a quantum field theory.'
Which immediately brings us to the finite foundation of the transfinite network.
Finite and infinite are relative terms [in terms of size and boundaries].
'. . . ordinary tensor product which is used to describe a composite system.'
[page 222]
Tuesday 23 February 2010
Streater & Wightman page 96: Field was invented to provide a connection between events at different points in space (time) so as to avoid the notion of action at a distance. We can achieve the same result by particles travelling from one place to another carrying messages from their point of origin to their point of interaction. These particles, like fields (or ambassadors) may have their own internal degrees of freedom so as, for instance, to be able to translate the message from one language to another. In this way we can preserve the locality of action in a spatially extended system. Before the development of space everything is local and so we can see local action representing the layer of the network that precedes the emergence of space.
The root question is the matter of mapping logical space to physical space and the human matter / spirit 'dilemma' revolves around this mapping: physical space is material and spiritual space is logical.
ANT The theological question. Each science can in a way be reduced to the solution of a set of fundamental problems. The theological question is creation: where we came from gives meaning to our existence.
creation / matter and spirit /
It is the spirit (ie the higher layers)
[page 223]
ANT: The physical world : god's body
: The logical world : god's spirit
The human soul has long been held to be both a material and spiritual form, and the whole Christian salvation story is based around the notion that the matter (the world and us) should be totally confined by the Spirit (God). The sin of Adam and Eve broke the confinement.
I read and write, using chunks of the book I read as letters in an alphabet (material) to construct the theological edifice that exists as least aspirationally in my mind.Ths work is sinspired by my participation, with the help of a series of goddesses, on the creation of new people and by the realization that all created life eventually ends due to the accumulation of errors.
Streater and Wightman page 97: 'Typical of states in which fields cannot be defined are those for which the expectation value is infinite [whereas the expectation of a certainty is 1]. This is familiar from elementary quantum mechanics where the position operator is not definable on states Ψ(x) which are normalizable: ∫|Ψ(x)|2 dx < ∞, but are such that ∫ |x|2Ψ(x)|2 dx does not converge.'
This points to a radical misunderstanding of the nature of space. It is not continuous and analytic, as the whole of physics assumes, but a discrete set of 'event locations' ie space is pixellated or granular because it is a logical entity built by assembling a lot of initial singularities into an addressable dynamic logical system. [the whole Universe is a set of children of the initial singularity]
[page 224]
Mathematical physics is an attempt to map elements of logical space to elements of physical space and the fact that this mapping is possible tells us that physical space has elements. The error, noted above, of current physics is the assumption that space is infinitely fine grained and Archimedean, so that mathematical analysis applies to it at all scales, which it does not. Analysis applies only at the lowest layer [before error and quantization]. Archimedean property - Wikipedia
The stock exchange unites the way of the hunter (speculator) with the way of the farmer (producer)
EXPLORER vs PRODUCER
We assume that the Universe is at all times closed so that almost every process within it is cycling, returning to its starting point after a certain number of operation. This explains the use of complex numbers in quantum mechanics. The cycle length of the initial singularity is 1, ie it returns to its original form after every action. A ticker has a cycle length of two, tick, tock, tick, and so on up to myself whose cycle length is of the order of 10E60 (Mc2 / ℏ T) where M is my mass, c the velocity of light, ℏ is Planck's constant and T is my lifetime in seconds, so we have 100 (kg) x (3E8)2 x (6 x 10E-34) x (2E9) = 3E61. This calculation depends only on mass and lifetime.
Streater and Wightman Axiom 0, page 97 assumes that the Lorentz transformation resulting from the relative motion of the particles must be taken inside the Hilbert space of the particle via the transformations represented by SL(2, C). The hierarchical network model suggests that we do not
[page 225]
transform the quantum machinery inside the particle but rather the output of the particle. This leads to the same results, since we have already agreed (page 7) that a symmetry operation like the Lorentz transformation leaves all transition probabilities unchanged |(ψ', φ')|2 = |(ψ, &ph;i)|2.
This article (creation) is written as a commentary on S&W's brilliant little book PCT. Spin, Statistics and All That
'There is an invariant state ψ0
U(a, A)ψ0 = ψ0
unique up to a constant phase factor (uniqueness of the vacuum)'.
ie the vacuum is immune to Lorentz transformations, meaning that velocity has no meaning for it, meaning that it does not see space (or time?) meaning that it is isomorphic to the initial singularity. The Universe is constructed by isomorphs of the initial singularity emanating within the initial singularity and this pattern is recursive, so that the layers of the cosmic network are sets of sets of sets . . . of copies of the initial singularity (is), causality being established by containment.
The internet shows us that logical space is not like physical space because the distance between different files is a function of URLs and processing time rather than the physical locations of the files addressed.
Processing time is not so much dependent on the length of the physical links, traversed at c as the amount of
page 226]
processing (switching) necessary to get a file to a user's screen ('horizon'). Thanu Padmanabhan
S Streater and Wightman page 98: 'Assumptions about the domain and continuity of the field.'
Test functions are on space-time; operators are on Hilbert space.
The big problem of quantum field theory is mapping logical Hilbert space onto physical space-time.
