Notes
[Notebook: Transfinite Field Theory DB 56]
[Sunday 23 November 2003 - Saturday 22 November 2003]
Sunday 23 November 2003
Monday 24 November 2003
Tuesday 25 November 2003
[page 22]
Wednesday 26 November 2003
Aristotle's work provided a foundation for physics as well as metaphysics. The principal features of classical physics are an amalgam of the ideas of Aristotle and Euclid. Newton accepted the notions of continuous space occupied by material particles but introduced new ideas about what actually animated these particles - the four laws of motion.
Negative numbers are necessary to design an analytic periodic function (ie bounded range) on an infinite domain, since we need positive and negative infinities to cancel out to give a finite result,
We have been talking about the number line which can be seen as the naturals, integers, rationals, reals, complex, matrix . . . series. But the introduction of complex numbers takes us out of the line into the plane, the Argand diagram. This gives is a geometric intuition of something that seems arithmetically impossible. Since physics, particularly quantum
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mechanics would be literally inconceivable without complex numbers, we must conclude that as these numbers are isomorphic to the Argand diagram, they are isomorphic to some deep feature of the world.
Here all the words, god, world, Universe, all that is, the whole etc all point to the same meaning, which is the superposition of all of them. Wittgenstein talks of showing and telling. Wittgenstein The whole cannot be shown (Cantor's paradox and other inconsistencies get in the way) it can only be told. This has led to a lot of crazy stories about god and our relationship to him/her/it (another superposition).
It is very easy to say that everything is fucked and lets smash the lot of it and start again with something decent, but that is not possible, so we spend our latter years either being a suicide bomber at one extreme, or carefully filtering through history as a guide to finding the best way forward in a Universe which we see as a continually evolving massively parallel mathematical proof, working itself out in time. The formal constraint is that each step forward must be consistent with its environment, ie its past light cone.
So for a long time have rejected Lonergan's distinction between proportionate and transcendent being. Lonergan pp 657 sqq Now we can say that the proportionate and transcendent being are not really distinct, but (here is a good form of words) proportionate being is the part of the transcendent being that we can see. When we turn on the light we can see more of the divinity but what we see changes as we look about, and so the boundary between proportionate and transcendent being is fluid, different for everybody (every entity) at every moment. Nor should we demand that proportionate being be consciously known. So more generally, proportionate being (for any entity) is the
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part of transcendent being that it is communicating with at any moment. This gives us also a picture of revelation.
This leads to another way to look at the empirical residue. Lonergan pp 50 sqq It is not so much the unintelligible dross of a material world as all that part of the world that is not in communication with the entity whose empirical residue we speak of, ie the rest of god. This easily fulfill the definition of prime matter nec quale nec quantum nec aliquid eorum quibus ens determinatur. Russell's paradox equates God and nothingness, as a mystic might be pleased to see.
The whole understands itself. Each act of communication, (we theorize) is isomorphic to an act of insight, and also isomorphic to the 'collapse of the wave function' but this isomorphism (in print at least) is inherently dual because motion can only be described by two fixed points known as before and after. 'Tempus est numerus motus secundum prius et posterius' [time is 'number of movement in respect of the before and after'] . Aristotle, 220a24
Natural line is a number dictionary. We give the natural numbers different meanings (real, matrix etc) in different contexts. They are the universal index set, because they have distinct names and a natural order. Communication can have no meaning without distinct symbols )marks - a space is a mark, the mark which is no mark, ie the closure of the set of marks). The inherent binaryness of communication is captured by our understanding of the empty set, which, (since sets are defined by their elements) is a unique but undefined entity. It is unique because it is undefined, since it has no features which might distinguish empty set one from empty set two. It can as well model the divinity as the initial singularity, both unique.
Predictive deconvolution uses a window of the past to predict the future, which prediction may be subtracted to
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reveal events not predicted by the past. So seismic processing gives us a model for history if we expand the linear time series of a microphone channel into the multidimensional time series which is reality. As a first step, we see the world not as a time line, but as a time tube, a stack of Argand planes stretching from the present plane into the past and future. From this we expand our vision to a tree of Hilbert Spaces whose most jejune representation is the transfinite number line stretching from the initial singularity to god. Although this line is extended in time, 'spatially' each subsequent point on it contains all its predecessors and is causally related to them in the same way that we cannot write out a set of cardinality aleph(n) until we have written our aleph(n-1)
Squinting at this tree to get the general picture, we see each subsequent moment as a superposition of all the moments that went before. The weighing of different structures in this superposition enables us to calculate the amplitudes for different events and so predict what will happen next (up to a probability = |amplitude| squared,.
