Notes
[Notebook: DB 62 Interpretation]
[Sunday 24 February 2008 - Saturday 13 February 2008]
Sunday 24 February 2008
The epistemological foundation of the Christian hypothesis us institutional authority and personal belief. The second is a consequence of the first, since religious institutions generally ensure that the young learn to fit in.
There are three different ways of specifying the energy, by the frequency of an amplitude, by the energy in the classical sense, or by inertia. They are all equivalent; they are just different ways of saying the same thing. Feynman page 7-2. [from a cardinal point of view] Feynman
Space and time: 'If a particle has defined energy, it also has defined momentum. If the uncertainty of momentum is zero, the uncertainty relation delta p.delta x = h bar tells us that the uncertainty in position must be infinite, and that is just what we are saying when we say that there is the same amplitude to find the particle at all point in space.' Feynman
[page 193]
DEFINITE (E, p ) ==> INDEFINITE (t, x )
'In order to have the probabilities change in time we have to have the interference of two amplitudes of two different frequencies, and that means we cannot know what the energy is.'
Quantum mechanics allows perpetual motion because it is complete and energy never gets lost, and all situations have a solution.
Quantum mechanics is indifferent to actual energies: 'The choice of origin for our energy scale makes no difference, we can measure the energy from any zero we want.'
All that counts is relative energies, ie relative rates of communication.
Quantum mechanics is about relative phases, and given the finite velocity of communication relative phase is a function of space and time, whereas if communication were instantaneous at infinite velocity there would be no momentum and no space.
Monday 25 February 2008
Potential = energy whose derivative gives a force. Derivative with respect to distance. How do we fit this to the idea that test is a potential? As we read along a text (its 'spatial' dimension) we experience a force (emotion) which rises from the meaning of the
[page 194]
text. Although often the emotion I experience when reading technical stuff is despair, because I cannot derive a clear meaning. So when we 'read' a hill, we experience a force moving us downhill.
. . .
Feynman page 8-2 '| = SUMi |i ><i | ' where i indexes a complete set of base states. In a free system without any exterior input, we would expect such states to be equiprobable so the base system represents maximum entropy, equilibrium no possibility of increasing entropy and so in a sense perpetual motion, as we find in the quantum layer of the Universe.
The classical layer is the quantum layer communicating with itself. Quantum 'teleportation'. Nielsen & Chuang
Incorporation - Abstraction
Fair Trade - Peerage
Prospectus - Trading value. Value is measured in quanta of action
like hours of work, number of units processed or kilometres
travelled.
What the theology company is marketing is a method of reaching peace by respecting reality.
[page 195]
The natural religion project: reaching peace by respecting reality.
Sameness and difference: the evolution of difference from sameness and he detection of sameness in difference. This is the cycle of the Hilbert Oscillator. What oscillates is the symmetries, ie those structures that are outside time (ie constant) in the spacetime region of interest.
Formal complexity operator. Oscillates between transfinite cardinalities. It is a transfinite number oscillator which acts by order and permutation. The order makes the permutation possible and the order hidden in the permutation allows us to extract a set of basis states or letters of an alphabet which appear in strings from a source with different frequencies.
Given enough boundary conditions, quantum mechanics allows us to calculate the traffic on channels. gravitation tells us how there channels are to be configures to get the maximum ratio of information (entropy) to energy.
Gravitation shapes the network (ie spacetime) in response to traffic (energy) at different points. It is not concerned with the moaning of the traffic, just the volume.
Site assumptions:
value for value / fair trade;
accountability / (ultimately) public company
Universe is divine / trustworthy / not defective
We stand opposed to all those beliefs that say we are some sort of special aliens who will eventually find our true home.
[page 196]
The world is home.
Incorporation: and the Word was made flesh. John 1:14
The Hilbert oscillator oscillates from talk to action. The word is made flesh (phenotype) and the flesh is made word (genotype).
Base states are an abstract version of a space which is 'filled in' by making vectors whose components are the products of a base vector with a number (real or complex).
'The complete description of an electron, so far as we know, requires only that the base states be described by the momentum and the spin. ' Feynman 8-5
One binary, one continuous parameter.
'We do not really know what the correct representation is for the world.
COUNT <==> SAMENESS (I count buttons, units)
Feynman 8-6 'Does a proton have internal parts?' [ie an alphabet?]
Energy scale measures 'hardness' or imperturbability. You have to hit a proton pretty hard to reveal the quarks.
IMPERTURBABLE = CONTROLLED
So we finally begin to penetrate something when we communicate with it faster than it can respond and keep its set point.
[page 197]
'Hard' states are relatively invisible and do not take any part in processes involving soft states. The nucleus is almost completely oblivious of the electron.
