Notes
[Sunday 19 April 2009 - Saturday 25 April 2009]
[Notebook: DB 66 Turing Field]
[page 117]
Sunday 19 April 2009
The path integral (functional integral) approach to neural networks. A neuron gives a signal when the algebraic sum ('phase') of its inputs passes a certain threshold. Beale and Jackson Beale & Jackson
Guess that the enormous complexity of quantum field theory arises from the roundabout way of doing things, observing and measuring the outputs of the world in spacetime and trying to explain it by mathematical methods appropriate to continuous spacetime without understanding the underlying mechanism which both creates spacetime and the events we observe 'in' it. Feynman's intuition, through the functional integral, reduces this spacetime complexity to a single amplitude for an event which is a measure of timing, so that if certain events coincide in time another event will occur. The role of space also appears as time via velocity, particularly the velocity of light. So we travel to a meeting, arranging our departure to arrive 'on time'.
Newton's law of the flip-flop: a flip-flop remains in a given state until reset. Clements page 95. Clements
[page 118]
Processes in real computers are distributed in space, and so signal propagation delays must be taken into account. This can be done crudely by making clock pulses so far apart that their interval exceeds the largest dimension of the computer.
I am a neural network, that is a computer network, a subset of the universal network, so that the effort to understand the Universe is essentially an effort to understand myself, where I fit in. Traditional religions see this problem in terms of masters (gods, kings, bosses) and slaves (slaves, subjects, sheep, goats, the faithful etc), whose wants come from the master and whose raison d'etre is to serve the master either for reward (heaven) or to avoid punishment (hell) or a bit of both. Locally, I am my own master and slave since while I can decide what to do and do it, I am nevertheless constrained in my actions by the need to obtain the resources necessary to continue to live and act., ie I must 'work for a living' unless by some accident of fate I should be endowed with 'independent means'.
Device failure rate= rate of radioactive decay. Clements page 130.
From a logical point of view self awareness can be expanded into a relationship between two semi-independent entities, me and me watching (measuring, communicating with) me. The ancients modelled this by the procession of the word, in God a distinct Person, the Word. In this way an understanding of our own psychology became the paradigm for the nature of the Universe a la Lonergan. Lonergan Perhaps Lonergan came as close to identifying God and the World as his Faith would allow but now, having ditched the Faith, we can go all the way.
[page 119]
LOOP DIAGRAM = CREATION DIAGRAM (which will naturally, like flies, continue to grow until they fill the Universe). This does not happen due to countervailing forces like lack of food.
Renormalizable --> coupling constant is dimensionless Peskin & Schroeder page 323. Peskin & Schroeder
Monday 20 April 2009
Tuesday 21 April 2009
Much of the dialogue in quantum field theory is between momentum and position space, controlled by the uncertainty relation delta x . delta p = h bar, with the implication that delta x --> 0 ==> delta p --> infinity, with all the consequent mechanism of renormalization to get points in space (Dirac delta functions) with reasonable and measurable associated momenta. The encoding and decoding in this dialogue is the Fourier transform between space and momentum representations of the interaction of interest.
The interpretation suggested by network theory is that we view individual Feynman diagrams as snippets of the universal network which are (apart from scale) isomorphic with the universal network and whose vertices are Turing machines. So input particles (packets of data) meet and transform one another to other particles (packets of data) that go on through the network. The Feyman picture postulates a propagator that continuously translates states from one point in spacetime to another where they interact in a manner controlled (ie bounded) by the various symmetries of nature. In the logical picture there is no reference to propagation through spacetime and spacetime continuity, all we require is logical continuity, so that the results of one halted process are the input to another process, which will halt in its turn. We
[page 120]
see here an ordering of processes (since each one follows from others) of definite lengths measured in units of the quantum of action (one complete step in a computation). This relates the abstract mathematical view of computation to the physical reality, and introduces time as the cardinal parameter of local network order t1 > t0 means that locally an event occurring at t0 comes before and may be the cause (incoming message) of an event [at] t1 (outgoing message). This is the system described by quantum mechanics, the formal framework of physics which is isomorphic to network theory.
