Newsletter 7

Pythagoras Foundation Newsletter No. 7. December 2006. Website http://www.stichting-pythagoras.nl/ E-mailadres nico.bader@stichting-pythagoras.nl Editors Nico Bader, Marie-Anne de Roode This semi-annual Newsletter gives articles and a summary of literature, book reviews of recent publications concerning Pythagoras and Pythagoreans. Interesting internetsites, work in progress and conferences are included. We will be very pleased to receive information of books and (journal, internet) articles to keep our lists up to date. Nico Bader - Chairman of the Pythagoras Foundation. “Well known intellectuals through the Antique texts of Plato, Aristotle, Plutarch, Cicero, Ovid, Nicomachus, Macrobius, Martianus Capella, Boethius, and many others, the image of the brilliant yet humble sage from Samos had been slowly reconstructed through medieval times, when he was admired by many influential Christian scholars from Cassiodorus to Petrarch. His admirers were to be found in Spain and England as well as France, Italy, Constantinople, and the Arab world.” From: Joost-Gaugier, C.L. Measuring heaven. 2006. p 76. Contents: Introduction by M. de Roode Pythagoras Foundation Library information by N.G. Bader Acknowledgments Colophon, copyrights Ecology, Mathematics and Pythagoras. Mita Darbari L.Zhmud. Fellowship at the NIAS in Wassenaar, The Netherlands Numbers are male, said Pythagoras and the idea persists. M Wertheim Grand design in the work of Leonardo, Vitrivius, Plato and Herodotus. L.Greenhill Recent publications: Books Forthcoming books Recent publications: Chapters in books Internetsites Conferences / Presentations Recent publications: Book reviews Recent publications: Compact discs Recent publications: Journal articles 1 p 2 p 2 p 3 p 3 p 4 p 6 p 7 p 9 p 10 p 13 p 13 p 15 p 15

Introduction On Friday the 23th of September we went to the Buma Library (information centre for Classical Antiquity: part of TRESOAR) in Leeuwarden, Holland. It was the Library’s 130th anniversary and the th 68 meeting of the Dutch Classical Union. (Nederlands Klassiek Verbond). There were lectures, a guided tour through the Library and excursions to various places. We went to Franeker, a former university town. An impressive program and a pleasant event. Our compliments for the organization. The Library of the Pythagoras Foundation will be visited by the head collections Tresoar, L.A. de Vries and by the secretary and librarian of the Buma Library, H.A. Haagland. We like to thank everyone who did send us payments for expenses. The next newsletter will be issued in June 2007. We would appreciate to receive articles and information half of May 2007. With very best wishes for the New Year, Marie-Anne de Roode Pythagoras Foundation Library Information. The Library collects all publications concerning Pythagoras and Pythagoreans. The library is a lending library; also copies of articles can be ordered. Copy costs and postage will be calculated. The Foundation is a non-profit organisation; our Newsletter is free of charge. Donations, also in the form of articles or books are very welcome. The Pythagoras Foundation Thorbeckelaan 46 1412 BR Naarden The Netherlands Postbank: giro 27423. International Bank Account Number (IBAN): NL84 PSTB 0000 0274 23 BIC: PSTBNL21 Coming soon: article database available via our website. The article database contains about 4100 records (bibliographic information about journal articles, chapters or parts of books, internet articles, conference papers, etc.). A rich source of information about Pythagoras and Pythagoreans. We would like to make this information public via our website in May 2007. By using classification codes, it will be easy to select specific titles of items or articles. Book reviews. In our paper archives there are hundreds of book review articles. A start has been made to structure this interesting source of information. The next step will be to put this information into a database. We will keep you informed. Nico Bader

We would very much like to add the following books to the Library: Cumont, F. Cumont, F. Dieterich, A. Eden, K. Harms, W. Longrigg, J. Sijakovic, B. Tejera, V. Lux Perpetua, Paris, 1949 Recherches sur le symbolisme funeraire des Romains. 1966. Nektyia. Beitrage zur Erklarung der neutestamentischen Petrus Apkalypse. 1893. Friends hold all things in common. 2001. Homo viator in bivio. 1970. Greek rational medicine. 1993. Bibliographica praesocratica. 2001. Rewriting the history of ancient greek philosophy. 1997. Acknowledgements The Pythagoras Foundation thanks the following individuals for their contributions and generosities: Konstantine Boudouris, Geoff Bowe, Mita Darbari, Leslie Greenhill, Kristi Jauregi Ondarra, Graham Pont, Tony Preus and Leonid Zhmud. Corrections and additions. Re the article “Pythagorean communities: from the individual to the collective portrait” from Mr Zhmud, in Newsletter 6 (June 2006), the author’s information and a reference lacked. Leonid Zhmud is Professor at the Institute for the History of Science and Technology in St. Petersburg. He has published on ancient science and medicine and on early Greek philosophy and religion, especially Pythagoreism. He worked at numerous research institutes, including the Institute for Advanced Study at Princeton. His books include Wissenschaft, Philosophie und Religion im frühen Pythagoreismus (Berlin, 1997) and The Development of Technological Ideas in Antiquity, Middle Ages, and the Renaissance (St. Petersburg 1995, in Russian). The reference in the article is to Rose: Rose, V. Aristoteles pseudepigraphus. Uitgever: Hildesheim: Olms.1971. (Reprint Leipzig, 1863) Contains: Fragmenta Aristotelis philosophica; Fragmenta historica cum appendica Anecdotorum Aristotelicorum Colophon Pythagoras Foundation Newsletter. Semi-annual Newsletter of the Pythagoras Foundation. Editors: Nico Bader, Marie-Anne de Roode. Address: Thorbeckelaan 46. 1412 BR Naarden. The Netherlands. E-mail : nico.bader@stichting-pythagoras.nl Website: http://www.stichting-pythagoras.nl/ Editorial Board: in progress. Advisory Board: in progress. ISSN: 1872-3241 (online version); 1872-3233 (print version). COPYRIGHT / USAGE NOTICE: PLEASE READ Contents of the Pythagoras Newslettter are copyright 2006 by the Pythagoras Foundation. The newsletter may be freely distributed in electronic or print form provided its contents are not altered and credit is given to the Pythagoras Foundation, Thorbeckelaan 46, 1412 BR Naarden, The Netherlands. If you wish to unsubscribe to this Newsletter, send an e-mail message to info@stichting-pythagoras.nl

