vol VII: Notes
2018
Notes
Sunday 21 January 2018 - Saturday 27 January 2018
[Notebook: DB 82: Life and Death]
Sunday 21 January 2018
Monday 22 January
Tuesday 23 January 2018
[page 116]
Wednesday 24 January 2018
. . .
[page 117]
How good is my book? So so. What is missing? Tails off towards the end. What is missing? A proper exposition of the increase in entropy [and therefore meaning] as we move up the transfinite scale. Needed to explain why I am more complex that and equivalent mass of gas. In a gas the roles of all the molecules are essentially identical. In me every molecule (or a large proportion of them) have a specific role, ie it is a point in a much larger space than the space associated with each molecule in a gas. Is this right? Can we express it in terms of Chaitin's measure of complexity, the shortest program necessary to generate each level of the transfinite hierarchy. How big a program does it take to generate all the permutations of n objects, ie all the states of the permutation group. Chaitin: Information, Randomness & Incompleteness: Papers on Algorithmic Information Theory, Heap's algorithm - Wikipedia
Thursday 25 January 2018
Friday 26 January 2018
Given digital to the core, continuous mathematics has no place in first order modelling of physics. Nevertheless the enormous effort that has gone into its development is not wasted, since it finds application in the theory of probability where the concept of measure zero describes the relationship of ℵn to ℵn+1. See Kolmogorov Foundations of Probability. Kolmogorov: Foundations of the Theory of Probability
Saturday 27 January 2018
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Further readingBooks
Click on the "Amazon" link below each book entry to see details of a book (and possibly buy it!)
Chaitin, Gregory J, Information, Randomness & Incompleteness: Papers on Algorithmic Information Theory, World Scientific 1987 Jacket: 'Algorithmic information theory is a branch of computational complexity theory concerned with the size of computer programs rather than with their running time. ... The theory combines features of probability theory, information theory, statistical mechanics and thermodynamics, and recursive function or computability theory. ... [A] major application of algorithmic information theory has been the dramatic new light it throws on Goedel's famous incompleteness theorem and on the limitations of the axiomatic method. ...'
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Finkbeiner, Ann, The Jasons: The Secret History of Science's Postwar Elite, Viking Adult 2006 Amazon Editorial Review: Publishers Weekly 'If necessity is the mother of invention, then the U.S. government's midwife for much of the Cold War was a small, brilliant and fiercely independent cadre of physicists who assembled each summer to make scientific reality out of pie-in-the-sky ideas. Ingenious problem-solvers to a man (they were, for decades, an all-boys club), "the Jasons" (a nickname of uncertain origin; it's either taken from the Greek myth, Jason and the Argonauts, or an acronym for the months of July through November) agreed to help the government-and cash its checks-on the condition that their work be free from political influence; if the Pentagon or White House proposed a project the group found absurd or ethically reprehensive, they would say so in their typically blunt, intellectually arrogant manner. However, the smartest people in the room weren't always the savviest, and the Jasons found their work manipulated by the military to suit its own purposes. At least that's the story as told by Finkbeiner, who spent two years interviewing dozens of Jasons past and present and doesn't hesitate to give them the benefit of every doubt that's arisen in the group's shadowy, five-decade history, particularly those dealing with the Jasons' involvement in Vietnam. Nonetheless, Finkbeiner offers a rare and valuable look at the intersection of world politics, military strategy and scientific discovery.'
Copyright © Reed Business Information, a division of Reed Elsevier Inc. All rights reserved.
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Kauffman, Stuart, At Home in the Universe: The Search for Laws of Complexity, Oxford University Press 1995 Preface: 'As I will argue in this book, natural selection is important, but it has not laboured alone to craft the fine architectures of the biosphere . . . The order of the biological world, I have come to believe . . . arises naturally and spontaneously because of the principles of self organisation - laws of complexity that we are just beginning to uncover and understand.'
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Khinchin, Aleksandr Yakovlevich, Mathematical Foundations of Information Theory (translated by P A Silvermann and M D Friedman), Dover 1957 Jacket: 'The first comprehensive introduction to information theory, this book places the work begun by Shannon and continued by McMillan, Feinstein and Khinchin on a rigorous mathematical basis. For the first time, mathematicians, statisticians, physicists, cyberneticists and communications engineers are offered a lucid, comprehensive introduction to this rapidly growing field.'
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Kolmogorov, A N, and Nathan Morrison (Translator) (With an added bibliography by A T Bharucha-Reid), Foundations of the Theory of Probability, Chelsea 1956 Preface: 'The purpose of this monograph is to give an axiomatic foundation for the theory of probability. . . . This task would have been a rather hopeless one before the introduction of Lebesgue's theories of measure and integration. However, after Lebesgue's publication of his investigations, the analogies between measure of a set and mathematical expectation of a random variable became apparent. These analogies allowed of further extensions; thus, for example, various properties of independent random variables were seen to be in complete analogy with the corresponding properties of orthogonal functions . . .'
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Pears, Iain, An Instance of the Fingerpost, Random House 1997 Jacket: 'Anyone who reads this will want to tell their friends about it ... This novel combines the simple pleasures of Agatha Christie with the intellectual subtlety of Umberto Eco ... don't let it pass by unread.' Sunday Times
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Pierce, John Robinson, An Introduction to Information Theory: Symbols Signals and Noise, Dover 1980 Jacket: 'Behind the familiar surfaces of the telephone, radio and television lies a sophisticated and intriguing body of knowledge known as information theory. This is the theory that has permitted the rapid development of all forms of communication . . . Even more revolutionary progress is expected in the future.'
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Papers
Nature, Editorial, "News: Open-access journal will publish first, judge later", Nature, 445, 7123, 4 January 2007, page 9. 'A radical project from the Public Library of Science (PLoS), the most prominent publisher in the open access movement, is setting out to challenge academia's obsession with journal status and impact factors. The online-only PLoS One, which launched on 20 December, will publish any paper that is methodologically sound. Supporters say the approach will remove some of the inefficiencies associated with current peer-review systems -- but critics question whether a journal that eschews impact factors will manage to attract papers. . . . '. back |
Links
Heap's algorithm - Wikipedia, Heap's algorithm - Wikipedia, the free encyclopedia, 'Heap's algorithm generates all possible permutations of n objects. It was first proposed by B. R. Heap in 1963. The algorithm minimizes movement: it generates each permutation from the previous one by interchanging a single pair of elements; the other n−2 elements are not disturbed. In a 1977 review of permutation-generating algorithms, Robert Sedgewick concluded that it was at that time the most effective algorithm for generating permutations by computer.' back |
Massimo Faggioli, Obsessed with Continuity, 'Edgardo Mortara was the Jewish child kidnapped by the papal police force in 1858 from his parents’ home in Bologna, Italy, then still part of the Papal States. Having been baptized by his Catholic nanny during an illness, he was declared a Catholic by the local inquisitor, who ordered the abduction on the grounds that Catholics could not be raised in Jewish households.' back |
Rolf Qua, Fossil jawbone from Israel is the oldest modern human found outside Africa, 'New fossil finds over the past few years have been forcing anthropologists to reexamine our evolutionary path to becoming human. Now the earliest modern human fossil ever found outside the continent of Africa is pushing back the date for when our ancestors left Africa.
The fossil, an upper left jawbone with most of the teeth attached, comes from Misliya Cave in Israel and dates to 177,000-194,000 years ago.' back |
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