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Notes

[Notebook: DB 57 Language]

[Sunday 24 April 2005 - Saturday 30 April 2005]

[page 118A]

Sunday 24 April 2005

We distinguish (Sprott) a logical set from a system. A set is simply a collection of items [ any collection into a whole M of definite and separate objects m  of our intuition or our thought. Cantor, 85], whereas in a system the items communicate with one another and cooperate toward some purpose ['set' contains 'system']. In biological system the fundamental purpose is maintenance of the system, that is continue to live, more succinctly, not die. Not dying is the lowest standard of living. Higher standards arise from more productive ways of structuring an operating the social system, ie better

[page 118B]

government. To govern is to control, and control depends upon the principle of requisite variety. F Heylighen and C Joslyn In order to have sufficient variety to control a human group, the government must either increase its own variety or repress the variety of their subjects. Often both strategies are used. In order to minimize repression, the variety of the government must be maximized. The maximum variety available to govern a population is the population itself, the ideal of democracy. At the other end of the scale is absolute monarchy, where the variety of the whole system is depressed to the variety of the monarch.

VARIETY = ENTROPY = INFORMATION.

Monday 25 April 2005

Diamond Collapse page 110: 'That the size of the statues has been increasing may reflect not only rival chiefs rival chiefs vying to outdo each other, but also more urgent appeals to ancestors necessitated by the growing environmental crisis. Diamond

The 'two year old' phase of development: very efficient at demanding input; not too god at acquiring it for oneself.

Tuesday 26 April 2005

The essence of the Christian good news us that our world was created by an almighty and benevolent power for our benefit. There has been

[page 119]

a hiccup, known in English speaking Christian tradition as the Fall. This turned out to be a happy fault, however, because god became human and walked among us and by allowing himself to be tortured to death by the Romans, put n place a correction to the Fall which will become manifest (apocalyptic) at the end of this world (as we know it). The story and the promise it hold of eternal; bliss and the conquest of death, has entrained billions of believers.

What is the good news in a scientific Theology? In a nutshell, it is that complexity makes stability possible. This needs some explication, which is the subject of the rest of this article.

1. The role of language (including mathematics)
2. Physics --> mathematics --> quantum mechanics
3. quantum mechanics -- > network
4. Network --> God (= whole)

The world of mathematics is the world of numbers, by which we mean discrete ordered symbols. This may be considered to be a world of messages, each possible message being represented by a certain ordered set of discrete symbols. Although there are many "s"'s in the previous sentence, each, because of the way it is embedded n the sentence (and the sentence in the world) is as distinct

[page 120]

symbol. The space of such symbols is known as the Cantor universe, or more poetically, Cantor's paradise.

We start to construct the paradise with the natural numbers 1, 2, 3, ... n, ... . Each of them is in the abstract a discrete symbol which may be represented concretely by some numeral, which may be something written like 1479 or a mob of sheep, or an arrangement of electrons in a computer.

Cantor made a clear connection between numbers and sets.

We are being practical model builders rather than mathematicians, and so we repeat Cantor's straightforward 'naive' description of sets to begin with and turn to the axiomatic approach, confident in the notion that these two formulations coincide almost everywhere.

Let us propose that religion underpins human cooperation where genetic forces leave off. In other words, it carries the structures found in sociobiology beyond the kin group to the wider tribe, city, nation, confederation of nations and so on. Given this assumption, we start building our religious castle in the air and then use ideas from physics and biology to give it a foundation on the earth.

Wednesday 27 April 2005

'Greenland was a hierarchical society, with great differences of wealth justified by the Church, and with disproportionate investment in Churches. Again we moderns have to wonder

[page 121]

if the Greenlanders would not have been better off had they imported fewer bronze bells and more iron with which to make tools, weapons to defend themselves against the Inuit, or good to trade with the Inuit in time of stress. But we ask our question with the gift of hindsight and without regard to the cultural heritage that led the Greenlanders to make their choices. Diamond, Collapse page 245.

The motivation to write (at least for long periods) is often hard to come by. Digging holes or working on the care seem more attractive, or any of all the other jobs for different people that are waiting to be done. But writing is a construction job too, and like all construction jobs, we are trying to make an efficient (and possibly beautiful) product. All the steps toward such a product are error prone, so that efficient production requires adequate error correcting mechanisms to achieve the desired product. We encounter a similar situation in quantum computing (Knill) where we find that increasing numbers of error per gate requires an increasing amount of error correcting overhead in the form of extra gates.

The network theory gives s a way to construct a general 'error model' that applies to societies in their environment as well as to computers, quantum and conventional.

As the overhead goes up, so, with given resources, only smaller problems can be tackled. In social error models much emphasis may be placed on corruption, the leaking of value from acceptable (legal) channels.

[page 122]

A viable society (computer) is partitioned from the non-viable by a threshold theorem: 'if the EPG is smaller than a threshold, then scalable computing is possible.

