Notes
[Notebook: TURKEY DB 55]
[page 238]
[Sunday 13 April 2003 - Saturday 19 April 2003]
Sunday 13 April 2003
Interference: two coherent sources (or more) establish a spatial structure which is lost if the coherence of the sources is broken by observation. Is quantum no-cloning in here somewhere?
[page 239]
Leaming Monroe 162: 'Marilyn was not floating any more - she had a direction again. Leaming.
Energy, momentum, structure (potential structure) which is realized by an interaction (a measurement). Epistemology: producing and testing symbolic models of the world.
Measurement is the comparison of one part of the world to another. Depending on their relationship to one another (consistent or inconsistent) a coherent measurement creates 'interference' that makes a certain structure observable.
The elements of an event. Once we have a general description of an event, we have it all. An event is a setup (in say all the memories of a computer chip) followed by execution (triggered by the clock pulse) followed by output, again a stable state of the system. We describe the action by defining the inputs and outputs. The input of god is nothing, the output is god. What does this tell us about god?
Present, past and future: often this sort of work seems unattractive because it seems hopelessly beyond my reach to emulate my heroes and say something new and valuable about the dynamics of the world. This is a consideration, but on close reflection I think I am drawn by what little progress I do make to realizing (or discerning) a dream. As the model firms up, so the structure that will consistently interfere with the structure of the world slowly grows in my mind. The checking process is still home made and conscious, but it seems clear that one day I (or somebody) will be able to write down consistently my still unexpressed feeling for the world, the human condition, and the experience of people near me.
[page 240]
On the scale of the Universe Saddam Hussein (or at least what he represents in the public mind) is isomorphic to a blocked sewer. The world is being held up around him with pathological consequences.
The particular psychological problem for me is acting alone. It would be better to have colleagues. There are probably some somewhere, and my best chance of finding them is probably the internet. My personality does not seem to suit academia, but maybe it is still a case of 'travels fastest who travels alone', and one can expect no collaboration until there is a clear and consistent formal statement of the hypothesis/ This. above all, is what I seek.
All 'interference' implies duality. Communication: if there is inconsistency, it dies (I do not want to talk to you). If there is consistency it grows, with energy proportional to the square of the amplitude (?)
Can we distinguish between the statements 'energy can neither be created nor destroyed' and 'energy is created and destroyed in equal amounts in any closed process'. No? This is a sort of principle of equivalence, and enables us to say that the energy of the Universe is zero?
ie energy / frequency / time are complex quantities, ie produced by bifurcation, destroyed by reunion. So when an atom radiates, the energy lost by the electron is carried away by the photon, as an encoded structural change in the atom, ie a permutation - one thing swapped for another.
Energy is concentrated by consistency, dispersed by inconsistency.
Energy, we might say, is a boson? and momentum a fermion.
Do I want an apple or not? Would an apple meet my desire? Seems not. A glass of wine then!
Leaming page 194: 'Before long [Vivien Leigh] discovered she loved Kazan's direction. It was a crushing defeat for Olivier, and one he would
[page 241]
never forget'. Why are we so interested in controlling one another's lives? A boson thing?
Feynman page 38-9 'We do not know we are stupid until we 'stick our necks out', so the whole idea is to put your neck out.
39-3 Force, communication, momentum, information.
40-3: Boltzmann's law
the probability of finding molecules in a given spatial arrangement varies exponentially with the negative of the potential energy of that arrangement divided by kT.
Is this the dominant force arranging molecules? Or are their 'higher' forces that create an object like myself? I have been created by the manipulation of potential energy in order to make my current state a very probable one. From the point of view of my molecules, they are just doing their thing according to the local potential.
EpisXXMetaphysics Essence and existence/ potency and act. But we are giving these words different meanings from those assigned by Aristotle,. Thomas and the RCC.
Perhaps we should start physics with statistical mechanics, since that gives it a direct link to our contention that the proper view of the world is through an information theoretical approach.
What does life add to Physics? Probably almost nothing, or something in the ratio of aleph(n)/aleph(n+1). All the laws of physics hold for life, but we also add reproduction. While the number of atoms in the world is somewhat conserved, the number of each particular molecule is less so, and the number of particular species even less
[page 242]
so. The rarity predicted by Boltzmann is offset by the power of reproduction. We have this idea from Dawkins. Dawkins.
Feynman page 40-4: 'That, then, is the distribution of particles in space. This is the end of classical statistical mechanics, practically speaking, because if we know the forces, we can in principle find the distribution in space and the distribution in velocities is something we can make out once and for all, and is not something that is different in different cases. The great problems are in getting particular information out of our formal solution, and that is the main subject of classical statistical mechanics.
41-2: 'As a mater of fact, if we know where the damping of the oscillator comes from, it turns out that that is always the source of the fluctuations also, a point which we will come back to.
