Notes
[Notebook: Transfinite field theory DB 56]
[Sunday 6 June 2004 - Saturday 12 June 2004]
Sunday 6 June 2004
Monday 7 June 2004
[page 103]
Tuesday 8 June 2004
Intelligence is closely related [to] frequency and can be parametrized by frequency. Some entities can solve problems (ie decode their input) faster than others. One imagines that if Einstein or von Neumann had taken on the natural religion project they would have figured it all out in a matter of months, something that will take me the best part of fifty years, an intelligence ratio in the realm of 500:1. Lonergan has noticed this to a degree, but the apparently instantaneous functioning of our senses (although we are aware of the world only after a 0.xx second delay) blinded him to the fact that the senses too have intelligence and judgment in the moment to moment guidance of animal motion.
Wednesday 9 June 2004
Thursday 10 June 2004
Physically low energy processes may be more or less significant (and we base our model on 'significant digits') depending on their place in the transfinite tree. The duality of space and time gives us two dimensions of significance, one based on timing and the other based on text (space)
The power of survival comes from productivity which we might measure 'fitness obtained per unit of input' or the relationship between fitness and input. This is a very complex relationship which involves the whole of a species' 'survival technology'. including ours. Measuring productivity is not easy and in fact perfectly subjective "what's in it for me?" is the fundamental question of any organism undertaking a (costly) task (we assume that all tasks have a cost in fitness which is hopefully recouped with profit.
Friday 11 June 2004
Lonergan's schemes of recurrence are a natural feature of the transfinite network, since small sets can only fill big sets by repetition. So the ℵ1 copies of the ℵ0 natural numbers requires ℵ1 copies of each natural number. We think outside space and time to begin with, but introduce tome as the dynamic of succession.
Saturday 12 June 2004
I suppose my position is meliorist (christian?) in that I see that the best can be the enemy of the good and that in a dynamic system the ideal is always lagging the reality, or is it reality lagging the ideal? We are looking for boundaries on behaviour ('thou shalt not kill') meaning kill people, meaning kill our allies, since killing enemies may be seen as necessary, like the occupation of the 'promised land'.
Lonergan's schemes of recurrence: Quantum mechanics and astronomy have given us deep insight into periodic motion, the only sort that is predictable (?) But the real interest lies in aperiodic events. They are the news. As Chaitin has observed, apparently random sequences (texts) are the most meaningful (compressed). Chaitin The only way to make sense of them is not to Fourier analyze them, but to have the 'software environment' necessary to decode them. We move from an harmonic (wave equation) description of the Universe to an information processing (functional, Hilbert space) description of the Universe. Fourier, being an integral transform, blurs all this information, since it must all pass through the dot product normalization process which abstracts from the data as an ordered set and provides us with an histogram (spectrum) of the data. Sop we might do a statistical analysis of the letter or word frequencies in the bible and obtain an abstract histogram which carries insufficient information to reconstruct the Bible. Is this true of Fourier:
[page 105]
the same information is available in the time domain as the frequency domain as long as we take note of the phase which controls the interferences (adding) of the pure frequencies to give the transformed version of the information available.
Field is Fourier transform of particles and vice versa.
PHASE - COHERENCE - CORRELATION
Schemes of recurrence: correlation increases probability. So in a random scheme the probability of P and Q and R is pqr, a small number since p, q and r =< 1 Now let us suppose that P caused Q caused R, then the probability of P and Q and R is simply p. If R causes P, then the cycle may start with P or Q or R, whose probability is p + q + r.
The Cantor Universe provides a natural framework for thinking about abstract and concrete. The abstract is the more physical, coming right down to mathematics, where we abstract from particular meanings (models) and deal only with the symbols, manipulating them as physical objects with certain rules and seeing what happens. We can vary both the number of the objects and the number of rules to see what happens. What a theologian is looking for is a structure that us independent of the number of objects and the number and nature of the rules, here called complexity invariance.
Path integral method: there are many paths from A to B, but only a set of measure zero paths is the best. Lagrange; Maupertuis; Feynman.
One of the most interesting mappings in physics is between events in 4-space and events in Hilbert space. This is akin to the mapping between physical and logical in a computer. We work in the logical realm producing in our minds and on our papers logical models of the physical world.
[page 106]
Lonergan seeks to constrain the physical world by working in logical space, the space of insight.
