Notes
[Sunday 12 April 2009 - Saturday 18 April 2009]
[Notebook: DB 66 Turing Field]
Sunday 12 April 2009
The Universe of events can be divided into predictable and unpredictable, although the boundary is not sharp. Predictable events are the subject of work, the foundation of survival. Classical thermodynamics, through the second law, established a relation between physical work and temperature at constant entropy through the Carnot cycle.
One cannot work with unpredictable substrates. Graziers long ago discovered that some animals like goats, sheep [people] and cattle are 'bosonic' and can be rounded up into mobs and moved as a unit. Others, like kangaroos, are 'fermionic', tending to act as individuals and refuse to be mobbed.BOSON vs FERMION PERSONALITIES
[page 105]
The velocity of light completes the space of motion. A space is complete when it contains its own boundaries, a la Hilbert space under the inner product measure. A complete space may function as an element of a larger space, as we like to imagine the Hilbert spaces of individual particles as elements of space-time which communicate by exchanging messages in spacetime.
The fundamental pleasure is completion ranging in expression from scoring a goal to having an orgasm to finishing a unit of work, like building a house or capturing and preparing food sufficient for a good meal. And, of course, having a baby, the primary act of survival.
ACT == COMPLETED PROCESS. I have done the dishes = past perfect in the traditional grammar. As opposed to future (somewhat) unpredictable.
Workable projects must have strong couplings so that the screwdriver always screws the screw and the bolt holds the structure together with bonds of adequate strength for the task. So too the cable must not break, nor the brakes fail.
A tool is a machine for increasing the probability of a given outcome. This is why tools are digital, to achieve suitable fit with a reasonable number of steps, like sizes of spanners. Reduction of the tool set reaches its maximum in the binary digital computer. The unary digital computer, represented by the energy network, cannot convey meaning. This begins with the binary bifurcation which is the foundation of all complexification.
[page 106]
We make the fundamental digital tool by increasing the signal to noise ratio, ie the gap between the binary opposites.
In order to do a job efficiently one needs a spanning set of tools, that is ideally a set of tools capable of making each step deterministic so that one can go from a to b without error.
The first time we do something we are writing software in ourselves for subsequent performances and refinements. Once the job is perfected (as in a factory) every step goes according to plan, unlike once off sitework, where the plan has to be worked out step by step as circumstances change.
While the simplest tool is a two state system (a bit) the most complex in the human layer is another person, a true and faithful servant who does what s/he is told without error or complaint, a situation only just in modern eyes if there is adequate reward for their compliance.
Since all information and computation are realized physically, one can construct deterministic logical (workable) processes only from deterministic physical processes, or by a process of error correction. In the quantum regime this is described by quantum information theory, in the classical regime by classical information theory. What is the formal difference, if any? The level of control required is measured by the entropy of the space of possibility, so minimal control is needed in a binary digital system.
Huang page 139: 'Statistical mechanics . . . does not describe how a system approaches equilibrium, nor does it determine whether a system
[page 107]
can ever be found to be in equilibrium. It merely states what the equilibrium situation is, for a given system.' Huang
ie statistical mechanics is formalism, states, not dynamics.
Huang page 139: "We might suspect that . . . -- the method of most probable distribution -- would enable us to discuss the equilibrium situation of not only a dilute gas but also any macroscopic system. This indeed is true. The generalization is classical statistical mechanics.'
The canonical equations of motion 'completely contain' a dynamical system. The heart of this representation is the Hamiltonian which couples each possible 'after' state to all the 'before' states.
'Postulate of equal a priori Probability: when a microscopic system is in thermodynamic equilibrium, its state is equally likely to be any state satisfying the macroscopic coordinates of the system.
'The fundamental quantity that furnishes the connection between the microcanonical ensemble and thermodynamics is the entropy.'
Huang page 146 'The temperature of an isolated system is the parameter governing the equilibrium between one part of the system and another.'
TEMPERATURE = f(VIOLENCE) ie the flow of interaction between particles in the ensemble.
Monday 13 April 2009
A novel is a point in string space. For communication theory,
[page 108]
all points are equivalent but in novel space only good stories count. Fritz Lieber The Girl with Hungry Eyes - Little Shop of Horrors - Feed me.
Christianity may be seen as a step forward in that it emphasized social control by moral persuasion (based on notions of good and evil, guilt and punishment) rather than outright violence as seems to have been the norm in the Roman Empire. It is by no means perfect, however, since it defines us (incorrectly) as defective sinners who must submit to the self-serving discipline of the Church if we are to be saved. Ultimately, the sharp distinction between God and the World belittles humanity by enslaving it to the narrow vision of the authorities who have devised and codified traditional religion
'Original sin' has a vestigial foundation in the evolutionary tautology that they survive best who will do anything to survive, uninhibited by rules that favour the survival of the using classes over the used classes.
