Notes
[Notebook NAKEDICAME, DB 53]
[Sunday 12 November 2000 - Saturday 18 November 2000]
[page 77]
Sunday 12 November 2000
Monday 13 November 2000
Thunderstorm, no compute. Working on revision of natural theology and it is going well.
[page 78]
The application of this model to the world begins in the section on Physics, but here we note a few correspondences. First, the natural numbers provide a model for counting and arithmetic that applies to all unique objects in the Universe, dollars, sheep, ticks of the clock etc etc.
Second, we notice that the changing world behaves very much like a permutational process, things are swapping positions all the time: a leaf falls and its place is taken by air.
We now turn toward animating the Cantor Universe here constructed.
ECONOMICS = SOCIAL PHYSIOLOGY
Tuesday 14 November 2000
[page 79]
Keynes 409 ". . . the next development in politico-economic evolution will emerge from new experiments directed toward determining the appropriate spheres of individual and government action." Harrod 409.
Here is where the new theological Lagrangian comes in, guiding the trajectories of human particles in the national space.
Communication is a force that deals with exceptions - we only communicate when some uncertainty arises due to changing circumstances etc. Between communications a body at rest remains at rest and a body in motion continues to move in a straight line. In QM communication means exchange of particles which is a gauge thing - since the world is full, one thing can only move if two things move - the little one said roll over.
Wednesday 15 November 2000
Thursday 16 November 2000
Religion works in the space of all possible configurations of the human mind just
[page 80]
as biology works in the space of all possible genomes. Let us call the space of religion M (we cannot use R because it already belongs to the set of real numbers).
The actual genomes of living animals each occupy a point in the space of all genomes G. Now the space of all genomes is very big but not infinite. If we take the human genome 3 gigabases. 4 bases so 4 Exp (3Gb).
PHYSICAL vs METAPHYSICAL PERMUTATION
PHYSICAL vs LOGICAL PERMUTATION
Viewed simply as a large object, G is not very interesting. But when we observe the distribution of real genomes in G, we begin to notice structure. This structure arises from the evolutionary relationships between genomes. This relationship arises in turn because genomes are not arbitrary strings of code, they have meaning. When executed in a competent
[page 81]
cell the genome controls the life of an organism and determines, as least to some degree, whether the organism will successfully reproduce (and so bring a similar genome into existence) or not.
M and G are spaces within U.
We postulate a general lust to reproduce that has its roots in Cantor Space and communication theory. The basic equation
a) an error free space may be more complex
b) a complex space may be more error free.
It has taken a long time to sort out the religion project, but now it is well on the way and things can begin to fall into place. What we may look forward to is a website a bit like the Summa, a lot of short articles = pages. Thomas has 3000. Here currently looking at 4 x 8 x 8 x 8 = 2048 or 84 = 642 = 4096 which allows room for 3000+
RCC is like cattle breeding, preventing
[page 82]
natural evolution to keep the genome in a space defined by human desire: Darwin and animal breeding. So the old religions are like farms, breeding people for the benefit of the organization rather than themselves.
POWER = VARIETY REDUCTION
Keynes: BRETTON WOODS
Genes create an organism with a large number of degrees of freedom which must learn how to navigate the space it is born into. One question is how long does one remember sensory inputs, decisions and outcomes? For the moment, or for a lifetime, ie is behaviour genetically determined or does it change over time along a 'learning curve'.
Communication and duality. The communication link between two spaces of dimension (digital measure) aleph(n+1) can have measure aleph(n). The encoding and decoding from aleph(n+1) to aleph(n) and from aleph(n) to aleph(n+1) establishes
[page 83]
an orthogonality between the two aleph(n+1)'s that are linked by this channel. This can be understood as what goes on between two state vectors when they communicate by "collapse". We understand this in function space, that is mapping space that is permutation space, that is meaning space. Meaning requires union which requires communication. To capture this we make function space = Cantor Universe happen with computers.
We have finished squinting the eyes to try to defocus onto the big picture and getting ready to begin filling in the detail of the space of recursive descent which has become clear to me.
