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Old 07-19-2007, 02:41 AM   #1
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Default The Archimedes Codex

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Nicetas Choniates was on the spot to witness the greatest calamity that ever befell the world of learning. In April 1204, Christian soldiers on a mission to liberate Jerusalem stopped short of their goal and sacked Constantinople, the richest city in Europe. ....

The looted city had many more books than it had people...Its inhabitants still considered themselves to be Romans and the city held the literary treasures of the ancient world as its inheritance. Among these treasures were treatises by the greatest mathematician of the ancient world and one of the greatest thinkers who had ever lived. He approximated the value of pi, he developed the theory of centres of gravity, and he made steps towards the development of the calculus 1800 years before Newton and Leibniz.
The Archimedes Codex (or via: amazon.co.uk)

I am really enjoying this, bought serendiptitiously yesterday!

Little tidbits that belief in one god an be traced back to Archimedes and his followers, that Pythagorous and Euclid were not that important, that the world of learning by focusing on the philosophers and poets has missed the plot, that Hagia Sophia was only possible because of Archimedes, that the xian curriculum of salvation by ignoring Archimedes has seriously biased all our modern thinking.

This book is about the beginning of a revolution in our thinking - the

http://en.wikipedia.org/wiki/Antikythera_mechanism being the other part of turning our understanding of the ancient world upside down.

Where was Archimedes work found? On parchment that had been scraped off and used as a prayer book. How was it reconstructed, using the best of modern science and technology and conservation and imaging techniques.
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Old 07-19-2007, 06:05 AM   #2
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Nicetas Choniates was on the spot to witness the greatest calamity that ever befell the world of learning. In April 1204, Christian soldiers on a mission to liberate Jerusalem stopped short of their goal and sacked Constantinople, the richest city in Europe. ....
The renegade force originally assembled for the crusade and hijacked by the Venetians were instantly excommunicated, of course.

For the sack of Constantinople was indeed a tremendous catastrophe. The list of works last referenced in Photius and Constantine Porphyrogenitus in the 9th century is very great.

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This book is about the beginning of a revolution in our thinking - the
http://en.wikipedia.org/wiki/Antikythera_mechanism being the other part of turning our understanding of the ancient world upside down.
Michael Grant did a book on ancient technology. Few realise, for instance, that the vending machine existed, or street lighting.

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Where was Archimedes work found? On parchment that had been scraped off and used as a prayer book.
The ability to recognise and use palimpsests has given us a number of lost works. The new multi-spectral imaging technology would be very useful, if more widely available.

All the best,

Roger Pearse
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Old 07-19-2007, 06:08 AM   #3
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Pythagoras and Euclid not as important as Archimedes? What about the axiomatic approach to geometry?
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Old 07-19-2007, 06:40 AM   #4
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I don't remember them working on absolute and potential infinities and calculus!

And were the four horses at St Marks Venice stolen then?

It seems Hero - who had automatically opening doors and steam engines - was dependent on Archimedes - which may mean number one mind, and is found in Diomedes, the mind of Zeus (or God). They may have worshipped the beauty and order of the cosmos.

On Euclid

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But Archimedes wouldn't think very highly of them, as they consist mainly of basic mathematics.....

The Christian curriculum necessarily included some ancient authors - Homer was necessary for Rhetoric and Euclid for Geometry; but Archimedes was not included in the curriculum of Salvation.
How much are we still affected by this thin gruel of knowledge that was passed on?
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Old 07-19-2007, 07:21 AM   #5
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I am going to quote a chunk from page 48 about squaring the parabola. The logical step by step process of Archimedes, of how he proves something, is I think directly related to the arguments we have here.

I was wondering about where to put this thread - here or S and S, and I chose here because I do see Archimedes as having developed a form of argument that is very powerful and appropriate but not much applied in bch.

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Three times in his career Archimedes proved that the parabolic segment - a certain curved object - is four thirds the triangle it encloses. This was his favourite measurement. .....we must first acquaint ourselves with Archimedes' geometrical method itself - based throughout on the combination of indirect proof and potential infinity. It is an extraordinarily subtle argument, one that even professional mathematicians have a hard time unravelling. It is like an affirmation based on double double negation....
To summarise, he argues first assume the curve is greater than four thirds of the triangle.

He then separately builds the curve up using very small triangles, which of course will be smaller than four thirds.

We now have two objects - the curve itself and an almost curve of very small straight line edges of triangles. - the jumble of triangles is an object bounded by straight lines.

But four thirds of an enclosed triangle is also bounded by straight lines.

He has two results - one greater, one smaller. This is impossible.

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Therefore the curve is not different from four thirds the enclosed triangle - the curve is therefore four thirds the enclosed triangle. Indirect proof and potential infinity together have brought us here.
I hope people can see something else - there is a relationship between curves and straight lines!

And it is probably this sort of stuff that led me to dumping religion and xianity as illogical, not thought through, unfounded, and eventually led me to ask questions about OK, how did this social structure xianity get going, was there a founder or is myth and story the more logical explanation?
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Old 07-19-2007, 09:33 AM   #6
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And were the four horses at St Marks Venice stolen then?
I believe so. Originally they stood in the Hippodrome.

The renegades also looted and destroyed the imperial tombs in the Church of the Holy Apostles, going back to Constantine. IIRC the whole lot was destroyed by the Moslems after 1453, and the church levelled.

Apparently some parts of Blachernae palace are still extant.

All the best,

Roger Pearse
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Old 07-19-2007, 10:47 AM   #7
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I strongly recommend this book, not least for the superb description of how they have worked out what Archimedes originally wrote and thought - including probably with reasonably accurate copies of what he drew, and the effects of several changes of operating systems and technology over the centuries!
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Old 07-19-2007, 11:27 AM   #8
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I hope people can see something else - there is a relationship between curves and straight lines!
Hmmm, sounds a lot like calculus.

http://en.wikipedia.org/wiki/Archimedes

http://en.wikipedia.org/wiki/Calculus

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Calculating volumes and areas, the basic function of integral calculus, can be traced back to the Egyptian Moscow papyrus (c. 1800 BC), in which an Egyptian worked out the volume of a pyramidal frustrum [1] [2] Eudoxus (c. 408-355 BC) used the method of exhaustion, which prefigures the concept of the limit, to calculate areas and volumes. Archimedes (c. 287-212 BC) developed this idea further, inventing heuristics which resemble integral calculus.[3] The method of exhaustion was rediscovered in China by Liu Hui in the 3rd century AD, who used it to find the area of a circle.
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Old 07-19-2007, 08:05 PM   #9
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I actually got to see this manuscript when it was undergoing analysis at the Walter's Gallary in Baltimore. I was not aware that there was a book about it. Thanks for the tip. I'd definately like to read it.
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Old 07-21-2007, 08:55 AM   #10
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Off topic - strange line in the middle somewhere - "evolved or intelligently designed" - do Americans feel they have to qualify the word evolve now? It could be a joke...
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