Mita Darbari Ecology, Mathematics and Pythagoras Pythagoras and Mathematics is understandable but Ecology is, comparatively, a new term and what it has to do with Pythagoras who lived almost two thousand and five hundred years ago? Pythagoras is, according to Bertrand Russell, intellectually one of the most important men that ever lived.(1) The term “ecology” is derived from the Greek word oikos meaning “household”.(2) The house (oikos) is a place where its inhabitants relate to one another and dynamically interact. As the house provides a shelter for people to live, in the same way, the universe provides a haven for the infinite manifold of unanimated and animated forms to exist and evolve together. Pythagoras may have been the first to use the term cosmos (3) to imply that the entire universe has order, which could be understood by mathematics as he postulated that the natural laws of harmony of the microcosm of music, of the human soul, biological life and of the cosmos were identical. Pythagoras, considered as the father of pure mathematics, not only studied Mathematics but tried to answer many philosophical questions, which are still uppermost in the minds of those who are concerned with existence, ethics, the human condition, and our relationship to the nature. For Pythagoras, Mathematics and geometry were sacred tools for uncovering the true nature of the universe. Pythagoras taught that the entire universe is one vast system of mathematically correct combinations. Among the Pythagoreans the monad was the first thing that came into existence. It was the number one, identified by the Pythagoreans with the unit point that was the epitome of exact objectification. From the unit point came all the numbers, and from numbers came the whole universe. The Pythagoreans considered the Monad as the beginning of all things, just as a point is the beginning of a line, a line of a surface, and a surface of a solid, which constitutes a body. A point implies a preceding Monad, so that it is really the principle of bodies, and all of them arise from the Monad. (4) Pythagorean dualism is expressed in terms of ten contrarieties (The Ten Pythagorean Principles): limit and unlimited, odd and even, one and plurality, right and left, male and female, resting and moving, straight and curved, light and darkness, good and bad and square and oblong. The contrarieties odd and even, square and oblong are related to the Pythagorean representation of numbers as patterns of dots. FIGURE 1 The reconciliation of these opposites creates harmony. For human behavior, this was harmony resulted from behaving temperately or by exhibiting moderation. One, the Monad, was the principle of Unity from which all things begin. Two, the Dyad, was Duality. It was both the beginning of strife and the possibility for the development of relationships between things, as everything is no longer the same. The Triad, Three, forms a bridge, allows relation between the two extremes. According to Porphyry, Things that had a beginning, middle and end the Pythagoreans denoted by the number Three, saying that anything that has a middle is triform, which was applied to every perfect thing. (5) The Pythagoreans called the number Four the "Key-bearer of Nature." This was because, as mentioned before, numbers are an arrangement of points. One point represented the number one, the beginning of all geometrical matter. A point has no length, breadth, or thickness (with zero dimensions). When the number one goes from the world of concept to the world of matter, it is

extended and becomes divisible, thus allowing for two. The first extension into the first dimension is a line. The line has length, but no breadth or thickness (one dimension). It is the dyad, polarity. A triad is superfice with length and breadth. It is the visible (two) dimensions. Three points represent a surface. It is a trinity. The number four may be described geometrically as the first solid: It has length, breadth, and thickness. It takes us into the third dimension. (Figure 2) It has been described as the first descent into matter. Four is also, coincidentally the number of elements that exist: air, fire, earth, and water. From these elements comes the world. FIGURE 2 Pythagoras taught that both man and the universe were made in the image of God; that both being made in the same image, the understanding of one predicated the knowledge of the other. He further taught that there was a constant interplay between the Grand Man (the universe) and man (the little universe). Pythagoras said that man was a microcosm; which means, a compendium of the universe not because, like other animals, even the least, he is constituted by the four elements, but because he contains all the powers of the world. For the world contains Gods, the four elements, animals and plants. All of these powers are contained in man. He has reason, which is a divine power; he has the nature of the elements, the powers of moving, growing, and reproduction. However, in each of these he is inferior to the others. For example, an athlete who practices five kinds of sports, and diverting his powers into five channels, is inferior to the athlete who practices a single sport, so man having all of the powers, is inferior in each. Than the gods, we have less reasoning powers; and less of each of the elements than the elements themselves. Our anger and desire are inferior to these passions in the irrational animals; while our powers of nutrition and growth are inferior to that in plants. Constituted therefore of different