Notes
[Sunday 2 March 2008 - Saturday 8 March 2008]
[Notebook: DB 63 aTheology]
Sunday 2 March 2008
[page 6]
Monday 3 March 2008
Let us say that the root of quantum mechanics is a real time system without memory. Processes can only communicate if they coincide in time. When we introduce space and memory a process can get to a certain point and then either wait or move through space to obtain the resources for the next step. Here lies the selective advantage of space, multiplying the chances for a process to find the resources for completion and so paying for
[page 7]
whatever costs are involved in constructing memory. With memory timing ceases (to some degree) to be of the essence. A juggle can leave his balls in the air and come back later to complete his act.
MATERIAL = MEMORY Kauffman N452:77. Zentrum Paul Klee Bern, Kauffman
Tuesday 4 March 2008
Why do we do stuff? Because there is dissipation and error in our processes that must be created. We split capital (or better cashflow) into two streams, capitalization, ie the creation of fixed points in the dynamics, and consumption, ie the execution of the dynamics, the processes. In the model the capital is the messages and the dynamics is the execution of the Turing machines that transform the dynamics. These Turing machines are themselves messages. So we arrive at the definition
MACHINE = FIXED POINT IN THE DYNAMICS
where the entropy of the point is measured by the entropy of the space in which the machine operators.
Wednesday 5 March 2008
'Every decoding is another encoding' Lodge, Small, page 25. Lodge
Omnes Quantum Philosophy (Original title Philosophie de la science contemporaine - much better). Omnes
[page 8]
A Turing machine, being inherently deterministic, is not observable.
Let us say that the cardinal of the dynamics is always greater than the cardinal of the fixed points within that dynamic. The fixed points are the alphabet, the dynamics the set of all possible permutations of the alphabet.
Power is a boson thing: the aim of the powerful is to get everyone into the state of your choice, which must be a boson state otherwise only one person can occupy it, solipsist - fermion.
Lodge p 59: 'What we really lust for is power, which we achieve by work'.
Money is a boson; money attracts money.
Simple Harmonic Oscillators occupy a 3D parameter space of phase, frequency and amplitude, all of which can be captured by complex numbers, except phase is closed so it cannot be counted, like astronomical Julian dates. Quantum mechanics is not so concerned with this confining itself to timeframes measured by the lowest frequencies of interest. All frequencies from there on up are superposed to give the end result. This happens in the frequency/time domain and does not require memory or space. It is worked by the ladder operators which are in a sense blind to the structure which arises from their operation, although it is mathematically possible to derive the form of the ladder operators from the black body curve and vice versa. They are the local implementation of a
[page 9]
global algorithm, the alphabet of interaction which explains the statistics but not the details of interactions, which arise in the layer using the alphabet. Physics provides the alphabet (an at least countable infinity of states) and all else is written in physics, ie it is applied physics. Thus is life.
Quantum Harmonic oscillator has a growing number of states.
Harmonic oscillator is what goes on in a potential well. The solar system is a superposition of harmonic oscillators operating in a potential well created by the whole system dominated by the sun.
The simple harmonic oscillator has two stationary states at each end of its swing. Its amplitude and phase are initial conditions (imposed by the higher and lower layers).
Our basic heuristic principle is that the fixed points in our Universe from which we can navigate ourselves through life can be placed into correspondence with mathematically consistent formal structures, like computers, which do a lot of the work that can be written out in a functioning algorithm like (eg) bookkeeping in all its forms, that is creating a paper model of reality, like a business.
How do we see the Harmonic oscillator as an inhabitant of code space, transfinite (?) code space. No, countably infinite code space modeling symmetries in a transfinite world.
The transfinite spaces are created by ordering their alphabets, card (aleph(n) ! ) = aleph(n+1).
[page 10]
These cardinals are counting ordinally distinct structures which all share the same cardinal (the cardinal of the alphabet) ie the entropy per letter at, say, equilibrium = equiprobability.
What we look for is a path from equiprobability to the proliferation of highly improbable entities like ourselves. Dawkins
Do we underestimate the world: DENSE CODING IS INDISTINGUISHABLE FROM NOISE.
Instead of rabbitting on about interpreting texts (see Theological Studies) we would do better to look at and interpret the world. Theological Studies A core belief of natural religion. Practical love of neighbour by charity, fair trade, peerishness (neighbourliness) and so on.
In computing, thing are connected by an address. So to communicate with another computers, I write things into an address which is logically and physically connected the the other machine.
More thinking time makes for better writing? Up to a point where more is to be learnt by writing than by thinking. And writing has the further economic feature that by propagating attractive writings one might attract value to oneself, ie build oneself a potential well (like an ant-lion) and sit at the bottom of it collecting the spoils. Antlion The economic motive creates the temptation to write for the popular mind rather than trying to discern some symmetry or truth on our existence.
Universe: everything in it pulsates like the Hilbert Oscillator, is the complexity oscillator [the oscillator of birth and dying].
