Notes
2010
Notes
[Sunday 15 August 2010 - Saturday 21 August 2010]
[Notebook: DB 70 Mathematical Theology]
[page 6]
Sunday 15 August 2010
Harriet Beecher Stowe: a theological debate on slavery starting from the apparent fact that the Bible (true to its time) condones it, but weighing against that arguments drawn from human nature, specifically that slaves are also human and have souls. Stowe
Stowe page 449: Dies Irae Dies Irae - Wikipedia
page 450: '"Now is all the time I have anything to do with," said Miss Ophelia.' [ie local space-time]
page 452: 'If we emancipate, are you willing to educate?'
An evil empire I have known. Evil empire - Wikipedia
What we are searching for is a clear expression in layered network terms of the symmetry 'all people are equal'. [including Jesus of Nazareth]
Stowe page 481: 'taken, reputed, adjudged in law, to be a chattel personal. US slave legislation. Harriet Beecher Stowe
[page 7]
What am I after? First some income for myself and my family; second the feeling that I have done something for the peace and wellbeing of the Earth and all who sail in her.
Stowe page 485: 'When one nigger's dead I buy another; and I find it comes cheaper and easier, every way.'
One of the most potent forces in the Universe is the retry motivated by error detection. The other is the correction, possible if one is using an error detecting and correcting code.
DUALITY: no point without space, no space without points.
The epistemological foundation of classical physics was laid by Einstein with the notion of the general covariance of coordinate systems.
Religion, theology and navigation
. . .
Radical errors:
1. Motion, stillness
2. error, sin, control
The notion of pain entering the world through sin is silly when viewed in a cybernetic light.
The strategy is to fit in until I am in a position from which I can speak and be heard. No message can be interpreted out of its proper space. The transfinite network, like the immune system, can, in principle, decode all messages.
[page 8]
Stowe page 492: 'The slave is always a tyrant, if he can get a chance to be one.'
My specific target must be the Pope, the slave who enslaves us all.
Machine = incarnation of an algorithm
Stowe page 514: 'If we suffer with him, we shall also reign, Scripture says; but if we deny him he will also deny us.
No rule of law, only personal relationships.
page 622: 'Is man ever a creature to be trusted with wholly irresponsible power? And does not the slave system, by denying the slave all legal right of testimony, make every individual owner an irresponsible despot.
page 623: 'Nothing of tragedy can be written, can be spoken, can be conceived, that equals the frightful reality of scenes daily and hourly acting on our shores, beneath the shadow of American law, and the shadow of the cross of Christ.'
Stowe page 8 [Ann Douglas Introduction] 'Compromise of 1850' 'Fugitive Slave Law' Compromise of 1850 - Wikipedia
Monday 15 August 2010
Pentagon Papers and Cambodian bombing Coleridge page 92 Coleridge, Pentagon Papers - Wikipedia, Operation Menu - Wikipedia
A mathematical theory is a network of mappings whose primary fixed points are a set of axioms,
[page 9]
freestanding, orthogonal (independent) and isolated, like the axioms of the Universe god, lightspace, mass space (closed system space), isolated quantum system, Turing machine.
1. god as defined by Aquinas
2. Minkowski space, the space of embodied communication
3. Riemann space, space of spaces of embodied communication (particles)
4. Hilbert space - quantum mechanics interpreted as the description of a network.
5. Computable space: the transfinite computer network.
Another subjectively glorious morning in the sun, having had a smoke and worked out the above outline for chapter four of the MTh, The Model.
The axioms of building are sand, clay, rock cement, wood, metal, ceramics and so on and the various parts of the building process are both constrained by the axioms and exploit their stationary features to construct more complex elements of a building like bricks, pipes, valves, windows, and so on.
AXIOM = ALPHABET of a SPACE
One can imagine that over the hundred thousand years or so of modern human history there have been hundreds of thousands of different theologies, that is theories of everything designed to explain the human condition and provide clues about how to deal with it. Xianity is but one of these. [these religions form a tree, descended from Africa through socialization of the children.]
The rise of science is a very recent development in human history, and is closely related, as Galileo noted, with the mathematicization of science.
[page 10]
Tuesday 17 August 2010
Getting down to the keel (nitty gritty).
On Veltman: we might take the view that quantum mechanics is effectively outside (prior to) space-time and therefore 'obnoxious' [invariant with respect to] to Lorentz transformations. What needs transforming [is the event, not the processing behind it] Veltman
Wednesday 18 August 2010
Particles interact when they are in contact, ie the nterval between them is effectively zero, ie joined by null geodesic.
We are engaged in the exegesis of the natural language / mathematical texts of physics utilizing a sort of copernican revolution moving from continuous mathematics to discrete mathematics.
Basically, the Pope is an absolute monarch and uses his power to suppress the creative evolution of a true human picture of the world. What would happen to theology if the oppressive power of the pre-scientific outlook was suddenly removed.
On the Political direction of Intelligence: Intelligence has two meanings, data and insight into data. Newspaper ownership and direction. Paper Tigers Coleridge.
