VII Notes
2010
Notes
[Sunday 3 October 2010 - Saturday 9 October 2010]
[Notebook: DB 70 Mathematical Theology]
[page 96]
Sunday 3 October 2010
Smith page 491: 'Graves differs from most men [?] in his feeling that any sort of resistance to romantic love is itself a kind of sine: a refusal of the Goddess, of what the Goddess means to him. Seymour-Smith
page 564: 'He had by now connected the practice of love directly with the observation of decency in human affairs.'
[page 97]
Cosmological Physics. Theological Physics. For a book, the title is the root of the tree which expands to the leaves, the part we see and from which we learn the passage from leaves to root.
The trunk of thje tree is the metric that couples the dual branches and roots, rootlets and root hairs. The tree is the metaphor.
Monday 4 October 2010
Empty head. No problems. Nothing to motivate me to think. The divine Universe seems all wrapped up in my mind and I seem to have nothing more to learn from all the books in the house or even all the books in the world. Such nirvanic content seems good, but like heaven, boring. Perhaps this view is partly connected to the fact that it has rained for three days straight and does not look like stopping, but at the back of my mind is the need to do something about my pleasure, to export it to other by promoting it, making natural religion a natural religion. This desire is partly taken care of by my decision to enter academia next year, but I also feel the need to do something now, to go on writing it out and seeking publication so as to spread the good word. Personal peace cannot be achieved without some degree of global peace. My immediate problem, however, is to take care of my very aged parents which creates a dilemma, since I will have to leave my children somewhat in the lurch to do so.
Why act? We are always acting as we live. Since action is conserved, the question is really why this act and not that? The conventional answer is that we act from potential or desire, and that our desires are a product of evolution, education and
[page 98]
the current situation.
So what next? Read Zee again. Zee
Special relativity covers the bifurcation of action into energy and momentum, ie spatial and temporal frequency.
Zee page xv '. . . in a path integral the bosonic fields are just number-valued fields . . . '. Cardinal fields, ie how many are there.
page 3: quantum field theory = {quantum mechanics, special relativity}. The big question is what is the internal structure of the set qft, an ordered set that can be represented in books. What do these books mean. Here we must consider their context, beginning with the 'physics industry' and extending to the whole human society and ultimately the Universe. From an information point of view each point in the Universe represents as much information as the entropy of the Universe.
A little book about peace: a beginners guide to information and entropy. Particles and counting.
As with the influences on human mental states, so, at a different scale [environment influences quantum systems].
I though i was stuck but now I am going again. I have found a step forward in my 'phase space', and am automatically motivated to start writing again, to get it down, a physical / mathematical picture of the transfinite space through which I move. I am a particle.
[page 99]
We have been blindfolded for centuries by the notion that God is invisible and mysterious.
'It is in the peculiar confluence of special relativity and quantum mechnics that a new set pf phenomena arises: particles can be born and particiles can die. It is this matter of birth, life and death that requires the development pf a new subject in physics, that of quantum field theory.'
Why is this connected to relativity? In quantum mechanics every observation is the detection of a particle created by the 'collapse' of some wave function. This collapse involved the transfer of energy from quantum state to particle and vice versa, as when an atom emits or absorbs a photon.
Relativity arises when particles and anti-particles are involved? [space and time, memory and change of memory]
'In quantum mechanics the uncertainty principle tells us that the energy can fluctuate wildly over a small interval of time. According to special relativity energy can be converted into [can be seen as] mass and vice versa. With quantum mechanics and special relativity the wildly fluctuating energy can metamorphose into mass that is into particles not previously present.'
These are 'virtual' energy fluctuations and 'virtual' particles. To get a real particle we need real energy.
Does special relativity really tell is that energy can be converted into matter, or is this just a fact of lice, all matter has energy and all energy is materially embodies, except in the fantasy of the field theorists who propose 'field' as an unobservable carrier of energy.
[page 100]
Has physics degenerated into a series of false cliches?
f = ax2 + bx + c means that there are values of the variable in f that are consistent with f = 0, and if we impose the condition f = 0, we variables will become fixed to rthe solutions of this equation, x = (-b +- sqrt(b2 - 4ac)) / 2a.
There may be no better cover for doing evil than a good reputation.
Quantummechanical amplitude ius the ampklitude of an unobservable conplex periodic function.
All we mean in mathematics when we say a number is infinitely large is that the relevant algorithms are logically correct no matter how large the numbers involved.
Continuum limit: although the computational mechanism of mathematics is considered to be continuous, the practical unit of operation is Planck's quantum of action, and computations more precise than this are to a large degree useless because the relevant complex exponentials almost all cancel except those near the 'classical path' for the particle.