powers, we have a difficult life to lead. (6) Although dualism was evident throughout Nature, the fusion of opposites held the secret of balance. Only in Oneness was true identification with God possible. God was equated with love, which pervaded the entire universe. The soul of the individual and that of the Earth and universe were intimately linked. There are even some faint allusions that both Pythagoras and Plato seemed to regard the living beings of the Earth as the eyes and senses of God. This microcosm-macrocosm idea, which seems ever more pertinent today in a world racked by fragmentation, is in fact strikingly similar to the contemporary concept of deep ecology, which believes in the absolute relativity of existence. But to Pythagoras, this was not merely confined to the material world. He viewed death as a passageway on the continuing journey of the immortal soul, whose re-incarnation would be determined by the values of previous deeds. A devout vegetarian, who considered animal sacrifices in the temples to be a sacrilege, (7) he believed that pain inflicted upon Nature would inevitably return to haunt humankind, both spiritually and physically. According to Porphyry, (8) Pythagoras taught that the soul was immortal and that after death it transmigrated into other animated bodies. After certain specified periods, the same events occur again; that nothing was entirely new; that all animated beings were kin, and should be considered as belonging to one great family. And hence Pythagoras taught that friendship was the truest and nearest perfect of all relationships. He declared that in Nature there was a friendship of all for all; of gods for men; of doctrines one for another; of the soul for the body; of the rational part for the irrational part; of philosophy for its theory; of men for one another; of countrymen for one another; that friendship also existed between strangers, between a man and his wife, his children, and his servants. (9) Pythagoras taught that all animated beings were kin, and should be considered as belonging to one great family and so he believed in universal friendship and hence he commanded: (10) Not to destroy or injure a cultivated tree, nor any animal either which does not injure men. Pythagoras not only saw vegetarianism as the key to peaceful human co-existence but also recognized the health advantages of a meat-free diet.

… he even forbade men to kill animals at all, much less would have allowed his disciples to eat then, as having a right to live in common with mankind.(11) For Pythagoreans, all souls spring from the same source and inhabit every living thing. It follows from this that all living things are related and there is literally a kinship of nature. Their beliefs about the soul in conjunction with their view the Cosmos is harmonious leads them to the ethical position that the task for human beings is to ensure that they live in conformity with the harmony of the cosmos. This can be achieved by following the ethical principles laid down by the community. Mita Darbari. Head of Department, Mathematics, St. Aloysius College, Jabalpur. References and notes 1. Russell Bertrand; History of Western Philosophy; Rouledge; London; 2004; Page 38. 2. Encyclopedia- msn.Encarta. Online. Cited on 13-02-2006. http://encarta.msn.com/encylopedia_761576703_4/Ecology.html#howtocite. 3. Diogenes Laertius, Life of Pythagoras; XXV. 4. Anonymous Biography of Pythagoras; 7; Preserved by Photius. Online. Cited on 07-02-2006. http://www.completepythagoras.net/volume1/photus.html 5. Porphyry; Life of Pythagoras; 51. Online. Cited on 07-02-2006. http://www.completepythagoras.net/volume1/porphyry.html 6. Anonymous Biography of Pythagoras; 15; Preserved by Photius. Online. Cited on 07-02-2006. http://www.completepythagoras.net/volume1/photus.html 7. Diogenes Laertius, Life of Pythagoras; XIX. 8. Porphyry; 19. 9. Iamblichus; Life of Pythagoras; XXXIII 10. Diogenes Laertius, Life of Pythagoras; XIX. 11. Diogenes Laertius, Life of Pythagoras; XIX. L. Zhmud, Fellowship at the NIAS* in Wassenaar, the Netherlands. 1 September 2006 - 30 June 2007 Leonid Zhmud, born in Lvov, USSR (now Ukraine), in 1956. Ph.D. from St. Petersburg University. Research Fellow at the Institute for the History of Science and Technology, St. Petersburg. A HISTORY OF EARLY PYTHAGOREANISM My research concerns one of the most vexed problems in early Greek philosophy and science. Pythagoras, arguably the most influential thinker among the Pre-Socratics, is at the same time the most elusive one. He was not the only Pre-Socratic who left no writings, or the only one involved in religious and political activity. It is rather a peculiar combination of these (and many other) circumstances that made him such a controversial figure. Most of the Pythagoreans, however, were as 'normal' as any other Pre-socratic. Their 'normality' ensured the continued existence of Pythagoreanism as a philosophical and scientific school, after the political domination of the Pythagorean societies in Italy was destroyed and the legend of Pythagoras became a part of popular tradition. Continuing my earlier studies in Pythagoreanism my future book attempts to analyse in detail every major aspect of Pythagorean activity against its own background: religious, political, philosophical and scientific. Wissenschaft, Philosophie und Religion im frühen Pythagoreismus. Berlin: Akademie Verlag, 1997. 313 p. Überlegungen zur pythagoreischen Frage, in: Frühgriechisches Denken. Ed. by G. Rechenauer. Göttingen 2005, 135-151. The Origin of the History of Science in Classical Antiquity. Berlin: W. de Gruyter, 2006. 332 p. http://www.nias.knaw.nl/en/research_group_2006_07/zhmud_l * The Netherlands Institute for Advanced Study (NIAS) in Wassenaar offers "A year to think" to approximately fifty carefully selected fellows each year. Scholars who have already made a significant contribution to their field are given the opportunity to devote themselves exclusively to their own academic projects for a ten-month period, individually or as part of a research theme group.