Theology: software for humanity.
Since all the particles in the world are children of some parent particles they all interact and they are all entangled.
Wednesday 24 February 2010
S&W Transformation Law of the Field page 99.
Page 96: 'One expects the analogue in relativitsic quantum mechanics of a classical observable field to be a set of hermitean operators defined at each point in space-time and having a well defined transformation law under the appropriate group.'
Like general relativity, this is a continuous representation of a discrete process (set of events) which really gives no clue as to how the group symmetry is implemented. We understand classical probability via balls and urns; what underlies
[page 227]
quantum probability to explain the peculiar way we compute it.
We think of a field as a countable infinity of superposed oscillations represented by vectors in a complex, separable Hilbert space, that is a set of superposed processes of different 'lengths' (times to completion) whose net result is the creation and annihilation of various particles at various points in a pre-existence spacetime.
FIELD =- NUMBERS IN SPACE
The rather complicated mathematics of distributions is needed to deal with the infinitesimal pixels of classical analytical space where an event with a probability greater than zero can occur in an infinitesimal pixel, ie 'at a point', so necessitating an object like Dirac's delta to make sense. Dirac delta function - Wikipedia
Here we love the network model in that it gives us a picture, a la Dirac, which explains not only how space is built out of the initial singularity, but how everything else is built in the space so arising. In particular, because computation deals with recursive functions, we have an explanation for the ubiquity of complex exponents in quantum theory. All we need (?) to understand is why p = |<b||a>|2 and we are home.
Higman: 'There are an infinite number of representations [matrix realizations] of a given group, but they are all built up from a relatively small number of so called 'irreducible' ones, and the number of these for any group is the number of classes in it.' Higman
I am starting to get excited about the theology company
[page 228]
which means that it no longer feels like drudgery work but I am keen to get on with it (painlessly) whenever opportunity present. I presume that excitement is the only condition under which non-work-ethical animals work. Much of the power of humanity is that we have learnt to do (or make the slaves do) unpleasant things in order to gain pleasant outcomes. War.
Thursday 25 February 2010
Ultimately, love conquers all, as does gravity, probably said that before: search! [25 March 2007, 15 March 2010, looks like I am going in circles]
The simple task before me is to express the ideas of Streater & Wightman in terms of a network of computers bound by the 4 theorems, Cantor, Gödel, Turing and Shannon (CGTS) and the assumption of the relativity of transfinity so that these theorems operate in any system where there is a b > a.
Apple: 'An object is the instantiation of a class definition.' Apple Inc.
Class, eg class of particles includes photon, electron, etc as children.
What I want to say motivates the effort to learn the computational techniques necessary to publish it. There is the added advantage that we think that the Universe works like an object oriented computer so that everything we learn about publishing the content helps us to develop the content itself.
[page 229]
If it can be deterministically presented in a maths book, ie if a finite string of characters has the variety necessary to fix the computation unambiguously, then it is a computable function, although it may take an exponential time to halt [if ever].
A TURING MACHINE IS A DIFFERENTIAL EQUATION [ie something formal that is an invariant of the dynamics]
ANT:method - differential_equations.html
The point set approach to the study of continuous functions nevertheless leaves us in the ultimate analysis with the only causal connection between distinct points being closeness, which is no stronger a connection that the concept of logical connection used in the network model, and generally much weaker and less intuitively satisfying, as indicated by the fact that all our mathematical proofs are ultimately logical operations on sets of points.
Human parallel processing: NY Times, Benedict Carey Benedict Carey
Streater & Wightman page 21: 'The vacuum state looks the same to all observers. It has zero energy, momentum and angular momentum.'
On the average? Particles can be created and annihilated within the vacuum state as long as they obey the uncertainty principle? Casimir force. Padmanabhan. Thanu Padmanabhan
It is hard for me to experience the potential consequences of my own ideas which are don't worry be happy, we can trust the world and we are not subject to the arbitrary whims of cranky old Gods like Greeks, Hebrews and
[page 230]
Christians. My happiness is to a large degree in my own hand (mind) and I should get used to it. At my stage of life I can go for broke without seriously inconveniencing anybody else.
Friday 26 February 2010
I like to think that I am in control: can I get this job done in the time available or will there be a panic? Take it slow and look a long way ahead, knowng all the time that there will be interruptions.
Computation of probabilities: Classical probability theory, based on the integers and introducing continuous functions as an explanatory abstraction, is concerned only with counting (cardinal) numbers and has little to say about order except as a way of generating cardinals (Boltzmann, Bose, Fermi counting). Then we come to take account of order and matrices and con-commutativity enter the picture. Non-commutativity starts with energy and time, and so points to some complexity there. Maxwell-Boltzmann statistics - Wikipedia Bose-Einstein statistics - Wikipedia Fermi-Dirac statistics - Wikipedia
Castles in the air: Wall Street and the Roman Catholic Church Partterson. Patteron
The banks deluded people into lending them money by bogus mathematical models with very weak coupling to reality. Some financial products are viable, some, like securitized sub-prime mortgages, are not.
