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Old 12-09-2008, 04:44 PM   #1
Antaletriangle
Avalon Senior Member
 
Join Date: Sep 2008
Location: U.K.
Posts: 3,380
Default GÖDEL'S INCOMPLETENESS THEOREMS-Math's dirty secrets.

http://www.bbc.co.uk/radio4/history/...20081009.shtml

In 1900, in Paris, the International Congress of Mathematicians gathered in a mood of hope and fear. The edifice of maths was grand and ornate but its foundations, called axioms, were shaking with inconsistency and lurking paradox. And so, at that conference, a young man called David Hilbert set out a plan to rebuild them – to make them consistent, all encompassing and without any hint of a paradox.

Hilbert was one of the greatest mathematicians that ever lived, but his plan failed, spectacularly, and it did so because of the incompleteness theorems. These were the work of Kurt Gödel and they changed the way we understand maths, took us to the very limits of logic and sent challenges spilling out into the worlds of physics, philosophy and beyond.

Contributors

Marcus du Sautoy, Professor of Mathematics at Wadham College, University of Oxford

John Barrow, Professor of Mathematical Sciences at the University of Cambridge and Gresham Professor of Geometry

Philip Welch, Professor of Mathematical Logic at the University of Bristol

VITALISM
http://www.bbc.co.uk/radio4/history/...20081016.shtml
On a dreary night in November 1818, a young doctor called Frankenstein completed an experiment and described it in his diary:

“I collected the instruments of life around me, that I might infuse a spark of being into the lifeless thing that lay at my feet…By the glimmer of the half-extinguished light, I saw the dull yellow eye of the creature open…”

Frankenstein may seem an outlandish tale, but Mary Shelley wrote it when science was alive with ideas about what differentiated the living from the dead. This was Vitalism, a belief that living things possessed some spark of life, some vital principle that lifted them above dull matter. Electricity was a very real candidate.

Vitalists aimed at unlocking the secret of life itself and they raised questions about what life is that are unresolved to this day.

Contributors

Patricia Fara, Fellow of Clare College and Affiliated Lecturer in the Department of History and Philosophy of Science at Cambridge University

Andrew Mendelsohn, Senior Lecturer in the History of Science and Medicine at Imperial College, University of London

Pietro Corsi, Professor of the History of Science at the University of Oxford

Last edited by Antaletriangle; 12-09-2008 at 04:48 PM.
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