Notes
[Notebook: DB 59 Draughts]
[Sunday 20 August 2006 - Saturday 26 August 2006]
Sunday 20 August 2006
Monday 21 August 2006
[page 125]
The structure of the transfinite network of such that permuting symbols in any layer affects many elements of the whole network. So we manipulate the hardware for our spiritual survival.
We can imagine the transfinite network as choirs of angels. The dynamics o the whole choir limit communication to differences of eigenvalues of the communicating systems. An equivalence class of this system can be described by the harmonic paradigm. The harmonic paradigm, like written music, is a bridge between finite text (sheet music) which captures the 'backbone' of a piece and actual performance, which may add other tissues to the backbone.
Evidence based ordering. [A] shed.
The traditional position in physics is that we are entities outside the systems we are studying. This position has been assaulted by quantum mechanics (eg the Tao of Physics etc) but
[page 126]
not yet taken. In the traditional theological position we are outside the world in the same way that the traditional god is outside the Universe He created. Here I put myself inside the system. I am a subsystem of the boundless class f systems which constitute the Universe. There is only one Universe, yet it is a common name (no capital)
Periods of high erasure are periods of high energy consumption, witness what we have been able to do to the earth since we began to eat fossil fuels.
The effective management of any choir (any ensemble of players) requires a certain amount of agreement on the notes to be sung and the tempo of the piece. The mathematical mechanism of quantum mechanics enables us to describe the conventions used by the universal harmony to a high degree of precision and hence (like evolution) it is unassailable from an evidence based point of view. But it remains limited in its interface with gravitation, and all other interfaces have a lot of free parameters.
The operators of quantum information theory are universal and so can represent any allowed operation. They are in a sense a set of building blocks (systems) for the Universe.
A muon is a simulation of an electron which takes a lot more processing to handle the same input and output as an electron .
Shine on you crazy diamond.
Tuesday 22 August 2006
[page 127]
PERSONA = INTERFACE
The problem is to go from predicate calculus in the transfinite network implemented y Turing machines. From this 'deterministic' Universe we extrapolate to the non-deterministic features of the world, for although a Turing machine is deterministic its input (and therefore its output) are not necessarily so. . . .
Turing showed that there is only a countable number of Turing machines. Since there are an uncountable number of functions, only an infinitesimal fraction of functions are computable. Let us assume that the alphabet of the Universe is the set of Turing machines (that halt, ie give an output).
Every observation is a count. We characterize the energy of a photon by a count of its frequency.
Our various Turing machines cover a spectrum of efficiency from those that calculate their result by the shortest possible algorithm, to those that fooster around for weeks to do the same job. We will call the parameter productivity, ie how much good work results per unit of input.
the biggest enemy f the environment is image scoring. I've always wanted to tour the country in a converted greyhound bus, but it is an image thing. What about a bike?
[page 128]
CRIMINALITY = SELF-INDULGENCE at the cost of OTHERS.
Do the Turing machines form a group? No because they erase? What about per permutation machines, assumed to form the permutation group? Some (few) permutations can be represented by an algorithm (and so compressed to a finite text), the rest can only be represented by 'lookup tables'. Finite representations of infinite permutations indicate the presence of symmetry.,
We elucidate the network model a little by applying three theorems to it: Gödel, Turing and Shannon.
Slavery, in the sense of controlled activity, would appear to be essential to survival and is modulated by religion which reflects the prevailing levels of justice, equality, etc. What we look for is maximum entropy slavery self-imposed (ie voluntary) in the light of clear need and applied with maximum productivity. This is plain in my part of the building industry, where we are continually doing new things [and climbing 'learning curves'].
The conflict between quantum field theory and general relativity (general covariance) lies in the conception of the vacuum. Quantum field theory assumes that the vacuum has the energy of fluctuation. Each 'fluctuation' has positive definite energy which contributes to the E50 - E 120 discrepancy between relativistic cosmology and quantum field theory.
[age 129]
How do we deal with this. One approach is to assume that the 'harmonic' vacuum is an artifact of the model, and that such an artifact does not appear in the network model, which contains nothing that even remotely resembles division by zero,
A Turing machine fed a problem from the '[incomputable] domain' will never halt. The job cannot be finished, it is infinite. An unfinished task is worthless except as progress toward a profitable completion. So the pressure to make something publishable out of all these pages of notes.
We note with glee that this picture raises more questions that it answers, since there is plenty of scope for future work. As I go along new problems emerge out of the mist, and my current one is how to use the symmetric network to unite gravitation and quantum theory. My hunch is that gravitation is in effect the dynamic geometry of any communication network.
Power of a computer is measured by the product of the clock frequency by the complexity (entropy) of the operation performed at each clock cycle, (say log(nands)).
