Notes
[Notebook: Language DB 57 ]
[Sunday 26 December 2004 - Saturday 1 January 2005]
[page 50]
Sunday 26 December 2004
Nature [Commentary?] From physics to metaphysics: we trace again the path taken by Aristotle from change in the sublunary world to the unmoved mover - ie constant potential.
[page 51]
A study of molecular biology [and creativity in general] reinforces the feeling that there is no obstacle in the Universe that cannot be overcome by suitable capital investment, that is the development of a dynamic structure (process) to bypass the obstacle. de Soto This is the technological analogue of the idea that every problem has a solution. But does it? This problem has been carefully studied in the mathematical realm. Here it is found that the processes required to solve some problems require unlimited resources in (memory) space and the number of operations (counted by time). This was proved by Turing. Turing, Davis But are Turing machines the boundary of computing? A metaphysician may be inclined to say no, that there are resources for understanding situations and working out how to deal with them available in the divine and spiritual world that are unavailable in the material world.
The Greek philosophers postulated a connection between the spiritual and material worlds. Plato, fearing chaos, postulated a non-chaotic world of organized bodies of information (ideas, forms, ordered sets) that somehow impressed themselves on the material world [and human minds] to give is the structures we see and the understanding of them we have. So pure non-constructive mathematics is sometimes called Platonic.
These ideas became central to Christian modelling of the world and remain deep in the foundations of many people's world views.
[page 52]
People have dreamt for some time that quantum theory may provide us with a new window on the relationship between matter and spirit.
We might see quantum mechanics as the most interesting result so far of the program enunciated by Galileo: . . . Galilei
Prandtl Nature 432:807 16 December 2004. Narashima
This notion that the world and mathematics are somehow images of one another took a vast leap forward in Georg Cantor.
Linguistic space / chemical space / Cantor space. Dobson
Barasch N 432:811 'So what happens when bacteria grow in a host that also covets iron (mammalian blood serum has just 10-26 M free iron), or when two microbes compete for the same source of metal. Essentially, thievery reigns. Barasch and Mori p 811
Monday 27 December 2004
Tuesday 28 December 2004
[Systems] designed to handle (rare) worst cases spend most of their time effectively not stressed at all, ie in heaven.
Metric space: Every technology is founded on a metric, eg entropy and information theory.
Wednesday 29 December 2004
Thursday 30 December 2004
Cybernetics allows us to partition the set of events into various versions of controllable and uncontrollable using the principle of requisite variety (Nyquists's theorem). Ashby, Justin Romberg
CONTROLLABLE = COUNTABLE
Like Plato, Aristotle and Newton, Cantor was a theologian looking for a space in which to model the relationship between heaven and earth. In each case the search is for invariants: things that remain the same as we change our position in spacetime. Plato began with separated forms, an early version of the idea Cantor expresses as an ordered set : 'The concept of 'ordinal type' developed here, when it is transferred in like manner to 'multiply ordered aggregates' embraces in conjunction with the concept of 'cardinal number' or 'power' everything capable of being numbered that is thinkable, and in this sense cannot be further generalized. It contains nothing arbitrary, but is a natural extension of the concept of number.' Cantor page 117
Plato was inclined to derogate the visible world, but Aristotle began a move in the opposite direction. In his Physics and Metaphysics (and other books) he developed a model for the sublunary world which he then extended to the heavens. In a nutshell, this world has the attributes of potential and action (inherent in the notion of motion) whereas the heavens are pure action. In other words, every possibility in the heavenly sphere is activated, whereas in our world, only some possibilities are activated, and the activation may change from one to another.
This diarised approach tries to capture connections (forms of words) as they surface in my mind. Ultimately this set of 'shots' is to be cut and pasted into a more coherent (better ordered) construct.
[page 54]
GEOMETRICAL PROOF - CONSTRUCTION
Although Plato, following Pythagoras, was aware of the importance of mathematics, it took Newton's introduction of calculus to mathematics to enable a static formal description of a dynamic process. For Plato and Aristotle, form did not change. The evolution of species was not possible. Like other forms, species are immutable.
Calculus shows us how to deal with the dynamic transformation of forms. Dynamics revolves around the interface between countable and uncountable, which required the 300 years between Newton and Cantor to solve.