We cannot say if the universe is open or closed, and, in principle, we cannot find out because we cannot look outside. This is because the universe is not a set.

CLOSURE: (Kreyszig) 'A subset M of a metric space X is said to be open if it contains a ball about each of its points. A subset K of X is said to be closed if its complement (in X) is open, that is K^C = X - K is open.'

OPEN SYSTEM = element of a network. Insofar as the universe (by definition) communicates with nothing outside itself (because there is nothing outside itself) it can be said to be a CLOSED SYSTEM. A dynamic understanding of Cantor's theorem, however, might lead to the proposition that every closed system, by mapping onto (communicating with) itself can behave like an open system and grow in an unbounded way.

Thursday 28 April 2005

Lost it again. I stand in the midst of a flowing noetic landscape populated with fragments of order, connections which I try to capture in words. But I have to be quick. It flits past, I see it briefly, but there are visitors, and by the time they have gone I have forgotten. Things seem to come back, however, and sometimes they can be tracked down (like dreams) by writing out impressions, like this, and trying to see connections: The discussion was about the levelling of class, moving from a spectrum between monarchs and slaves to a situation where we are all peers on the human network.

Christianity used to explain life for me and show how everything fitted into its place, but now I can see it is fundamentally a load of bullshit, but it succeeds because it unites people in a common (if fictitious) communication protocol, ie a set of unquestioned invariants through which all

[page 124]

communications flow. In a digital system, such a protocol would be the range of voltages/currents/whatevers that meant yes (1) and the range that meant 0 (no).

My ideal would be a global set of protocols which are not fictitious in the sense that even though they are fictitious, they fit reality much more closely than the Christian protocol, which is centrist rather than distributed.

Do these words mane any sense to you?

The network model. Each node is an onion whose inmost core is the physical link, expanding out through layers to the user level. [or vice versa, the outermost level the the physical link and the user nestles at the core.

FREE == USER (CLIENT)
BOUND == SLAVE (HOST)

PEER = EQUALITY (neither user nor slave

peer = equivalent (CARDINAL, CANTOR)

The set of peers is the permutation group of all ordered sets of the cardinal number peer(n) The law of requisite variety say that deterministic communication is possible within a peer cardinal, but that most communications are indeterminate (?).

Electrons are peers. What is their cardinal number? Ordinal numbers spin up, spin down (in whatever basis)

[page 125]

Friday 29 April 2005

The Xian model, by making the universe created makes it also finite, this separating it form the infinite God. Quantum mechanics gives us a model for the interaction of a deterministic continuum {'wave equation'] with a random quantized output.

Saturday 30 April 2005

Both sides are somewhat to blame in the theology/science saga. On the one hand we have the conservatism (momentum) of huge and ancient institutions like the Roman Catholic Church. On the other hand we have the revolutionaries who started up outside the institutions and eventually became institutionalized themselves, in institutionalized opposition to their historical parents. Here in institutionalized opposition, we have a potential tragedy in human affairs whose most blatant manifestation is war, but which exists at all scales in human society where options are arbitrarily fixed. Tension is released by motion, so we should expect more fluid systems to be less tense than more solid. So the Roman Catholic Church rejects a scientific foundation (ancilla to the Biblical/Patristic foundation is as far as we'll take it) and the academic views ranging from 'opium of the people' to 'obsolete anachronism' give no welcome to theology.

Scientific progress is constrained by models and data. Where we have no model we cannot go, ie imagination is the front line of science. From imagined models we can devise methods for testing. Of course, imagination

[page 126]

is not constrained to science. It is the core of the cybernetic model of survival, look, process (ie think, imagine, calculate), act. If you succeed good, if not try again with new models or more precise execution of the old model.

Mind control.

Let us propose that some transfinite peer group in the transfinite network is of the same power as human mind space. That is, insofar as human mindspace is represented by discrete symbols (messages) there is sufficient variety in the chose peer group to establish a cone-to-one correspondence between elements of real mindspace and elements of the model. The nodes in mindspace are human minds. We take a mind to be the total experience of a human individual. Each mind is embedded in a deep network extending to the physical layer (hardware) and individual minds are able to communicate through the physical layer by communicating through the various organs of information transmission and reception ranging from reproductive signals to music and metaphysics.

Let uncontrolled mindspace be a mindspace where every possible mental state is allowed. Such a situation can exist in reality as long as the mindspace in question (one or more individuals) can maintain physical integrity. In other words does the fact of communication constitute a system comprising a set of peers without regard to the 'meaning' of the communication. Can we gain insight into this question via quantum mechanics

[page 127]

and quantum field theory. Transfinite network provides a route to giving clear meaning to the terms subjective and objective. More subjective = more concrete and more specific. More objective more abstract and general.

Insofar as the task of religion is to integrate a community of people, it must be able to control the behaviour of elements of the community to avoid divisive behaviour and promote integrating behaviour. In a network, the basic divisive behaviour to either not to communicate or to communicate error, ie do something that a trustworthy node would not do.