Friday 17 November 2000
Perfect market = perfect communication. But in fact systems often do not say anything until they have been out of equilibrium for a certain time - friction, hysteresis, quantization etc all contribute to this, since communication itself
[page 84]
has a certain cost which will not be expended until the expected return exceeds the cost of communication ie until the cost of disequilibrium exceeds the cost of communication.
J M Keynes: The General Theory of Employment, Interest and Money. Keynes
5: wage = marginal product of labour
utility of wage (when a given volume of labour is employed) =
marginal disutility of that amount of employment.
Real wage (potential) forces actual amount of employment.
Sin-Itiro Tomonaga: The Story of Spin Tomonaga
9 spinning = not spherically symmetric.
Saturday 18 November 2000
What we set out to do in physics is to expand the physical particles from points to larger sets and show
[page 85]
how the laws of quantum mechanics look to a macroscopic observer looking at macroscopic systems. This is made possible by Cantor Symmetry,
So we want to export the complexity invariant elements of field theory beyond its physical basis to the whole spiritual Universe.
eg relativity + quantum theory -> antimatter.
1: In attempting to incorporate special relativity into QM it is necessary to invent spin ie action.
2. Spin is twice as effective at producing magnetic moment as orbital angular momentum.
So we come again to Lagrangian
classical L = KE - PE, ie energy of motion - potential energy.
Now we want to minimize L, ie maximize PE, minimize KE, ie keep energy in structure rather than
[page 86]
motion. [insofar as Lagrangian integrates over time, it is blind to time?]
[Diagram]
Aristotle thought the world was a form of matter or potentiality. The moderns see the world as forms of action, since only action is sensible. Form of action = boundary of action. But action puts bounds on itself because it is quantized and we may see energy as rate of action. Both PE and KE have the same dimensions, so PE + KE are both rates of action. What is the distinction? [depends on frame of reference?]
Conservation of energy KE + PE = const. So the conservation of energy says that the rate of action in an isolated
[page 87]
event is constant and the movement between KE and PE is controlled by the requirement that the Lagrangian be extremal (to handle whatever sign conventions we attach to energy).
So does negative energy correspond to negative action? Negative time?
What if the total energy of the Universe is 0? Maybe ℵ0 = 0 on the spiritual (Cantor) scale.
Let us generate physics from the conservation of action (angular momentum), energy and momentum. [angular = rotational = closed. Two entities with equal and opposite angular momentum give zero action!]
We see no absolute in size, but in action, and to get physics off to a good start we identify the quantum of action with the natural numbers [or perhaps the integers].
Prepare "On the Representation of the Word" for publication in Theological Studies.
[page 88]
Symmetries of the Lagrangian and Noether's theory:
space - momentum
time - energy
spin - action
Dodd 42: "In practice all these different invariances are ensured by requiring that the equations describing any system are covariant under the group of Lorentz transformations of special relativity. Dodd.
Continuous symmetries = proper Lorentz. Discrete symmetries.
PARTICLE <-> WAVE
DISCRETE <-> CONTINUOUS
C, P, T p. E, h
Here we come to a sticking point which has occurred to me for thirty+ years, since the sixties. It is a dimensional thing. The dimensions of action are energy.time, or momentum.distance. Now how do I calculate how much action is involved in an action like writing a word?
[page 89]
I move the pen through a certain trajectory. A path integral along this trajectory should yield an action. Now action and momentum are conserved in this process, ie there is a flow of p. E and I through the tip of this pen which leaves the desired line and is then dissipated on the rest of the world. Although all three are conserved, the relationship between them is complex, so one unit of angular momentum may be correlated with very different energies depending on the quantum numbers of the transition which the radiating electron has before and after its change of state.
What I have learnt out of all this is that I know bugger all. If there is one thing I've learnt in life it is that learning never taught me nothing (Mrs Yellowbeard)
[page 90]
[diagrams]
Any attempt at writing is an attempt to compress the world.
