Notes
[Notebook: Transfinite Field Theory DB 56]
[Sunday 16 November 2003 - Saturday 22 November 2003]
Sunday 16 November 2003
[page 17]
Monday 17 November 2003
Back to reading Lonergan Insight and Nielsen and Chuang simultaneously looking for enlightenment. Lonergan, Nielsen and Chuang I am still trying to understand how Insight convinced me that the Catholic model (which distinguishes god and experience, claiming that experience of god is something for another life) introduces unnecessary complexity into our understanding of reality. Morally, the defect arises from the conviction that human intelligence is unique in the world, and that all the rest of it is just dumb and inert, needing a puppetmaster to operate it. This is the stuff of emotional experience. On the technical side, where we hope to make a breakthrough, we can see that knowledge (defined as secure abstract representation) is ubiquitous in the Universe and that the whole thing is in effect ordered by its own intelligence.
We might say that Christianity, like all the old religions, suffers from having anthropomorphic gods who embody the complexity of human affairs. We might do better to build our concept of divinity from the size, power and complexity of the Universe
[page 18]
in which we find ourselves.
METAPHYSICS == MATHEMATICS == QUANTUM MECHANICS
To prove the second identity, we note that mathematics is anything that can be done by a universal Turing machine, which is equivalent to the set of all halting Turing machines (a subset of all possible Turing machines) [Turing machines produce permutations of the natural numbers] Now we assume that a quantum computer can do anything that a Turing machine can do, so that the formalism of quantum mechanics provides an isomorphic representation of the formalism of mathematics. In the world of formalism, complete isomorphism is equivalent to identity.
Tuesday 18 November 2003
Wednesday 19 November 2003
Thursday 20 November 2003
Friday 21 November 2003
Thought of a form of words this morning on the way to work nearly worth crashing the car for and now it completely escapes me. Perhaps it will come back. Perhaps about the Procrustean truncation of the human spirit by the vows of poverty, chastity and obedience! These vows are designed to make living people small enough to fit into the dead literary models of the RCC.
Such spiritual compression without a safety valve is liable to lead to explosion. This model may help to explain the relationship between terrorism, and the attempted restriction of the creative (expansive) force of reality - the 'pressure of dark energy which makes the Universe expand'.
Saturday 22 November 2003
Morning again. Will I become conscious of any new steps on my path to my grail? I am aware that my consciousness is the outcome of a gigantic process
[page 19]
which I call mind and understand to be (ultimately) all the information processing that goes on within me from quantum to neural. All these processes mind me, noticing and heading off (where possible) deviations from the 'fit' set of states of my being (or better), the set of fit states of my being . . . . 'Fit state' means a state calculated (with respect to my environment) to best maintain my fitness.
We are embedded in God. God is wild, so that anything that survives, survives in a wilderness.
We cannot comprehend the whole because our cardinal number is less that the whole. Cardinal number corresponds to energy. We say the energy of the Universe is countably infinite. At the local level, energy is finite and characteristic of a state (though two states may have the same energy (be degenerate) locally, we guess that degenerate states are always split by the environment (gravitation eg) so that they are all unique. Is the gravitational splitting of states in fact the overall structure of the cosmos?
Nor can we control the whole, because we do not have the requisite variety. Because it is (from our point of view) uncontrollable, it is wilderness. Different wildernesses have different energy (temperature) which parametrizes the fluctuations and the violence of the interactions in that wilderness. A characteristic of wilderness is death, because although it is finite it is creative so that new beings can arise only if old beings fall. No subset of a wilderness can maintain its independence from the wilderness forever, but must ultimately fall prey to (fatal) circumstances beyond its control.
The classical world is the world of classical objectivity where all phenomena are open (in principle) to
[page 20]
the eyes of all, and is finite. Here we are interested in the relationships of things to one another. The quantum world id private - no cloning. Every interaction is unique in a certain context in the history of the world. This private world is infinite(continuous).
So we might say divine = private
Infinite - reversible.
Insight is not reversible.: it 'collapses the wavefunction', leading to a classical measurement expressed as a vector in a certain basis (idea in a certain Universe of discourse, structure of synapses in a certain animal nerve system, and so on).
How do we mate Hilbert space with transfinite network? In quantum mechanics, though the basis states are discrete, their coefficients a and sqrt(1 - a2) are elements of a continuous domain. . . . How do we represent the discrete basis states and the continuous (and complex) parameters in terms of the transfinite network?
It seems natural to map the set of basis states onto the natural numbers, so that each dimension in the resulting Hilbert space is identified by a unique natural number. Now while a number is simply a named empty set (?) (set of empty sets), whereas there is more in a dimension than that, it is a vector, the geometric equivalent of an ordered set of numbers taken from some domain. We can choose a set of orthonormal basis vectors and represent these by the set of sets [ [1, 0, 0, . . . ], [0, 1, 0 . . . ], . . . ]. So good. Now we come to vectors which are the superposition of basis states like a|0> + sqrt(1 - a2)|b>. The continuum enters here but it is not directly observable but only guessed at by repeated measurement.
[page 21]
So we think the parameters of certain vectors are drawn from the 'transfinite cloud' surrounding any countably infinite system. This brings us to the question of the control of quantum states (and consequent measurements) and quantum computation.
Ultimately we want to see the structure of the Universe in a suitably chosen set of quantum states. Our perception of the Universe is ultimately based on a set of measurements of various quantum states (as when a photon is recorded by my visual system).
She spiritual controls the material is the same as saying the higher powers overcome the lower. So we see that control of a quantum system does not involve changing the cardinal number of the basis space but in adjusting the 'weights' coefficients of each dimension. Here are complex numbers, which give is a perfect arithmetic model for vectors n Hilbert space. All subprocesses of the Universe are by their definition bounded and cyclic, and so are able to be represented by superpositions of complex exponentials.
If quantum mechanics is metaphysics, what it says to us about bonding may be applicable at all scales including ourselves. Quantum mechanics says things will bond if the bonded state has lower energy than the unbonded states. (Is this a completely universal statement?) If so it may show us the relationship between love and energy.
An insight embodied in the Hitchhiker's Guide. Adams Concrete and abstract are relative terms related to the resolution or complexity of data. The Universe as a whole is fully concrete or complex and subsets of the Universe, being less complex, are abstract versions of it, as Dent was an abstract version of the world [Earth]. The Hilbert oscillator mediates between levels of concreteness and abstraction.
[page 22]
The driving force behind this quest is the lust for life. The history of life shows that salvation often requires great effort., This is the effort that maintains homeostasis in he face of fluctuations and so lives to live again.
We need to think about renormalization in quantum theory and the transfinite hierarchy - the avoidance of infinite self interaction, collapse to a point, and so on.
SPATIAL EXTENSION = MOMENTUM UNCERTAINTY. . . .
Monastery: this imprisonment cannot be real.
Morality - the force toward individual adaptive modification. Politics - the force toward collective adaptive modification