[page 11]
The potential wells occupied by the simple harmonic oscillator and the quantum harmonic oscillator are formally different, but both define a certain space by the potential existing in it, and then see how things move that feel the potential move. In the simple harmonic oscillator the absolute value of the potential varies as the square of the distance from the equilibrium (stationary) state.
The archetypal formal explanation of dynamics is the differential equation, a fixed text that describes the boundaries or fixed points of a motion. So simple harmonic motion is the totality of motion allowed by a potential described by the differential equation for simple harmonic motion.
. . .
The design of a programming language means finding a suitably related set of transformations that can do anything in the way of manipulating texts (in put and output, messages) easily and transparently: generating random numbers, translating from one human language to another, and so on.
Thursday 6 March 2008
So the principle is how things move is bounded by the potential in which they exist. My movement is bounded by the contradictions between Catholicism and the religious space I feel would best help is toward peace, sustainability, love and excitement.
The simple harmonic oscillator oscillates between potential and kinetic energy.
A lot of computing decisions are between local and remote, server side or client side. Perhaps we might say processor intensive, server (which is probably the more powerful machine) vs communication intensive client (since the cost of communication is probably the clients biggest cost.
Quantum harmonic oscillator oscillates between numbers of photons in various state. The attractive potential is the boson potential, where the attractiveness of a state is proportional to the n umber of 'particle' occupying it (Feynman). Feynman This 'force' is balanced by the difficulty of getting from one state to another, which grows exponentially with the energy barrier between the states,
So is the real estate market, where we are always attracted to live in metropolises but repelled by the high cost of getting there.
Dedicate this work to Giordano Bruno who saw that the Universe was infinite and died by fire for the ideas expressed here. Giordano Bruno - Wikipedia One is lucky to have been not only too insignificant to notice, but to be born in an age when dissidents are merely expelled form the Church, not burn alive.
Omnes page 27: 'The present situation is fluid -- which perhaps explains Kepler's whimsical personality -- somewhere between yesterday's failure and tomorrow's hesitant promise.
page 28 'A novel idea will then slowly begin to ripen: would it be possible that lifeless nature should obey an order
[page 13]
imposed [described?] by mathematics?
Omnes: 'With Kepler, astronomy has fulfilled its role as midwife in the birth of science, by revealing the existence of empirical laws shaped in mathematical form.'
Force p 29. Stevin and statics. Statics - Wikipedia
Galileo: Motion without force. Newton Force ==> acceleration and differential equations.
From Galileo's law perpetual motion becomes a point of equilibrium as well as perpetual stasis: they are the same : a body at rest remains at rest and a body in motion continues un uniform motion in a straight line unless acted upon by a force.
Einstein: rest = motion
acceleration = formal (connection of 'matter 'and 'space'
ELASTIC: You leave as you came
PLASTIC: The interaction has changed the interagents,
Omnes p 33: 'Newton's first task is to establish to plausibility of his theory. He does it by a method that will show up many times in the development of physics: recovering some results, already known in the form of empirical rules, as logical and mathematical consequences of newly stated principles.'
page 34: Action = information
page 35: 'More efficient calculations do not entail higher conceptual
content'
[page 14]
Unless we see the world as calculating itself and accept that there is perhaps natural selection among algorithms that favours the 'fittest' elements of algorithm space where fit correlated with 'efficient calculator' (as is the case with modern 'guided' weapons.
Omnes page 36: optics / Dynamics
We se the global computer as a space full of agents which interact directly with one another rather than communicating through a central processor (God) who drives everything. When we say the Universe is divine we say that it is a network of local gods.
To be in a potential well is to be bound rather than free. To be bound is to be in communication with one's environment, that is to be in some way a dual or correlate of the environment, a copy, a knower.
Omnes page 37: 'space is also matter'.
Huygens: Superposition of waves. Christiaan Huygens - Wikipedia
. . .
page 57: 'In mathematics what matters is not the nature of things,
[page 15]
but the relationships that exist among them.'
Which can be represented by messages in a network of natures. By their messages you shall know them.
Omnes page 58: A geometry is always associated with a group.
'From a science that possesses its own traditional objects of study [mathematics] is becoming the universal science of relations; in a certain sense the science of the structures that may arise in any science.' [ie formalism]
page 61: Classical mathematics: the final result 'that paradise which Cantor created for us' as Hilbert called it, was indeed the only possible paradise.'
Epistemology
Page 62: 1. the world is faithfully represented by our mental
images and ordinary language;
2. the world is essentially different from our perceptions of it.
page 69: 'Thus perception appears as an extremely complex process where the outside world is first decomposed into a multitude of attributes well before its meaning can be grasped. This analytic feature of perception, which begins by breaking down the image before proceeding to its synthesis, has gradually imposed itself during the last few decades and philosophy can no longer ignore it.