The path integral operates only secondarily in space-time. its quantum mechanical function is to examine the possible paths between states [which have no particular spatial representation].
The overall misconception of quantum mechanics is the projection of discrete logical states onto an abstract continuous space-time. There is no such thing, There is merely a network of
[page 101]
communication served by invariant particles (messages) which gives the appearance of the world to its inhabitants. We can introduce this network by comparing its features to quantum mechanics.
1. quantized
2. computed - the eigenvalue equation amplitude and reality
3. control and the Lagrangian.
We are in God, the giant intelligence mirrored in our own brains. How doe we infer consciousness: by the presence of control.
The path integral method proceeds by dividing the path from state a to state b into tiny segments of action and then adding them all up. Each path is a permutation of the continuous line and the resulting space of paths can be Fourier analyzed into a superposition of an infinite set of periodic functions whose sum squared is the probability of stating in state 1 and ending in state 2. The practical use of all this is that with the sum of outcome probabilities normalized to 1, the action associated with any transformation is 1 = h.
The messages and processors of a network correspond to the invariants and dynamic of the physical world, which are coupled, in a closed layer, by fixed point theorems. The discrete fixed point theorem. Fixed point theorem - Wikipedia
So to Feynman. Feynman The continuous formalism of quantum field theory is our best approach to the discrete reality but continuous mathematics does not have the variety to properly map the discrete world. Cantor exposed the duality of the continuum. its cardinal is the cardinal of the set of countable
[page 102]
ordinals, countable being the cardinal of the alphabet set from which the word set is generated. Different permutation of the alphabet give different words. Every incarnation of a letter is an addressed discrete relationship.
Why does the logical world look like the physical world and vice versa? Our physical world is an interpretation if sense data [which are all ultimately quantum events like the absorption of a photon or phonon].
We image the path integral in terms of screens and holes and the rules indistinguishable states add, consequent states multiply, so mapping it onto space-time. in quantum space, however, whose only dimension is frequency (energy) what? The Lagrangian which is the action is structured in discrete steps, measure of physical implementation ħ.
Let us suppose that the observable correlate of a logical operation has the measure ħ which we project into space-time, momentum-energy.
Which may be interpreted as a periodic function describing the process of a computation proceeding step by step [scaled by the action, which measures the rate of processing per interval ε].
'Further analysis led to the use of the exponent of the
[page 103]
time integral of the Lagrangian (in this volume referred to as the action) as the transformation function for finite time intervals However, in the application of this function it is necessary to carry out integrals over all space variables at every instant of time.'
ie to integrate over the whole configuration space of a passage from one state to another.
Feynman page 2: '. . . in nature the laws of combining probabilities are not those of the classical probability theory of Laplace.' What we are looking for is the logical explanation how of the quantum mechanical probabilities come to act as they do. The most interesting feature is that the calculations are carried out in the complex domain and only reach reality via the |ψ|2 prescription. The vectorial nature of the complex numbers allows for negative feedback (inhibition as well as positive feedback (promotion) as we find in all societies, promote this kind of behaviour, inhibit that.
What we think is that quantum mechanics is a description of discrete logic.
Probability amplitude is a complex number, ie a vector with two degrees of freedom constrained by normalization.
Feyman page 5: φ = probability amplitude, P = probability
P = |φ|2, φ = φ1 + φ2, P1 = |φ1|2, P2 = |φ2|2.
page 8: 'When we watch the electrons to see through which hole they pass we obntain the result P = P1 + P2. When we do not watch we get the different result P |φ1 + φ2|2 ≠ P1 + P2.
[page 104]
Complete processes are real, incomplete processes are complex.
Feynman page 9: 'We shall state the uncertainty principle as follows: Any determination of the alternative taken by a process capable of following more than one alternative destroys the interference between the alternatives.' Interference = [vectorially] adding amplitudes φ1 + φ2.
Waves are a consequence of the logical confinement represented by a periodic function that does not go anywhere. In quantum mechanics, confinement causes eigenfunctions.
page 14: 'The concept of interfering alternatives is fundamental to all quantum mechanics . . . when alternatives cannot possibly be distinguished by experiment, they always interfere.
The answers in physics are cardinals, but we argue to them through complex ordinals, constructing wavefunctions for different systems by trial and error (guided by some principle) until we come up with the right probabilities, ie the right ratios of various numbers to one another, ie frequencies. How often does that follow this, etc.
