Notes
[Notebook: DB 60 Spotlights]
[Sunday 19 November 2006 - Saturday 25 November 2006]
Sunday 19 November 2006
Monday 20 November 2006
Tuesday 21 November 2006
[page 32]
Wednesday 22 November 2006
The computable manifold is the observable subset of the transfinite network.
The principle of requisite variety and the relative cardinalities of the computable and incomputable functions means that available observations do not have the power to comprehensively represent the incomputable features of the Universe. Hence the uncertainty in quantum observations, they are ever only part of the story and the whole story requires a representation of equivalent cardinality which, while we assume it to be real, can only be sampled, not comprehended, by systems of smaller cardinal. [teleportation]
We have talked at length about the boundary between finite and infinite systems. We now have to say more about this boundary, particularly the recursive occurrence of boundaries between cardinalities which occur in the Cantor Universe. To clarify this picture, we introduce the idea of relativity of transfinity, a property that arises because the notion of set is indifferent to size. The consequent 'symmetry with respect to complexity' gives us a wormhole to pass from one transfinite peer group to another.
Machine infinity: and the size of the hydrogen atom.
To model evolution, we need some sort of memory and a system where resources are limited and possibilities are unlimited, so there is competition for the resources to realize
[page 33]
the possibilities. This selects for the 'fitter possibilities', those better able to garner bandwidth for themselves.
All observable information in physically encoded.
Quantum mechanics and relativity describe the basic network structure of the Universe, and can be applied a any level of complexity, but what about the detail, the gossip, the actual messages that are pass over the network. It is of the essence of a network that it be able to convey any possible message. In alphabetic terms, all possible (ie 'well formed') strings are transmissible. The designation 'well formed' being related to the protocol or grammar which partitions the full set of permutations of a string of letters into grammatical and ungrammatical utterances (or observations). How is this partition implemented? The answer seems to be evolution by natural selection. Evolution can occur at any scale and so we propose that it is ubiquitous in spacetime. This occurs because the transfinite number of possibilities in each situation is much greater than the number of possibilities that can actually be realized in physical observations. This means that the entropy of the observable [and controllable] is too small to completely constrain he entropy of the unobservable - Chaitin's principle or the law of requisite variety.
It happens that out of all possible network events (ie messages) some are self sustaining (ie closed) and some are not. Of those that are self sustaining, some are better [at] it than others. All the self sustaining are strings of Turing machines in the computable manifold - C infinity - each Turing machine in a string corresponds to a differentiation,
[page 34]
a connection between two points which yields a value.
The possible paths along an evolutionary tree are transfinite but the local rate of differentiation may be very small (digital) s one may postulate more determinism and predictability in simple systems rather than complex ones.
NOISE vs CARDINALITY
Television series explore all possible permutation of a relatively small set of characters moving in an environment created by themselves and other irregular characters and circumstances.
In [zero] dimension there is no connection , in one dimension 1, in 2 dimensions a countable number (defined by resolutions of connections n a plane) in three dimensions n uncountable number because all possible connections are direct and do not need to touch one another. So printed circuits are layered = 3D.
You can either sit still and let the music go through you or dance with the music, thereby establishing . . . immobility relative to the music. By moving at the Nyquist frequency one can transform the music completely away and enter a stationary state.
1. Every event has a unique 'signature'
2. Communication between events (causality) is ordered by time, ie not instantaneous and capable of being placed into correspondence with the natural numbers.
[page 35]
Due to the delay, the order of events may appear different to different observers, but at each locality events are well ordered in local proper time.
Ziggy report: critique Ziggy Switowski
Reading Agatha is like looking out the window as one drives along and thinks. The Body in the Library. Christie
Christie page 125: 'The trouble in this case is that everybody has been much too credulous and believing. You simply cannot afford to believe everything that people tell you. If thee is anything fishy about, I never believe anyone at all! [general covariance - we constrain the possibilities only by their connections] You see I know human nature so well' [ie all nature]
Covariance - commutativity - shared basis
The Agatha Christie story = applied satisfaction theory = only one solution fits all the constraints = deterministic communication.
qubit/qualeph
Bombed into the stone age by a remote and unaccountable imperial power.
Equus and general covariance: one can construct a space in which any behaviour appears reasonable. Shaffer The 'preservation of the alphabet' paradigm says that this construction should not be put into practice when it tends toward the death, rather
[page 36]
that the life, or the organism and its descendants.
There is a school of thought that we can do whatever we like on earth and we will be smart enough to survive it, even if we can't fix it.
Quantum mechanics began as 'wave mechanics' and gave rise to the so called particle wave duality. This duality is epistemologically asymmetrical however. We observe particles. We postulate waves. By waves we mean periodic functions, which make us think immediately of continuous functions like sine and cosine. But there is digital periodicity too, as the name recursive function theory applied to the theory of computation suggests. Ultimately any computer implements a network with just one function, the Sheffer stroke or nand executed rapidly both serially and in parallel. We have cycles within cycles, subroutines of subroutines all built up out of strings of Turing machines.
