vol 7: Notes
2004
7 November
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... to restore theology to the mainstream of science
Notes
[Notebook: Language DB 57]
[Sunday 7 November 2004 - Saturday 13 November 2004]
Sunday 7 November 2004
Monday 8 November 2004
[page 29]
Tuesday 9 November 2004
Summa Theologiae I, 50, 1: 'I reply that it is necessary to postulate certain incorporeal creatures. What God principally intended in created things is the good that consists in assimilation to God. The perfect assimilation of an effect to a cause is noticed when the effect imitates the cause in that very feature through which the cause produces its effect, as heat makes heat." Aquinas 261
The cause-effect relationship is a communication link. Communication correlates the recipient of a message with the sender. In full duplex communication, both terminals play both roles (simultaneously? or) sequentially. For meaningful communication, the roles must be sequential, ie I listen to you before O reply, and if the conversation is to get anywhere, my reply should be relevant to what you have said, provided that is relevant to what I last said, etc. In a
[page 30]
'meaningful' conversation, each message builds on the last in a convergent series that ends in the communicants taking well defined positions with respect to one another. POSITION == STATE. Coordinates in a reference frame.
The entropy of a set is a function of its cardinal number.
Sharing : communication (other things being equal) (ie partial derivative) the more one shares the more powerful one becomes.
Symmetry with respect to complexity means that there are common solutions to problems at all levels of complexity. This immediately suggests that the best strategy is to narrow a problem down to the binary case and study this carefully to get clues to how things work in the transfinite domain, cantor's.
Stock market: picking turning points in a time series of prices.
I lead a heavenly existence, drawn and pushed forward by a stream of glimpses of divinity.
Economist 6 November 2004 page 14: '... the left emphasizing individual rights in social and civil matters, but not in economic life, and the right saying the converse.'
Wednesday 10 November 2004
Thursday 11 November 2004
Method is the 'differential equation' that governs the acquisition of true knowledge. It shows us how to construct an infinite series that converges on the truth.
Eigenvalues are invariants, things that are effectively unchanged by the action of the operator - stationary points.
FORCE == COMMUNICATION
Newton's 3 laws tell us the basic features of the interactions pyres between bodies. The law of universal gravitation particularizes these laws to forces with a particular set of properties (inverse square, proportional to mass = cardinal) Since N's time we have discovered three new forces which still obey the three laws. Newton
Natural theology and natural religion need no institutional specification of doctrine as we find in the Christian Churches because doctrine is already determined the the nature of the world and all we have to do is to look with insight to see what we need to (and need not) do.
Friday 12 November 2004
Saturday 13 November 2004
Further reading
Books
| Newton, Isaac, Philosophiae Naturalis Principia Mathematica , Harvard University Press 1972 One of the most important contributions to human knowledge. First translated from the Latin by Andrew Motte in 1729, Amazon back |
| Newton, Isaac, Principia volume II The System of the World, University of California Press 1966 back |
| Whitehead, Alfred North, and Bertrand Arthur Russel, Principia Mathematica to 56, abridged (Cambridge Mathematical Library), Cambridge University Press 1997 Amazon back |
| Newton, Isaac, and Julia Budenz, I. Bernard Cohen, Anne Whitman (Translators) , The Principia : Mathematical Principles of Natural Philosophy , University of California Press 1999 This completely new translation, the first in 270 years, is based on the third (1726) edition, the final revised version approved by Newton; it includes extracts from the earlier editions, corrects errors found in earlier versions, and replaces archaic English with contemporary prose and up-to-date mathematical forms. ... The illuminating Guide to the Principia by I. Bernard Cohen, along with his and Anne Whitman's translation, will make this preeminent work truly accessible for today's scientists, scholars, and students. Amazon back |
| Newton, Isaac, Philosophiae Naturalis Principia Mathematica , Harvard University Press 1972 Amazon back |
| Whitehead, Alfred North, and Bertrand Arthur Russel, Principia Mathematica (Cambridge Mathematical Library), Cambridge University Press 962 The great three-volume Principia Mathematica is deservedly the most famous work ever written on the foundations of mathematics. Its aim is to deduce all the fundamental propositions of logic and mathematics from a small number of logical premisses and primitive ideas, and so to prove that mathematics is a development of logic. Not long after it was published, Goedel showed that the project could not completely succeed, but that in any system, such as arithmetic, there were true propositions that could not be proved. Amazon back |
| Goedel, Kurt, and B Meltzler (translator), R B Braithwaite (Introduction), On Formally Undecidable Propositions of Principia Mathematica and Related Systems, Dover 1992 A translation of Uber Formal Unentscheidbare Satze der Principia Mathematica und Verwandter Systeme I, Monatshefte fur Mathematik und Physic, 38(1931) 173-198. Jacket: 'In 1931 a young Austrian mathematician published an epoch making paper containing one of the most revolutionary ideas in logic since Aristotle. Kurt Gödel maintained, and offered detailed proof, that in any arithmetic system, even in elementary parts of arithmetic, there are propositions which cannot be proved or disproved within the system. It is thus uncertain that the basic axioms of arithmetic will mot give rise to contradictions. The repercussions of this discovery are still being felt and debated in 20th century mathematics.' Amazon back |
| Goedel, Kurt, "On formally undecidable propositions of Principia Mathematica and related systems, I" in Solomon Fefferman et al (eds) Kurt Goedel: Collected Works Volume 1 Publications 1929-1936, Oxford UP 1986 Jacket: 'Kurt Goedel was the most outstanding logician of the twentieth century, famous for his work on the completeness of logic, the incompleteness of number theory and the consistency of the axiom of choice and the continuum hypotheses. ... The first volume of a comprehensive edition of Goedel's works, this book makes available for the first time in a single source all his publications from 1929 to 1936, including his dissertation. ...' Amazon back |
Links
| Aquinas 261 Whether an angel is altogether incorporeal 'I answer that, There must be some incorporeal creatures. For what is principally intended by God in creatures is good, and this consists in assimilation to God Himself. And the perfect assimilation of an effect to a cause is accomplished when the effect imitates the cause according to that whereby the cause produces the effect; as heat makes heat. Now, God produces the creature by His intellect and will (14, 8; 19, 4 ). Hence the perfection of the universe requires that there should be intellectual creatures. Now intelligence cannot be the action of a body, nor of any corporeal faculty; for every body is limited to "here" and "now." Hence the perfection of the universe requires the existence of an incorporeal creature.' back |
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