Notes
[Notebook: DB 61 Warm]
[Sunday 13 May 2007 - Saturday 19 May 2007]
[page 56]
Sunday 13 May 2007
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The logical equivalence principle.: the logic of the Universe is constrained by the same principles as the logic of our minds, ie the Universe may be modelled as a mental (formal) structure and those parts of it that are not formal cannot be formally modelled.
Hidden variable theory is a search for a deterministic explanation of the statistics of quantum theory.
TURING MACHINE = ENZYME, introducing determinism and so increased speed (spacetime resolution) into a process.
Weinberg [Three Minutes} page 63: 'It is critical to the argument of this book that the Universe has once passed through a state of thermal equilibrium. '
Neural networks: Beale and Jackson. Beale and Jackson
'. . . in order to see what properties we expect for the observed microwave radiation background we have to ask: what are the general properties of radiation in thermal equilibrium with matter.?' Planck.
page 65: 'Planck's formula can be summarized quantitatively as follows: in a box filled with black body radiation, the energy in any range of wavelengths rises very steeply with increasing wavelength, reaches as maximum, and then falls off steeply again. This Planck distribution is universal. . . . '
page 69: 'The average distance between photons in black body radiation is roughly equal to the typical photon wavelength.'
[page 58]
'. . . in black body radiation the rule is that the number of photons in a given volume is proportional to the cube of the temperature.'
Energy density of black body radiation is 4.72 T4 eV per litre.
page 70: Photon wavelength is coupled to the size of the Universe (measured in atomic diameters, say), suggesting a relativistic origin.
3000 K = 1 micrometre; 3K = 1 millimetre.
What does the network have to say about the 'recombination' when electrons became bound to protons and photons were no longer impeded dropping the radiation pressure by a billionfold.
page 80: 'The enormous energy density of radiation in the early Universe has been lost by the shift of photon wavelengths to the red as the Universe expanded, leaving the contamination of nuclear particles and electrons to grow into the stars and rocks and living things of the present Universe.'
Radiation energy has become gravitational potential, ie a sort of gravitational formalism, the large scale structure of the Universe.
page 86: 'Given enough energy, it is always possible to create any kind of particle-antiparticles pair in a collision with pairs of photons.
event: energy in = energy out
momentum in = momentum out
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action minimized in
structure in (eg 2 photons) --> structure out, (eg electron + positron).
Hardware is conserved but software (meaning) changes are ubiquitous. Is there any entropy change in 2 photons -- > electron + positron?
page 87: 'Conditions of this sort, with temperatures so high that particle-antiparticle pairs are as common in thermal equilibrium as photons do not exist anywhere in the present Universe except in the cores of exploding stars.'
page 91: 'The really remarkable thing about a system in thermal equilibrium is that all its properties are uniquely determined once we specify the values of the conserved quantities. . . .'
1. Electric charge; 2. Baryon number; 3. lepton number.
page 96: '(Strictly speaking, the quantity which varies as the inverse cube of the size of the Universe us not the number of photons per unit volume but the entropy per unit volume. . . . )'
ie the entropy of the Universe is constant. Where did it come from in the initial singularity, entropy 0?
Photons have no charge, but nevertheless interact with charged particles, like electrons. Charge is irrelevant to a photon, only energy.
charge = protocol.
Equilibrium among a set of particles is maintained by communication ('collision' in the bang world), so when
[page 60]
communication breaks down populations may develop independent temperatures.
The argument for initial simplicity is strong, so speculate about Turing machines and 4-space. The Minkowski metric is near as we can get to the identity in a space where the spacetime symmetry is broken. In the local rest frame the 4-momentum vector is purely timelike.
So let our simple Universe begin with one dimension, time. Time couples to energy via action in the Planck-Einstein equation E = h bar nu. From a computer point of view we may consider each tick on the time vector to be an operation (in fact the no-operation identity operator) and associate a quantum of action with each operation. For mathematical convenience we can think of this as a 1 dimensional plane wave represented by a complex exponential. Such a Universe is 'pure energy' and we can imagine that when particles are annihilated and created the intermediate state is 'pure energy' that then assumes some structure, that is becomes converted to potential energy. Every particle carries an amount of potential energy measured by its four momentum. In an interaction this is the contribution of each incoming particle. Not all the structure (potential) of a particle need become kinetic in the course of the interaction, so that the structure of the outcome is constrained by the structure of the input.
