Notes
[Notebook: Transfinite field theory DB 56]
[Sunday 4 April 2004 - Saturday 10 April 2004]
Sunday 4 April 2004
[page 61]
Monday 5 April 2004
A function from R to N is necessarily periodic since card(R) > card(N).
Most historical religions seem to have taken the view that we need to control and constrain nature in order to survive. But consider the birds of the air, who carry on their busy and energetic lives with no preachers or monks urging them on. Of course, we say that it is our advanced levels of culture, technology, civilization etc that makes all this controlled action necessary. One might think, though, that complex social organization, technology, etc would make life easier and freer rather than more contracted and more difficult. Is this inevitable, or is it a model dependent feature of human life. If it is the latter, then we may be able to approach the theoretical optimum much more closely. So we need a theorem like Shannon's, which establishes the limits of possibility and then some creative development to devise paths from the present system to one which is constrained only by physical and logical limits.
You can take my job and share it. This is the fundamental question. Religion tells us how to work for heaven. Some religions of the past have placed heaven in another life and have accepted that [this] life is a pain to be endured nobly. We do not feel that that is the whole story. A modern effective religion should be able to deliver meaningful; and effective algorithms for executing the tasks of survival on a painless and even pleasurable manner, so that we are inclined to sing rather than grumble at work.
[page 62]
We do not make a sharp dichotomy between capital and current spending, but instead recognize a spectrum of durability from the momentary to the eternal. We tend to make expenditure more efficient if we increase its durability in terms of the number of operations it can achieve before decay, what we might call technological Q. From a quantum mechanical perspective, the Q of the Universe is infinite, something which perhaps proves that the full unitary system is full. Observables have the same cardinality as the natural numbers.
So pure capital ==> Q = infinity, and this is like eternal (divine) text.
Perhaps we can postulate that the simplest way for two entities to communicate is directly. Then second order etc effects come in when other entities become involved in the communication (gossip) muddying the waters. We can counteract this effect by demanding that the information we work on is first hand, or at least trustworthy for other reasons.
3 legs: democracy, socialism and capitalism, seen operating in the TN.
A change at one point in the Universe propagates as changes in other points. Because propagation takes time, each effect has its cause, and this in turn gives us special relativity.
For capitalization (and stable corruption) production (of wealth in all forms) must exceed consumption, ie construction must exceed destruction. But how do we measure these? Economics is isomorphic to physics in that it relies on the unitary measure money where physics relies on energy. Both money and energy are measures of value, but, in the more complex world of politics
[page 63]
religion, etc, there are other measures of value. [it is the market that measures these values against money]
energy and motivation : convert potential to actual, ie work to make ideas (dreams?) come true, like getting and keeping a good job.
The struggle always is to get real, that is to perform effective actions in every domain from bodily function to political preferment.
A treatise on the powers of memory, communication and creation, expressed as a memory.
Quantum computation tells us that every time a third party (noise or worse) gets onto the line communication between the two parties is reduced, and they are able to become aware of it.
We do not expect to make money from intellectual property 'per se' (as they say) but rather from the physical embodiment of such intellectual property in a text, patent or thing like a trade mark or a well governed community,
Mathematically, creation comers from the exponential power of union.
The transfinite network is the space of all possible complexity arising from permutations of permutations of . . . sets of cardinal ℵ0. This huge system is cut down to size by the requirement of unitarity. In other words, no matter what transfinite permutations of the natural numbers are possible they are constrained to having to express themselves through the natural channel which we identify with observable reality.
Our make is the Universe, and our making is not all that mysterious if we consider in detail the
[page 64]
long process by which we came to be, 13.x billion years by last count (Wilkinson Microwave Explorer? C L Bennett et al.
We may divide the events of the world according as the love that drives them is unconstrained, or must jump a series of hurdles before consummation.
Temptation (droop) may confirm us in our certainties, as the error in a system points it back toward the preset standard.
