L'horlogerie suisse rend hommage à ses illustres prédécesseurs

Cette machine d’Anticythère n’en finit pas de nous étonner. Sa complexité est telle qu’immédiatement après sa découverte certains esprits très imaginatifs crurent qu’ils s’agissait d’un artefact extraterrestre. Rien que ça! Aujourd’hui, la firme Hublot rend hommage au génie grec qui fut à la base de l’horlogerie suisse et jurassienne Cette machine permet le calcul des posirions du Soleil et de la lune mais aussi des éclipses. Et vela il y a près de deux mille ans. Les savants grecs se sont basés sur les travaux de Geminos et d'Hipparque. Actualité récente Pour la première fois depuis 2.200 ans la machine d'Anticythère quitte la Grèce dans le cadre d'une exposition en Suisse

Algorismus, a well-known translator

Translator of Diophantus and Brahmagupta Algorismus, iranian translator [1] beter known during the arab occupation as Al-Khwarizmi, is without any contest the diophantus translator ever better known in the history of mathematics. He has not "created" algebra , it is only an arab’s legend [2]. Other cases of usurpation in mathematics — The Fermat ’s theorem was proved by Andrew Wiles. Fermat only talked about the theorem saying that he possessed the solution without any demonstration. Today the theorem is quoted asd Fermat-Wiles. Tomorrow the theorem will be quoted as Wiles theorem. — The hindu-arabic digits are in facts hindu digits. During the arab invasion of India, Arabs has exterminated the many part of the indian population (indian genocide or Hindu Kush), and copied (plagiarism) the hindu digits. What the historical sources exactly says Fallowing the works of Jens Hoyrup, professor at the university of Roskilde, we learn that Al-Khwarizmi (Algorismus in latin and in french) does not create the art (of mathematics) nor the manner to calculate. According to him, Al-Khwarizmi only produces a digest of all the mathematical techniques existing at this period [3]. He is not the «father of algebra» , he is only the translator of the works of Brahmagupta and Diophante. Al-Khwarizmi confessed in a letter adressed to the sultan that he was not the author of the techniques that he describes in his treatise. Rosen, who translates in english Al-Gabr w’al muqabala tell us that the vizier has demanded to Al-Khwarizmi to translate mathematical books and has encouraged him to write a treatise (Rosen : «That he was not the inventor of the Art is now well established»), synthesis of the different translations[4]. According to Morris Kline, emeritus professor at the Courant Institute of Mathematical Sciences (New York University), the Arabs don’t use the symbolism. The «algebra» they used use purely rhetorical, and in comparison to Hindus and Diophantus , a step behind[5] (page 192). According to him, they introcuced even a regression in arithmetic because they refused to use negative numbers, well-known at this period [5]. Nicolas Bourbaki, famous group of french mathematicians, in the chapter devoted to the evolution of algebra don’t talk about Arabs, except to evoke the translations of the results of greek and hindu mathematics. [6] (page 70). In the chapters devoted to linear algebra and commutative algebra, no trace, no quote of any Arab. [6] (pages 78-91), One can summarize this by saying that the contribution of the Arabs in the great history of mathematical is microscopic. When we open the "Encyclopedia of mathematics" and we read the heading "algèbra" , there is no contest : «Arithmetic of Diophantus (III rd century A.D.) has had a major influence on the development of algebraic ideas and symbols"(...) François Viète, end of XVIth century, was the first to use the letters of the alphabet to indicate the constants and the variables of a problem. Most of the symbols of today were known in the middle of the XVIth century, who is a benchmark of the end of the prehistory of algebra [7] (page 73) Morris Kline [10] take his time in his book «Mathematical Tought» to explain the origin of the word algebra, coming from the latin algebra. He explain that the word algebra is issued from spanish "algebrista", meaning «medical doctor and barber» , coming from al-gabr (name ot the book of Diophantus’s translation done by Al- Khwarizmi). By insisting on the origin of the word, we have no doubt that Morris Kline means that algebrista is a tribute to doctors who saves life and not to a mean translator. See akso The fabulous machine of Antikytera Références [1] Wikipedia : Algorismus, Disputatio : interpres ?,Wikipedia latin [2] Saqr Abou Fakhr, Non, l’Occident ne doit rien aux Arabes, Le Courrier International, 29 juillet 2004, http ://www.courrierinternational.com/article/2004/07/29/non-l-occident-ne-doit-rien-aux-arabes [3] Jens Hoyrup, "Algèbre d’Al-gabr" et "algèbre d’arpentage" au neuvième siècle islamique et la question de l’influence babylonnienne in D’Imhotep à Copernic, Cahiers d’Altaïr, pp 88-89, Peeters-Leuven, 1992 [4] Rosen, traduction anglaise d’Al-Gabr w’al muqabala, http : //www.wilbourhall.org/pdfs/T heAlgebraofMohammedBenMusa2.pdf [5] Morris Kline, Mathematical Thought From Ancient to Modern Times, Volume 1, Oxford University Press [6] Nicolas Bourbaki, Eléments d’histoire des mathématiques, Masson, 1994 [7] Reidel, Encyclopedia of mathematics, Volume 1, Kluwer Academic Publisher, 1998 Akso availabke in french and in english :