All possibilities are envisaged and the consistent ones realized. CONSISTENT = FUTURE LIGHT CONE
We set out, in the quantum non-cloning and empirical residue essay to show that Lonergan's empirical residue does not exist. In the absolute sense proposed by Lonergan, this proof is still good. How now do we make the map between quantum mechanics and the new definition of empirical residue that it is the part of god that is not being revealed to us at any moment, ie this moment while the ideas are being revealed to me by the current operation of my mind on all the little treasures I have collected since birth.
Quantum mechanics - revelation - collapse of wavefunction - communication. There is no communication without meaning, ie a
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a complete communication requires that a message be both sent and received, and we see as 'consistency' the conditions needed in the sending and receiving entities for complete communication to happen. The establishment of such consistency is the solution of a problem, ie an act in insight which we model quantum mechanically by the evolution of a set of eigenvectors and the communication of an eigenvalue corresponding to one of the eigenvectors of the eigenfunction (code?) shared by sender and receiver ie past and future, or here and there (t1, t2. p1. p2)
All this palaver may help with the problem of mapping quantum mechanics into/onto 4-space and the resulting generation of particles / states / structure etc.
Feynman QED [Quantum Electrodynamics] page 49: '. . . in order to calculate properly the probability of an event in different circumstances, we have to add all the arrows for every way that the event could happen - not just the ways we think are the important ones!' Feynman
How to make money: 1)work for $x per hour. Slow but sure. 2) gamble. One a losing game this is bound to make a loss in the long run.On a constant game, one will break even and on a winning game (like a rising stock market) one will, if playing at random, win. The outcomes of random play can be improved by knowledge eg where is the real oil; what is the fast horse, etc. In purely probabilistic games, no knowledge is available. Here we have the quantum thing - getting the knowledge may change the game.
Adding amplitudes in a complex space is a way of measuring consistency.
The theory that God rewards the good is often used by the well to do to prove their virtuousness, but this is not necessarily a valid inference. The alternative is a theory of fluctuations, noise and overcoming noise.
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Thursday 27 November 2003
Some people (all people!) surround themselves with other people, they are 'dressed' in the physical sense (Nature ?), acquiring mass as they do do.
Agatha: 'There is nothing so inhuman as the mask of the good servant' Vicarage, p 97. Christie
CLASS is defined by NON-COMMUNICATION. We do not 'talk to one another outside our class'. 'Talk' has many meanings which might be ordered by the 'intimacy' (complexity) of the talk, from conversation with a machine, a servant, through to a lover or a child.
Quantum mechanics and probability: ''Ah!' said Miss Marple. 'Bit I always find it prudent to suspect everybody just a little. What I say is that you never really know, do you.
There is a conserved flow at each peer level and we might in fact use the symmetry of conservation [conversation?] as a defining feature of a peer level, a level or depth of meaning. So, we say, there may be a way to describe a conserved flow of meaning, that is a meaningful conversation about something. Such a conversation we may understand do be an analysis of some situation, be it the workings of an atom, a game, or the network of intrigue woven in the Vicarage.
The drug laws (eg) are well established and have a momentum which is very difficult for a single individual to overcome unless that person can acquire similar momentum, that is 'dress' itself. Here we find a clue to the might of the pen, since a single decision by the high court might set all the drug laws at zero. - by declaring drugs (psychotropic) as matters in the internal (spiritual) forum and so not a fit subject for parliamentary (or any other) law.
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We can understand political violence in terms of the 'political pressure' in a state, which determines the energy of collision of the particles in that state.
We may describe a human as a 'state' using a natural transfinite extension of the quantum mechanical formalism. This transfinite quantum mechanics is what we equate to metaphysics.
Feynman claims that the little arrows representing amplitude remove the need for the 'collapse of the wave function.'
Feynman QED page 76: '. . . these arrows are probability amplitudes [analogous to the amplitude and phase of a wave] that give, when squared, the probability of a complete event. *
* 'keeping this principle in mind should help the student avoid being confused by things such as the 'reduction of the wave packet' and similar magic.'
But the fact remains that we only observe by measuring, and every measurement selects one out of a formal array of possibilities with a probability which depends on the squared length of a certain arrow, which we may think of as constructed by summing or multiplying other arrows.
The 'normalization' of transfinite quantum mechanics gives us an inverse series to the transfinite numbers, 1/ℵ0, 1/aleph(n) etc.
The Hilbert oscillator operates by binding and separating states - entanglement and disentanglement. Everything is a little bit (1/aleph(n)) entangled with everything else, but we can identify systems that are not entangled and so evolve (as the whole Universe evolves) unitarily.