USED (Marx) <> WORKER
When headroom is scarce society tends to be violent because there are more errors. Adequate headroom protects against error and so gives a more peaceful society because there is adequate processing power to solve more potential conflicts amicably. We maximize headroom by localizing processing. What can an isolated Hilbert space do? Rotate in multidimensional space, a rotation being understood as a change in the angle between two vectors. It is relative motion in the nature of a flow of fluid (entropy) rather than rigid motion from place to place.
[page 109]
We imagine the world being constructed through topological barriers and linkages, ie regions where messages cannot go and regions where they can. In human society this corresponds to out right to silence, to keeping our knowledge to ourselves, ie privacy balanced by our right to know the direction of the res publica
For each generation, the good news (if any) relates to the progressive removal of various 'evils' such as violence, sickness, poverty, homelessness, unemployment and so on. We see all these things as dangerous failings of the old system which need to be remedied by closer attention to the details of what is going wrong, in fact and in cause.
STRUCTURE = SET OF PROHIBITIONS (thou shalt not fall down), ie no-go zones or boundaries for various processes.
So the conservation of probability is the basic prohibition in quantum mechanics: the rate of events in the Universe is constant = energy is conserved. What is changed is not the overall rate of events but their meaning arising from how they are structured by prohibition. The Universe cannot stay in a state of contradiction. Such a state ultimately decays.
Perfect correlation of states (determinism) requires a coupling constant between events of 1, a must follow b as night follows day, so a Turing machine steps unfaltering to its conclusion.
Continuing in the Christian direction, we start to develop a moral code which enhances peace and survival by selecting behaviour conducive to increasing the bandwidth of social communication. Here meekness and gentleness correspond to high
[page 110]
bandwidth that is high fidelity communication. So it may take a document of the length of a novel to capture the nuances of a human situation that the novelist has chosen to explore. Hemingway, The Old Man and the Sea. Endurance.
Controlling desire. Control is the foundation of error free communication and careful control is needed to survive in complex changing environments. The aim of religion is to create a human space fit for the home of humans. As our understanding of humanity grows, so do our criteria for a suitable society seen as human habitat.
The function of prohibitions (symmetries) is to guide the execution of potentials into fit channels. In a peaceful society we expect behaviour to be guided by public spirited reason, where we seek to spread 'good' as widely as possible.
From the physical point of view, the human system can be seen as a closed network of material transport driven by solar energy.
We make much of the defectiveness of human nature, but as we gain deeper understanding of how we came to be how we are, it is likely that we will see that on the whole our life stories are optimal relative to our environment.
Tuesday 14 April 2009
Calculate cross section = calculate traffic in a channel, ie the flow of action = energy of the channel.
[page 111]
We move from quantum theory to thermodynamics via statistical mechanics. The essence of statistical mechanics, as in the theory of probability, is to start with a set of equiprobable events and see what we can deduce from them about complex random events. The idea being that a set of small random events can in same way generate a set of larger random events, that is random events requiring longer and longer cycles of elementary events to complete themselves.
A cycle is completed when it returns to its starting point, in a suitable space. the structure of the world lies in the generation of larger events (like building a house) out of many smaller events, like hammering a nail.
Some cycles have a sharply fixed frequency, other recur, but at random times, like the disintegrations of a particle with a certain half life. Biological reproduction cycles in all their diversity, exhibit a complex mixture of more random and more deterministic elements that lead to enough reproduction to make the species grow. Each of our lifetimes is an enormously complex chain of events leading from conception to death.
Each cycle from a network point of view is the verified transmission of a message. So do we see the photon stepping through spacetime at a frequency f = E / h, matching the length of its steps to its frequency to that it always appears to move at the same velocity, c. This suggests a pixellation of space-time constrained by the velocity of light alone. We imagine this geometrically by the light cone (more generally the communication cone) constrained by the fact that it
[page 112]
takes time to go a distance because it takes lots of steps and each step takes time. The frequency of the stepping is energy or at least frequency x size of steps (measured in quanta of action)
A digital Universe steps like a walker.
A continuous Universe rolls like a wheel.
Wheel is simpler, walker more versatile (eg climber),
How do we build civilization out of the feral world of quantum mechanics? Or is it so feral? Insight = collapse of wave function (isomorphic up to a cardinal number; isomorphic up to a phase).
Physical measurements are carried by phase and they interact isomorphically to complex numbers, or in other words, we add amplitudes represented by complex numbers.
Insight is a random cycle which nevertheless makes progress by communication as we see in the scientific community of communities. In spacetime elements of a community may be widely distributed but unified by communication.
We might see some sort of correlation between the size of an insight and the frequency of its occurrence. Thus revolutionary ideas come about once a century in physics, but the enormous number of lesser insights that lead to the revolution are everyday or even every minute occurrences. Religious revolutions, on the other hand, have a characteristic time of thousands of years. Natural religion
[page 113]
is a millennial event.
