Notes
[Notebook: DB 59 Draughts]
[Sunday 9 July 2006 - Saturday 15 July 2006]
Sunday 9 July 2006
[page 60]
Monday 10 July 2006
Dirac page 80: 'dynamical variables referring to different degrees of freedom commute' so that a message string that gives a sequence of values of independent degrees of freedom is an observable. Dirac
As in quantum mechanics, we can distinguish an abstract communication C from its representation (in Greek, English, mathematics, etc)
Can we say that communicating entities are entangled?
[page 61]
We may think of the difference between dictatorship and democracy in terms of specific heats, where dictatorship suppresses individual human degrees of freedom, giving low heat capacity, while democracy reveals individual degrees of freedom, leading to high specific hear, ie a small temperature change for a large input of energy (fluctuation, tsunami, etc). We can imagine almost all disasters as sudden releases of energy, bomb, earthquake, etc.
Since the two slit experiment works an electron at a time, we can say that the electron interferes with itself and say the same for the initial particle n the Universe, whose self-interference (communication, consciousness) has given us what exists now.
Light cone: everything that we can see can influence our current state, which can be generalized to 'communication cone',
Conversation between independent entities (degrees of freedom) is observable [to them, but maybe to noone else - quantum cryptography]
Dirac writes: 'We assume on physical grounds hat the total energy of a system is always observable. For an isolated system, it is constant and may then be written H. Even when it is not a constant we shall often write it simply H, leaving its dependence on t understood. If the energy depends on t, it means the system is acted upon by external forces. An action of this kind is to be distinguished from a disturbance caused by a process of observation, as the former is compatible with causally and equations of motion, while the latter is not.' Dirac Principles, page
[page 66]
(from page 61)
Is this so? We assume that all forces are due to exchanges of particles, as are all measurements, so under the communication paradigm, 'force' and 'measurement' are the same.
Quantum field theory is stuck on the problem of singularity a a source which becomes more attractive as you get closer to it without limit. Quantum mechanics solved this problem in the case of the atom by postulating a ground state below which (in energy terms) the electron could not go. Why can we not do the same thing with the self energy of the electron? We might suspect that the ground state of the electron is split into two, spin +- 1/2.
My habitat has grown more complex over the years, so it is often hard to find things out of their 'proper place' and to estimate the shortest route between two points, given changes of level and a limited number of doors and corridors.
We cannot have movement without a space to move in. The moving object may possibly be found at any point in space (spans the entropy) but is only found at a given point at a given time, the rest of the space being filled with other things, so that all movements are closed or grouplike [permutationlike] in that a closed chain of things must move if one is to move, and the probability of this movement is related to the sequential occurrence of the circuit of moves. This sequence may be random (as in spacefilling Feynman integral) or in
[page 67]
some sense controlled.
If the medium is the message, vector algebra is what the world has to say for itself. We can find a matrix to transform any vector into any other. The rules of quantum mechanics place constraints on these matrices which hopefully make them resemble transformations which actually take place.
When we come to coding and information theory we note a similar phenomenon, since the vectors and matrices need to be spaced out as far as possible from one another to avoid confusion. This is akin to speciation in the living world.
Tuesday 11 July 2006
Transfinite algebra takes us around the transfinite network. Our first step is to show the effects of the implementation of Shannon's ideas in this system. The transformations of information theory are limited to those which can be implemented with strings of Turing machines, ie functions of functions, each one transforming the output of its predecessor. Such a string is the propagator of a calculation.
All things move by calculation = proof.
page 69]
(from page 67)
Wednesday 12 July 2006
. . .
This is a work about the idea of work. Our model should naturally fit the way things actually are, the interplay of the actions and interests of parts and wholes. And, then, hopefully tell us how to secure our interface with the natural world to avoid the fate of those populations that grow beyond the carrying capacity of their habitat.
The quantum loose rein.
Is god capable of intelligent design? Arguments both ways? Classical and incomplete. Gödel's theorem in the flesh. The Word made Flesh, ie expanded to a viable entity, as Bernoulli's theorem ==> aeroplane. The full technological development of an abstract idea.
. . .
Survival - decision = survival - modelling - decision.
At the physical layer the Universe uses unary (Roman, Cuisenaire) notation so that wavefunctions are simply additive. Once meaning enters, we can begin to abbreviate.
Quantum mechanical formalism mimics the behaviour of the world, but what is the actual mechanism?
Two sources can communicate by sharing the same database, as do genetic and flu researchers etc. A photon travelling between two sources is in the nature of an element of a database.
The degree of cosmological redshift tells us how 'far' a photon has been.
The Universe gains structure by division, like cell division, either symmetric or asymmetric. Morrison Nature 441:1068 Morrison
The genes are in effect the parts (the alphabet) from which we are constructed. Or, if proteins are the alphabet, the genes are an abstract representation of the alphabet, needing transformation by ribosomes, etc.