Thursday 19 August 2010
[page 11]
The finite velocity of communication enables us to establish a time ordering of causes and effects which can be represented by a communication cone. In the one dimensional world of quantum events, this cone is simply a 'timeline' which may be very short, since quantum mechanics has no memory all we can do is calculate the next state from the one before.
We begin with a stripped down version of quantum mechanics ['naked quantum mechanics'] as it exists in its own one dimensional space and then turn to the creation of spacetime and the projection of quantum events onto the space-time manifold.
Continuous mathematics assumes that there is always more detail to be resolved (as in the high hopes of quantum computation) It jibs at quantization and the resultant 'uncertainty'.
Constructing probabilities with a computer network. Building up from simpler constructions with coins, dice, roulette wheels and urns to the probabilities of halting (thus becoming an event).
What science is trying to do is elucidate the reliable (invariant) structures of the Universe that is the processes that can be represented by isolated Turing machines, which are equivalent to eigenfunctions.
Physics Today On modelling the world. or Physical Review D.
We cannot observe instances of a quantum process because isolated computers (ie determinstic) 0nly their outcomes which are predicted by quantum mechanics So we model fixed points in the Universe by deterministic comp;uters or algorithms
[page 12]
From this point of view, a fixed point is equivalent to the software loaded into a universal Turing machine to compute a particular instance of a particular function.
Quantum mechanics has no memory so it follows a purely random path, the probability of each state does not change as we repeat identical preparations.
Camus Sisyphus 'O my soul, do not aspire to immortal life, but exhaust the limits of the possible.' Pindar, Pythian iii Pindar - Wikipedia, Camus
We hypothesize that the quantization of the Universe results from conformity to the requirements of the theory of communication, that messages must be digital to allow perfect deterministic recovery.
The Pope is a politician exercising political control over the Catholic communication network, censoring some messages deemed dangerous from the Pope's point of view as tending to undermine his franchise.
not-p is orthogonal to p, in that their product is nothing, in probabilistic terms p and not-p is impossible [probability 0].
The promised land was beautiful advertising but a tawdry, bloody, genocidal reality.
[page 13]
Camus Introduction (James Wood) page ix: 'While Kierkegaad insists, in The Sickness Unto Death, that Christianity '
begins' with the concept of sin, Camus insists again and again that we are innocent. While Kierkegaad argues that paganism is no more than being in a state of despair but being ignorant of it, Camus delights in paganism, and in a paganism that is not ignorant of itself, but thoroughly self aware and relentlessly vigilant. While Dostoevsky proposes suicide as the only logical response to an awarness that God does not exist, Camus proposed that the man without God must not kill himself, but realize instead that he is condemned to death, and live his life saturated with that terrible knowledge; Camus proposes awareness itself.'
Christianity, Melville, Pierre 'Silence is the only voice of our God . . . how can a man get a voice out of silence? Melville
The natural God chatters on non-stop at about 10100 words per second [within any horizon].
Wood, page x: 'Camus is forced into his own leap, which is the assertion -- and it is not much more -- that we must oppose the world's meaninglessness with our revolt, our freedom, and our passion.'
All of which are meanings built into human nature by selection.
page xi: 'Death only becomes a problem for those religious believers who see life as something more than material existence, which is why Christians must announce that death os conquered. . . . Camus cannot evade death; instead, as it were, he will (in both senses of the word) entertain death, keep it busy.
Natural religion trades eternal life for being temporarily part of God
[page 14]
Wood page xi: Camus: 'in a Universe suddenly divested of illusions and lights, man feels an alien, a stranger. His exile is without remedy since he is deprived of the memory of a lost home of the hope of a promised land. The divorce between man and his life, the actor and his setting, is properly the feeling of absurdity.'
Because camus has not learnt to decode our real place in the divine Universe.
page xii: 'The stranger or exile is the absurd man, awake to the impossibility of reconciling himself to his situation.'
Formal mathematics assumes an infinite resolution, whereas real mathematics has to build itself up from the empty set, implementing error correcting systems powerful enough to resolve the emergent levels of complexity.
One cannot understand real mathematics without including the mathematicians. Tymoczko
Most mystical literature seems to bean exercize in obfuscation designed to increase the political power (= f(number of followers) ) of the guru in question. Jesus was much more concrete.
One might say that this model of the Universe is impersonal but we are persons and we are part of it so it is at least partially personal and when we apply Cantor symmetry to this proposition we see that the Universe is an infinite set of personalities, that is of independent sources, as the Person of the Trinity are imagined to be.
[page 15]
Veltman page 15: 'In a quantum mechanical description the state of a free spinless particle is completely specified by its three-momentum.
V assumes the existence of a background space-time and overlooks the one dimensional nature of quantum mechanics in itself.