Feynman page 28 2-2 "the Quantum-Mechanical Amplitude
'. . . the quantum mechanical rule. We must say how much each trajectory contributed to the total amplitude to go from a to b. It is not just that the particular path of extreme action contributed, it is that all parts contribute. They contribute equal amounts to the total amplitude, but contribute at different phases. The phase of the contribution from a given path is the actionS for that path in units of action ħ.
[page 105]
Feynman page 29: '. . . in the classical limit some particular path becomes most important.'
'no path needs to be considered if the neighbouring path has different action; for paths in the neighbourhood cancel out the contribution. But for the special path, x, for which S is an extemum, a small change on the path produces, in the first order at least, no change in S All the contributiuons from the paths in this region are nearly in phase, at phase SCL, and do not cancel out.
How does all this fit a computational model? First note that quantum mechanics is the alphabet from which space and time are constructed. It is the heart of dynamic meaningless logic where we are dealing with physical quanta alone (like sheep) with no meaning given to these quant by incorporating them in some more complex structure. Say again, quantum mechanics is one dimensional field theory, a superposition of rational frequencies; event a happens a times, which event b happens b times so that their relative frequency is a / b.
What do we mean by conservation of probability? There is always something happening, so the probability of something happening is 1, at every moment, like a Dirac's delta.
Feynman page 31: '[In the quantum case] No particular trajectory is of overwhelming importance.
page 31: 'The number of paths is a high order of infinity, and it is not evident what measure is to be given to the space of paths.'
In the network model, the 'space of paths' becomes the transfinite computer network, each path being a message between two points.
[page 106]
Feynman page 37: 'Amplitudes for events occurring in succession in time multiply [phase is a measure of 'time' that is of process]
Tuesday 5 October 2010
Wednesday 6 October 2010
Thursday 7 October 2010
They key to quantum mechanics lies in the complex amplitudes.
Time: successive events multiply [causality]
Space: independent events interfere [communication]
Quantum mechanics occupies only a 1D complex space, there are no independent events, all we have is a sequence, ie 1 path in the path integral. The question then becomes how do we map a complex multiplication onto a logical operation. Answer see quantum computation. Nielsen & Chuang
I am not Zee's bright young physicist, but a dull old theologian who may have been able to emulate a bright young physicist by plodding steadily for forty years under the influence of a strong emotional (motivational) field.
Evolution leads us from pure undifferentiated action to differentiated (chosen) actions.
The key to quantum mechanics is the synchronization of processes, which synchronization is expressed by the eigenvalue equation which seeks 'harmonics' in the infinite dimensional Hilbert space in a manner analogous to the harmonics of a vibrating string or de Broglie's view of the Bohr orbit as an integral number of wavelengths of momentum.
Unsynchronized processes are just as likely to undo one another
[page 107]
('go back in time' [like Feynman's view of an antiparticle]) as to complement one another (at least in a basic two state system, Feynman's ammonia molecule). So we have 'constructive' and 'destructive' interference.
Energy varies as amplitude squared, for both real and complex waves. What does this mean, from a processing point of view? First we interpret 'wavelemngth' as the length of a process. Some processes (those that do not halt) have an infinite wavelength, ie we never see a whole period where the system comes back to its starting point. We model a process as a sequence of logical operation or events, each of which involves classical action, nh 1< n< ℵ0, ie n is a natural number, an element of ℵ0.
Let us consider the wavelength of a multiplication, the number of operations required to fill the register c with the product of the state (ie numbers) registers a and b, >i>c = ab When the multiplication (or Turing machine) has finished, it returns the value c and awaits the next call with the inputs a and b Let us assume that the 'execution time' for the multiplier is independent of the sizes of a and b, and that this time is measured as a count of elementary events. The physical time to execute the multiplier is then a function of the time frequency of elementary events, that is the 'energy' of the processor.
Now how are we to understand energy = amplitude squared?
How do we map probabilistic frequency to space and time frequencies, ie energy and momentum? This is the world of quantum mechanics, ie it is the mapping algorithm for taking us from the abstract theory of probability to concrete
[page 108]
physics.
Abstract: We take Wigner's thesis to its logical conclusion. The Universe is mathematics incarnate, realizing Landauer's hypothesis that all information is represented physically. Mathematics talks about the infinite, but we cannot produce an infinite object since we cannot see something which is not defined. Mathematical talk about the infinite occurs in the spiritual realm of meaning and definition: an infinite set, they say, is one that can be mapped onto a subset of itself, ie it is indeterminate.