We now explore possible scenarios for the generation of space by the paradigm above, using quantum mechanics in its abstract Hamiltonian form of conjugate quantities without any reference to space, time, momentum and energy, only action action and reaction. From this point of view everything in the network is normalized (measured) by the quantum of action and there is no action associated with processes that do not halt. It follows from this that if we do succeed in creating spacetime from the computational network, the resulting spacetime will be pixellated by the quantum of action. Since, in the network, everything is finite, when we come to think in terms of four momentum and spacetime position we do not find geometric points with infinite 4 momentum but regions (pixels) which 'contain' or represent one halted process each. Since a halted process may be a set of halted processes ('exited subroutine') such spacetime regions may be of any size.
The Fourier transform of a Dirac delta requires infinite four momentum to be faithful.
A person is a group, transforming itself into itself through time.
[page 121]
KISS - Gene Simmons [ISBN] 0712623353 Simmons
Simmons page 3: 'Someone, perhaps Machiavelli, once said that it is better to be feared than loved. I understand that. Love is evasive. Love has its needs. You have to be giving. You have to be concerned with someone else's happiness. Power is a cleaner idea, a cleaner concept. I want to walk into a restaurant and be waited on. I want to have women want me, although not necessarily because I want them. Women understand these notions very well. A woman wants to make herself as attractive as she can . . . because she wants every man to want her, although she may not be interested in any of them.
Breakthrough = halt. POWER <==> POTENTIAL (WANT)
User pays removes the moral hazard of temptation to bludge. Should I really be taking social security payments just because I fulfill the requirements? I am happy with my situation because I think my work here will ultimately be worth more to my taxpayer nation that I have received from the nation as sustenance which I bring this job to a productive finish, which always seems to be getting closer while standing an indeterminate distance away, a process that cannot predict when it will hlt. So I am taking a 'moral punt' but the older I am the better the chance of a payoff and the bigger the payoff, since a formally unassailable theology would be a benefit to the planet devastated by people who do not yet see it as part of their own flesh and blood.
A want is something that you do not have causing a tension (potential gradient) toward getting. Without wanting to live we would not live
[page 122]
because we would no go after the needs of life.
BPHZ Theorem '"for a general renormalizable quantum field theory, to any order in perturbation theory, all divergences are removed by the counterterm vertices corresponding to superficially divergent amplitudes.' P&S, page 338 Peskin & Schroeder
'. . . we will investigate one detailed example of a two-loop calculation, which demonstrates explicitly the appearance and cancellation of non-local divergences.'
We might see the transition from quantum field theory to network theory as analogous to the transition from muon to electron where a complex and inefficient algorithm is replaced by a simple efficient one that depends on a new way of looking at things.
As the fundamental universal algorithm becomes simplified energy is released to run more and more copies of it in parallel so, say, a Universe with just one electron becomes a Universe with a large number of electrons, where we define an electron as a certain mapping from input to output which can be implemented in different more or less massive ways.
The function of mass in physics is to connect momentum and energy.
We may see the history of mathematics as a dialogue between arithmetic/algebra and geometry, a dialogue also present in the history of the Universe. However meaningful dialogue must ultimately be discrete rather than continuous so from a realistic point of view logic/arithmetic/algebra takes precedence over geometry.
[page 123]
The fact that renormalization is a) necessary and b) works suggests that it is a fiction of the continuous formalism that requires the existence of pointlike particles with infinite momentum.
Tuesday 21 April 2009
[sic]
Requisite variety works in both space and time insofar as a feedback system that is trying to control a variable must respond quickly and frequently enough to stop the variable exceeding controllable bounds and the 'word length' or complexity of the controller must be sufficient to take care of all the degrees of freedom of the controlled system. Thus a fascist bureaucracy must take regular readings on every individual in the community and check frequently enough to stop any one of them getting out of bounds. In physical terms, the 4-momentum of the controller must exceed the four momentum of potential error.
