The mystery of the manuscript of Archimedes

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The Law Of Archimedes, «Eureka!» Archimedes screw, «Give me a fulcrum and I will move the Earth!» And finally, «don’t touch my drawings!» These words and expressions exhausted almost everything that we learn about the famous Siracusa in high school. We know that Archimedes, the great mechanic of antiquity and the hero of the resistance to the Romans. But this legendary man, especially, was one of the largest Greco-Roman mathematicians.

The ancient mathematician

Not self-taught, he received an excellent education in Alexandria, the main scientific centre of that time. Archimedes life was in correspondence with scientists there. And the legendary Alexandria in the III century BC were collected achievements not only of the peoples of the Mediterranean basin, but, thanks to the campaigns of Alexander the great, and many mysterious civilizations of Mesopotamia, Persia, and the Indus valley.

However, even before the Renaissance, when for the first time in many hundreds of years have developed an interest in serious mathematics, came very little of the original writings of Archimedes. Greek manuscripts, even copies, translations, or just quotes. Not to mention the detailed proofs of the formulas and theorems. Archimedes-mathematician was long known to scientists no more than Einstein student: very smart, did a lot of something very important.

Тайна рукописи Архимеда

Domenico fetti Archimedes 1620

Preserved little information on that in the treatise «Method of mechanical theorems,» Archimedes explained in detail their most amazing mathematical discoveries. But the treatise this for about thousands of years numbered among lost forever to mankind.

One of the most famous Bible scholars of the nineteenth century, Constantin von Tischendorf in the 1840s, he worked in the libraries of Constantinople. From there he brought home a page of items of interest for the manuscript, which was discovered some half-erased complex mathematical calculations in Greek, similar to the work of Archimedes. Alas, the scientist just ripped a page out of the book when the librarian was looking the other way. This act of vandalism was futile − neither Tischendorf nor anyone else gave the text of any special value.

The real merit of opening the book, seen by Tischendorf and later became famous as the Palimpsest of Archimedes, belongs unknown to the Turkish librarian. He quoted the strange mathematical calculations in the newsletter worldwide directory which fell into the hands of the Danish historian and philologist Johan Ludwig Heiberg. He was intrigued so much that immediately went and acquainted with the book personally in 1906. What he saw shocked him to the core.

At first glance, quite ordinary liturgical book of the XIII century from the monastery of Mar Saba in the desert of Jerusalem. But if you look across the liturgical text was barely visible line on the earlier Greek, full of scientific and philosophical terms.

The term «palimpsest» means «re-erased». Because of the value of the parchment in the Middle ages of unnecessary books are often divided into separate leaves, clean them from the ink, then sewed and wrote new text. In the Palimpsest of Archimedes, each of the sheets were still folded in half, to get a book of a smaller format. Therefore, the new text was written across the old. As of the writing material unknown monk used the Byzantine collections of scientific papers of approximately 950 years. But cleaning was not performed very carefully, and the original text was visible.

The joy of Haberga no bounds when he realized that a larger number of initial texts is a copy of the works of Archimedes and that among them there is almost full of the coveted «a Method…».

The library was forbidden to take out the manuscript from its premises (who can blame them after the visit of Tischendorf?), so a scientist hired photographer, pereslavskogo for him the whole book. Then, armed with only a magnifying glass, Heiberg engaged in a detailed transcript of the photocopy. The final result, and then the English translation was published in 1910-1915 years. The opening caused a lot of noise and even got on the front page «new York times».

The continuing adventures

But then came the First world war, the end of which the Ottoman Empire ceased to exist. Among the devastation in Constantinople, soon became Istanbul, was not quite up to ancient manuscripts. In the 1920-ies a large number of Turkish values and moved to Europe. Only much later were able to establish that a certain Frenchman was able to purchase and take a Palimpsest in Paris, where for a long time just became a collector’s rarity.

Interest in the works of Archimedes was revived only in 1971. Specialist in ancient Greek culture, Oxford Nigel Wilson drew attention to some of the words in the document of the Cambridge libraries (the same page of Tischendorf), which, in his opinion, was used only by Archimedes. Wilson received permission for a more thorough investigation of the document and not only confirmed that the page refers to the Palimpsest, but also proved that with the help of previously inaccessible technologies (such as ultraviolet light) the text can be recovered completely. The case remained for small – to find sunk into oblivion code. The academic world began an intensive search, but they in what have not resulted.

In 1991, employee of the auction house Christie’s received a letter from a certain French families wishing to auction supposedly the same Palimpsest. The news was received with skepticism, but subsequent examination has rendered unexpectedly positive verdict. The result is a sensational bidding document was sold to an anonymous billionaire for $ 2 million.

Тайна рукописи Архимеда

The Palimpsest Of Archimedes. Visible inscription made by a scholar

All scientists of the world held its breath – after all, at the behest of the new owner of the book can just close the box forever. Fortunately, fears proved unfounded. When Dr. will Noel, curator of manuscripts Art Museum of art the Walters in Baltimore (United States), addressed to the agent of the owner with a request to provide a code for research, his initiative was received with enthusiasm. The billionaire earned his fortune in high technology, and because he was not so far from science and its interests.

From 1999 to 2008, a group of specialists worked with the Palimpsest of Archimedes. The document, by the time caught in a terribly bad condition, has been carefully restored. When the code expanded on separate sheets, it was discovered that a line of text of Archimedes was concealed inside cover because previously inaccessible. Among them were the key points in the proof of the theorems. And the latest scanning techniques (in the range from infrared to x-ray) and computer processing have helped to restore everything possible, even invisible to the eye letters.

But why is it so important?! A long time ago it was known that Archimedes was often connected to large numbers and very small values. For example, to calculate the circumference of a circle he has entered it in a polygon with a large number, but the short length sides. This brings to an important in mathematics is infinitely large and small quantities. But whether Archimedes is able to operate a true mathematical infinity?

It seems that infinity is just an abstraction. But it is the Foundation of mathematical analysis is fundamental for virtually all modern engineering, physical and even economic calculations. Without it you cannot build a skyscraper, construct a plane or calculate the output of the satellite into orbit. Modern mathematical analysis were laid by Newton and Leibniz in the late seventeenth century, and almost immediately the world began to change. It work with infinity gave our civilization its technological power.

Thanks to the discovery and restoration of the Palimpsest of today, we do know that Archimedes infinity was calibrated instrument. His calculations were perfect, and the evidence is kept a careful inspection of modern mathematicians. It’s funny, but Archimedes quite often uses what in modern mathematics is called Riemann sums, after the famous mathematician… of the nineteenth century.

However, some of his methods apparently came «from another world», to the modern scientist, they are alien and unnatural. They are no worse and no better than the present, they are just different. It is rocket science, «genetically» has nothing to do with the modern.

What have we lost?

Sorry, but the discovery of the lost manuscript of Archimedes belatedly. In the XX century it became a sensation, but only in the history of science. What would happen if the manuscript fell into the hands of scholars for hundreds of years before? If its for another school read Newton? Or Copernicus? Or Leonardo da Vinci?

Even for mathematicians of the nineteenth century this work would be of more than academic interest. For scientists of XVII-XVIII century the value of it would be immense. And in the era of the Renaissance, once in the right hands, he would have produced a bombshell, completely redrawing the future development of mathematics and engineering. What we lost, lost for centuries access to the ancient book? Cities on Mars, interstellar space ships, clean fusion reactors? About it is anyone’s guess.

George CHALECKI

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