Notes
[Notebook: DB 59 Draughts]
[Sunday 13 August 2006 - Saturday 19 August 2006]
[page 117]
Sunday 13 August 2006
. . .
It seems clear that the 'software' described by quantum theory and relativity is operative throughout spacetime from the initial singularity until now, and no reason to believe that it will not continue to operate for the rest of time. They are therefore the broadest and simplest constraints on the world, and we should expect constraints on the Universe to become more complex as we burrow down through the subsets of the Universe to the most complex.
On the other hand, as constraints get tighter, elements of any permutation become better defined and so complexity increases rather than decreases with constraint (which here therefore acts in the opposite way to constraint == imprisonment. Freedom thus has two aspects, one arising from energy (potential freedom) and the other arising from entropy (actual freedom).
General covariance in a network. I can become part
[page 118]
of a network if I share its protocols so that the messages I receive have meaning for me and the messages I transmit are meaningful to the rest of the network. We may say that the protocol gives meaning to the message, just as the physical and logical structure of a computer give meaning to every bit within it. Meaning an protocol are duals, or relative, maybe like covariant and contravariant quantities.
Formal mathematics is not concerned with meaning (semantics, models) but simply with the combinations of various symbols. It is therefore appropriate to the initial singularity in which we propose that there is minimal structure and minimal communication.
Symmetry breaking is a feature of meaning. We begin with a world like is which can have as many meanings as there are propositions a is b. A 'newborn' computer has a lot of hardware in an 'erased' (indeterminate) state which becomes determinate when it is switched on and booted up. It can then log onto a network and communicate with its peers, but we might say that the hardware layer has no meaning, it is just a set of physical states that interact as they are told to by the software.
We interpret quantum mechanics as a form of network traffic analysis whose coupling constants reflect the probabilities of communication between various entities (in physics, between the world and measuring instruments) and whose symmetries reflect the general content of the messages exchanged and their effects on their transmitters and recipients.
[page 119]
On our definition of the Universe ('nothing outside') we interpret Newton's first law to say that the Universe states in its 'state of rest or uniform motion'. The second and third laws constrain events within the Universe. (F = ma, action and reaction are equal and opposite) to be conservative local gauge theories, where the gauge is the message.
. . .
Why are the transformations of quantum mechanics constrained to be unitary? We answer because they are logically (ie continuously, indistinguishably), correlated to the 'conservation of probability'. Conservation of probability on the graphic user interface corresponds to unitarity if allowed quantum operators. THEOREM = OVERLAP = CONTINUITY.
Difficulty is manifested by increasing error rate which leads to tension because the probability of fatal error is felt to increase.
Heisenberg's x ansatz (?) [basic approach] gives us a way to eliminate complex numbers form our model of the world. Physicists can only explain observations and all observations are classical. There is no need to introduce complex numbers to our description of the mechanism of the world if a classical description is available. Of course interpreting this classical description (particularly because of its size) might still best be done using the harmonic paradigm which has dominated the world of physics for centuries. The route from the formal system driving the world to the harmonic paradigm
[page 120]
is spanned by the notion of recursive or cyclic behaviour which is beautifully modelled by the complex exponential. But computer programmers know that we can also create loop structures with digitally encoded software.
All we know is what we observe. The rest is modelling designed to help us work out the implications of our observations and what to do about them.
Given the marvellous success of the harmonic paradigm, we can only justify the transfinite network if we can find a way to make it yield the same results and hopefully embrace general relativity in the same breath.
Unitarity enter the source entropy through the condition sum over the probabilities of the possibilities = 1.
How do we write factorizable software? Non factorizable software, ie what is the software equivalent of pure states, entanglement, etc?
Exciting things happen after despair. It is a cycle.
Map quantum field theory onto the network: birth and death of messages.
At this abstract level of the network we se no difference between emptying a tank of water and downloading information through a server, but the information is not consumed, it is copied. No cloning says all the mater in the Universe is bound up in representing all the states in the Universe and there is no room left over for copies. There are no copies in the symmetric Universe. [yes and no. We have to make many copies of each element of a set in order to write out all the permutations of that set,]
[page 121]
And therefore no absolute truth?