The crowning glory of the Newtonian approach is quantum mechanics. Through the works of Cantor and Hilbert, However, Quantum mechanics addresses a much larger space than Newtonian physics.
Deighton 'Only. . . page 109: '. . . Its love alright. And like a lover, he keeps pushing the relationship to the brink of dissolution. 'Disillusion corrected Bob. Deighton
We all seek a comfortable relationship with our environment (people, animals, plants, things). We can imagine two ways of creating such comfort which we will call the developmental and the Buddhist. (active, passive) Active change the environment; passive, change yourself. We then use some sort of extreme principle to decide the
[page 55]
optimum balance.
[diagram]
Descartes alerted us to the need for clear and distinct ideas. Descartes Three hundred years later information theory has shown us how to use clearness and distinctness to overcome noise [error] in communication and showed us how to communicate clear and distinct ideas over a noisy channel. Shannon Throughout, we consider Descartes 'clear and distinct idea' to be isomorphic to Cantor's ordered set.
Plato, Aristotle, Newton, Cantor all theologians trying to discern the bond between heaven and earth.
In questions of survival, time is of the essence since continued life requires continued input.
"Their knowledge and observation of the ways of the world put them into a position of wealth and power and they held onto it [?]
Unitarity - justice - due process - conservation
In the transfinite realm, unitarity is imposed upon the network by the limited size of the natural
[page 56]
numbers with respect to the transfinite numbers. This statement may sound mystical, but the aim is to so embed the mysterious side of global in our understanding of the observable features that any pejorative connotation of 'mystery' and 'mystical' is removed from our glossary, except in the case of false mysticism, ie that not consistent with the observed world.
The global quantum network (transfinite network) is unitary and subsets of it may be (approximately) unitary. The distance of each point from a unitary condition is a product of its communication (interference) with the rest of the world.
One may understand adiabatic in the sense of unitary, that is a system effectively (or abstractly) isolated from the rest of the Universe. This is the dream of quantum computation. Although this dream cannot be achieved on the first iteration, quantum error correction allows us to move asymptotically to perfection [provided we have the necessary resources, ie spare entropy]
Functional analysis
One of the key ideas of a mathematical metaphysics is unitarity.
Let us then treat our input (our experience) as the output of some gigantic entity each of us calls 'my environment'
. My environment is a history, a lifeline of where I've been.
[page 57]
The animal stories communicate an abstract picture of human nature from generation to generation. The same, at the opposite end of the spectrum, as the work of normative educational institutions like the Roman Catholic Church.
On the evolution of country roads (communication channels)
'odium [theologicum]' theological hate: burning at the stake; torture, terrorism etc, ie being in a state that 'justifies' [makes probable] anonymous and indiscriminate killing.
To unify religion we must see theological hate as an error to be eliminated. We can see, on the competition model, why peoples should strive to eliminate one another; we wish to propagate the cooperation side of the model which says it is best for me to promote (rather than impede) my neighbour's welfare.
Many say that global welfare can be maximized by free trade, that is allowing any two individuals to enter into any relationship of exchange which is mutually agreed, ie a deal or a continuum of dealing.
Information ages at all timescales and it requires sampling at the Nyquist frequency to keep up to date.
Tsunami: disaster on a large scale, a big 'error', transient, and now we are in the decay period. One
[page 58]
proxy for this is the death rate, the number of people being killed per day. Initially this is very high ('prompt deaths') and then the rate decays. The more quickly it decays (due, eg to prompt aid), the smaller the integral of death (and suffering). Suffering can be reduced even more by preparedness. So, given sufficient capital, all habitations on earth are designed and built to minimize the risk from all sources, to the inhabitants. This is a consequence of the harm minimization approach to problems (at all scales)
One's 'integration interval' is one's life so far. As we get older, we integrate a large range of event.
So imagine that every point on the 'natural' line (ie row of points) is an event, and that these events may be arranged in any order, ie we think of them as abstract network protocols that each gives us insight into some concrete situation. So physics is generally a case of applying the dominant paradigm to more and more cases, always on the lookout for the case that lies outside current doctrine.
CANTOR replaced the notion of point with set. The information content of a point is a function of the dimensionality of the space in which it lies and the definition of the coordinate at the point in each spatial dimension. Cantor's theory suggests that most of the information is carried by the dimensions, since they are all orthogonal ie perfectly separated from one another like entropy free symbols.