Insofar as the Universe is error free and deterministic (which is not very far, but essential to the existence of an durable structure at all) every event is unique and can be seen as the exchange of a specific message through a specific piece of time corresponding to the interval between sender and receiver and the acknowledgement and verification of this message. Communication is indifferent to (abstracts from) specific messages and simply regards messages as a string of symbols emanating from a source with certain statistics. For Khinchin, sources are ergodic. Khinchin In quantum mechanics, the statistics of each equivalence class of sources is determined through the Feynman diagram and rules for such sources. For a typesetter, the source emanating this very text can be represented by a spanning set of glyphs, each occurring with a certain frequency, normalized over the set to one, so
[page 124]
that exactly one letter is emitted for every keystroke, presuming a one-one correspondence between keys and glyphs. Since there are millions of glyphs in use, practical typesetting systems with practical keyboards break the selection of a particular glyph into a series of operations: choose language, font . . . choose specific glyph. This approach can be constructed as a binary tree distinguishing between the hundreds of languages, fonts and characters in common use. If we see the act of observation (measurement, communication) as the emission of a symbol, we can imagine the process behind this emission as a hierarchical system of choices capable of moving us from the initial singularity to a specific moment.
There is a war on between fascism and freedom. Here, for me, the archetype of fascism is the Roman Catholic intellectual property ranging from prescriptions for governance to prescriptions about the beliefs that underlie that governance. Basically, we are all poor sinners in need of regimentation by the Church as Vicar of God, empowered to execute God's Will. The archetype of freedom is the theory of the transfinite network embodies in a transfinite interpretation of the quantum mechanical formalism, where we replace Dirac's [. . . ]
COMMUNICATION --> LANGUAGE --> FONT --> GLYPH
Each step can be broken into steps down to the quantum of action. In practice the 'unit of action' is determined by the resolution we are using to examine the process. A communication is a process taking place at constant cardinality but represented in a space of higher cardinal, the tensor product of the interacting spaces / particles.
[page 125]
We understand the interaction of particles by integrating over their spaces. We understand the spaces by differentiating over the particles.
Looking at mathematical physics, we see that almost every quantity involves differentiation and/or integration plus other arithmetic and algebraic symbols.
SENSUAL --> SEXUAL
KINEMATIC --> DYNAMIC
The derivation of the functional integral begins (as ever) in a discrete lattice and is then, by the rules of calculus, taken to the continuum representation on the assumption that the world is continuous. Also, since a continuum contains no information, this is equivalent to an abstraction that ignores the details of individual discrete steps. The computer network model, on the other hand, proceeds by discrete steps [each with a definite address in space-time] which can in some cases be modelled by a continuous curve and in other cases not. Classically we bridge this gap with Fourier analysis, introducing high enough frequencies to model the detailed steps in a process which may ultimately be represented by a digital string describing the tree that bore the process. Every moment has a string of events connecting it to the initial singularity.
So we can use the Fourier transform and the sampling theorem to prove the equivalence of the transfinite computer network and quantum mechanics.
Quantum field thery looks a bit like a box of mathematical tricks that can be performed in sequence to give computations corresponding plausibly to observed events.
[page 126]
Why quantized: begin with the phase space [transfinite network] and tie everything to that form the initial singularity on.
Celebrities (Madonna, Hitler, the Pope etc) mark boundaries of human space and this makes them celebrated, the first to climb Mount Everest naked, etc.
The emergence of structure from the vacuum? No, the vacuum is by definition lowest energy, most stable, the ground state of the Universe and so corresponds to the formalism. Here we say the vacuum is the transfinite computer network. We introduce dynamics by seeking rules for the interaction of formalisms, that is change. This is possible because no formalism can excite all its its states simultaneously, since this would involve contradiction? What we are saying is that formal restraints on the size of the alphabet of a formal system mean that we can only represent all possible words written in this language sequentially, not simultaneously. This is why God (classical) cannot be the fullness of being in any real sense [unless we include time and dynamics]. The simultaneous excitement of all possible formal states is formally impossible, so we have motion and uncertainty.
QUANTUM OF ACTION = MOMENT OF 4-MOMENTUM
space-time pixel (4xel) 3xel = voxel. minxel.