First extract the alphabet ('attributes') then use it to render the picture.
page 72: 'The significance of reason in modern cognitional sciences would rather take into account two simple but essential ideas which were still missing in the eighteenth century [Kant]: that thinking takes place in the brain and that reason and logic in particular, was acquired and developed by humankind through a long historical process. It has a strong social component, involving communication and culture.'
page 81 'The fracture is . . . there in the fact that these laws [of science] are when seen through the ideas of average intelligence or classical philosophy, absolutely unintelligible. In a nutshell, the more we know, the less we seem to understand.'
page 84: '[Mathematics] is the abstract study of form' - POTENTIAL
Kant's a priori's are features of a [neural] network.
Friday 7 March 2008
More Omnes
Quantum mechanics tells us that the world is inherently dynamic at the level of the free system. Heracleitus was right here. Heraclitus - Wikipedia But a theorem tells us (Brouwer?) that every motion has a fixed point. It is the existence of these fixed points that makes complexification and life possible because they provide memory, which in turn guides the dynamics to create more fixed points, as we see (?) for instance in the quantum harmonic oscillator and all the other oscillators like the atom and the solar system.
[page 17]
Omnes p 108: 'What is mathematics, . . . This question , , , attracts only a small number of philosophers and mathematicians. Who else would care?
And how big is the mathematical theology community. It would be nice to find another one!
Mathematics is sacred text. The Bible is sacred text. All text is sacred in the sense that it is the foundation of knowledge, life and everything added to pure act to give us this world.
In physics, structure results from potential.. The swinging pendulum has two fixed points and spends most of its time near them, Calculate the probability density function for simple harmonic motion, which we can illustrate with a stroboscope whose period is incommensurate with the period of the pendulum, if we wait long enough.
Biology: Our view is that just about everything is alive. By life we mean actively maintaining a very improbable state by feedback, and on this definition it is to be found everywhere where Shannon's theory of communication is implements by exploiting entropy to correct and prevent error. From this point of view the domain of life is the domain of cybernetics which can come into existence as soon as memory is available. And memory is a product of control, but control imposed by logical continuity.
Saturday 8 March 2008
A fleeting glimpse has escaped again without getting written down. Copying out page 5 above. But no I've got it. Let us say that any particle with mass is alive,
[page 18]
since the existence of (rest) mass points to internal process, that is, life (as Aquinas and Aristotle would say, self motion). So we begin biology with massive particles, leaving physics to deal with the massless, ie photons.
Arguments from continuity are arguments from meaninglessness where there is no mapping or order so all we can do is count things to arrive at a certain measure. Physics relates measures to one another by equations, but it has been found in particle physics that equations by themselves are not enough. They must all be coupled into a network with different coupling constants (eg Feynman diagrams)if we are to be able to calculate a parameter of a probability such as the g factor of an electron etc.
An algorithm is a set of fixed points that guides the dynamics of a situation. We begin with simple harmonic motion and work through quantum harmonic motion to transfinite harmonic motion.
Cardinals do not of themselves evolve, and so we have the conservation law. Ordinals do.
The amount of energy in a state is its cardinal which is identical to its frequency. But cardinals have a natural zero whereas we say that we can put our zero of energy anywhere. What we can say is that
[page 19]
kinetic energy + potential energy = 0, ie there are two counts of energy and one is the arithmetic negative of the other, ie add one kinetic unit to one potential unit and you get 0, if you manage to count all the (superposed) potentials and motions.
How does this relate to action? Energy is the time rate of action (as momentum is the space rate). Action is the ur-thing like the empty set of action, an act with no content, some might say pure act. The evolution of structure five it content. So can we have time without space? Maybe not, but we can have energy without space, but we cannot measure energy until we can measure [frequency] and to do this we need an oscillator with a fixed frequency as a standard, ie we can compare different states of fixed energy and read off rational numbers, being the ratio of the two frequencies determined by counting oscillations.
A particle can only change energy (or momentum) by communicating. [Which means that all motion is bound to the universal flow of four momentum]
What is change? Uniform motion is not, it is a stationary state. Newton saw that every change of state requires communication of force (Galileo before him) Acceleration is a change of state. Does this make gravitation (like all fields) a state changer? A field is that whose gradient is a force. [a field is the integrated effect of a large number of acts of communication] This defines potential and a field define potentials which 'control' the dynamics, creating and annihilating.
We unite communication of force with communication of information by Landauer's hypothesis that all information'
[page 20]
is embodied physically
The core idea of quantum mechanics is in the nature of a fixed point theorem: confinement breeds structure which can be understood by Fourier analysis and superposition in wave mechanics and through the eigenvalue equations in matrix mechanics. Wave and matrix mechanics carry us from constraints to structure. We learnt a lot about it from sound, light, music and colour.
CANTOR FORCE == CANTOR POTENTIAL
Potential wells bind and create structure. What makes the potential wells? They are something formal, as Einstein found with gravitation. While they exist they are eternal but they can change kinematically,
We finish physics with the roots of evolution, that is motion and stillness, process and memory.
All potential wells are Cantor potentials. What might that mean (first permute the words, then see what they mean)?
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