Edges map nodes to nodes, while nodes map edges to edges. The difference between a node and an edge is that an edge has just two ends and a node may have an infinity of ends (input/output points)
Recycling requires signal channel (the product). garbage channel (the waste)
Feynman page 8-8 'The limiting case of U(t1 , t2 ) as t1 approaches - infinity and t2 approaches + infinity is called S, and what [the physicist] wants is <chi | S | psi >, ie a map of everything that happens to change psi into chi.'
The U matrix moves an event along its generalized geodesic from t1 to t2 , like my U matrix has transformed me slowly from egg to middle age.
'Each amplitude at t + delta t is equal to all the other amplitudes at t multiplied by a set of coefficients'. The next step into the future depends on the whole of the past. Special relativity says this cannot be so and limits causal influences to the past light cone. Each individual is attached to a light cone which samples a tiny fraction of spacetime, except in the indefinite past and future where it affects and is affected by everything else (but not in an expanding Universe(. So independence ==> expansion.
[page 198]
The base states of the Universe: the divinity hypothesis tells us every possible basis, with a certain probability which is in the end decided by network constraints. Our hypothesis is that the only constraints on the Universe are network constraints which fundamentally relate to resolution and bandwidth,
We only fight hen necessary, or apparently necessary.
We are all witnesses to god's activities.
I am a party of one, but as the platform slowly emerges from the mist, I hope to get others to exercise their boson nature and join me in this state. it has taken me a long time to get here so I do not expect a crowd for quite a while yet, time to get my act better together.
In the end it will go on presentation: whether it is perceived as a route to salvation from our growing awareness of our situation. We must curb our heavenly aspirations with the boundaries of physical reality and assess what our fair share of the world's resources must be. This also is part of fair trade - not to kill the golden goose.
Ammonia molecule and the quantum harmonic oscillator.
It began with a theory of peace: peace comes through adequate space; and we an grow pace exponentially on a fixed energy budget if we exploit the power of order which manifests dynamically as the power of algorithms to work for is on cash registers and car engines [not to mention the social algorithms which make our society possible].
[page 199]
Can we derive all the physical properties of the Universe from the proposition information is always incarnate, ie represented physically. There is no pure unphysical (spiritual) representation of information. Whatever can be physically represented is the boundary of information transmission.
What distinguishes quantum from classical? Certainty. Classical allowed unbounded certainty because formally certainty has no cost. In reality, however, precision is expensive but can often pay off.
A wonderful thing about quantum mechanics is that it can describe so much in so few symbols because the symbols are given deep meaning by mathematical function theory, the theory of mappings finite, infinite and transfinite.
Ammonia molecule: Feynman page 9-2: 'We have found two special solutions in which the amplitudes do not vary in magnitude and furthermore, have phases which vary at the same frequencies. These are stationary states as we have defined them in section 7-1 ['if a thing has a definite energy and if you ask any probability question about it the answer is independent of time, Although the amplitudes vary with time, if the energy is definite they vary as an imaginary exponential and the absolute value does not change. That's why we often say that an atom in a definite energy level is in a stationary state page 7-2]
Fixed points in the dynamics - energy levels.
Diagonalization: finding stationary base states for
[page 200]
observables, since observables are by definition stationary. The spectrum of an atom tells us the stationary states, the line intensity measures the traffic between them. Nothing an change its state without communicating with its environment.
The biggest abstraction: it is all just a flow of data through a network.
Feynman page 10-8: 'In the 'particle' theory of electromagnetism, the process of virtual photon exchange gives rise to all the phenomena of electrostatics.
Exclusion energy page 10-9
Tuesday 26 February 2008
Classically the power of a simple harmonic oscillator varies as the square of the amplitude and frequency.
[To DB 63: ATheology]
[paged 1]
With growing confidence I think that I can make a first pass at a theology, putting together all the bits and pieces that I have collected over the years. These ideas first appear in these notebooks (usually) and then slowly diffuse into the development of a theology and a religion.
The name atheology reflects our attempt to take a neutral stance, halfway between theism and atheism. It all depends on what you mean by god. We model this situation quantum mechanically as a two state system, a qubit. Qubits exist in two dimensional Hilbert space and are formally manipulated with unitary operators represented as 2 x 2 complex matrices. Abstractly there is only one 2D Hilbert space and one qubit represented in it. We can however build up more complex systems out of qubits just as we represent the natural numbers with finite strings of bits.
Differentiate between qubit and classical bit.
If an atom is to be bound its binding (low energy) states must be considerably more probable that disintegrating states, eg U238.