MINXEL = quantum of action projected into Minkowski space. Minkowski space - Wikipedia
Rain: thank god for the roof and the fire.
[page 127]
The Classical God is the Determinist, and we might see the visible elements of God (the past) as determined, but complex enough to have an indeterminate future (Gödel incompleteness, Turing incomputability). Gödel's incompleteness theorems - Wikipedia Turing machine - Wikipedia
The network version of the generating function of the path integral approach is a Turing machine.
Fourier components of different wavelengths [periods] are orthogonal.
As mathematics abstracts from detail by projecting discrete events onto a continuum, so does the Universe, removing degrees of freedom in the process, hopefully arriving at an easily manipulated analytic expression that tells us a little something about an exceedingly complex reality.
An important feature of quantum mechanics is that the number of effective degrees of freedom is a function of energy, cf Einstein on specific heats etc. PaisAlbert Einstein - Wikipedia
MEANING(x) = f(role of x in a process).
Statistical mechanics is concerned with the most probable distribution of states = messages in the network? No, of nodes in the network as a result of exchanging messages = collisions.
Cardinal of a message = size = energy = mass and takes no notice of the meaning of the message. From a cardinal point of view all books of n words are the same.
Quantum Field Theory: a set of algebraic rules for rewriting strings of
[page 128]
symbols subject to the constraint of maintaining equality = cardinal measure
Research: sniffing out fixed points (trajectories) a la path integral
Statistical mechanics begins, like all theory of probability, with a principle of equal a priori probability (by some measure). Huang, page 141.Huang
Every now and then I feel that I am on a terminal approach to something and then it appears that there is another mountain to cross on my way to the true vacuum (the true formalism).
The principle of general covariance is the principle of treating all messages the same, the abstraction that gives us gravitation. Using the notion of abstraction and complexity invariance, we see that the ontological structure of the Universe is also its explanatory structure.
STATE = distinct entity representable by a distinct symbol. So the Classical Trinitarian God is a state represented by the Word, that is the Representation.
No cloning says all representations differ.
A symmetry is broken when the Postulate of Equal a Priori Probability is violated by some 'meaning' being given to a set of symbols by a higher process which alters the probability of emission of the symbols in the set.
[page 129]
The introduction of meaning shifts the equilibrium distribution of the symbols from a previously stationary source.
Equal a priori probability = maximum Shannon entropy = equilibrium. Entropy (information theory) - Wikipedia
'Correlation function' measures the rate of communication = amount of energy shared by the communicants (perhaps as a proportion of their total energy) A particle that decays shares 100% of its energy with the decay products. Atoms exchanging light photons are exchanging approximately [one billionth of] their rest energy.
Although we think we are rather smart to have invented writing with durable materials (and therefore memory) it turns out to be ubiquitous in the Universe and some particles like photons, neutrinos, electrons and (most likely) protons never decay (although they may be destroyed by interaction) and so are a foundation for eternal memory and precisly defined formalism corresponding to zero energy, ie no quanta of action are to be found in an eternal memory since by definition it does not change (act).
Almost all these sentences are almost tautologies but taken all together they seem to be slowly moving into new territory.
From a quantum field theory point of view the digitalization of the Universe is a matter of choosing suitable cutoffs that prevent us from following a continuum to an unacceptable conclusion. Everything stands to reason only up to a certain point, and then things change: two is a company, three is a crowd.
As war shows, people will do anything to survive, including
[page 130]
killing others and running the risk of personal injury or death. This demonstrates also that social organization is a powerful as the biological organization which leads us to prefer broken limbs to head injuries. The way to eliminate war is to eliminate the need for war by visibly implementing global fair trade. This is a definition of fair trade: a kind of trade that makes war unnecessary and unprofitable. Global organization seems necessary to achieve this, since everyone must agree on an environmentally sensitive 'level playing field'.
Wednesday 22 April 2009
Quantum field theory imagines fermions interacting by virtual bosons whose existence is controlled by the uncertainty relations so that they can exist for arbitrarily high energies for arbitrarily short times, and the same for momentum and the size of the interaction zone in space. The point is that these products always correspond to one quantum of action and so give us a foundation for the mapping from logical space to physical spacetime.