The harmonic Universe is a cardinal model of the symmetric Universe, in other words its foundation lies in measure theory [measuring probability]. The symmetric Universe is an ordinal model of the Universe.
We are inside the Universe as we are inside logic. In the old days when people thought god was outside the Universe, people also thought that we were outside the Universe, exiles in a strange land. Now that the Universe itself is divine, we can move in with god. This is the heaven (and the hell) that they were telling us about.
I feel that I am coming to a climax. I hope that is not a delusion.,
All physical observation comes down to counting the elements of a certain set, and set of sets . . . . So our eyes count the incidence of photons in various energy bands at various points on our retinas.
This is for all those who have seen their lives stunted by the requirements of institutionalized religion. Worms turning.
What is the topological structure of the Universe. This will reflect what it looked like as a baby, tubes for photons to circulate through (Poincare) Weeks
Every permutation describes an operation which is to rearrange the elements of the permutation from their natural
[page 122]
order to the permutation in question.
Monday 14 August 2006
Purely formal mathematics eschews meaning, ie semantics? Does not look like it since everything depends on mapping = meaning. The formal part arises because we do not ask what 'holds the correspondences together' but simply assume that given sufficient memory and ordering, they can be created formally without gaps or inconsistencies. Dynamics introduces forms which are held to account for correspondences.
The manic-depressive cycle s natural in that in pursuit of some goal one may exhaust one's capital (depression) before getting the payoff (mania).
Theology:
The purpose of this article is o flesh out the series of equations Planck/Boltzmann = h/k = radiation/matter = quantum / classical = hidden / observable = ℵ0 / aleph(>0).
We start with the final term.
The actual meaning of the symbols a / b in the above list remains undefined. It is not to be interpreted so much as division as dichotomies between different aspects of the world. The motivation for this work is to
[page 123]
cast light on the ancient traditional dichotomy between God and the World.
God has perpetual motion. The world does not. Kirchoff set the quantum ball rolling when he proved that the spectrum of radiation emanating from as hot black body must be a function of temperature and frequency only. His proof depends upon the hypothesis that there is no 'perpetuum mobile of the second kind'. Pais 365, Kuhn 4. Pais, Kuhn
All the mathematics of encoding and decoding can be accomplished using a network of Turing machines
TURING MACHINE = PROOF
From the formal point of view, propositional calculus, set theory and mapping make talking about mathematics in finite books possible - back to the Hilbert Oscillator of old. A formal or software oscillator based on some loop construct.
The size of the world is measured by time division multiplexing and the conservation of probability. The probability of the whole Universe at any instant in 1. So time also is defined by probability.
Tuesday 15 August 2006
Wednesday 16 August 2006
They do it because they can; no inhibition, or as
[page 124]
Lonergan would say, virtually unconditioned.
Unitarity is observed in the quantum regime and we have a perfectly incompressible flow of quantum amplitudes that become observable as events whose probability relative to the observe is 1. The past is the set of all events whose probability was 1, and unless they have been erased, remains to (?).
On the other hand we hold that entropy always increases n the classical regime. How do we understand this? The two world';s first met explicitly in Planck's derivation of the black body function, a product of what we now call the quantum harmonic oscillator. Can we model this with a Lonergan like software structure that takes random inputs (the vacuum) and gives black body output, ie constrains the random to a certain entropy. The level of constraint is given, on a domain of cardinal n, log n - entropy of black body function.
Thursday 17 August 2006
Friday 18 August 2006
Creation. The ancients decided that possibilities can only be realized by a preexisting reality. The visible Universe, they concluded, must be realized by some agent which is already real. To avoid infinite regress they postulate a totally real entity called god. Here we propose a mechanism for creation that appears to extend
[page 125]
this answer by showing that a theory of creation may pave the way to identifying god and the Universe. If god and the Universe are one, scientific theology becomes an option because god is observable. We take the position that every experience is experience of god.