Many is the idea that feels gorgeous in the mind that will no go easily into words.
At the centre of religion, as with all
[page 91]
technology, lies TOLERANCE. How much tolerance can we allow? As much as does not compromise the operation of the system. In the diameter of a crankshaft it may be a fraction of a millimetre, in the voltage in a computer, it may be 20%. In more complex species it gets greater and greater through the combinatorial and exponential powers of information theory - ERROR CORRECTION.
I have become convinced that a major restriction on theology is
the use of natural language, and that serious progress requires us to
turn to mathematical models in theology. non-mechanical
constraint
SIMPLICITY
Every harder layer decodes and encodes (ie gives meaning to) the layer below it.
[page 92]
The central problem for physics and all the sciences that like to see their results written down is the contrast between the static nature of text and the dynamic nature of the Universe. One can only write an eternal text about those elements of the Universe that never change. So no matter when or where we work, F = ma, E = mc2 and H = k log n, and we have no reason to think that these equations will ever fail to be found in physics textbooks. Since we can look back billions of years, we can gain confident that these fragments of text have always mapped onto some real features of the Universe, in other words they mean something real, although the nuances of that meaning depend on one's wider view of reality.
The central fact of dynamics as a science is that if we want to write it down, we require a minimum of two symbols to describe a motion, a representation of before and a representation of after. Of what happens between the before
[page 93]
and the after we cannot say, except that we consider it to be a process that transforms the initial state into the final state.
This insight is at the heart of the mathematics of motion we call calculus. In the intuitive geometric picture, we picture the trajectory of a point through space to be a line. We may consider a line to be an ordered set of points which we name with numbers. The natural numbers 0, 1, 2, . . . may be used to name isolated points one unit apart. This is not enough, however, and we must name the points in between, for which we use the rational and real numbers.
Calculus used ordered sets of numbers to describe the for and after. The intuitive view of calculus is described in the illustration, which is a two dimensional slice of spacetime relating before and after in time to before and after in space. [Whereas we can really go in both directions in any spatial dimension, we can only go in one direction in time (following 'time's arrow')] Now I said above that we can describe the before and after in symbols and can take the motion as ineffable, but calculus
[page 94]
uses a limiting process of bringing the before and after together closer and closer to arrive at the relative rate of change over an infinitesimal interval. We can perform this mathematical limiting process in our imagination, and much research has gone into determining which relationships between variables (ie functions) are differentiable and which are not. In general physics has worked on the idea that a function that faithfully represents some physical process is by this fact continuous and differentiable because we assume the Universe is continuous (one) and differentiable.
But here we run up against the quantum idea that suggests that universal process is not infinitely analyzable, but there is in fact a limit to the fineness of the Universe, and at a certain level of resolution we discover that, if we take action as the quantity to be represented by a line (a line of action) that line is not continuous, but instead consists of discrete points each one quantum of action apart, and that inquiring what
[page 95]
goes on between the points has no reality that can be captured in writing. So a line of action comprises a series of discrete points just as does the integer number line. Whatever process leads from one integer to the next can not be expressed in integers any more than what goes on between points one quantum of action apart. It is strictly inexpressible. So the static structure of the Universe, that is the structure that can be expressed in writing, has a fundamental graininess. [like writing itself]
This is not to say that the Universe itself is not continuous, for quantum mechanics envisages a continuous process (represented by the wave function) that fills in the gaps between discrete observable events, but is not itself observable or recordable.
So we think that motion is a seamless continuum bounded by two discrete static points. The written description of
[page 96]
the Universe therefore has an inherent duality which is represented in mathematics by complex numbers. The wave function has two expressions psi and psi-bar. When we multiply them |psi| squared = psi.psi-bar, we get a static representation of the dynamic underlying event which we express as a probability, that is a real number that describes a discrete event (or an ensemble of discrete events).
On the next page we will go on to say more about the continuous world behind the discrete observables, thereby returning to the transfinite numbers described on page 2. [We may consider long durations as providing the continuity behind short durations]
