VII Notes
2010
Notes
[Sunday 12 September 2010 - Saturday 11 September 2010]
[Notebook: DB 70 Mathematical Theology]
[page 56]
Sunday 12 September 2010
TRUTH <--> SURVIVABILITY (defence in depth)
Mind: Freud -- untrustworthy; Descartes -- guaranteed by God.
[page 57]
Robertson page 113: 'Let us say the mind is what the brain does', a phenomenon rooted in a physical substrate. Robinson
Monday 13 September 2010
Facing the depressing thought of having to wade through a year of Christian studies to get to the PhD level - my penance for not having done a good job in my honours year. However this should give me a chance to consolidate from critique of Xianity and perhaps recruit a few academics to my point of view.
Awareness Robinson page 118: 'By self-awareness I do not mean merely consciousness of one's identity, or of the complex flow of thought, perception, memory and desire, important as these are. I mean primarily the self that stands apart from itself, the questions, reconsiders, appraises.' ie the critical layer, or as Lonergan would say, the judgement layer, testing for and if possible correcting errors.
[in ISO, the error correction layer, every layer corrects (controls) the layer below it in order to insure its own survival - the fundamental bootstrap Tanenbaum]
On the theory of tolerance. It is the search for safety that drives us to extremes. Each layer of the network has a limit and the layer above it is built on this limit, which may be a complex quality represented by an ordered set of some cardinality.
The key to it all, which makes binary possible, are the stationary points of the dynamics.
A continuous symmetry means nothing happening: via negativa Lie Algebra and [continuous mathematics].
Theorems become operative when their conditions are
[page 58]
fulfilled and there is computing power available to fulfill these conditions.
Ideas are stationary states of the mind, like genes (which far from dominating the dynamics, are merely its stationary points, contra Dawkins? Dawkins
I am advised that my personal faith journey cannot be an ingredient in a reseach thesis. On the other hand, any model of the Universe must include me, so my experiences are data in the quest for a theory of everything.
Robinson: Thinking again, μετανωησις or something like -- deconstructing and reconstruction. [opening a vulnerable period when one is changing one's shell]
The reconstruction: we have bnee deconstructing long enough. Now it is tome to filter the bathwater for babies.
Do you get the story?
The Universe is a simple dynamic system, what the ancient and medieval philosophers called pure act or pure being, something happening here and now.
Continuous mathematics is in a way the study of isolated points, each allegedly identified by a vector of real numbers with some basis in the space of points.
Robinson page 118: 'Those who claim to dismiss the mind/body dichotomy actually perpetuate it when they exclude the mind's [= our] self-awareness from among the data of human nature. By self awareness . . .
[page 59]
see above.
Tuesday 14 September 2010
Quantum mechanics is a hybrid between continuous and discrete mathematics: the dimensions of Hilbert space are discrete entities, but the parameters associated with each basis vector are complex and continuous.
Robinson page 122: 'On the one hand we have the most ancient and universal theological intuition, that the order we see exists by divine fiat, that the heavens proclaim the glory of God. And on the other hand we have this late development in cosmological peculation, the nation that the reality we experience is arbitrary, being one manifestation of an infinitely greater potentiality.'
Yes, and a continually changing manifestation that explores the potentiality with certain probabilities of occupying any point in the configuration space.
Robinson page 123: E O Wilson: On Human Nature: "The core of scientific materialism is the evolutionary epic. Let me repeat its minimum claims: that the laws of the physical sciences are consistent with those of the biological and social sciences and can be linked in chains of causal explanation; that life and the mind have a physical basis; that the world as we know it has evolved from earlier worlds obedient to the same laws; and that the visible Universe today is everywhere subject to these materialist explanations."
But what if the constraints on the material world are spiritual? ie meanings established by the relationships of physics symbols to one another, like this writing.
[page 60]
The dynamic layering paradigm deals with all these matter/spirit problems. [requisite variety says more complex layers can control simpler ones, but not vice versa]
How do we get from the axioms of quantum mechanics to the axioms of the transfinite network.
Axioms = software: a set of constraints to exploit the structure of the machine to achieve certain ends. Software calling software: layering is local
Debuggers add another layer emulating the program to be debugged [so we can see it in action]
Let us say that the Universe is written in object oriented (local) software. The object contains its personality within in, and given certain input, will produce a certain output.
Equations of state constrain paths in configuration space.
Since everything goes through the hardware, every communication is a somewhat ordered set of quantum events.
Wednesday 15 September 2010
Robinson page 127: 'If I were not myself a religious person, but wished to make an account of religion, I believe I would tend to the Feuerbachian view that religion is a human projection of humanity's conceptions of beauty, goodness, power and other valued things, a humanizing of experience by understanding it as structured around and mirroring back these values. Then it would resemble art, to which it is strongly associated.'