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Local time is always digital, measured by some two state device and a counter.
Now we break the symmetry of tick and tock into a duality, one dimension of space and one dimension of time. This introduces momentum, orthogonal to energy as space (1-D) is orthogonal to time.
[diagram]
Velocity, dx/dt enters the picture. Space = memory. To measure velocity we must measure two positions and two times. To arrive at instantaneous rather than overage velocities we must go to the limit where these positions and times differ infinitesimally.
This space can be parametrized by frequencies. This takes is to the Hilbert realm where frequencies are orthogonal to one another. A hilbert space of countable infinite dimension can represent the natural numbers.
Confinement in space creates quantization in energy and momentum, as in atoms where the electron is confined by the electromagnetic potential.
Around and around. Turing machines tell us that universal computing machines need four degrees of freedom: L-R position on tape, character on tape, printer, machine state [which correspond to] CLOCK (TIME), SPACE, SPACE, SPACE.
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Hobson page 176: 'We must . . . obtain a set of equations that describe quantitatively how the curvature of spacetime at any event is related to the matter distribution at that event. These will be the gravitational field equations . . . '
Source of spacetime curvature is the energy-momentum of matter. This is considered to be a deterministic quantified relationship X matter <==> Y curvature.
'Einstein's equations are . . . a set of second order partial differential equations . . . for the metric coefficients gum, nut of spacetime.'
Second order differential equations give us constraints on the constraints on the matter of interest. Gravitation is second order, quantum mechanics first order.
acceleration determines velocity, velocity determines position.
Shaping my mind by contact with books.
The notion of scale invariance is that my communications with my peers provides a model for electrons communicating with their peers and so on. One communication by me involves trillions of electrons interacting with one another.
Initial singularity = 2 state system = clock, qubit, energy H, frequency i/hH.
Simple = digital = easy as 1, 2, 3, , , , Gravitation = communication without meaning. Communication = passing on a state.
Monday 14 May 2007
Feynman's path integrals assume the existence of space-time whereas we are trying to create the whole Universe, including spacetime from a point using the differentiation of networks as an explanation.
Weinberg's Universe is dominated by photons which are coupled to spacetime. When their energy is greater than the rest mass of various generations of particles the appropriate particles are created and given the equipartition of energy (by collision = communication) the number and energy of these particles may be equal to the number of photons.
I have a building site with lots of pieces lying around but still no clear idea about how they fit together.
In physics, particle formations and bindings all depend on energy states, ie energy per particle = 1/number of particles. The particles corresponding to the Planck energy scale are Plancktons!
Relative velocity changes the appearance of one particle form the point of view of another (assuming that they can communicate) but the particles remain the same in their own rest frames. If it is moving it looks different. If it looks different, it is moving. Since everything is moving in a timelike manner there differences can only occur if spacelike degrees of freedom are available.
Give initial singularity E = 1. h = 1, nu = 1. If it splits in two, we have two particle existing simultaneously (spacelike
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separates) E = 1/2. h = 1. nu = 1/2 each and so on.
Initial singularity momentum = 0, two particles, p1 = p2 and so on . . .
Weinberg page 160 1087 photons in the Universe. Weinberg
The bootstrap. Complexification is achieved by ordering alphabets. The minimal alphabet us two letters. We know we can say nothing meaningful with an alphabet of 1 letter and that this is not just a constraint on human knowledge, but on all differentiation.
Current physical models no not discuss the details of interactions but instead try to predict the properties of individual interactions but rather they are a sort of network traffic analysis a bit like the divorce rate. This traffic is described beautifully by quantum mechanics in what we might call a kinematic way. The dynamics are the dynamics of mind, constrained by the bounds on formalism.
QUANTUM MECHANICS = TRAFFIC THEORY
Shorten busy links, ie simplify the code, ie tolerate a bit more error because repetition is cheap.