NYTimes, October 3, 2006 Numbers Are Male, Said Pythagoras, and the Idea Persists Margaret Wertheim. When I was a physics major in the late 1970’s, my very few fellow female students and I had high hopes that women would soon stand equal with men in science. But progress has proved slower than many of us imagined. A report last month by the National Academy of Sciences documents widespread bias against women in science and engineering and recommends a sweeping overhaul of our institutions. While there may indeed be subtle biological differences contributing to the scarcity of women in the top ranks of science, interviews make clear that many female scientists continue to experience both overt and covert discrimination. The academy’s report is welcome, yet there is reason to believe that when it comes to the mathematically intensive sciences like physics and astronomy, it is not just bureaucracies that stand in the way. Female physicists, astronomers and mathematicians are up against more than 2,000 years of convention that has long portrayed these fields as inherently male. Though women are no longer barred from university laboratories and scientific societies, the idea that they are innately less suited to mathematical science is deeply ingrained in our cultural genes. The problem goes back to the ancient Greeks, particularly to Pythagoras, the philosophical giant who dreamed the dream that became modern physics. Pythagoras almost certainly learned his famous theorem about right-angled triangles from the Babylonians, but we owe to him a far greater idea: “All is number,” he declared, becoming the first person to say that the physical world could be described by the language of mathematics. Pythagoras also gave us the idea of the “music of the spheres,” a set of mathematical relationships that would describe the structure of the universe itself. His vision would eventually give rise to the scientific revolution led by Copernicus, Kepler, Galileo and Newton. The search for a theory of everything today is the latest version of the ancient Pythagorean quest for divine “cosmic harmonies.” Though many cultures have developed sophisticated mathematical traditions, including the Chinese, the Arabs, the Indians and the Mayans, the West is the one that came to see the material world as an embodiment of mathematical laws. And from the beginning, the search for such laws was viewed as an innately male activity. The Pythagorean society of the fifth century B.C. was a cradle of mathematical research, but Pythagoreanism was also a religion, and like many Greek cults its beliefs were dualistic. For Pythagoreans, reality consisted of two parts: on one side were the mind and spirit and the transcendent realm of the gods; on the other side were the body and matter and the mundane realm of the earth. Like many Greek thinkers, the Pythagoreans associated the mind/spirit side of reality with maleness and the body/matter side with femaleness. Pythagoras introduced numbers into this mix and put them on the male side of the ledger. In the Pythagorean system, thinking about numbers, or doing mathematics, was an inherently masculine task. Mathematics was associated with the gods, and with transcendence from the material world; women, by their nature, were supposedly rooted in this latter, baser realm. At the end of the Middle Ages, Pythagorean interest in a mathematical approach to science began to gain ground, and it is here that we begin to see the seeds of modern physics. “The creation of number was the creation of things,” Thierry of Chartres wrote in the 12th century, when the first universities were formed and academic learning was formalized. The universities were founded to educate the clergy, and since women could not be priests they could not attend. Many university departments did not admit women at all until the early 20th century, and physics departments were often among the last to accept students and professors who were women. The Pythagorean association of mathematics with transcendence was easily imported into a Christian context, giving rise to the idea of the Judeo-Christian god as a mathematical creator. When Stephen Hawking links a theory of everything to the mind of god today, he is reiterating an essentially Pythagorean view. But this godly-mathematical connection also sat easily with the Catholic tradition of a male-only priesthood. Thus, from the start, women were excluded from this academic field and its associated sciences. When the early scientific societies formed in the 17th and 18th centuries, most continued this misogynistic trend. Henry Oldenburg, an original secretary of the Royal Society in Britain, wrote that the organization’s mission was to “raise a Masculine Philosophy.” Not until 1945 did this bastion of science admit a woman as a full member. Female physicists have continued to confront deep-seated prejudices. Emmy Noether, who discovered that all physical conservation laws were associated with mathematical symmetries, was