43-3: 'In order to borrow an excess energy W over the average, the odds are e to the minus the energy that we have to borrow over kT'.
Thermal equilibrium is an equilibrium of communication. Each atom is receiving as much information as it emits.
42-9: The Principle of detail balancing.
Agatha Christie Appointment with Death page 21: 'Dr Gerard said gravely: 'I believe at least one of the chief tenets of the Christian faith - contentment with a lowly place. I am a doctor, and I know that ambition - the desire to succeed, to have power - leads to most ills of the human soul'.' Christie.
Christie page 44: Can one person ever be helpful to another?
Feynman page 44-10: Entropy is conserved in a reversible (quantum mechanical) system.
Monday 14 April 2003
Tuesday 15 April 2003
The 'peace theorem' is an outcome of the statistical mechanics of the transfinite network. The most interesting duality in the network is the dynamic interaction between its layers which is called the transfinite or Hilbert oscillator in these notes. We can describe this through a few questions.
Why particles? (ie discrete entities) - required by theory for error free communication.
Why waves? (ie interfering/superposing entities, not discrete.)
The dual is the whole and part. While writing one tries to avoid too much revision. This is like not putting a foot down until one is sure of the ground. If the footprint will not bear the load, revision is required, and we cannot continue our journey unless we can find another safe place to stand in the environment within a 'pace' of our present position. One needs a similar discipline in the writing business where each sentence (or other symbolic unit) is a footprint which must be sound (make sense, have meaning) in terms of the environment in which it is found. Let us take meaning as the most general term for the relationship of part and whole. Because the whole is divine (never repeats itself) different instances of the same utterance (footprint) are similar but not the same, as Lonergan would have us believe.
Wednesday 16 April 2003
Back to Agatha Sparkling Cyanide and the search for a fit. Christie. A fit may have any number of dimensions depending on the complexity of the situation. The most complex fit in human affairs is love, but we can go down to simple fits like PV = RT and more generally the fit expressed by 'constructive interference'
[page 244]
Whodunnit? Who fits all the subtly placed clues? A's denouements often seem a little glib and one wonders whether there really are enough clues to support the outcome (and is too lazy to check - suspending disbelief), but the principle is good.
In an evolving Universe environment is constrained by individuals and individuals by environment, giving us a non-linear system as in GR where energy configures spacetime and spacetime configures energy.
We are going to apply statistical mechanics (often disguised as information theory) to the transfinite network to derive some results pulling in and interpreting such symmetries as the invariance of energy with time, momentum with space and action (angular momentum) with cardinal number. [Still don't know what this means, but the hunch is that no matter how complex a structure, one act of the structure is measured by the quantum of action - this is the power of spirit over matter - this idea has been with me for a long time, but has seemed to be an outlier, too far out.]
In this statistical mechanical scheme of things, the transfinite transition can be modelled as a phase change induced by the elements of the smaller set changing from being fixed to being able to permute themselves in any order [from solid to liquid - what happens when we go to gas? permutation by order and change of distance apart]
Feynman 46-8: Ordering [in the present] is not due to fluctuation, but due to much higher ordering at the beginning of time [when the entropy of the Universe was zero?]
47-3: 'This problem of explaining new phenomena in terms of old ones, when we know the laws of the old ones is perhaps the greatest art of mathematical physics.
The statistical mechanics of a superposition of Hilbert oscillators.
48-8: 'A quantum mechanical system, for example an atom, need not have a definite energy, just as a simple
[page 245]
mechanical system does not have a definite frequency; but no matter how the system behaves, its behaviour can always be represented as a superposition of states of definite energy.'
This comes from confined waves, The harmonic oscillator is confined by spatial relationships of force. The Hilbert Oscillator by logic.
Thomas de Quincey 'Confessions of an Opium Eater'. de Quincey.
'. . . the expansion of benign feelings incident to opium is no febrile access, but a healthy restoration to that state which the mind would naturally receive upon the removal of any deep seated irritation of pain that had disturbed and quarrelled with the impulse of the heart originally just and good.
anaesthesia = closure = unperturbed Universe.
'. . . the opium eater . . . feels that the diviner part of his nature is paramount; that is, the moral affections are in a state of cloudless serenity; and over all is the great light of majestic intellect.'
Why do we push each other around so much? This is a question of theological dynamics. What is the origin of the forces between humans. The spiritual forces respond to the physical forces, arise form the physical forces.
All information is encoded physically, including my feelings and consciousness, which by this hypotheses correspond to some physical states of myself.,
de Quincey: a language of representative feelings.
Thursday 17 April 2003
Our descriptions of infinity are in effect meta-descriptions, ie descriptions of processes (Turing machines) that carry us to infinity by putting the infinities in finite boxes (variables, symbols, sets). So we define 'limiting processes' which approach more and more closely, by an infinite series of steps, to a result of infinite precision. In other words, infinite recursion,
von Neumann: Measurement, fit, fitness, fittingness. von Neumann.