We can only resolve what is resolvable in the Universe, the lesson of quantum mechanics. Hidden variable
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theories try to make quantum events deterministic. We are in a way free to insert indeterministic elements in the theory as long as they are isomorphic to the existing formalism. There is plenty of space for this in the transfinite function spaces and their finite models.
Transfinite addition a + b = max {a. b} . . . .
To work, my laboratory, ie a system through which to view the world.
If knowledge in some sense grows exponentially, then persistence will always win over skill unless the skill is applied persistently. Tautologies are not vacuous, they are transformations to a new reference frame.
Given the appropriate Turing machine, every deterministic transformation is effectively a tautology in the sense that it could not be otherwise.
Tuesday 15 May 2007
Hofstadter: I am a strange loop. Hofstadter
At school my teachers stressed the value of organic matter in the soil. In the lab, however, we were taught the rudiments of plant nutrient requirements demonstrated by hydroponic methods. Now we have gone a bit hydroponic, and it would be interesting to see how much we could stabilize global temperature by encouraging farmers to build up the
[page 66]
organic portion of their soil and landscape.
The set of all sets does not exist means no system can fully control itself because it cannot deal with all the possibilities of a much more complex environment. The only way is total lockdown. Be a dark matter. Autistic.
Dark matter has no structure to be discerned it is pure noise, in other words a communication network in equilibrium. All of the world we observe is far from equilibrium, the basic driver being hydrogen bonding to become helium and so on.
Natural religion take the religion out of religion by embracing all religions in a common model of superhuman (supraindividual) structures. (In the nuttiest possible shell).
Natural religion is something to be discerned, not constructed. It already exists. We just have to learn to see it.
I grew up with a martyr mentality but lived to see that it is far from optimal behaviour, from the point of view both of the individual and the community. Author.
Documenting an exploration
Eichler: 'In our home countries we are all in similar positions politically - we fight for financial support from our governments and from other funds in order to gain high-quality results. In this respect, every scientific
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community in the world speaks the same language.' Nature first author
Nature 447:2 'Like gun control _ an idea that cannot speak its name, even in the wake of last month's horrific shootings at Virginia Tech - the abandonment of missile defence seems to be politically out of bounds'. Nature editorial
Marks on Linnaeus, 447: 28 Marks
The scale invariance of communication networks is a wormhole that allows us to consider the personalities of nations, people and quarks in the same model Like nations and people, quarks are asymptotically free but find it very difficult to get away from one another and cannot exist independently.
The world is a fossil of varying age.
Everything changes (Heracleitus) but at different frequencies (spanning a range of about 10100 ).
The no-cloning property of the symmetric Universe is a gauge, a non-abelian one, which may in some manner relate to the non-Abelian gauge theories of physics (I wish). The no-cloning property normalizes the symmetric network by establishing each particle as its won reference frame and joining them by general covariance.
Hardware = gravitation = continuous. Maybe attempts to quantize gravitation are misguided.
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Wednesday 16 May 2007
Thursday 17 May 2007
Creation is by time division multiplexing. One cannot pay full attention to two tasks at once. But many tasks must be completed to stay alive. Therefore time division multiplexing, creating longer cycles, lower frequencies.
There is no need for a continuous space in general relativity. The shape of the Universe can be described by a discrete number of points and that is all that we will ever observe. Nevertheless the requirement of continuity (= symmetry, lack of definition) is a strong constraint on the gravitational field equations.
Two metric containing 16 different entities can connect pairwise (by entity) in 256 different ways,
Symmetric Universe is not a manifold because it cannot be continuously parametrized. Every point in it is represented by a symbol or string of symbols drawn from some alphabet. The smallest number of dimensions in the Platonic world is countable infinities, but in real world implementations the existence of error scales the detail down to the finite natural numbers.
Continuity and differentiability add up to a strong constraint, the 'contact' or nearest neighbour constraint.
In general relativity, the logical space defined by the
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symmetric Universe maps to the four dimensional space of experience.