a contemporary to Einstein and helped work out some of the math of general relativity. She did so without a formal academic position and mostly without pay. Lise Meitner, who developed the theory of nuclear fission, was not included when the Nobel Prize was given for this work in 1944. The Harvard University physics department did not give tenure to a woman until 1992. This week, the Swedish Academy announces the Nobel Prizes in science. It will be remarkable if any women are on the list. Marie Curie won a Nobel in physics in 1903; the only woman to follow her was Maria Goeppert Mayer in 1963, when she shared the award for her theory about the structure of atomic nuclei. In mathematics women have fared even worse. The Fields Medal, the mathematical equivalent of a Nobel, has never gone to a woman. Many women who have gone into science since the 1970’s continue to be stunned at how slow change has been. Gail G. Hanson, distinguished professor of physics at the University of California, Riverside, and the only woman to have won the W. K. H. Panofsky Prize in experimental particle physics, said by phone: “At this point there seems to be an acceptance of women in science at relatively junior levels. But once we get to more senior levels, a kind of antagonism sets in.” As a postdoctoral fellow at the Stanford Linear Accelerator Center, Dr. Hanson discovered quark jets, the work for which she would later be awarded the Panofsky Prize. Yet throughout her research career, she said, she has continued to be treated like a junior colleague, not like a leading researcher. Dr. Hanson is the subject of a chapter in a new book tracing the lives and work of 40 outstanding female physicists of the past century. Called “Out of the Shadows” and edited by Nina Byers and Gary Williams, physicists at the University of California, Los Angeles, the book recounts the barriers many of these women faced — and continue to face today. A number of younger female physicists contacted for this article agreed that bias remained real, but they did not want to be quoted on the record. With sadness and anger evident in her voice, Dr. Hanson said: “I thought these kinds of things only happened in the 1950’s. It’s appalling that women still confront these hurdles.” She added: “And when you get the prizes, you’re often treated even worse. Men can tolerate a woman in physics as long as she is in a subordinate position, but many cannot tolerate a woman above them.” The National Academy’s report states that we still have a long way to go. Compared with their male colleagues of similar experience, female scientists and engineers are underpaid, undervalued and underrepresented in the top tiers of science. Given the long history of antipathy toward women of a mathematical bent, it was perhaps naïve to think we could change our institutions in a generation. It is not just bureaucratic will that needs to shift; it is the cultural zeitgeist. Margaret Wertheim is the author of “Pythagoras’ Trousers,” a cultural history of physics and women. New York Times. October 10, 2006. Letters To the Editor: Pythagoras and Gender Re “Numbers Are Male, Said Pythagoras, and the Idea Persists” (Oct. 3): Margaret Wertheim is absolutely correct in noting the scarcity of women in the top ranks of science, and that while there may be subtle biological differences that come into play, the most important contributing factor is women’s experience of both overt and covert discrimination. However, presenting Pythagoras as a prototypical example of male chauvinism in the science of antiquity is a less than perfect choice. While the Pythagoreans may have been male-dominated, they provided a fairly favorable social climate in which women could pursue scholarly studies. There is evidence that women were active members of the Pythagorean school, not only as students, but also as scholars and teachers. One of the most prominent women in ancient mathematics was Pythagoras’ wife, Theano. So here is another aspect of the unequal treatment that women in science have received throughout history: our society’s selective amnesia in regard to women in science. Caroline Herzenberg, Chicago To the Editor: Blaming the ancient Greek philosopher Pythagoras for the persistent bias against women in the sciences is an interesting idea, if perhaps a bit far-fetched. However, claiming that Pythagoras held that numbers as such are inherently male is misleading. On the contrary, as we are told by Aristotle, the Pythagorean school (always interested in binary oppositions) considered odd numbers male, but even numbers female. In a world that is all number, women thus do have their natural place. Katharina Volk, New York

New exposition (8600 words) Grand design in the works of Leonardo, Vitruvius, Plato and Herodotus Leslie Greenhill © ABSTRACT Leonardo da Vinci’s image of Vitruvian Man, man the microcosm, is the most famous illustration of its kind. Da Vinci’s layout of man’s body in a square and a circle is derived from a formulation found in the influential treatise The Ten Books on Architecture written some two thousand years ago by the Roman architect and engineer Vitruvius. Using original text and material from authoritative sources, it is demonstrated that certain critical design elements in the body’s layout can be linked to other historically significant designs found in Vitruvius’s treatise, in the famous layout of Atlantis as described in Critias by the Greek philosopher Plato (as well as in the philosopher’s description of the structure of the Soul in the Timaeus), and in a number of inventive formulations in a renowned classical work The Histories by Herodotus. The influence of Pythagoreanism on the designs and formulations is examined. The material in this exposition radically changes notions of design and the nature of Greek and Roman measures in antiquity. (A short presentation that demonstrates the substance of these claims is available on request.) Vitruvian Man as rendered by Leonardo da Vinci Further information Author’s email address: lesgreenhill@yahoo.com.au Tel: (Melbourne, Australia) 9583 6771 • Mobile: 0417 926 592