[page 61]
As we say frequently religion is the art (ie technology) of peace.
Robinson page 127: Freud Civilization + Discontents: Religion: "The whole thing is so patently infantile, so foreign to reality, that to anyone with a friendly attitude to humanity it is painful to think that the great majority of mortals will never be able to rise above this view if life." Freud
Did Freud rise above it?
page 128: Steven Pinker: 'Religion is a desperate measure that people resort to when the stakes are high and they have exhausted the usual techniques for the causation of success.' which is to mistake the tip for the iceberg, the complexion for the deep reality. (How the mind works) Pinker
Pinker again: "Maybe philosophical problems are hard not because they are divine or irreducible or meaningless or workaday science, but because the mind of Homo sapiens lacks the cognitive equipment to solve them. We are organisms, not angels, and are brains are organs, not pipelines to the truth."
Nevertheless, a neuron is equivalent to a Turing machine, and a network of neurons has power bounded only by its cardinal.
Robinson page 130: 'The questions to which science in its most sophisticated forms has come would have been the imponderables of philosophy a few generations ago, of theolofgyu a few centuries ago, of religion a few millennia ago. Why this ancient instinct for the greatest question?
Yancy I Was Just Wondering Lima Inquisition 1570 - 1820. Yancey, Peruvian Inquisition - Wkipedia
[page 62]
Thursday 16 September 2010
Generating memory. Like the wheel,mathematics is extremely simple at its roots. We can do it all with a few symbols and lots of imagination, and we can imagine that the human creation of the mathematical Universe is isomorphic to the Universe's creation of itself. From walking step by step to the wheel is the archetype of the transition from discrete to continuous.
Another good thought flashed through my mind but I have lost it by trying to finish the paragraph above before taking off at another tangent. It was the equation SYMMETRY = EQUIPROBABILITY. Broken symmetry [on] the other hand means one possibility reaching a probability of 1 at the expense of all the others = the wave function collapsed = 1 possibility out of many chosen = judgement.
COLLAPSE OF Ψ = JUDGEMENT (like drawing balls out of an urn, but perhaps there is an explanation for the particular choice of ball.
CREATION = GENERATION OF MEMORY [generation of control]
Father <--> Son two copies of the same God (omnino simplex) differing only because one is not the other, they are orthogonal.
It would be amazing of the digital construction of the Universe turned out to be true, ie as useful as the wheel.
[page 63]
The not function can be used to construct a wave, a square wave maybe but we can just as well think of it as a [digitized] complex exponential wave. Quantum mechanics works in the wave domain and it has no memory. Read Feynman again. . . .
. . .
Orchestra: superposition. Are quantum mechanical superpositions real or are they simply putting bck together a unity which we have analyzed into parts, like the mapping of a line of music through fourier analysis onto an infinite set of orthogonal frequencies.
So we can generate the harmonic paradigm from the logical paradigm but not vice versa, and the logical paradigm expresses itself harmonically as random noise, like the conversation of modems.
The Catholic idea historically and presently imposed on women and children is that you tolerate abuse because it is said to get you a better place in heaven, although it is hard to see how the vision of God admits of degrees.
Wave is a) periodic [from the point of view of a memory] and b) differentiated, ie it embodies NOT.
So a wave has two complex components represented by complex numbers exp(i ψ).
CREATION bootstrapping cardinality by resolution, obtaining resolution by ordering: so creating an ordered reflecting surface
[page 64]
(extended memory) increases the angular resolution of a telescope.
X-ray telescope: approximate the ideal reflecting surface to the nearest molecule. Harvard-Smithsonian Centre for Astrophysics
At the simplest level all communication is spectroscopy - frequency based. [and both motion and gravitation modulate frequency]
After a long excursion into mathematical (formal, logical) metaphysics, I am coming back down to earth, building a concrete Universe inside the initial singularity. The atom of structure os two sources and a link between them, two fermions and a stream of bosons.
The Bose property; the Fermi property, defined for [sets of] identical particles.
Quantum mechanics has no memory and operates in the energy / frequency domain. Its manifestation in the momentum/resolution domain is a projection of quantum mechanics into a structure with memory.
My picture is simple because I am not able to comprehend anything more complex than loving my friends. [the Age of the Spirit the Age of Alzheimers]
Friday 17 September 2010
From the point of view of quantum field theory quantum mechanics in one dimensional. From the point of view of four-space, we might be inclined to identify this dimension with time, but since we regard space-time as an
[page 65]
emergent entity, and we understand time in relation to space, we must simply look at quantum mechanics as a one dimensional process without prejudice to its properties, which may be envisaged mathematically as a sequence of actions one following the other with no memory of the actions that preceded it so no constraints, pure action, preformal (the existence of form requires memory, a stationary point in the dynamics - the first stationary
The motion of a perfectly symmetrical wheel is unobservable.