Hobson:' . . . in general we do not require the whole of a manifold M to be covered by a single coordinate system. Instead we may have a collection of coordinate systems each covering some part of M, and all these are on an equal footing. We do not regard any one coordinate system as in some way preferred.' Let us call each coordinate system in the Universe an ego and say that all egos are equal, and that every ego observes the other egos from its own local (logical) frame of reference which (shaped by evolutionary history) enables the ego to understand the other egos and act for its own survival.
In N dimensions the transformation matrix has N2 entries (channels of communication). A message is a differential, or is a differential a message - how to construct the next link in the chain.
dy/dx is a relationship (or communication) between y and x defined by Lim a--> 0 of ( f(x+a) - f(x) )/a.
Friday 18 May 2007
4-D spacetime, 16-D metric, 64-D connection, 256 D curvature, of which we experience only the 4-D and postulate all the other dimensions to explain the 'shape' of spacetime, which they appear to do perfectly and with logical consistency given the hypothesis of continuity. And it is the logical consistency which is the clincher. The Universe is logically bound.
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Traditional theology explains the world by an impenetrable mystery called God. Physics explains the world by illogical continuity. Neither explanation is mechanistically satisfying, like the explanation of an internal combustion engine extracting mechanical energy from a potential.
Energy potential <--> engine <--> kinetic.
A chain is a mechanistic explanation of its own strength.
Traditional religions reflect their education / ruling subset origins in basing their salvation on military power. God is the ultimate (metathermonuclear) weapon that justifies the use of all other weapons.
The gutless ones who go to war. The alternative, of course, is trade which complexifies by creating a web of relationships between nodes, which provides a niche for each node. To be 'funded' a node needs a niche.
Governments tax, and spending use their spending to guide the 'ship of state' (another gubernatorial concept)) If the ship of state expands to embrace everyone it need no longer be guided because it fills the whole of the available space. It has only to avoid error (injustice) which moves it away from equilibrium by decreasing its entropy (error = confusion = reduced resolution = reduced cardinality = reduced entropy).
Writing sometimes relaxes, sometimes stresses.
Relaxation between points. Gravitation is a smooth
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surface passing through (containing) all the points (events) in the Universe. Geosurveys and the calculator implementation of a differential equation . . . a radially weighted average of values interpolated by contouring a set of gravity meter readings corrected (barometrically) for altitude.
Every incident in m life has contributed to forming the person I am now, modelled by memory.
We model computers not by their changes of state but by the sequential states of memory. The changes of state of a Turing machine form a group a subgroup of the permutation group whose cardinal is the number of internal states of the machine (?)
. . .
Quantum mechanics: temporal average of traffic on various routes. Routes are different when the symbolic representation of one differ from that of another.
The nub of experimentation is the design of apparatus, a matrix (with certain eigenvalues) through which to look at the Universe, in other words a sensitive coordinate system.
Agatha Flood page 172: '[Frances Cloade] had the same appreciation of a good cook of a good parlourmaid as she would have
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had for a good pianist.' Christie
Modern society depends on the clock, the basic requirement for time division multiplexing and computation, in which each step is mapped to a particular time.
The speed of execution of the logic is of no concern to the logic as logic. It is a physical question. It may, of course, relate to the survival of the physical entity embodying the logic.
Communication there: where error is a possibility, delay is necessary to exclude the possibility. Error only becomes possible when we introduce meaning, so that some strings advance the overall process and some hinder it.
MEANING = ORDERED PROCESS = MECHANISM = MAPPING
I am a field of one (so far as I have seen) looking to attract others into the investigation.
Like a permutation, a vector contains just one of each letter of its alphabet, which in this case is the coefficient of a basis vector.,
Naturaltheology.net Yahoo Explore URL
Mathematics is the epitome of mechanism, mathematicians can do anything that a Turing machine (or network of Turing machines) can do.
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We connect two Turing machines by connecting the output of one to the input of the next.
What is curvature in network terms? In flat space velocity of transmission is constant, ie coding delay is constant. In curved space we have variable coding delay which is nevertheless always greater (slower processing) perhaps as a result of congestion or error in heavily trafficked networks. Slowing of heavily used networks creates a selective pressure to make them shorter.