Recent publications. Books Arslan, A. I lkc ag felsefe tarihi Istanbul Bilgi Universitesi. 2006. ISBN: 9756176601 Subjects: Philosophy, Ancient History. Pythagoras and Pythagorean school. Birnbaum, J. Der Apollontempel von Didyma: Analyse einer pythagoreisch-platonischen Entwurfskonzeption Hochschulschrift: Berlin, Techn. Univ., Diss., 2006 Anmerkungen: Dateiformat: tgz, Dateien im PDF-Format Brunaux, J-L. Le Druides et autres legendes celtiques. Broché. 2006. ISBN : 2020796538 Commentaires: Des druides, nous avons l'image confuse - et fausse - de magiciens aux pouvoirs surnaturels, de prêtres en toge blanche sacrifiant au coeur de profondes forêts. Plus de deux mille ans de commentaires antiques, de rêveries romantiques puis d'idéologies nationalistes ont façonné cette image qui ne peut aujourd'hui satisfaire l'historien. À ces fantasmagories, il faut opposer l'image - plus réelle - de druides philosophes. Les Grecs font en effet des druides gaulois les maîtres de Pythagore. Nous sommes loin de l'image de Panoramix, et plus proches de Platon. Ellis, E. V. Squaring the circle: The regulating lines of Claude Bragdon's Theosophic architecture Virginia polytechnic institute and state university. 2005, 407 pages Abstract: Traditionally, squaring the circle has been about bringing the incommensurable work of the gods within the realm of the commensurate by using infinite cosmic principles to regulate the finite world. The American architect Claude Bragdon (1866-1946) squared the circle using his Theosophic architectural theory that was based on a neo-Pythagorean emphasis on Number, which he believed to have contained the secret of the universe. America at the turn of the 20th century was interested in Eastern spirituality at the beginning of an age of scientific relativity when the world and universe were being questioned due to new scientific discoveries based on higher-dimensional mathematical speculations that challenged relationships between humankind and the cosmos. Paralleling this scientific search was the Western conquest of the world on earth, which brought back speculations about the Near and Far East, including translations of their ancient scriptures and encyclopedias of their architecture. The fourth dimension was an imaginary mathematical (re)creation of great interest to Bragdon and common to scientific relativity and Eastern spirituality; two cultural constructs that altered the perception of time and space to affect the American imagination and architectural production. Within this context, Squaring the Circle investigates the relationship of theory to practice by considering Bragdon's architecture as the material manifestation of his Theosophic architectural theory. Empedocles. Peri physeos / Empedokleoys. Alpignano (Torino): A. Tallone, 2006. Note: Issued in a case. - Greek text with Italian transl. and critical essays - 150 num. copies printed. Cont. 1 text by Jean Zafiropulo (pp. 63- 69). - Author's name on t.p.: Empedokleoys Fauvel, J. Music and mathematics : from Pythagoras to fractals. Oxford Univ. Press, 2006. ISBN 0-19-929893-9 Fichtner, L. Apel·les Fenosa - die vier Elemente, the four elements: auf den Spuren des Empedokles; 28.01. - 26.03.2006, Hessisches Landesmuseum Darmstadt; [anlässlich der Sonderausstellung Apel·les Fenosa. Die Vier Elemente] Fenosa, Apel·les [Ill.]. 2006. ISBN: 84-343-1089-9 Freyburger, G. et al. Sectes religieuses en Grèce et à Rome dans l'Antiquité païenne Paris: Belles Lettres, 2006. Serie Collection Realia. ISBN 2-251-33820-9 Gómez Pérez, M.A. Pitágoras México, D.F. Grupo Editorial Tomo, 2005

Graham, D.W. Explaining the cosmos : the Ionian tradition of scientific philosophy Princeton, N.J.: Princeton University Press, 2006. ISBN:: 0691125406 Contents: The Ionian program -- Anaximander's principles -- Anaximenes' theory of change -- The generating substance theory as an explanatory hypothesis -- Heraclitus's criticism of Ionian philosophy -- Parmenides' criticism of Ionian philosophy -- Anaxagoras and Empedocles: Eleatic pluralists -- The elemental substance theory as an explanatory hypothesis -- The atomist reform -- Diogenes of Apollonia and material monism -- The Ionian legacy. Graf, F. Mystica, Orphica, Pythagorica / Walter Burkert . Göttingen: Vandenhoeck & Ruprecht, 2006. Kleine Schriften / Walter Burkert ; Band 3. (Hypomnemata. Supplement-Reihe) . ISBN: 3-525-25272-2, 978-3-525-25272-7 Im Zentrum von Burkerts Forschungen: Religion Dieser Band der Kleinen Schriften Walter Burkerts ist einer der vier Bände (von insgesamt acht), die der religionswissenschaftlichen Forschung Burkerts gewidmet sind. Er konzentriert sich auf seine Schriften zu Pythagoreismus und Orphik. Walter Burkert ist einer der profiliertesten und bedeutendsten Forscher zur griechisch-römischen Antike der Gegenwart. Der vorliegende Band der Kleinen Schriften konzentriert sich auf Pythagoreismus und Orphik. 