Notes
[Notebook: DB 57 Language DB 57]
[Sunday 21 November 2004 - Saturday 27 November 2004]
[page 33]
Sunday 21 November 2004
Trading in a market to build a personal capital, vs collecting a number of personal capitals into a shared (cooperative) exercise.
Relativity of transfinity / machine infinity. We describe the set of natural numbers by saying that we can find any natural number we choose in it.
[page 34]
A 'machine infinity' puts a (physical) bound on this choice and allows us to model the physical constraints on the representation of numbers.
The natural numbers are an ordered set of distinct identities. Ordered means that if we choose any two elements of an ordered set we can see by looking at them how they fit into the order, ie which comes before (or after) which. An ordered set, to make sense, must contain at least two distinct elements (symbols, letters, entities)
Sets are not necessarily ordered? - consider a set of identical particles distinguished only by their spacetime-coordinates. These coordinates are ordered, so we may impose an ordering on these particles using an algorithm which reduces one set of spacetime coordinates to a number which can be compared to the number corresponding to another of the coordinates, and the sets then ordered by the order of these numbers. Such an algorithm may be degenerate, reducing many orderings to the same number so that they are all peers, that is, enjoy the same rank. The structure of the transfinite network and its need to communicate through physical channels introduces a high degree of degeneracy which cannot be broken by physical observation. The only way to break this degeneracy is to model the transfinite space lying 'behind' finite (ie local) space. We relate the local to the global by differentiation and integration, so we can imagine these operations taking us up and down the transfinite scale.
[page 35]
The smallest 'machine infinity' is probably 1, the machine whose only working part is 0 < 1. A machine whose infinity is two allows us two symbols, 0 < 1 and 1 < 2, ie 0 and 1. By juxtaposing such machines in a ordered sequence, we can represent numbers of unlimited size by countable strings of binary digits, given that 2 aleph((0) = ℵ1. At the other end of the scale of complexity, but equal in transfinite arithmetic whose machine infinity is greater than ℵ0 ie aleph (1). For such a machine we can write ℵ0ℵ0 = ℵ1 so we have the peculiarly degenerate transfinite arithmetic statement 2 ℵ0 = ℵ0 ℵ0 = ℵ1 and generally 2 aleph(n) = aleph(n) aleph(n) = aleph(n+1).
This vagueness captures the symmetry that when we find a property of the infinite set aleph(n), we can find that property in each of the lesser finite sets, n.
When two entities touch (are bound) they in some way become one entity. The abstract model for this unity is communication which correlates (identifies) certain aspects of each entity.
Information, entropy and coding.
CODE = FUNCTION
lossless/lossy 'compression' = coding.
Monday 22 November 2004
Back to 'Lonergan's metaphysics and quantum theory'
[page 36]
Tuesday 23 November 2004
Back to site work, as a systematic way to clear my head and progress toward writing of the isomorphism between Lonergan's metaphysics and quantum theory.
Note the distinction in the share market between 'real' and 'paper' profits and losses, similar to real and virtual reality. Virtual reality exists through meaning where there is more to a physical structure than meets the idea [eye?]. So this is not just ink on paper, but a sentence that means something to someone that speaks the language.
TRUTH = ADAEQUATIO = CORRESPONDENCE
If it is to have a non-trivial meaning, it must be other than strict identity. I am true because I am the same as myself is the same as saying god is true because he is identical to himself.
Truth exists when two distinct parts of the Universe are correlated with one another, like the kitchen in front of me and the image on my retina. The lens of my eye is in some was
[page 37]
truth preserving.
Le Carre Honourable Schoolboy page 327: 'we're fighting for the survival of Reasonable Man. le Carre
Le Carre page 489: 'He's mention that to George one day, if they ever, over a glass, should get back to that sticky little matter of just why we climb the mountain. He's make a point there - nothing aggressive, not rocking the boat you understand sport - about the selfless and devoted way in which we sacrifice other people, such as Luke and Frost and Lizzie. George would have a perfectly good answer, of course. Reasonable. Measured. Apologetic. George saw the bigger picture. Understood the imperatives. Of course he did. He was an owl.'
'One of them, Caiaphas, the high priest for that year, said, "You don't seem to have grasped the situation at all; you fail to see that it is better for one man to die for the people, than for the whole nation to be destroyed. He did not speak in his own person, it was as high priest that he made this prophecy that Jesus was to die for the nation - and not for that nation only, but to gather together in unity the scattered children of God. John ? 49-52.
ENDGAME
He needed to move in order to find direction 503.
Life is cheap for Xians (and Muslims) because they do not really die and death, pain and suffering are good because they lead to a better paradise.
[page 38]
le Carre page 521: 'Nobody wants a deal, they want a commodity. The deal obtains for them the commodity. What do you want?
Why do we wish to present religion as an industry? Because we wish to exist within the law, not above it.