Patterson, page 207: 'All the bad news made it clear that many CDOs
[page 231]
were worth far less than most had thought.' I have done the same as the banks (Lehmans) - lured people into lending to me then gone slow on repayment.
Patterson page 222: '. . . the market was acting in a way that defied any pattern Rothman, or any other quant, had ever seen.
Because all the patterns they saw were delusions. [?]
Saturday 27 February 2010
Since money is a public good, all amounts over a certain minimum should be publicly tracked to give a real time picture of money flows as we do with the roads and traffic flows.
Patterson page 224: 'The carnage, . . . revealed a dangerous lack of transparency in the market.'
page 227: ' "Quant managers tend to be a bit secretive; they don't reacxh out to each other. It is a bit like a poker game [overlap, common subroutines]. When you think about the Universe of large quant managers, its not that big. We all know each other. We are calling each other and saying "Are you selling?" "Are you?" " '
Like string theory, quant mathematics is all virtuosity, no contact with reality.
Lehman (page 232) Turbulent times in quant land.
Much of this problem would be solved of there was a minimum profit ratio on the market, ie quantization, induced by a ratio tax on financial transactions a la the Bank of Earth.
[page 232]
The basic error in the money markets, as in quantum field theory, is an unfounded belief on con continuity reflected in titles like 'Continuous Time Finance'. Merton
Ideas, like the formal identification of the initial singularity and God begin as wild guesses (fluctuations) and then slowly weave themseves into the fabric of the hypothesis. Quantum fluctuations - Wikipedia Diffusion - Wikipedia
Secrecy, Patterson page 240; 'The most terrifying aspect of the meltdown was that it revealed hidden linkages in the Money Grid that no one has been aware of before.'
We might see the market as the foolproof foundation of the capitalist system, but we imagine that a similar model works wherever capital, that is structure, is developed out of non-structure and (if things go wrong) may revert back to non-structure as the market sucks out their value and deploys it elsewhere.
page 244: 'The worst fear of quants such as Asness was that their Chicago School guru, Eugene Fama, had been right all along: the market is effective, brutally so. Long used to grabbing up the short term inefficiencies like ravenous piranhas, they'd had a big chunk taken out of their own flesh by forces that could neither understand nor control.'
Here we see again a place for the hypothesis that contradiction creates energy which is the change needed to remove the contradiction.
[page 235]
ENERGY = RATE OF CHANGE = velocity d(something) / dt.
Patterson page 247: 'The light at the end of the tunnel is an oncoming train.'
The quant meltdown is a sign of the errors of physics propagating from science into technology. [? more likely the quants overlooked the fluctuations and chaos of physics]
page 249 Lo & Khadani What happened to the quants? Amir E Khadani and Andrew W Lo
page 263: Greenspan: 'In recent decades a risk management and pricipng system has evolved combining the best insights of mathematicians and finance experts supported by major advances in computer and communications technology. A Nobel prize was awarded for the discovery of the pricing model that underlies much of the advance in derivatives markets. [Black-Scholes Black-Scholes - Wikipedia} The modern risk management paradigm held sway for decades. The whole intellectual edifice, however, collapsed in the summer last year. 23 October 2008 Alan Greenspan
All complex structures, like myself, are castles in the air if they lose contact with their foundations, in my case the input of enough low entropy to keep my error rates within acceptable bounds.
The visible part of god is error control. No news is good news, so every message can be interpreted as a move to keep the system together motivated by the perception that something needs to be said. Love is saying and hearing the things that need to be said to keep love alive.
Patterson page 280: Secrecy ==> no control ==> doom
[page 236]
. . .
My property is private but the money attached to it is a public asset and must be driven according to certain road tules by licensed drivers.
Patterson: Wilmot: 'Certificate in Quantitiative Finance'.
page 292: Wilmott, Phil Trans Roy Soc, 2000 'The Use, Misuse and Abuse of Mathematics in Finance.' Paul Wilmott
page 293: 'The mad scientists who'd been running wild in the heart of the financial system for decades had finally done it: they'd blown the system up.'
More damage than all the terrorists put together, calculated in life years lost through consequent poverty induced by loss of capital.
page 293: Wilmott and Derman 'The Financial Modeller's Manifesto Emanuel Derman and Paul Wilmott
page 294: 'The truth is that there are no fundamental laws in finance.' Except those imposed by open communications. There can be no law in secrecy because secrecy implies no communication, correlation or control.
page 294: Modeler's Hippocratic Oath = to Epistemology
page 297: Mandelbrot: 'The only serious criticism of my work, expressed by Cootner, was that if I am right, all our previous work is wrong. Well, all of their previous work is
[page 237]
wrong. They've made assumptions that are not valid. The models are bad.
'Boom in Dark Pool: trading networks . . .' Patterson and Luchetti . . . Scott Patterson and Aaron Luchetti
Quantum computer = elaborate interferometer Burkard, Science 327:650 Burkard
Yovel et al 'Optimal Localization by Pointing Off Axis' Science 327:721 Yovel High gradient - precise localization.
Continuous time finance: what we are loking for is the algorithm by which the Universe decides to allocate its energy to the realization of different structures. Merton.