Tragedy of the commons - overcome by control. Diamond page 429. Diamond

Maximum control is optimal bandwidth sharing between individuals.

'All information is represented physically' puts physical limitation on the bandwidth available for sharing and so makes sharing necessary to maximize complexity.

Newton: Absolute 4D [3+1 D] space
Einstein special relativity: 4D with delay
Einstein general: 4D space with delay and energy-momentum conservation
quantum: normed infinite dimensional - -> normed transfinite dimensional.

[page 128]

transfinite network: unbounded with aleph(0) bandwidth.

For stability, ruling class must live the same life as everybody else (or in fact be 'everybody else'

RELIGIONS; down on sensuality. Not does. Or a mixtures, not-does for us, does for them, since they must suffer to keep us in our world of pleasure.

A modern religion must undertake a serious study both of ideal states and of routes to get to them, and also of the failure modes of such states. This means in a way finding the least complex basis for the elements of a complex society.

BANDWIDTH

Different layers of a transfinite network may use different embodiments in the chain to the physical layer.

'Performance anxiety' is related to the perceived probability of error (what are my chances of getting killed, embarrassed, if I try this?). As we become more familiar with actions through repetition our anxiety decreases as we become more certain of success.

Anxiety, tension, peace etc are all points on a scale of error probability, damage caused, etc. We like to stay down near the zero end of the spectrum, the end where all goes well. Small accidents like burning the soup or losing your glasses prompt more care, when dealing with our environment, while doing minimum harm, and serve

[page 129]

as paradigms for worse things which could happen like a fatal fire in the kitchen (a possibility which should as far as possible by excluded by design, so as to make fatal human error less probable.

Probability arises because a countable set does not have the bandwidth to fully represent an a countable set. The countable set can only provide snapshots, which are analogous to the symbols in a message.

Quantum mechanics is notorious for its counterintuitivity (at least to those who encounter it in later life). We cannot imagine it in three dimensional space, even with the help of Brandt, in the way that we can see and feel the motions of Newton's planets. But we can make it intuitive if we see it not as the three dimensional space, but as a network analogous to all the other networks we experience in life. Brandt

The ability to visualize a system gives us the power to play with it. A set i easily visualized, since it is a distinct object that can be put into correspondence with other objects. So this pen is an easily grasped example of a set. Set theory also enables is to visualize a communication network of sets swapping elements with one another. This is analogous to a group of people swapping images and ideas (that is states) with one another. Any state can be represented by some transfinite ordinal number.

[page 130]

We can easily imagine the interaction of the cosmic community of atoms by exchanging photons between one another

We can imagine the world of quantum mechanics as a network communicating by the exchange of particles. The exchange particles are in principle observable even though the changes of state within the sources and sinks are not, and must be deduced from the exchanged particles. We must imagine each of these exchanged particles as a message, physically realized.

We proceed by analogy with technological communication networks to recognize a layered structure in each node of the network which runs from the physical layer at the bottom to the user layer at the top. Tanenbaum.

We have identified four distinct network protocols in the physical layer of the universe, gravitational, electromagnetic, strong and weak, each involving the exchange of different sets of particles.

Now the deepest mystery of quantum mechanics after the uncertainty principle is the so called '

collapse of the wavefunction'. Before a hydrogen atom radiates, we model its internal state as a weighed superposition of some infinity of 'basis states'. From this infinity it chooses two, and radiates a photon corresponding to the difference in their energies. The atom has a spectrum of transitions that occur with different probabilities under different conditions (preparations).

[page 131]

Let us anthropomorphize the situation and consider me sitting here writing this. My mind is a superposition of an infinity of states, some of which in some way correspond to what I am writing here. You cannot observe the state of my mind (any more than you can observe the internal state of an atom ) but you can observe (read) this writing and by processing t through the states of your mind that correspond to our common language, acquire a mental state that corresponds to my mental state.

Historically, quantum mechanics has given special attention to the observer with physicists in mind. But on the ground that we occupy no special place in this universe we can see our observations of the world as subset of all the observations of elements of the world with one another, each observation being the process of communicating a message.

The network model of quantum mechanics also explains the strange interpretation of the calculations of quantum mechanics discovered by Max Born |phi| ² = probability of event.

This paper Can theology be a science is a PhD thesis for me, in other words (I hope) it gains me entry into the academic world so that these ideas may be supported and grow.

As in those sweatshops where the employees are forbidden to talk to one another, the designers of quantum computers wish to prevent the physical implementations of their qubits having unauthorized conversation with the environment.

[page 132]

MOSSBAUER

As the environment changes, systems get taken into spaces beyond their dynamic range and so potentially dangerous random elements enter which may create events beyond the system's error correcting or response range and it dies.

'As a result of such experiences ... ' (?)

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