One cannot distinguish observer and observed (parent and child) in an isolated (local) observation.
The differentiation of the Universe proceeds 'inside' the initial singularity.
AND requires two 'registers' (memories) for inout and one for output, it it is 3D, ie 3 orthogonal stationary states, each capable of two states, conventionally 1 and 0, as in the truth table. Quantum mechanics provides the clock for AND, NAND etc. CLOCK = NOT
AND = three interacting NOTs.
Then we connect ANDs together to make a computer.
Turing's genius lay as much in programming the Turing machine as inventing his machine in the first place. The notion of a Turing machine takes place in a series of steps each of which implies the step that follows it so that the machine proceeds deterministically from start to finish
[page 66]
(when it does finish, ie halt and emit a message), the result of its computation, which has been determined by the initial configuration of the machine.
Logical space is the configuration space of Turing machines. transfinite computer network is a phase space for Turing machines.
The cardinal of the set of countable ordinals is ℵ1
We can assign a cardinal to each complexity of Turing machine, stating with the two bit machine (2 inputs, one output) which is universal ion its truth table.
| Truth table for general two input one output device | |
|---|---|
| 00 | [1, 0] (EBNF notation) |
| 01 | [1, 0] |
| 10 | [1, 0] |
| 11 | [1, 0] |
The $64 jackpot is to explain how the computer network idea yields the same results as quantum field theory, where qft agrees with observation. ,p. A history of process controlling: counting.
There's a lot of truth in everything.
[this] Natural theology website is my Summa.
our assumption is the God and the Universe are ultimately very simple and therefore comprehensible.
[page 67]
Knowing and being, God knows everything by being everything.
Full duplex communication (represented by complex numbers) is intrinsic to the system because as you change me I change you like dual spaces revolving around the metric. The metric is the contact between the duals which is achieved by digital communication, rather like interdigitated gears.
Saturday 18 September 2010
Why does the Universe evolve: because of the remarkable ability of computations to implement Shannon's encodings enable the Universe to correct its own errors and move itself up the transfinite hierarchy.
Particles are messengers between quantum processes [visible manifestations of invisible processes] Messages are created and absorbed by these processes, the energy in the field (process) being just the same as the energy in the in and out particles.
Peacock page 273: 'It will be an excellent approximation to treat the Universe as if the matter content were a simple dissipationless fluid undergoing a reversible expansion.' Peacock
paghe 274: Early Universe radiation dominated. The redshift for matter-radiation equality is 1 + zeq = 23900Ωh2(T / 273K)-4
'Prior to matter-radiation equality, the speed of expansion is so high that fluctuations in the matter density cannot collapse
[page 68]
under their own gravity; only at later times can cosmological structures start to form.'
'Of course, matter and radiation are coupled by Thompson scattering . . . " Thompson scattering - Wikipedia, Klein-Nishina formula - Wikipedia
'The Planck time . . . sets the origin of time for the classical phase of the big bang. It was recognised at an early stage that there are some particular aspects of the initial conditions of the Universe at tp: these are the "fine tuning" problems that motivate modern inflationary cosmology . . . '
page 277: '. . . for radiation the entropy is just proportional to the number of particles.
'Although we do our best on a local scale to obey the second law and cause entropy to increase, these efforts are swamped by the immense quantity of entropy that resides in the microwave background.
Peacock page 282: The massive neutrino is the simplest example of a relic of the big bang: a particles that once existed in equilibrium, but which has decoupled and thus preserves a 'snapshot' of the properties of the Universe at the time when the particle was last in thermal equilibrium.'
Why do some interactions only occur at high energies = high frequencies of action?
page 283: 'In a sense most of cosmological theory comes down to solving the Boltzmann equation for photons
[page 69]
plus neutrinos plus collisionless dark matter coupled to the matter fluid via gravity in all cases and also by Thompson scattering in the case of photons.
The Father and the Son observing each other are the Holy Spirit: love is observation. Making love in the physical sense is mutual observation through sensors in our skin.
The 'guiding field' (Einstein Fürungsfeld) is logic as implements by computers.
Human relationships, since they involve two people, are more complex that we can understand and not therefor something we can control. They are one representative of a higher layer of complexity than the human layer and so are in effect 'made in heaven'. Given the social and political controls existing in most societies on most human relationships, they are subject to inputs from ever higher layers, for which we also lack the variety necessary to exert deterministic control.
