Notes
[Notebook: Transfinite field theory DB 56]
[Sunday 16 May 2004 - Saturday 22 May 2004]
Sunday 16 May 2004
[page 76]
Monday 17 May 2004
We seek to use scale invariance to carry the variational
[page 77]
method across from quantum field theory to society and the whole. How do we prune a fully connected network down to one which has powers of survival and reproduction? A fully connected network is bound to survive because it has maximum entropy and cannot go wrong. Every communication is good. It is only when it begins to break up into distinct local entities that what might be good for one is not good for another.
In a fully connected network, the probability of a link lij is independent of i and j. [all connections equally probably, a maximum entropy situation]. In a sparsely connected network, pij is a particular function of i and j.
War, Peace: Industry. Politics [is a] superposition of capitalism, socialism and democracy.
Tuesday 18 May 2004
DEMOCRACY = PARALLEL PROCESSING
Life is one: gossip, spin and truth.
transition = evolutionarily stable strategy = safe path. We have had adequate expression of violent revolution over the last few millennia. Now we seek a peaceful revolution. Violent revolutionaries 'smash the system' in the (apparently forlorn) hope that something better will grow in its place. For people with nothing left to lose this is a reasonable strategy.
On the hypothesis that any reasonable strategy will (sometimes) be implemented in a given set of circumstances, the reasonable strategy for eliminating violent revolution is to minimize the number of people with nothing left to lose. There are two ways to do this: murder and sharing. Historically,
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community organized murder has played and continues to play a considerable part in human affairs. It violates the principle of human symmetry, and therefore cannot be allowed. 'Human symmetry' is a mathematical restatement of the concept of human equality.
So we chose sharing as our route to peace.
Why all this work? We get sucked in by the possibility of added comfort and security. Individually perceived possibilities (like flying machines and this theology) attract us to seek realization. Much of the world today seeks comfort and security by 'violent' methods.
Wednesday 19 May 2004
The world is and remains a wilderness no matter what we do, although we can create peaceful entities within it given adequate sources of low entropy energy. The best description we have of wilderness is a stationary (minimal/maximal) Lagrangian. To understand this we need to see how the Lagrangian applies in quantum field theory and then see how quantum field theory fits the network to give an idea of how to compute the Lagrangian of a network. Finally, we can determine the properties of a network with a stationary Lagrangian, and then apply this, by Cantor symmetry, to human affairs.
Half work and half play for half pay.
Fermion is the field of a boson, structuring the energy spectrum of the bosons. Boson is the field for fermion, carrying the messages
[page 79]
that move the fermions around.
All comes down to symmetric and anti-symmetric wave functions for identical particles.
In a dynamic morality, we live the differential We know we are going in the right direction if things are getting better, and in the wrong direction when they are getting worse. When things are staying the same, direction become meaningless and we are in the realm of eternity ('the same' may be bad or good). What is good. It is when children are well fed and happy, social relationships are easy and income exceeds outgoings.
MATTER ENERGY INFORMATION
Quantum mechanics tells us how information is encoded and transmitted in a system constrained by conservation of momentum, energy and action.
RELATIVISTIC INVARIANCE - true for all observers near and far, fast and slow. It is a symmetry related to the speed of communication. This can easily be applied to a network, each link being assigned a characteristic delay (which is encoded in 4-space as the result of dividing distance by velocity 500 miles at 10, mph = 50 hours. The recipient of this information sees the distant situation as it was some time in its past. So each of us sees the other as the other was in the past and this delay may be taken as a metric on the space of human interaction.
Physics describes the hardware of information transmission. This gives us a sharp boundary between physics and metaphysics, but it also shows that while physics does not contain metaphysics, metaphysics does contain physics. So we can exploit symmetries between physics and
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information processing.
We'll figure it all out as we go. Hoping that a consistent master plan will lead to consistent details. The evil to avoid is double booking, because then we will become overworked trying to meet all our obligations.
So we invert the story : physics is the conserved part of information theory. To a first order, the computer stays the same as the information flows by, changing states within a stable shell. The stable shell is the alphabet. The process is the permutation and combination of the alphabet subject to the selective pressure induced by the boundedness of the alphabet, which imposes a set limit to growth, so that in the finite domain 2n < 3n < . . . nn.
The exciting thing is how broadly we have to think to even look like capturing the breadth of the Universe, and, in particular, to realize that the human individual system is open ended in its conceptions. By networking with one another, we transcend a transfinite discontinuity.
In order to prevent confusion, we maximize the distance between the code sequences in the space of possible code sequences.
Coding theory naturally works in n dimensional space, where n is the length of the code word [this is analogous to transcribing the natural line into a transfinite dimensional Euclidian space] We can define both a geometric and a Hamming distance between these code words, and calculate how much error we can handle before the words get confused.
The Universe operate sin a code space of ℵ0 dimensions, using ℵ0 distinct words from the ℵ1 permutations of the ℵ0 dimensions (non-commutative multiplication).
Some idea seem too weird to write down. One that has been in the back of my mind for a long time is
[page 81]
is that every action, no matter how complex, is represented by just one quantum of action (the master plan for that action, in effect) and all the other actions involved(in say the evolution of a galaxy or planet, the life of a person etc) are associated with different (partial) contributions to the action in question. This is naming taken to the extreme, since a quantum of action is 10-34 J sec and event like the sun 10 billion years x 4 E 26 Watts, = 1044 J sec = huge. But they may be something in it, since in the spiritual world we can encompass the whole life of the sun in four little words. This is meaning in practice. Every meaning can be associated with a quantum event. Any part of the Universe down to the smallest can represent the whole Universe, so that the whole Universe may be involved in as many meanings as there are particles (actions) in it.