[page 71]
We can condense a lot of talk about the Cantor Universe into probability spaces, which (Creutz page 8) have deep connections with statistical mechanics.
We want to describe the evolutionary paradigm in a transfinite network space which allows networks to reproduce themselves (like cells).
The initial singularity is the ur-stem cell of the Universe. Muotri
Thursday 13 July 2006
Friday 14 July 2006
The engineering heat death of the Universe approach sees entropy as a problem, a measure of disorder in the Universe, while the information approach sees it as a resource, since the information carried by a point is equal to the entropy of the space carrying the point, and entropy can be exploited to achieve error free communication, the foundation of order.
The attitude that entropy is an 'evil' rather than a 'good' means that the question of generation of entropy (and information) in the Universe tends to be overlooked. But we must ask, given the possible simplicity of the initial singularity, how does the Universe complexify itself? ie create the structure (information + entropy) that we see and are?
Physics achieves this by filling the whole of space with a population of 'fields' corresponding to the various observed particles and postulating that wherever there is enough energy, different particles will materialize with probabilities and properties determined by the symmetries of the fields. But what does this . . .
[page 72]
method of calculation point to in nature?
Ancient religions were ,marketed with miracles and wonders.
Christianity cracked onto the most miraculous and wonderful idea of
all, eternal bliss in heaven with god and all his mates. Natural
religion is the complete opposite, something very commonplace and
completely essential.
Here we define religion generally as a means of reaping the productivity gains that result from innovation and cooperation.
Religion is to the fore these days as he ancient rift between east and west projects itself globally.
What is the physics (mechanism) behind the mathematics of complex vector algebra? communication.
Saturday 15 July 2006
Quantum theory has long enjoyed a reputation for counterintuitive obscurity, but the advent of quantum information theory has set the coming out of quantum mechanics in motion by giving us an intuitively satisfactory [picture of what is happening]. We are born to communicate. The encoding and decoding of our interpersonal and intrapersonal communications occupies a good proportion of our central nervous system, a multiprocessor with some 1011 processors and 1015 interconnections. Muotri op cit page 1087 Quantum field theory is also a theory of communication. An abstract world of fields communicates with itself by the exchange of particles that is messages, which have a finite lifetime just like the sentences exchanged by people in
[page 73]
conversation. The following set of parallels between the quantum world and a communication network give some substance to this analogy between chat and particle physics. That it is more than a pretty picture can be shown by using it to pacify the problematic relationship between quantum theory and gravitation. I wish. But the payoff is so great that it is worth trying even though the chances of success are minuscule. So can be represented by a Dirac delta. We just have to hit the point x for which f(x) = 1 rather than zero.
We may consider the delta as a box 1/aleph(n) wide and aleph(n) high, whose area is therefore aleph(n)/aleph(n) = 1.
LOCAL = SIMPLE (since the addressable space is small)
ABSOLUTELY LOCAL = INITIAL SINGULARITY
The continuum version of quantum mechanics allows entropy and information to be packed o an infinite density, whereas there s a quantum limit in this too which describes the relationship between attract entropy and 4-space. Information packing density is a function of 4-momentum.
1, Soul and personality: the hidden soul [wave function] drives the observable personality.
2. Particulate communication : a consequence of Shannon.
3. Delay in communication : a consequence of processing needed for encoding and decoding.
4. Communication disturbance = uncertainty principle.
[page 74]
5. Superposition = states of soul = server
6. No cloning.
7. Teleportation (meaning) : a classical sentence transmits a quantum state.
We want to use communication to make space, and the resulting space to be the shape described by gravitation. What hope?
The source entropy (per person) of the human source is a large number, characteristic of the transfinite peer level of the same power as humanity.
In communication, 'distance' is something like 'Hamming distance', the number of letters that have to be changed to make two strings identical, regardless of meaning.
For strings, general covariance means that we are interested in the relative structure rather than the absolute values, so that we can replace all the letters in a string by their correspondents in some permutation, and the meaning would be the same, ie ab = ba when we substitute a for b and b for a. What matters is how these strings are encoded and decoded, and this depends on how the processor interprets the strings. So general covariance leads to the view that "I am hungry" has a meaning that can be encoded in an infinity of ways.
. . .
[page 75]
. . .
We might couple this idea of general covariance (something ordinal) with delay in communication (something cardinal) to get general relativity.
The soul controls the body because it is the 'disposition of the body' which leads it to process itself in a way that we can call soul.
Just as Boltzmann derived thermodynamics from hard sphere statistical mechanics, we want to derive the behaviour of the Universe from the statistical mechanics of networks of Turing machines.
Every point in quantum mechanics is a variable orthogonal to all the others and so independent of them.