Within the law = within the informed consensus of the people. By informed we mean that there has been enough public discussion to lead to a general agreement on the course to be taken. Religions are inclined to believe that they are above that sort of thing, but they are not. If we are to have peace, everybody must live within the consensus. Achieving consensus is not easy. It is easier, however, in the world of physics and biology than in the worlds of love, religion and politics. This is because in the world of physics and biology we can discern relatively clear optima (ie the best way to handle x) and work toward them. So the second law of thermodynamics gives a target for the design of heat engines.
Here we seek guidance in the more complex matters of love, religion and politics. All these things imply economics, because we live in a dynamic material world. Economics, in its turn, is constrained by environment, finance, technology and so on. It is from our relatively deterministic connection to the physical world that we feel our way into the spiritual world. Because all information must be represented physically to be communicated. Landauer
Technology extends our power to converse with the environment.
Capitalizer vs consumer
Wednesday 24 November 2004
Thursday 25 November 2004
Friday 26 November 2004
Deceit is only possible in systems complex enough to keep copies of the messages they send, in other words they can communicate without changing their own state, unlike an atom which changes its internal state when it communicates.
ORDERS CORRELATE : CHARGE!
The future of the system depends on how perceptive its auditors are. If the auditors fail to detect scams, things will go from bad to worse. If the auditors do fail, this is either because they are incompetent or complicit.
We can see many of the features of life as iterative processes rather like infinite series, where we go around and around a similar path every day but gradually come closer to a particular point, like finishing the house, getting to know a friend or even breaking off a relationship. At its simplest, a series is an ordered series of natural numbers indexed by themselves. Such a series is inherently divergent. If the elements of the series are integers, we may allow positive and negative integers of any absolute value whose sum may, nevertheless fluctuate around zero or some other small number and so not be divergent. Once we admit real numbers to our series, we can define and relate convergence of the sum and convergence of the terms towards zero. Much mathematics and practical value revolves around the transition from rational to real numbers. This transition is just the first in a series predicted by Cantor's Theorem however, and so the terms of a series may be numbers from the transfinite domain, ordered structures quite complex enough to represent entities such as ourselves as we move through our lives (or as our lives go past us - relatively indistinguishable = degenerate.
The whole plan is to identify the necessary and sufficient conditions for a peaceful, prudent, dynamic, safe and exciting society.
Committed to a course of action. At present the United Nations is in a power game with the disunited nations. The only way to resolve this game is to develop a new algorithm (protocol) for interaction which mirrors at a certain level of complexity, the global process. We see this process as forms competing for realization, that is for matter. I am represented by 85 kg of atoms. We need not heed all this detail, however, if we seek to understand the world through its symmetries, those things that state the same as we move through time and space. Spacetime.
We can abstract nationhood down to head of statehood and say that there would be peace between nations of there were peace between
[page 41]
heads of state. This is an example of the more general principle of invariance with respect to complexity. The form 'head of state' is an abstract version of the form 'state" or national community or whatever we want to call it. Features of statehood. Napoleoni page 65
We can allow for any amount of complexity in the states of mind of individuals in a community as long as they can all be traced back to the same root; in our case the physical world. So, to a first approximation, everything that us physically possible is possible in an open community. But does possible = desirable?
We see (in quantum states for instance) that different possibilities have different probabilities. Quantum mechanics is the formalism that attempts to compute the probabilities of the various possibilities. In the realm of measurement, quantum mechanical quantities can be computed and measured to ten or more 'significant figures' that is to one part ion ten billion or less.
You are not my real girl, you are my dream girl. It is easy to get them mixed up sometimes, but not if you can map romance into quantum mechanics. QM tells us that a certain formal set of 'wave functions' seem to govern the behaviour of the Universe. The mathematical machinery of quantum mechanics has been constructed in Hilbert space, [a sort of dream space].
Peace is only possible when there is one channel that unites us all. That channel is the physical (chemical, biological) channel by which we are represented in this world. What we do must be real. We do not offer our child bread and give
[page 42]
him a stone.
TRUTH is a feature of abstraction, A true idea is a true abstraction, ie a true compression of the process we mean it to represent.
G J Leigh page 94: 'The concept of gas is probably due to von Helmont of the famous tree experiment. Leigh
Gas is a symmetry. There are many distinct gases with the common property "I am a gas".
By 'true' abstractions, we can bring all people to the table as a united people, a prerequisite, it seems, for united nations.
Processing power = complexity of unit operation x rate of unit operation.
Unit operations occur at all scales, eg absorption of a photon, making a baby, formation of a galaxy, etc.
The Universe is (at least near energy sources like the sun) an exciting place. [Life] never stops, babies, weddings, fights, crashes etc etc. Despite the small population, things are always simmering along with occasional rarer and more extreme events.