This seems hard to comprehend, but maybe makes sense when we model meaning with transfinite recursion.
Fundamentalist constraints increase the temperature and pressure of society, and hence the possibility of inelastic collisions (ie collisions which change the cardinal number (entropy) of the system?) ie bits stick together, kill each other, have babies etc.
NEED, DESIRE A given definition of humanity constrains the definition of human needs and permissible desires.
The dynamic which we must understand is between aleph(n) and aleph(n+-1). This is the fundamental transition of the Hilbert oscillator, and the interface between individual and community.,
Pornography: a physical representation of a metaphysical state.
Under the conditions of the reversible heat engine, entropy is conserved and zero energy entropy extracted from the hot reservoir. These conditions are fulfilled by the Universe: unitarity implies (?) that entropy is conserved. The expansion of the Universe and the consequent drop in temperature means that the past is on average hotter than the future, so that work can be done between the past hot reservoir and the future cold reservoir. This work, we might think, is countable isomorphic to communication, the trade in entropy within overall constancy.
EXPANSION --> WORK --> STRUCTURE
--> ORDERING --> ENTROPY
The transfinite transformation shares some features of exponential and logarithmic transformations.
To me the most intuitively satisfying way to think of the Universe is in terms of plumbing or wiring, or traffic (communication) systems of any sort. Many different pipes and many different things flowing through them. In the abstract world of physics, we can invoke a number of different plumbing systems, carrying probability(entropy) energy, momentum and action.
Thursday 20 May 2004
Friday 21 May 2004
Saturday 22 May 2004
Justice too can be modelled as a flow and corruption as a leakage (error) in the flow.
The states in a superposition are points in a probability space. Each state has a certain probability, and the sum of all the state probabilities is normalized to 1. ie a measurement will yield exactly one state.
Physics studies the properties of conserved flows under different conditions. Metaphysics deals with non-conserved flow, ie the processes in the source that create the
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flowing fluid and the sinks where it disappears. By conservation we mean that the algebraic sum of the sources and sinks is zero (constant), so that we can map them all 'back to back' so that creation on one side is equivalent to annihilation on the other, in other words in physics me might say that existence is conserved.
This abstract physical position underlies the metaphysical detail that leads the physical system of our Universe to create entities like us and our solar system. Here we have the interplay of two forces known without history as order and chaos. In Genesis God did not create the world out of nothing (a view popular later) but out of [formless void]: 'the world was formless and void (Gn I:2).
Frank L Lambert: The second law of thermodynamics is time's arrow, but chemical [and physical] kinetic is time's clock. Frank L Lambert.
Politics: We are absorbed in applying the spectrum generated by the transfinite oscillator to human affairs. One level of complexity we have to deal with is the politics of community. The political spectrum is traditionally spread between left (lets all work together) and right (its every entity for itself). Reality is obviously a superposition of both these positions. We may regard the left as the integrating and complexifying force, moving the system toward a jump to the next level of complexity. This corresponds to a creation operator. The right, atomizing tendency, tends toward the next smallest level of complexity and corresponds to the annihilation operator. This struggle between power and cunning is the fundamental driving force of the Universe. We see it in evolution. The Lagrangian of a system is stationary when it reaches an optimum balance of power and meaning (existence and essence, energy
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intelligence. etc). It is our superior cunning which has brought us superior energy, which has led to our very rapid growth in the last few centuries.
Peer operations take place at constant entropy. Creation operators increase complexity and annihilation operators decrease it.
As Cantor modelled the path to higher transfinite numbers by ordering. From an ordered set we can create a large number of permutations. This ordering may be compared to differentiation, which takes into account the order of the points on a line to compute the local derivative. The opposite of differentiation, where we effectively ignore the order of the points and simply add them all up. Integration, annihilation and knowledge all decrease complexity and their opposites do the opposite. Differentiation, a la Cantor, reveals the hidden transfinite structure of the natural line.
Links
| Frank L Lambert Why Don't Things Go Wrong More Often? Activation Energies: Maxwell's Angels, Obstacles to Murphy's Law 2834 Lewis Dr., La Verne, CA 91750 'Students often invoke Murphy's Law when inanimate "things go wrong", when skis break or fires occur or instruments fail due to corrosion or tires unexpectedly wear out. But why don't similar upsetting events happen to everyone every minute? Unwanted combustion and corrosion of common materials, although energetically favored, are not kinetically instantaneous. (The second law of thermodynamics is time's arrow but chemical kinetics is time's clock.) Chemistry students learn that chemical changes are usually obstructed by activation energy barriers whose origins lie in the energy required for bond breaking as new bonds are formed. Thus, activation energies act as obstacles to Murphy's Law in being deterrents to undesirable reactions and, lightly, as our "Maxwell's Angels". The fracture of solids - whether surfboards or car fenders - also involves breaking chemical bonds. However, such incidents are classed as physical changes because the free energy of the fragments is not notably different from the unbroken whole. The micro-complexity of fracturing utilitarian or beautiful objects prevents assigning a characteristic activation energy even to chemically identical artifacts. Nevertheless, a qualitative EACT SOLID (actiovation energy of the sold?) can be developed. Its surmounting is correlated with the radical drop in human valuation of an object when it is broken.' back |