1962 hatte Burkert die Studien zum Pythagoreismus revolutioniert; zahlreicheArtikel aus jener Schaffensphase greifen einzelne Aspekte des Phänomens auf und sind bis zum heutigen Tag wegweisend geblieben. Die Arbeiten zur Orphik - einer religiösen Bewegung, die eng mit den Mysterien des Dionysus verbunden war - haben Burkert während seiner gesamten Forschungslaufbahn beschäftigt, nicht zuletzt deswegen, weil in den letzten dreißig Jahren immer wieder zentrale Texte publiziert worden sind, zu deren Verständnis Burkert Entscheidendes beigetragen hat. Huffman, C.A. Philolaus of Croton : Pythagorean and presocratic ; a commentary on the fragments and testimonia with interpretative essays Cambridge [u.a.]: Cambridge Univ. Press, 2006. ISBN 0-521-02471-4 Kai make s, P. Philosophia kai mousike : he Aristotele kai ton Plo tino Athe na: Metaichmio, 2005. ISBN: 9603757934 mousike stous Pythagoreious, ton Plato na, ton Kalogerakes, G. Apollonios Tyaneus. Theos ste ge; yper Apolloniu Tyaneos logos apantese stis christianikes sykophanties. Thessalonike, Dion. (2006). Lang, F. Mitt liv som Pythagoras Uitgever: Esbo : Schildt. 2005. ISBN: 951-50-1510-3 Malaspina, E. Cicerone il letterato, il politico, l' uomo. Novara, De Agostini scuola S. p. A. Petrini editore. Progetto Chorus. Gli autori. Somnium Scipionis e antologia dalle opere. IX, 2005. Marquet, Y. Les "Frères de la pureté", pythagoriciens de l'Islam : la marque du pythagorisme dans la rédaction des Epîtres des Iḫwān aṣ-Ṣafā Paris: S.E.H.A., 2006 Moran, B. Memories of divinity: The divine proportion in Whit Stillman's 'Barcelona' and Dan Brown's 'The Da Vinci Code' University of Manitoba (Canada). 2005, 147 pages Abstract: 'Memories of Divinity: The Divine Proportion in Whit Stillman's Barcelona and Dan Brown's The Da Vinci Code ' ties the divine proportion to celebrations of the divine feminine endorsing empire as betrayals the Pythagorean cosmology that founded the proportion. Fusing theology, mathematics, architecture, art, ideology and politics in republicanism, specifically in Plato's Republic, the legacy of the divine proportion has been ironically winnowed to create the aesthetic identity of empire, mirrored in the subversion through co-option of the republicanism inherent in early Christianity. Aesthetic reading of the icons of western cultures after Rome exhibits the tension between the imperial cooption of republican aesthetics and republican ideology. da Vinci's De Divina Proportione acts as a

Vitruvian fusion of ideology and aesthetics to create meaning, through the republican engine of symbolic metaphor in art. Whit Stillman's Barcelona exposes the ironic application of the republicanism inherent in both early Christianity and the divine proportion by dominant imperialist powers through the problematic celebration of beauty as the locus of memories of divinity in a postChristian world. Central in Barcelona is the enigmatic place of the imperialism of the American Republic, the difficulties of the imperial republican and the resulting challenge for a personal search for meaning. Pythagorean beauty defines meaning in Barcelona, whilst meaning is redefined into republican equivocality. Inversely, Brown's The Da Vinci Code, co-opts the divine proportion to claim an encoding of empire. Brown's Empire however is a tyranny of the divine, a suppressed rightful throne which reconfigures the republics of Christ and Pythagoras into the ultimate empire. Navarro Antolín, F. Comentario al "Sueño de Escipión" de Cicerón Madrid: Editorial Gredos. 2006. ISBN: 8424928512 Nisticò, G. Da Pitagora a Colombo : il sogno dell'America = From Pythagoras to Columbus : the dream of America Milano: Spirali, 2006. ISBN: 8877707348 Otaola, P. El De musica de san Agustín y la tradición pitagórico-platónica Valladolid: Estudio Agustiniano, 2005. ISBN: 8485985923 Pégolo, L. La música de las esferas : textos de Cicerón, Macrobio, Favonio Buenos Aires, Argentina: Secretaría de Cultura de la Nación, 2006. ISBN: 9879161130 Persons: Marcus Tullius Cicero; P Cornelius Scipio Aemilianus, Africanus minor; Scipio, Africanus Primavesi, O, Kosmos und Dämon bei Empedokles. Der Papyrus P. Strasb. gr. Inv. 1665-1666 und die indirekte Überlieferung. Vandenhoeck & Ruprecht. 2006, Hypomnemata 116. ISBN 3-525-25213-7 Raventós, J. Comentarios al sueño de Escipión Madrid : Ediciones Siruela, 2005. ISBN: 8478449264 Schmidt, H.J. Prof. Dr. Brian Teaser: Stationenlernen "Satz des Pythagoras" Köln: Aulis-Verl. Deubner, 2006. Schriftenreihe: Kopiervorlagen Mathematik. ISBN: 3-7614-2540-6 Sommer, A.F.W. Harmonices mundi libri V: Lincii Austriae, 1619 Wien: Im Selbstverlag, 2005. ISBN: 3902484969 Contents: "Quorum primus geometricus, de figurarum regularium, quæ proportiones harmonicas constituunt, ortu & demonstrationibus. Secundus architectonicus, seu ex geometria figurata, de figurarum regularium congruentia in plano vel solido. Tertius propriè harmonicus, de proportionum harmonicarum ortu ex figuris; deque natura & differentiis rerum ad cantum pertinentium, contra veteres. Quartus metaphysicus, psychologicus & astrologicus, de harmoniarum mentali essentia earumque generibus in mundo; præsertim de harmonia radiorum, ex corporibus cœlestibus in terram descendentibus, eiusque effectu in natura seu anima sublunari & humana. Quintus astronomicus & metaphysicus, de harmoniis absolutissimis motuum cœlestium, ortuque eccentricitatum ex proportionibus harmonicis. Appendix habet comparationem huius operis cum Harmonices Cl. Ptolemæi libro III. cumque Roberti de Fluctibus, dicti Flud. medici oxoniensis speculationibus harmonicis, operi de Macrocosmo & microcosmo insertis" -- Original t.p. Thiel, D. Die Philosophie des Xenokrates im Kontext der Alten Akademie München: K.G. Saur. 2006. Reihe Beiträge zur Altertumskunde ; Bd. 231. ISBN: 978-3-598-77843-8, 3-598-77843-0 Warm, H. Die Signatur der Spharen : von der Ordnung im Sonnensystem Hamburg : Keplerstern Verlag, 2004. ISBN: 3935958129 Das Buch enthält die erstmalige Veröffentlichung der Entdeckung einer vielschichtigen Ordnung, welche die Abstände, die Geschwindigkeiten und die Konjunktionsperioden der Planeten sowie die Rotationen der Sonne, der Venus und des Mondes umfaßt. Um auch dem Laien eine fundierte Auseinandersetzung mit der Thematik - sowohl in fachlicher als auch in philosophischer Hinsicht - zu ermöglichen, beinhaltet es darüber hinaus