This is the first time I have been up writing at 4 am since the Wahroonga days
The set of ℵ0 Turing machines forms an alphabet for universal action. Each machine embodies a computable function and may be thought of as an operator, transforming an input vector into an output vector. Let us, following quantum mechanical practice, associate [the Turing machines] with observables. As entities in the Universe, we are continually observing
[page 130]
and being observed. To see an be seen I absorb and emit photons. When we touch and converse there is also an exchange of phonons and all sorts of other, ultimately particulate signals. The experience of life arises from the integration of those signals y a system that has evolved huge complexity over four billion yeas. How this happened is our principal concern and we hope t explain it using the theory of networks. The theory goes beyond biology, which is the motivation for rooting it at the interface of general relativity and quantum mechanics.
Let us associate one quantum of action with the execution of one Turing machine (henceforth presumed to be a machine that finishes its task). In the abstract, Turing machines halt (produce an answer) or not. In the dynamic version, different Turing machines will take a different number of cycles to halt, depending on the complexity of the data they are given and the complexity of the transformation embodied in the machine.
Map the harmonic version of quantum mechanics into the symmetric network picture.
Hilbert space is a function space, like the symmetric space, derived from Cantor's set theory. From a cardinal point of view, the spaces of quantum mechanics and the symmetric Universe are equinumerous, so a one to one correspondence may be established,
The clue to the ordinal correspondence (isomorphism) seems to be the eigenvalue equation, which selects particular functions (eigenfunctions out of the continuous space of functions (Hilbert space).
[page 131]
Eigenfunctions are represented by vectors whose length (but not direction) may be changed by the operator in question. The computation of the eigenfunctions etc of an operator can be complex, but the results are verified to very high precision, so we cannot doubt this formalism too much. But how to explain it?
If each operator is a Turing machine, we may interpret the eigenfunctions as the set o inputs that enable the machine to halt and put out a vector which is the input vector multiplies by a scalar. All other inputs do not yield a result.
Selective pressure on operators (phenotypes) promotes some operators at the expense of others. We are left with energy momentum and spin, a set of operators that span the Universe (?) All these thins have a symbolic representation in physics, and the quantum mechanical foundation of the Universe seem quite simple until we come to apply them to real (ie complex) systems.
Wednesday 23 August 2006
Thursday 24 August 2006
Friday 25 August 2006
How can se see gravitation as an intrinsic property of a communication network?
First, there is selective pressure toward 'fit algorithms';
Second: Two nodes with heavy traffic between them can profit by
moving closer together;
Third: communication delay (special relativity) [security <==>
keeping up with environmental changes].
PHYSICS = TRADE = exchange of value.
[page 132]
Saturday 26 August 2006
As a step toward the physical interpretation of the symmetric network, let us assume that one quantum of action is associated with the execution of on Turing machine, ie one complete communication or one observation [message].
To every Turing machine Tm computing a function f there is a not-Tm computing not-f giving us unitarity and gauge communication. In other words, in a full divine Universe, every motion must be accompanied by its inverse, since overall the system cannot change. A sort of Archimedes principle.
If I am a network of Tm's, the Universe of my life is a corresponding network in my environment.
How do networks create? First connect new hardware and then 'educate' it by input from the rest of the network and the users. God is the top user.
,,,
West, Ringmaster page 228: 'Mystery was one of the props of power. West
I sit and sit until something ants to be said, and then write it down. A process halts.
Huang page 19: 'The only reversible way to transfer heat is to operate a Carnot engine between the two reservoirs. Huang
[page 133]
What is the difference between a Turing machine and a Carnot engine?
Turing machine is not reversible
Physics al comes down to cardinal numbers. Counts. Each count is located at a spacetime point, and is observed with a specialized structure, be it the modified cilia of the photon receptors in our eyes to the 2000 tonne monstrosities favoured by some high energy physicists. The reception structure gives meaning to the counts. In the case of the human visual system, the processing used to deliver the final picture to the 'user' (the person using sight to navigate through the world) involves billions of neurons with trillions of interconnections.
This has been an impressionistic sketch of the possibilities of theology, that is a synthetic rather than an analytic theory of everything. Traditional theology uses the concept of god as a point at infinity, an invariant which serves as a foundation for explaining experiences (measurements) of the Universe.
measurement = {measurement}
We assume spacetime addressing when we study things like Liouville's theorem in 'phase space'.
Exactly like counting sheep. We can run some sheep through a gate and count them, and so come up with a number. But what does this mean? The meaning of the number depends upon the environment of the counting. Whose sheep? Which paddock? How much each? etc etc.
[page 134]
Physics uses a lot of formulae which work (sometimes with apparently 100% precision) but which cannot satisfactorily be derived from 'first principles'. This is maybe because the first principles are wrong. We might guess that cardinal numbers (like IQ) are being unduly emphasized at the expense of ordinal numbers that exist in >1 dimensional space.
Trouble attracts energy> Trouble is energy?
At the root of every transformation is the Lorentz transformation, which arises because every transformation requires computation and every dynamic process occupies time. The Lorentz transformation encapsulates the casual structure imposed on the observed world by this delay.
The harmonic paradigm gives us a natural model for uncertainty in counting, by providing a 'loose coupling' between position and wavelength etc delta p delta x >= h bar.