Wednesday 27 February 2008
Thursday 28 February 2008
Fiddling with the web. I need a new content
[page 2]
management system since Frontier went too expensive for me. Want to integrate these sites
Theology company
Natural theology
Natural religion
A theology
A new theology
and make them interactive with some sort of voter dominated content control and spam removal. The choices seem rather limited but we seem to be coming back to Ruby on Rails which was the focus of my last effort to replace Frontier which died when I decided content development was more important than content management, but I wish to go much more publick now!
Forty years ago I wanted to update the Summa and lost my job as a consequence. Now I see a way to write a commentary in three columns: the latin text, my comments and the english text.
Friday 29 February 2008
The dot product measures the angle between two vectors, in quantum mechanical terms the relative phase and in computing terms the relative degree of completion of two processes, it the execution of two Turing machines. The quantum mechanical (and wave theoretical) principle of superposition hold that if two processes have the same phase their amplitudes add and the energy (or probability) of this situation is proportional to the square of the resulting [amplitude]. On the other hand, if the processes are exactly out of phase, they annul one another and the probability or energy goes to zero.
[page 3]
Although phase is always positive and increasing with time, it is not the phases that annul one another but trigonometric functions of the phase like sine and cosine. What does this mean physically? That a half finished process annuls a finished process? That a process going backwards annuls a process going forwards? What about 'beat notes' hen we superpose two processes with different periods (frequencies)?
Dot product is a multiplication and integration which is not commutative in quantum mechanics because our vectors are in a complex field so < x | y > = <y | x >*. Dot product compresses finite, infinite or transfinite dimensional vectors to a simple complex number, so we see it as analogous to abstraction or knowledge.
The use of 'gates' in quantum information theory in fact 'digitizes' operations which we know to be continuous. We are simply concerned with the initial and final states and do not worry about the dynamic process that carries one into the other. By analogy with macroscopic processes (which include the operation of ordinary digital computers) we think of the process between initial and final states as being continuous, so the initial and final states are connected by geometric continuity which underlies the idea of logical continuity. Perhaps the situation at the microscopic level is the other way around, or a superposition of both.
Complex conjugation reflects complex numbers in the real axis.
Thinking in communication theoretical terms, orthogonality is equivalent to error free communication, since < i | j > = delta ij, if the system is one one basis state, it has no probability of being in another.
[page 4]
Superposition is in effect a condensation of a number of events into one. So we may think of a source A which emits a normalized string of symbols ai as the 'expansion' of a superposition. By observing the source for long enough we can work out the relative probabilities of the ai and so their relative weights in the source superposition. This view, like communication theory, takes no note of any meaning which may constrain the emission of symbols from a so that they are in fact a determined string. The theory itself tells s that the 'meaning' of a string is maximized when its symbols are equiprobable, so no observer without the means to decode the string can decide whether it is purely random or maximally meaningful, ie carrying a maximum amount of information.
All quantum mechanical operations (like hammering in a nail?) can be represented both by matrices and by Turing machines.
Feynman III 8-5: What are the base states of the world? Anything orthogonal? no matter what the cardinal. These are observable base states. We can say nothing about unobservable base states, so we may as well not talk about them, they are hidden in the 'omnino simplex' divinity.
NAMING = BONDING
The name may be a physical bond, as in a molecules or spiritual bond, as in the meanings attributed to words, is 'brick' is bonded to [a picture of a brick].
[page 5]
Quantum mechanical amplitudes do not tell us what things are doing, but what they could do, and the rules of quantum mechanics enable us to compute the probabilities of these various possibilities.
Real probabilities are yielded by observations which depend on the state of both the observer and the observed, hence the use of the dot product, which tells us how close (in phase terms) the observer's state is to the observed's state. If they are exactly out of phase, the observer sees nothing. So in the two slit experiment, we station observers all over the screen who see particles at a rate proportional to the relative phase of the observed particles. We assume that the observers are all in phase, and that the phases of the observed particles change with their location in (relative) space and time.
The growth of complexity is driven by the exponential power of error correction which is in turn related to the exponential growth of message space as message strings get longer. The decrease on complexity comes form the occasional failure of this process, birth and death, the currency of the Hilbert Oscillator which describes birth and death at all scales. Here we see how death is a natural part of life, and reverse the Christian denial of death.
[page 6]
Saturday 1 March 2008
Virtuous circle: increased orthogonality of symbols increases message space allowing increases orthogonality of complex symbols which can be fed back to increase orthogonality of alphabetical symbols, and vice versa. The virtuous circle requires the evolution of codes that efficiently exploit the spaces created, ie maximum entropy codes. [the simplest code is repetition]
In physics we have two selective pressures (two potentials) toward lowest energy and highest entropy. In a sense we can see these as two sides of the same coin, since reducing the energy per state allows us to increase the number of states (entropy) per unit of energy, as we see in an atom very close to ionization where the potential approaches zero and the number of states approaches the free continuum.
On propagating through a network = on creating a network.
-->