The fundamental Christian error: we know better than our maker. It is also a significant comment on human nature that many people can make a living by mating (or appearing to mate) in public. The pornography industry is, at bottom, an expression of the Christian error, a version of the Platonic error, that information exists independently of its physical expression.
Can we say that a properly organized crime, especially if it is victimless, is part of the peace, and should be allowed to remain as long as its pays its taxes and behaves itself. What then is the basis for distinguishing crime from business as usual. Crime has victims.
We divine the world into 'programme' (a finite text of our own creation) and 'runtime', the infinite set of conditions necessary to execute the text.
In the light of quantum information theory, if though can be equated with information processing, all action is identical to thought [isomorphic, ie formal identity, different physical substrates (alphabets)]
But is there an irreducible 'matter' from which all symbols are formed? Do we need it? Do we need something which is nec quid, nec quale, nec quantum, nec aliquid eorum quibus ens determinatur? It adds nothing to the theory! [but does provide an intuitive interpretation of the abstract model]
[page 65]
Memory: state that does not change unless deliberately changed.
We may se quantum mechanics as a closed system which may be expressed by the natural numbers and so be complete, just as the particle interactions of the Universe are complete (?) This complete system, however, leads immediately to the vast incomplete system described by the Cantor Universe.
We might say that the multiplier effect of intelligence is so great that violent revolution is unnecessary if we have time t learn new ways before the old are overthrown - what we might call gradualism or social continuity. To be contrasted with the violent revolution first and then rebuild ethos of the US, various other terrorists and rogue nations, etc.
The human world is under pressure and we are all pushing against one another trying to expand and lower the pressure in our own lives. One way to reduce overall pressure is to increase the size of the overall space by creative union.
cf Muslim/Christian relations in Spain EB 17, 407c sqq.
The Roman Catholic Church probably embodies the biggest falsehood ever imposed on the human race, and continues to maintain the truth of its position through arrogance and political power.
We have a simple explanation of the 'unreasonable effectiveness of mathematics' if both mathematics and the physical world are networks of symbolic communication. We would then exploit the same rules to hold for both.
The most important [thing] a society or any organism has to do is maintain a viable interface with the
[page 66]
wilderness, ie the equilibrium surrounding it. Life, as we know it, is a state of disequilibrium. The full entropy of the symbol set is adequately represented by the entropy of the E-set. Is it uncertainty which defines the distinct classes, E-set and not E-set? This would be a wonderful connection, so we add it to our assumptions until we get around to looking into it mathematically. The overarching notion is the fullness of the world. Communication is fixed to ℵ0 and everything else is normalized to that. This is in effect conservation of energy. As the term 'entropy' began as a physical concept ('caloric') and was gradually purified into a mathematical concept, we must purify energy, momentum and action in the same way so that they become formal elements in a formal model. Quantum mechanics does this(?). The passage from dream fiction to mathematical consistency requires much of the sort of mental application that I shrink from. Here, however, we may need to practice self-constraint in order to realize an imagined good, work, in other words. The imagined good need not be conscious or communicable, as birds (and so many other creatures (all?)) have to work to preserve and propagate themselves. All that work (entropy restraint) is derived from the entropy difference between incoming sunlight and outgoing infra-red. We can analyze any organism in these terms. The transfinite network provides us with a workshop and test bed in which to make this analysis.
Tuesday 6 April 2004
Wednesday 37 April 2004
Thursday 8 April 2004
Friday 9 April 2004
Saturday 10 April 2004
Links
| C L Bennett et al First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Maps and Basic Results Abstract: We present full sky microwave maps in five frequency bands . . . from the WMAP [Wilkinson Microwave Anisotropy Probe] first year sky survey. . . . A best fit cosmological model to the CMB [Cosmic Microwave Background] and other measures of large scale structure works remarkably well with only a few parameters. The age of the best-fit Universe is t0 13.7 +- 0.2 Gyr old. . . . " back |
