Notes
[Notebook: DB 59 Draughts]
[Sunday 30 July 2006 - Saturday 5 August 2006]
[page 101]
Sunday 30 July 2006
The first thing we notice is the general conformity between the theory of evolution and the recursive
[page 102]
Function theory. Recursive function theory, however, does not include selection because it is a formal, rather than a dynamic system. Nevertheless we can use recursive function theory, in the form of quantum mechanics and information theory, to give us a selective principle which, formulated broadly, says that fitness correlates with the ability to modulate error rates in communication.
The trusted zone, and the rest.
We can distinguish two different regions of communication, 'the trusted zone' [pillow talk] and the rest. Mathematically we can distinguish them as deterministic and non-deterministic.
Recursive function theory starts with certain primitive functions and builds everything else out of [them]. We find, using propositional calculus that the whole formal system can be built with a sufficiently large collection of nand gates which in a practical (ie finite) computer are connected into a network, receiving the transmitting between their environment ('users') and one another.
How big should the network be to model the Universe?
A novel, or any original piece of literature, is a new coding, trying to express a new idea, the invariant behind the serial form, ie the whole.
TRUSTED <--> DETERMINISTIC <--> PREDICTABLE
NOT-TRUSTED <--> PROBABILISTIC <--> UNPREDICTABLE
[page 103]
Trusted and not trusted are relative, and a mark of co-religionists. Each degree of trust embraces a smaller and smaller community, in which we might find ultimate trust in oneself. Others, less self confident, may rely on trusted others (family, stockbroker) to guide their activity.
We trust in god. QED
Multiplexing has overheads (storing and retrieving states) and also advantages, so me expect to find an optimum somewhere between one process takes all and switching between processes so quickly that nothing ever gets done (photon mode).
1. EVOLUTION <--> RECURSIVE FUNCTION THEORY
2. SELECTION - COMMUNICATION THEORY.
Every job has a characteristic time, given the technology involved. This may be changed by overclocking or the invention of faster algorithms - technologies.
Many of the ancient scientists we know of, starting with Parmenides feel that true reality was unmoving and motion and time were in some way illusory. Why they took this view is a job for the history of science, but it is still with us in the common conceptions of god and eternity. In the evolutionary paradigm, spacetime is of the essence because it established an ordering in cosmic processes.
[page 104]
The time is coming closer when all this capital expenditure will yield an income.
How do we explain general covariance? By the consistency of the Universe, all versions (representations) of it are the same, ie mean the same. They are nevertheless different in detail and this difference may be an alphabet for the next stage of permutation,
Monday 31 July 2006
Tuesday 1 August 2006
Wednesday 2 August 2006
Zee, Symmetry page 186: '. . . physicists who enjoy having Nature as the ultimate arbiter, are not entrenched into warring camps as readily as other thinkers.' Zee
Invariant action = minimum action = most efficient algorithm.
Ancient and powerful cultural traditions have predisposed many people to European origins to see the Universe as an artifact. The artificer is commonly known as god. Although god is seen to have created a magnificent Universe it is felt that it could have been made differently. Here we wish to explore the idea that the Universe is not an artifact, but something existing in its own right.
On this hypothesis, our Universe is subject to no external constraint, and its structure and behaviours, are therefore constrained, if at all, only
[page 105]
by the requirement of consistency [at the same address]
Thursday 3 August 2006
The first crack in god is the Trinity, gleaned, it seems from the New Testament (or inserted by the authors, who wrote long after [the death of] the person, Jesus, whose biography they purport to record). Like good historical novels they contain plenty of truth. So do Father, Son and Paraclete have a prior history?
The Father s the Creator, 1000+ BC
The Son the Logos, 500- BC
Paraclete/Spirit/Holy Ghost
In our Judaeo-Christian tradition, we are apt to identify the god of the Old Testament with the Father,
When we look at the Universe in spacetime we see it beginning as a point and expanding through time to ever increasing spatial size. If we look at this development not so much as an expansion of space, but the growth of a geneological tree, it appears that every current event can trace its ancestry to the initial singularity. The ancestry of every point is a path through the Cantor Universe, which can be represented to a first approximation as a series of binary choices, a binary tree,
The initial singularity is the quantum of action which began as the tick if a clock and gradually complexified to things like my own life, considered as an event.
[page 106]
Encyclopaedia Brittanica, 14th Ed 1039 s.v. Trinity: 'The doctrine, them we may conclude, arose primarily from the conviction that worship of Jesus is consistent with Monotheism. Bit, if secondarily the doctrine when formed is defended as offering the best attainable conception of the Divine perfection, it follows that our sense of what is good and fitting, our aesthetic and religious instinct for perfection . . . are all relevant to its discussion'. page 480 Charles John Shebbeare.
As our most distant extant literate ancestors observed, we seem to inhabit two worlds, sometimes called spiritual and materiai. We see a similar dichotomy in the physical world, between events that appear to conserve entropy (that is information) and those beholden to the second law of thermodynamics that generally tend to increase entropy. We might identify the material world with entropy conservation. To the best of our current knowledge the events in the material world are described perfectly by quantum mechanics. True, there remain open questions where we do not know how to apply quantum theory. Quantum mechanics requires all of its transformations to be unitary. On the Born interpretation of quantum amplitude function, this is tantamount to the conservation of [classical] probability, which implies conservation of entropy. Consequently, material processes are reversible.
While entropy is conserved in the quantum world, it is not on our world of heat engines and dissipative process. Engineers and classical physicists were motivates to view the second law as a prophecy of the 'heat death' of the
[page 107]
Universe, taking with it all life as we know it. Huang page 20 Fortunately the end was some billions of years off, but it was consistent with the common belief that this world will eventually end (and may be replaced with something better, us being resurrected to enjoy it.)
How do these two pictures fit together? Mathematically the boundary might be modelled by Gödel's completeness and incompleteness theorems, Turing's theorem and Shannon's theorems.
The idea behind Shannon's proof is that we can reduce the probability of confusion between a given number of symbols by making the symbol space as large as possible and by placing the symbols as far apart as possible.
Implicit in the proof is the existence and properties of ordered sets, for it is by ordering that we gain access to exponentially growing spaces a demonstrated by decimal, binary or any other 'place significant' means of representing numbers.
Institutional (environmental) prohibition may breed obsession unto death. So we have always wanted to fly, but had to wait until recently to do it, and then without anything like the freedom of a bird.
Going into debt to achieve a purpose. This is the prime characteristic of he vacuum, which manifests particles with the boundaries of the uncertainty principle, that is accurate to about one quantum of action.
[page 108]
The cosmological constant problem arises because the fluctuations of the vacuum amplitudes are squared to obtain the probability of manifestation of a particle with positive energy, and all this positive energy is integrated to give us the energy density of the vacuum, unbalanced by any negative quantity. If this diagnosis is correct, how do we cure the disease?
The obvious answer to the religion problem was discerned by William Blake: 'All Religions are One' means that the material world provides a universal language of images, and that each man's imagination speaks that language with his own accent. Religions are grammars of this language. Seeing is believing and belief is vision: the substance of things hoped for, the evidence of things not seen. Frye, page 28
'"Everything possible to be believed is an image of truth"' is general covariance restricted only by consistent (and unitary) transformations.
