billpapa.org Reading (b)log

This is a collection of Chaitin’s more accessible articles. Most of these are an attempt to define his quasi-empirical epistemology, which is tries to be a dialectical transcendence of idealism and empiricism.

To present it he uses some very interesting quotes:

According to Plato, the world is rationally understandable because it has structure. And the universe has structure, because it is a work of art created by a God who is a mathematician. Or, more abstractly, the structure of the world consists of God’s thoughts, which are mathematical. The fabric of reality is built out of eternal mathematical truth. [Brisson, Meyerstein, Inventer l’Univers, 1991]

Furthermore, the attitude that theoretical physics does not explain phenomena, but only classifies and correlates, is today accepted by most theoretical physicists. This means that the criterion of success for such a theory is simply whether it can, by a simple and elegant classifying and correlating scheme, cover very many phenomena, which without this scheme would seem complicated and heterogeneous, and whether the scheme even covers phenomena which were not considered or even not known at the time when the scheme was evolved. (These two latter statements express, of course, the unifying and the predicting power of a theory.)” |John von Neumann, \The Mathematician”, 1947, reprinted in Newman, The World of Mathematics, 1956, and in Br.ody, V.amos, The Neumann Compendium, 1995.

The metaphysicist believes that the logically simple is also the real. The tamed metaphysicist believes that not all that is logically simple is embodied in experienced reality, but that the totality of all sensory experience can be comprehended' on the basis of a conceptual system built on premises of great simplicity. The skeptic will say that this is amiracle creed.’ Admittedly so, but it is a miracle creed which has been borne out to an amazing extent by the development of science.” |Einstein, \On the Generalized Theory of Gravitation”, 1950, reprinted in Einstein, Ideas and Opinions, 1954.

In my opinion, the fundamental point is this: The belief that the universe is rational, lawful, is of no value if the laws are too complicated for us to comprehend, and is even meaningless if the laws are as complicated as our observations, since the laws are then no simpler than the world they are supposed to explain.

Chaitin states that “the main idea of Algorithmic Information Theory (AIT) is that a scientific theory is a computer program, and the smaller, the more concise a program is, the better the theory.”. The theory/computer program parallalezation has a lot in common with Rosen’s modeling relation (Rosen 1985) and Naur’s programming as theorizing concept (Naur, 1985). Chaitin presents the following relations:

• Shannon information theory (communications engineering), noiseless coding: encoded message -> Decoder -> original message
• Model of scientific method: scientific theory -> Calculations -> empirical/experimental data
• Algorithmic information theory (AIT), definition of program-size complexity: program -> Computer -> output
• Central dogma of molecular biology: DNA -> Embryogenesis/Development -> organism
• Turing/Post abstract formulation of a Hilbert-style formal axiomatic mathematical theory as a mechanical procedure for systematically deducing all possible consequences from the axioms: axioms -> Deduction -> theorems
• Contemporary physicists’ efforts to find a Theory of Everything (TOE): TOE -> Calculations -> Universe
• Leibniz, Discourse on Metaphysics, 1686: Ideas -> Mind of God -> The World

The common thing among these relationships is that the left hand term is much smaller than the right hand (its model), and our goal is to make it as simple as possible as dictated by Occam’s razor. The reason for the application of occam’s razor in this situation i think comes from the argument that if the model becomes a as big as the modelled entity itself, then it’s a description-mirror image and not a model -there’s always such a theory (Leibniz).

References

• Naur, P. (1985). Programming as Theory Building. Microprocessing and Microprogramming, 15, 253-261.
• Rosen, R. (1985). Anticipatory Systems. Oxford: Pergamon Press.

This entry was posted on Wednesday, November 30th, 2005 at 11:42 am and is filed under modelling, philosophy, systems theory. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.