V: 'We do not postulate commutation rules, but we postulate that a particle of well defined momentum and energy is defined by a plane wave.'
ie by a periodic function! φ = exp(-iE / H bar)
page 26: 'Since the range of momenta is infinite [and continuous ? ] the space of a single particle is already of infinite dimension'
And on this assumption, is the space of two particles transfinite, ie the set of permutations of the space of one particle?
The mathematics of quantum mechanics seems to completely disregard the ordering of basis vectors in Hilbert space.
Veltman page 17: 'discretization' of momentum by assuming the Universe is a square box of volume V.
'What we are doing here is of course quite horrible: we are violating Lorentz invariance. A square box of volumeV is not Lorentz invariant.
Here arises the idea (obscured by the assumption of 4-space)
[page 16]
that unobservable quantum transformations are outside space (have no memory) and are not therefore subject to Lorentz transformation.
Veltman page 17: 'This plague, having to abandon Lorentz invariance in order to define the formalism, seems common to all approaches to quantum field theory. One always needs some kind of grid. The final results, the Feynman rules, do not suffer from this breaking of Lorentz invariance. We will, by necessity, ignore this difficult issue.
The 'grid' is the set of quanta of action, which is formally the set of Turing machines. A functioning machine is an isolated point that may be visualized as moving around a space of states (defined by Davis's tetrads [quadruples] Davis).
This article is inspired by some words of Veltman and a few ideas from Zee: First that it is time to go beyond the harmonic paradigm and second that quantum mechanics is one dimensional field theory.
Quantum mechanics describes permanent particles with well defined energies. Quantum field theory describes evanescent particles, ie particles which are elements of the universal memory whose states change as the process proceeds.
The 'permanent' particles of quantum mechanics can exit all at once in a superposition.
The Feynman rules tell us how to compute the probability of discrete events.
[page 16]
Veltman p[age 18-19: 'In fact, thinking of an electron, charge density must be proportional to probability current and probability density, with a conservation equation ∂μPμ(x) = 0 analogous to the conservation of electric charge.'
Probability density = event density (mapped onto 4-space) [= energy density].
. . .
A common religious claim is access to the real truth about the human condition. Our approach to this question is thorough history: if you want to know why we are here study our history. The power that made us is there for us to take advantage of: life is what we make it. Christianity has got us off to a bad start by branding us all sinners but once we see that this claim is motivated by politics rather than science, we can shrug it off and move on to studying the world and ourselves as it really is, a wonderful system honed by billions of years of trial, error and success.
Abbot is Catholic, Julia atheist. Tony Abbott MHR, Bella Counihan What is the difference? It is clear that we are part of something very much bigger than ourselves. Whether we call this god or not-god makes absolutely no difference to the reality; the rose by any other name would smell as sweet principle. A rose by any other name would smell as sweet - Wikipedia Here, then, enter the Greens. The foundation of greenery is a new theology: our lives are not controlled by some remote omniscient, omnipotent being. They are controlled by our habitat, our environment, material and spiritual. Greens say the Earth is Our Mother, and we must take care of Her. Very true. The Earth is also our God, creating us and judging us. If you fall off a very high place,
[page 17]
your judgement is very likely death. If you play your cards right, you will probably win in the end This is the judgement of reality. If we damage our environment we damage ourselves. The planet may be huge but it is very sensitive. Small changes in the arrangement of the solar system drive large changes in global climate.
Greenery is Islamic,. We must submit to the requirements of our environment if we are to survive. It is much bigger and more powerful than us, and if we step out of line we may begin the path to extinction.
Veltman page 19: 'Thus corresponding to a Lorentz transformation there is a big complicated transformation in Hilbert space.'
This conclusion (which I am inclined to think false) arises from Veltman's initial assumption to project all quantum states onto 4-space without developing the 4-space from the native one space formulation of quantum mechanics.
Quantum mechanics is the basic hardware code of the Universe.
We are inclined to match the opposition hardware software with the opposition permanent / ephemeral, but we know that software is of itself eternal, and a particular instance of software (eg the Bible) will last forever provided that its hardware foundation is renewed when it deteriorates,
[17]
by copying.
MEMORY = MATERIA PRIMA
Veltman page 21: V repeats in bold 'To every Lorentz transformation, or more generally a Poincare transformation, corresponds a transformation in Hilbert space'
'Since we want physics to be unique we will insist that this is a one-one correspondence.
So
'If the correspondence is unique then the product of two Lorentz transformation L1 and L2 must correspond to the product of two corresponding transformations X1 and X2 in Hilbert space. . . . We say that the transformations X in Hilbert space are a representation of the Lorentz group. Again, the matrices X are in general very different from the matrices L.'
The metric of the mind measures the association of ideas which can be crudely measured by the rte of communication between regions of the network representing the ideas whose distance is being measured.
Stationary point - point of stagnation. Stagnation point - Wikipedia
Friday 20 August 2010
Saturday 21 August 2010
FORM = A state of memory represented by (eg) a string of symbol;s which may be treated as a vector in a sufficiently symmetrical context, ie where the ordering of the basis states in the relevant Hilbert space is irrelevant, so all permutations are equivalent.