I think I have sort of thought this for a long time but this might be its first explicit statement, thanks to Peskin & Schroeder page 479 [renormalization group, asymptotic freedom]. Peskin & Schroeder Renormalization group - Wikipedia Asymptotic freedom - Wikipedia
Interaction turns off at high momentum means that at this momentum scale, the interaction 'software' (algorithm) does not yet exist, in keeping with the principle lower energies more complex algorithms, so we might guess that the product of frequency and complexity in each layer is constant, just as a constant amount of data can be sent down a serial channel (width 1) at
[page 131]
n symbols per second, or an a parallel channel of width n at one symbol per second.
Peskin & Schroeder page 481: A fundamental universal constraint 'The Lagrangian of a renormalizable theory can contain no terms of mass dimension higher than 4.'
Gauge symmetry = communication channel. So in quantum electrodynamics the Lagrangian is invariant with respect to local changes of phase which are variant signals in the invariant channel. The step from Abelian to non-Abelian gauge invariance corresponds to an increase in the complexity and coding of messages on the channel.
Stock prices are unpredictable because there are s many different personae communicating with the market, and predictable, insofar as all the actors are sharing the same information about the company traded and its prospects.
An independent symmetry transformation at each point in spacetime = independent message at each point in spacetime, subject to the requirement that the messages can be transformed into one another.
P&S page 482: 'From the modern viewpoint . . . gauge symmetry is not an incidental curiosity, but rather the fundamental principle that determines the form of the Lagrangian.
In other words, we want a Lagrangian with a 'flat response' to the spectrum of messages (frequencies) that the physical network needs to transmit.
[page 132]
Thursday 23 April 2009
Given that gravitation is not quantized (since it deals in pure energy and has no possibility of error) it must also be scale free, so that it is indiferent to atoms, fundamental particles, planets and galaxies.
Crombie: The more closely we study the history of science the smaller the discontinuities (steps) in the development of knowledge appear to be so that in the limit we may consider it a continuous process of the growth of understanding with time, sometimes fast, sometimes slow.
DRUG = PERTURBATION = MESSAGE
The more stable the system, the smaller the perturbation (coupling constant) caused by any given message.
GREED CONTROL: The system will remain stable as long as everyone takes only their fair share, ie a reward commensurate with their input.
Christianity promises an infinite reward for a finite payment, something that should alert us to the possibility that it is a scam, particularly because no one has ever demonstrably received that reward. The cult of saints is supposed to be evidence that some do receive this reward, but the evidence is tainted.
Early scientists applied cardinal mathematics to the study of the Universe. The rise of statistical mechanics
[page 133]
coincides with the introduction of ordinal mathematics into physics when we began to study ensembles with the same cardinal number of particles, the same volume and the same temperature (energy) but a huge number of different orderings of the elements of the ensemble, each corresponding to a different ensemble. Cercignani
The idea of the ensemble is both analytic and synthetic. First we analyze a situation into a fixed number of degrees of freedom - this is the analysis; and then we explore all possible ways of combining these degrees of freedom (ensembles) to see what they look like, and we are often rewarded by finding that they look like our world.
We have normal people who look round and say this is our world, and then we have exceptionists (extremists, idiots) who say that what you see and experience is not the real world at all, reality is something completely counterintuitive and mysterious and because that is so and we know it we have a right to kill you.
The slower the communication, that is the lower the bandwidth the more faith (= stability) is required to maintain the status quo between messages.
Theological Studies:
This article is written from the pragmatic point of view that science and technology contribute to our fitness, that is our probability of survival integrated over a certain period of time. It is clear that we are ultimately doomed by the death
[page 134]
of the sun but it seems that we can look forward to a few billion years of reliable service yet.Nn's funeral. Roaccutane alias isoretinol.
The rediscovery of the last century is that business is better than war. ie it contributed more to one's fitness, but, a certain environment is required for this proposition to become true, ie for all its conditions explicit and implicit to be fulfilled.