Each function in ℵ0 is a point in ℵ1, and generally each function in aleph(n) is a point in aleph(n+1) and vice-versa.
von Neumann page 207: 'Although we believe that after having specified phi, we know the state completely, nevertheless only statistical statements can be made on the values of the physical quantities [measured outcomes] involved.'
On the other hand the statistical character is limited to statements on the values of physical quantities, while the preceding and subsequent states can be calculated exactly. . . . The time dependent Schrödinger equations makes this possible, . . . since it determines the entire path of phi [provided no measurement takes place and the system is left free to evolve under its own steam, a practically impossible condition].
Is the wave function computable? Or, is the derivative computable - does the limiting process halt? Only conditionally, ie when things reach a certain level of infinitesmiality, or a stationary state (same thing, ie non-linear terms disappear very fast)
The exponential gain in power by using logarithms enables us to use countable systems to compute (some points in) uncountable systems.
[page 247]
Maybe we can say that those differentials are computable which can be expressed in explicit form eg
Since there is an explicit solution to Schrödinger . . . it must also be computable. How does nature write the equation? find the solution? By evolving logical confinement. States of probability zero may have no children!
And the number of children (and so the rate of growth) is in some way connected with the probability of the parent state? No! A very improbable parent state may have many children, so acting to make itself more probable.
Now a state is a function, operation, process. So a state of motion is a process of motion and even states of rest are states of motion whose activity is invisible to the observer (not measured).
von Neumann page 208: phi is uniquely determined, since the differential equation is of the first degree [and arbitrary constant, t0.
page 209: 'The explanation by means of hidden parameters has (in classical physics) reduced many apparently statistical relations to causal [deterministic] foundations of mechanics. An example of this is the kinetic theory of gases.'
page 210: 'This concept of quantum mechanics which accepts its statistical expression as the actual form of the laws of nature, and which abandons the principle of [deterministic] causality, is the so called statistical interpretation. It is due to M Born, and is the only consistently enforceable
[page 248]
interpretation of quantum mechanics today - ie the sum of our experiments relevant to the elementary processes.'
We can explain this by the definition of law. A law applies to > 1 case. It does not therefore account for the full details of the case, but extracts, from the full specification, elements relevant to the constraint it represents, being blind to everything else. The law is by definition blind, ie there are {parameters, variables, degrees of freedom} invisible to (hidden from) every law. Since law applies to > 1 cases, there must be at least one parameter hidden to energy law. A spanning set of laws, however, may define a fixed point as two lines do, but in QM the uncertainty (consistency) principle limits the precision of measurement, ie realization.
POTENTIAL - FORM - ESSENCE - TEXT, like this a static thing that just sits until it finds a reception somewhere, a reader. [it does not even know that it is being read] Then, by being consistent with the reader it becomes 'charged', dramatic, energetic being and causes excitement, recognition and action. So some texts leave us dead, some excite to dramatic action, and everything in between.
Here we see a glimpse of psychoanalysis, people finding their behaviour distorted by unconscious 'charged' texts (potentials) that need to be located and changed in order to bring harmony (consistency) to life. Pop psychology (eg dianetics) also adheres to this idea. For Hubbard, the (undesirable) charged texts are 'engrams' The art of being a best selling author is to write texts that become charged in the popular mind. As in physics, charge is a measure of the rate of communication.
Friday 18 April 2003
von Neumann
That's what sets me off writing in this book, when I dream up a text that has some charge for me
[page 249]
von Neumann page 206: P [ = the probability that in the state phi the quantities with the operators R1, . . . , Rl take on values from the respective intervals I1, . . . , Il is
where E1 (lambda), . . . , El(lambda) are the resolutions of the identity belonging to the R1, . . . , Rl respectively.R1, . . . , Rl ] is the most general probability assertion possible.
page 206: '2. The problem of P cannot be answered for arbitrary quantities r1, . . . , rl, but only for those whose operators R1, . . . , Rl commute with one another.
page 211: 'In the case of non-commuting R1, . . . , Rl.
So is P complete or incomplete?
page 212: In order to be clear on this point we must investigate more precisely what the measurement of a quantity r about which P makes a probability statement, means for the quantum mechanical method of description.'
Compton scattering.