Le foncteur d’oubli

L’exemple classique que l’on donne pour un «foncteur d’oubli» est la projection d’un cube sur un plan parallèlement aux arêtes et perpendiculairement au plan. Le carré obtenu par la projection est celui d’un «oubli» de structure ; la structure cubique ayant été oubliée dans le carré. Un très bel exemple du foncteur d’oubli est celui du passage d’un vecteur à ses coordonnées : Gamma : (0,0,0) -> (x,y,z) peut être transformé par un foncteur d’oubli FO FO : Gamma -> Gamma ' avec Gamma ' : Phi (ensemble vide) -> (x,y,z) Une autre manière de voir le foncteur d’oubli FO FO : Gamma -> Im Gamma Im Gamma : (x,y,z) -> (x,y,z) Autrement dit nous pouvons écrire le foncteur d’oubli de la manière suivante : Il opère sur le domaine en transformant (0,0,0) en (x,y,z) et en transformant l’image en ellemême (x,y,z) en (x,y,z). Ce que nous pouvons écrire en une ligne FO : ( (0,0,0), (x,y,z) ) -> ( (x,y,z), (x,y,z) ) Une dernière étape consistera à ne regarder que l’image du vecteur transformé. Cela s’appelle un transport de structure.

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Les nombres complexes généralisés

On parle aussi de nombres complexes fendus ou déployés. La généralisation procède de la manière suivante : 1 ere généralisation On considère que pour le nombre complexe usuel x + y i, le nombre imaginaire i est solution de l'équation x² + 1 = 0. On écrit alors le nombre complexe sous la forme x + y (solution de x² + 1 = 0). On généralise alors en remplaçant la solution de x² + 1 = 0 par la solution d'une équation du second degré avec Delta négatif. On écrit alors x + y (solution de x² + p x + q = 0). Et on appelle I = solution de x² + p x + q = 0 avec Delta négatif (Delta vaut p² - 4 q) 2 eme généralisation. On procède de la même manière mais cette fois on utilise un Delta positif. Soit E = solution de x² + p x + q = 0. On écrit x + y E Source : Les nombres complexes et leur application en géométrie, Yaglom, éditions Dunod

Les couples en mathématiques sont les seuls qui en se disputent pas

Les psychologues disent que celui qui cherche à se disputer veut en réalité exister aux yeux de l’autre. La femme délaissée par son mari ou conjoint cherchera d’autant plus noise qu’elle suspecte une infidélité et donc d’être devenue transparente aux yeux de son chéri. En mathématiques, les couples ne se disputent pas. Même s’il y a une domination de l’un sur l’autre, cela ne génère aucun conflit. Effet, un couple est une paire ordonnée d’objets dont l’un appelé origine a en quelque sorte préséance sur l’autre appelé extrémité. Le couple (a,b) est en effet différent du couple (b,a) , alors que la paire { a,b } est égale à la paire { b,a}. Une paire, en mathématiques comme ailleurs, ce n’est pas un couple. Dans le premier cas, le couple (a,b) représente en mathématiques l’existence d’une flèche (celle de Cupidon pour les amoureux) entre les objets a et b, une flèche n’étant rien d’autre qu’un fil invisible reliant l’objet a à l’objet b (fil abstrait). Dans le deuxième cas, la paire {a,b} représente deux objets a et b placés dans un sac invisible. Le couple représente une fonction là où la paire représente un ensemble.

