Notes
[Notebook: DB 62 Interpretation]
[Sunday 18 November 2007 - Saturday 24 November 2007]
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Sunday 18 November 2007
Aristotle's distinction into things that exist 'by nature' like trees, and 'by art' like wooden beds is echoed in the distinction between formal (as in formal mathematics) where the symbols are manipulated by some outside agency, like a mathematician, and dynamic (as in physics) where the symbols interact from their own nature.
NATURAL = FREE
FORMAL = CONSTRAINED
One may compare the layers of a network to the time ordered layers of literature of culture in general, each subsequent layer taking and elaborating meaning and inspiration from its recorded and remembered predecessors.
A complex number carries two channels of information, whose independence is marked by calling them real and imaginary, and which are additively independent through they interact in multiplication, since i2 is real. What does this mean?
Monday 19 November 2007
The natural development of complex numbers are vectors and matrices which carry n channels of information represented in n dimensional space). Quantum mechanics uses complex vectors, so embracing the complex protocol in the more complex protocol
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that embraces many pairs of channels, like a many pair copper telephone cable.
Byron & Greek Love: Louis Crompton Crompton
Page 197 Lady Caroline Lamb: 'Mad, bad and dangerous to know'.
I write much of this from love (and its consequences) trying to resolve real or imagined conflict between 'flesh' and 'spirit', whose origin, I believe, is this very false dichotomy promulgated by the Christian trend in theology which regards the world as a puppet of an invisible superior being and all of us here below who are in fact defective sinners. This paradigm creates a role for 'shepherds' who keep the mob together and control its direction, while making an income by selling the natural increase of their flock into the meat trade. So we replace the duality between matter and spirit with the quantum harmonic oscillator, which creates and annihilates the states of the Universe. We imagine the world as a space of all possible states. We consider a state to be created (moved from possible to actual) by the acquisition of energy. To be is to have energy, which we see as a measure of the flow of action in the Universe.
As plumbers, we imagine the world as an infinite closed pipe system in which there is a ceaseless conserved flow of action. We assign the cardinal ℵ0 to this conserved flow, since it can be measured in a fundamental unit, the quantum of action.
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Thus we hope to replace the violent duality of matter and spirit with an ever growing number of states separated by every smaller distances in terms of action, but ever greater distances in terms of complexity.
The flow of action is observable, that is visible to us and measurable. It is the dynamic cardinal of the Universe. We do not inquire about what the action is, but just treat it as a countable unit, a cardinal unit.
Photons (as in optic fibres) do not require a return channel (as in electric currents). This is because the current of electrons is conserved whereas photons can be created at one end of the fibre and annihilated at the other with a corresponding reverse flow of energy, which needs no specific channel, like a wire, to itself. Photons are one way wires.
CAUSALITY - DEPENDENCE. The software depends on the hardware, so we can have a hardware layer without a corresponding software layer, but not vice versa, since the principle of physical embodiment says the software cannot execute without the relevant layers of hardware down to the initial singularity, the quantum of action.
How does this relate to the light cone?
CAUSALITY IS A FORMAL FEATURE of the model and is an expression of ordering. From 'fully
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disordered' (purely timelike) action that gets exactly nowhere (because there is no observable difference between the different points (if any) in the state space), [to ordered].
From Quantum Harmonic Oscillator to Hilbert Oscillator whose fundamental symmetry is that there is just one abstract Hilbert space for each cardinal number of dimensions, that is the number of points resolved in the domain of the function represented.
Minimal complete Hilbert Oscillator is the 4-oscillator which exists in 4-space and explains the basic structure of spacetime. This protocol lies between quantum mechanics and partile family, and is thus the foundation of the communication network that exchanges the particles that we observe.
Quantum mechanics tells us how potential structure regulates traffic flow between states, as does statistical mechanics.
Consciousness is a part of experience, like all the others.
Tuesday 20 November 2007
POTENTIAL = SPACE. We (classically) think of potentials in space (4-space) as functions of four space-time variables. But Einstein identifies the potential with the space itself, so we no longer have a potential in space, but both have the same structure. We can nevertheless put this in carrier space to visualize it better, but in reality potentials are the forms that guide
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action: hard to avoid the dualism. In the dynamic view, potentials are computable transformation and an appropriate representation for an element of the alphabet of potentials is a Turing machine or algorithm.
Formally the Turing machine is the algorithm and we can construct an algorithm for addressing all possible algorithms to give us the universal Turing machine.
Things work better when imagination runs further ahead of construction, since there is more time to consider the deeper implications of each action and to avoid actions that might lead to failure.
Although we can work things out in two state systems, real wavefunction have both finite and infinite and transfinite dimensions. We have to content ourselves with summing over a finite number of 'principal axes' in order to model real processes.
Wednesday 21 November 2007
Thursday 22 November 2007
Friday 23 November 2007
In a time division multiplexed system the strength of a bond (other things being equal) is proportional to the fraction of time (0 <= t <= 1) devoted to it, ranging from indifference (0) to identity (1). This is in line with Lonergan's idea that to love someone is to think about them all the time. Lonergan It also fits the mystical view that seeks to identify with god, since in a divine
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world I am always communicating with god [without being a mystic].
Wilson Darwin's Cathedral. Wilson