The precise agreement between computation and observation gives us faith in our computational methods and assumptions. The agreements are averages of millions or billions of observations and the algorithms work from equiprobable events to the probabilities observed in reality. The probabilistic coupling constant, the inner product . . . of two vectors tells us how closely they are coupled.
Wednesday 15 April 2009
Suicide. If we were more reasonable about death maybe potential suicides would ask people for help with killing themselves and so be given reasons for living. Hanging is grisly and unless done very efficiently, terribly painful both physically and psychologically. Did he believe he would go to heaven after twelve years of Catholic education? Although they might teach that all suicides go to Hell, at least all 'private' as opposed to judicial suicides. But the Church has never given that option, choosing to kill its victimes by fire and sword.
We die through 'unfitness' ie inability to keep the life process going. Usually such unfitness shows at times of high environmental physical stress.
We might say that mathematics is straightforward but what does it mean? What is a superposition? In the real world something can be in one state at a time, whereas a superposition is seen as a weighed mixture of a possible infinity of states. In a network, a superposition is a set of memories to which the system under
[page 114]
observation may connect.
The Theology Company ambition - to develop and market a rational religion.
The quantum sustem is constrained to be continuous and linear because it is too simple to be anything else. CONTINUOUS = NO DETAIL
As soon as communication enters we have space and quantum field theory.
Now we can all afford the degenerative diseases of the rich, and also the discipline the rich learn to protect themselves from degeneration.
Peskin & Schroeder: The key to all this attempt to unite theology and physics is to interpret Feynman diagrams as local pictures of a transfinite computer network. Peskin & Schroeder
It takes work to remain healthy, that is to keep a complex system error free.
What is the logical interpretation of relative velocity = relative energy = relative momentum = Lorentz / Galilean transformation? Space and local motion, extended memory and systematic changes of memory state. Space is the vehicle for quantum fields? Quantum mechanics is the science of space? The physical realities of space are potential and locomotion, ie relative motion which requires communication for its observation / realization.
[page 115]
Renormalizable = digital?
Thursday 16 April 2009
Friday 17 April 2009
The psychological foundation for suicide is that one no longer fits into one's native society. An alternative is exile, so a failed Roman general has the option of falling on his sword or exile, the suicide being more 'honourable'.
An idea spreads by a chain reaction: someone understands it and sees that it is good and so is motivated (on the average) to tell more that 0 people. Provided no one forgets (ie the idea dies in them) this will lead to exponential growth en, where n is the average number of people who successfully pass the idea on. The internet so speeds up the [passing on] process that ideas can grow from one copy to millions in a very short time.
IDEA = ELEMENT OF SOFTWARE = TRANSFORMATION represented in quantum theory by a matrix of pairwise relationships between all the elements of a state vector. Since all our measurements are modelled on inner products, the details of an ordered vector are destroyed in the integration to obtain the observation, but this does not mean the details are not there. So quantum mechanics is indifferent to order, as we should expect, as the basis states of a Hilbert space or any other vector space have no natural ordering, allowing us to choose conventions for analytic exposition but then integrating this detail away. Indifference to order also means quantum mechanics does not need memory, each moment being independent, so that every event (moment) is the beginning of a new state of the system.
[page 116]
Quantum mechanics is 'outside' spacetime and 'outside' history. It is a theory of perturbation or reaction, every message being accompanied by its dual, every action by an equal and opposite reaction [so maintaining the unity and stability of the world?].
The fundamental ordering parameter is time: 'numerus motus secundum prius et posterius'. Aristotle
Saturday 18 April 2009
Peskin & Schroeder page 127: In the high energy limit cross section formula become very simple, which suggests that at higher energies (lower layers of the network), processes are much simple than at low energy (per particle) where we get complex processes like me, the complexity arising from the many payers of process which are using the fundamental processes.
Quantum field theory: How does the world compute all this stuff? Network = source of perturbations. Every time the phone rings my course through life is changed to some degree. The simplest life is that of the completely free particle, and the only completely free particle is the Universe itself.
In the Universe all information is represented physically and logical processes are implemented by physical motion in continuous 4D space. We would like to turn this around and say that all physics is implemented informationally, and all physical motion in 4D space is implemented by logical functions, like and, or, not etc. So we might ask does the body drive the mind or [page 117]the mind the body, and the answer is both. By thinking I work out what to do, but what I must do is to a large extent constrained by the needs of my body for food, shelter, sensuality, excitement, sex, reproduction etc etc. So once again the layered network paradigm helps, the higher layers establishing and maintaining their existence by manipulating the lower layers. The terms 'mind' and 'body' refer to layers n and n - 1 respectively.
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