The fabulous machine of Antikytera

This machine of Anticytera couldn’t help astonishing us. Its device is so complex that immediately after its discovery some imaginative people thought the machine has been made by alien. Today the watchmaker firm Hublot dedicates a watch in a special tribute to the genious greek mathematician who created the first mechanical computer. The plagiarism of the first greek mechanical calculator The discovery of mechanical arab astrolabs by the english archeologists entails that some of them has imagined thet the arabs legends could have one hint of reality, ignoring the fact that the mathematical background was Greek. They forgot the fake news generated by the arabs shopkeepers in order to make increase artificially the prize of incens by telling fantastic reports where the son of the shopkeeper would have climbed huge mountains, wrestled with fierce beasts, and run in a deserted country to find the precious material. The recent discovery of a machanical calculator in the sea in a area very close to the island of Antikytera, created by Greeks following the works of Geminos or Hipparcos, and older than all the arab mechanical astrolabs has completely erased the myth of a ancient glorious arab civilization that only propagandists continues falsely to assert. The machine of Antikytera possess a very complicated network of gearwheel that the machine is still studying today in order to know how it works, when the arabs astrolabs copying a small part of its complexity are simplier and easy to understand. The production of gearwheels formed a noticeable industrial activity in the Roman Greece and was at the origin of the first automatic machine created by Jews and byzantine Romans in Sicilia. The arab’s legends Masses of sites saying that Arabs has everything invented flourish on the web, saying that they were influenced by spirits or surnatural entities, the djinns, only existing in the world of dreams. Many people has reacted to this false stories or fake news[1]. Don’t forget the character of the arab population prone to create imaginary stories like «The Sherazad stories about 1001 nights». So they imagined they would have been the first to create a plane. In reality, a tipsy redneck falling from a tower opened his coat and has imagined he could fly like a base jumper do it today. Unfortunately for this poor guy, his technique was not good enough and he died when he hit the ground. But the arab’s legends continues to talk about a «flying coat» and «miracle» like they did for «flying carpets» ! Let us give to Caesar back what belong to Caesar. Let us notice like an important giving to science by the Arabs the non-scientific character of astrology and the construction in Persia of the first astronomy observatories. The myth of the Golden Age of Al-Andalous Some writers, like Ibn Warracq [2] (page 291), evoked the myth of the Golden Age of Al- Andalous, and according to him this myth was created during Middle Age by Hebrews in order to underline the poor conditions of living in Spain after the Reconquista. It was in order to forget that the Jewish has been complied to convert to islam or to wear a small yellow circle on their jackets, genuine ancestor of the yellow David Star (imposed by nazis during the second world war). It was a manner to reach the oblivion of all the persecutions that muslims imposed to non-muslims [2], what they called dhimmis, meaning slaves. During the Reconquista, Hebrews settled in North Africa and imagined a mythic world, heaven for spirit towards the repression of the Spanish people (and Inquisition) who convert them by force threatening with torture or death penalty if they don’t. The transmission of the greek knowledge towards the West by the byzantinian Romans monks who translates it The intellectuel Arab from Gaza Saqr Abou Fakhr [3] refute the fact that the West could not have access to knowledge without Averroès and Ibn Khaldoun. He assert that «the main part of nationalists arab writers and muslims novellists continues to maintain the idea of a glorious old arab civilization». The idea that the Arabs have transmitted the Greek and Roman knowledge to the West has been completely denied by serious studies [4]. It’s the Roman byzantine monks returning from Constantinopolis who really have transmitted the antique knowledge to the West. The Arabs only translated from Greek to Arab and thought falsely that knowledge give power and their aim was to appropriate the power of other people. See Also Algorismus (Al-khwarizmi) a well-known translator References [1] Forum kabyle, http://www.kabyle.com/forum/non-les-arabes-nont-pas-invente-lalgebre [2] Ibn Warracq, Pourquoi je ne suis pas musulman, L’Age d’Homme, 1999 [3] Saqr Abou Fakhr, Non, l’Occident ne doit rien aux Arabes, Le Courrier International, 29 juillet 2004, http://www.courrierinternational.com/article/2004/07/29/non-l-occident-ne-doit-rien-auxarabes [4] Sylvain Gougenheim, Aristote au Mont-Saint-Michel, Seuil, Collection L’Univers Historique, 2008