In quantum mechanics we construct wave packets (the Dirac delta Dirac delta function - Wikipedia) by superposition of plane waves of an infinite spectrum of frequencies, a very complex manoeuvre to try to connect continuum mathematics to quantum reality. Nevertheless, calculations based on this convention work, and it would be nice to know why.
Feynman Quantum 2-1: |ψ|2 = 0 --> ψ = 0. Feynman
The world is pixellated at the scale of h The action remains invariant under relativistic transformations of momentum and energy (space and time) [suggesting that action lies in a deeper layer than energy and momentum].
Quantum mechanics is reversible. We do not get irreversibility until we have memory and then there enters the cost of erasure (Landauer) Landauer
[page 109]
Feynman page 2-2: The wave picture gives a natural picture of the uncertainty principle which fits comfortably with the fact that the outcome of a computation is uncertain until it halts.
PAST == KNOWN / FUTURE == PREDICTABLE (to some degree predicted by quantum mechanics - ie a probability distribution).
WAVELENGTH = card(actions to complete a process)
Functions become periodic when they have limited complexity in a more complex calling environment so they are invoked repeatedly [like advertisements on TV].
What does force do? Changes things, like a message.
Phase = cardinal of operations. Subsequent events multiply. Multiplication of normalized phases effectively adds them, so the correct language in computation is that each interim result is multiplied by the next logical process to give interim result + 1.
Operations may be creative (relative to some goal if they bring us closer) or annihilatory (if they take us further away, travelling the 'wrong' way).
Feynman page 2-7 'If one electron is occupying a certain space, then another does not occupy the same space. More precisely, there are two spin cases, so that two can sit on top of each other, one spinning one way and one the other way. But after that we cannot put any more there. We have to put others in another place
and that is the real reason matter has strength [ie compressive strength].'
Energy levels: the stationary points in the Universe ar processing rates, and different structures correspond to different processing rates.
Change of processing rate = change of energy = change of algorithm from eigenfunction a to eigenfunction b.
Feynman page 2-8 Linearity (additivity) of energy levels = Ritz combination principle
'. . . waves in a confined space . . . exist only at definite frequencies.'
Periodic functions are a consequence of 'cardinal confinement', 'variety confinement' or 'entropy confinement'.
Sattareh Farman Farmaian: 'This story [is] for all young Iranians who . . . live in foreign countries and ask their elders< "whar did you do wrong there, that we too must live in exile far from our own land?" For the present, at least, the failure of my generation has dispossessed them of their Persian heritage. I want them to know what I think we did wrong.' page 12 Farman-Farmaian
Most of the ancient religions are spiritual prisons devised by rulers to keep the variety of their subjects down. Farmaian page 76, particularly women.
Persian national epic Ferdowsi Book of Kings Ferdowsi - Wikipedia
[page 111]
Farmaian page 81: Ayatollah = "Sign of God", 'the highest degree of religious learning to which a Shiite cleric can aspire.'
page 83: 'Like every sheltered pious Shiite woman [my mother] believed that all mullahs were highly spiritual men of stainless purity, sternly aloof from worldly matters and immune to sin.'
page 85: W Morgan Shuster The Strangling of Persia Shuster
page 87: 'For Moslems, disagreeing with a parent, or indeed any family elder, is among the worst of all sins, and its punishment is everlasting hellfire.'
page 99: Shazdeh [Sattareh's father] liven in constant fear of informers.'
page 101: 'Every adult I talked to thought that people's destinies were written on their foreheads from birth, yet my father told us every Friday that our futures depended entirely on how hard we studied and what we made of ourselves.'
page 109: ' 'In Iran,men and women who were not related were not even supposed to look at one another's faces . . . .'
page 110: The word "azadi" [freedom] . . . conveyed nothing to me except the opposite of being under house arrest or in jail.'
page 113: 'Satti, you are running - women cannot do that.'
page 120: Anglo-Persian Oil Company BP - Wikipedia
The continuum is a prison appropriate only to the lowest levels of
[page 112]
complexity.
Farmain page 277: 'America, I thought bitterly in my room that night, was truly a wasteful nation. It had thrown away affection exactly the ay it threw away food it did not want. Thinking only of its fear of communism and of the interest of American oil companies, it had used its great power to stifle our nation's aspirations to independence and dignity. The ay we felt about the United Stated would never be the same again.'
In a layered network, the structures at low levels also appear embedded in structures at higher levels. So, for instance, we find duality everywhere from the polarization of light and the spin of electrons to the shape of our hands and the inside-outness of our clothes.
At the binary level, logic and arithmetic are the same.
Friday 8 October 2010
Saturday 9 October 2010