Charge conservation: relative, not absolute phase (consistency) is what counts. Rate of interaction is proportional to consistency.
page 217: 'We have answered the question as to what happens in the measurement of a quantity r under the above assumption for its operator R. To be sure, the 'law' remains unexplained for the represent. This discontinuous transition from psi into one of the states phi1, phi2 . . . (which are independent of psi, because psi enters only into the respective probabilities Pn = |psi, phin|2, n = 1, 2, . . . of this jump) is certainly not of the type described by the time dependent Schrödinger equation. This latter always results
[page 250] in a continuous change of psi, in which the final result is uniquely determined and is dependent on psi (cf the discussion in III.2)'
consider the eigenvalue equation H phi = lambda phi, which holds when the effect of the operator H on the function phi is simply the multiplication of phi by the real [rational?] number lambda.
Here we have a considerable compression of the ordered set H down to the cardinal lambda. We might consider this process as analogous to insight, a mental process in which a complete set of data (H) is reduced to simple sentence (lambda). As in Lonergan we see by 'abstracting' from a lot of real wheels and other circular objects that a circle 'is the locus of a point that moves as a fixed distance r from a fixed point P.'
We would like to be able to say this that the cardinal of H is aleph(n+1) and the cardinal of lambda is aleph(n), n => 0. Insight, corresponding to the collapse of the wave function, is thus seen as a complexity reducing operation which extracts a law out of a much large volume of data, - eg Tycho Brahe --> Kepler --> Newton.
In this picture an insight corresponds to a measurement, that is the establishment of consistency among a set of states (as eg Kepler's laws are consistent with Brahe's data). As with insight, so we cannot make a measurement but instead establish certain conditions (preparation) and see what measurements come out. In general measurements are counts of events (eg how many electrons appear at P when we fire electrons at a barrier with two slits in it), and these events occur at random times which are nevertheless consistent with the relevant wave function. So too insight is a random event that occurs when a network of events in the brain reaches some point of consistency which becomes conscious and causes us to say eureka. This is a result of the tension of inquiry. So we see an electron in an energy state ni finding a way to absorb or emit a photon and so move itself into an energy state nj , the photon in a sense being the same as the utterance eureka.
[page 251]
von Neumann page 220: '. . . a quantity r can always (ie for each state psi) be measured exactly if and only if it possesses a pure discrete spectrum,'
A differential equation is [ie represents] a confining potential which causes the existence of a discrete spectrum of functions that are consistent with the differential equation.
When the spectrum is continuous we cannot measure it exactly, and so we are left, from a measurement point of view, with a discrete spectrum of intervals.
page 222: '. . . these quantities which (according to our intuitive picture of them) are quantized . . . it suffices to observe them with just sufficient precision that no doubt can exist as to which of these 'quantized' values is occurring. That value is then as good as 'observed' with absolute precision.
This is how Shannon's theorems operate in information theory where by forming complex symbols in a high dimensional space we increase the 'distance' between transmitted symbols to the point where the probability of confusing them drops to zero, allowing us to achieve error free communication over a noisy channel as long as there is enough spare entropy.
The power of error correction (avoidance) comes from the construction of an ordered set (symbol) from a set of smaller symbols. So by union we avoid error and increase fitness and survivability.
INSIGHT = DIAGONALIZATION
Pressure of time leads to improperly;y completed operations with increased error rates. For certainty, take your time. The basis of work and sport is to place some sort of time limits on operations. In sport this tends to force error, leading to a winner. In work
[page 252]
it appears as the aphorism 'you get what you pay for.
COOLING the system leads to slower and more certain activity.
The four forces vary in their intimacy, ie in the intrusiveness of their interactions - energy scale.[Gravitation] the most benign (in general) and powerful (black hole) of all forces.
Ditch theology (for the time being)
TRANSFINITE DYNAMICS
Time at last to cut loose from the Catholics and build from the ground up, crediting them nevertheless for the force which propelled me into a new orbit, STATE.
The change of STATE: revolution. Aristotle (?) the highest good is to serve the state (half true) to serve oneself (half true) [equipartition theorem]
The tutelage symmetry: bringing up nations is [quasi] isomorphic to bringing up children - emitting a particle in an interaction between two other particles . . . .
The Lagrangian of the standard model is quite a read. It describes the world as we find it, but it is quite prolix. Perhaps an historical (evolutionary) approach may make things clearer and more concise.
Saturday 19 April 2003
. . . the spiritual world, which we take to be as real as the observable worlds, just not so accessible to theoretical study.
New ideas lead to new structures. Note the permutational method used by sexual reproduction, which, in the absence of mutation and copying errors permutes the genome at all scales, ie permutes the power set of N.
[page 253]
ie we partition N into all the elements of its power set and permute these with the rule that sets must be exchanged only with sets of the same cardinal number. This process produces different ordinals.
To be a model of everything, we have to correlate it with quantum field theory, evolution, and relationship.
The naturals are enough to name every event within an horizon.
Each permutation of the naturals is a Turing machine.
How would this structure look to an element of itself, ie me?
Since n! > 2n [n > 3], there are many permutations that cannot be reached by 'mass production' methods and require individual treatment.