- eine Einführung in den grundlegenden Aufbau des Planetensystems - die Darstellung und Analyse der wichtigsten verschiedenen Vorstellungen zur “Sphärenharmonie” von der Antike bis in die Gegenwart - unter besonderer Berücksichtigung der Ideen Johannes Keplers - Erläuterungen der aktuellen wissenschaftlichen Erkenntnisse über die Entstehung und Zukunft des Sonnensystems, über den Ursprung des Universums und seine Strukturen - einen ausführlichen Anhang zu den behandelten Themen aus Astronomie, Musiktheorie, Geometrie und Arithmetik. Zhmud, L. The Origin of the History of Science in Classical Antiquity. Transl. by Chernoglazov, Alexander Walter de Gruyter GmbH & Co. KG, Berlin. 2006. ISBN 978-3-11-017966-8 Reihe: Peripatoi / Philologisch-Historische Studien zum Aristotelismus 19 Contents. Introduction. Chapter 1: In search of the first discoverers: Greek heurematography and the origin of the history of science. Chapter 2: Science as técnh: theory and history. Chapter 3: Science in the Platonic Academy. Chapter 4: The historiographical project of the Lyceum. Chapter 5: The history of geometry. Chapter 6: The history of arithmetic and the origin of number. Chapter 7: The history of astronomy. Chapter 8: Historiography of science after Eudemus: a brief outline. Forthcoming books Primavesi, O. Über die Lehrmeinung der Pythagoreer Berlin: Akademie Verlag Berlin, 2007. Schriftenreihe: Aristoteles - Werke in deutscher Übersetzung Aristoteles. Band 20/ II ISBN: 3-05-003734-2 Gemeinsam mit den Fragmenten aus Philolaos und Archytas bilden die Nachrichten des Aristoteles das Fundament für die Rekonstruktion des älteren Pythagoreismus. Während andere Überlieferungen einem eher vorsokratischen Wissenschaftsbegriff verpflichtet sind, decken die Berichte des Aristoteles die ganze Skala von der Pythagoraslegende über die urtümliche Lehre der Akusmata und Zahlensymbolik bis zur Astronomie des Philolaischen Systems ab. Spätestens seit Andronikos von Rhodos (1. Jh. v. Chr.) wurden die beiden speziellen Aristotelischen Abhandlungen unter dem Titel "Über die Lehrmeinung der Pythagoreer" zu einer Pragmatie in zwei Büchern vereinigt. Die erhaltenen Fragmente daraus werden hier in deutscher Übersetzung vorgelegt und kommentiert. Chapters in books Brague, R. Ni Empédocle ni Plotin. Pour le dossier du pseudo Empédocle arabe. p 251-264. In: Agonistes : essays in honour of Denis O'Brien / edited by John Dillon and Monique Dixsaut. Aldershot, Hants, England ; Burlington, VT : Ashgate, 2005. Dillon, J. Empedocles' cosmic cycle in the later Platonist tradition. p 211-218. In: Agonistes : essays in honour of Denis O'Brien / edited by John Dillon and Monique Dixsaut. Aldershot, Hants, England ; Burlington, VT : Ashgate, 2005. Gauger, J.D. Aristoxenos. I. Leben. II. Werk. III. Theorie der Tonfolgen. IV. Rhythmik. V. Zum Pythagoreismus. p 141-144. In: Lexikon des Hellenismus. 2005. Hrsg. von Hatto H. Schmitt und Ernst Vogt. Wiesbaden: Harrassowitz Verlag.

Lorusso, A.M. Dal semplice al complesso: valenza strutturale e didattica della tecnica dell' eco in Empedocle. p 109-124 In: Quaderni del Dipartimento di Filologia, Linguistica e Tradizione Classica »Augusto Rostagni«. Università degli studi di Torino. (Bologna: Pàtron Editore). 2005. Lucarini, C. Martinus: Filostrato e Apollonio di Tiana. In: Studi ellenistici. XVI. 2005. Biagio Virgilio (Ed.). Pisa: Giardini editori e stampatori. p 289-344 O'Brien, D. Empedocles: a synopsis. In: Frühgriechisches Denken. Georg Rechenauer (Hrsg.). Göttingen: Vandenhoeck & Ruprecht. 2005. p 316-342 O'Brien, D. Matière et émanation dans les Ennéades de Plotin. p 63-87 In: L' Alchimie et ses Racines Philosophiques. La tradition grecque et la tradition arabe. Sous la direction de Cristina Viano. (Histoire des Doctrines de l' Antiquité Classique. XXXII.). Paris: Librairie Philosophique J. Vrin. 2005 Philoponus, J. Refutation of Empedocles. p 49-60. In: On Aristotle's "On coming-to-be and perishing 2.5-11" / Philoponus ; translated by Inna Kupreeva Ithaca, N.Y. : Cornell University Press, 2005. ISBN 0801443369 Polycarpou, C.N. Chance and Necessity in Eudoxean Thought. p 80-91 In: Hasard et nécessité dans la philosophie grecque. Moutsopoulos, Evanghelos (dir), Athènes: Académie d' Athenes. Centre de Recherche sur la Philosophie Grecque. 2005. Abstract: According to Eudoxus, symphytos atychia is connected with the effects of the blood's state, whereas epeisactos atychia has to do with the medical view that it is not the nature of tyche to come "in response to one's wish". Now, being firmly convinced that providence is indissolubly linked to intentionality, Eudoxus rejected the so-called astrological fatalism. Moreover, being fascinated by the Pythagorean view that the existence of mathematically ordered elemental powers is what is required by necessity, Eudoxus never approved of the so-called Pythagorean doctrine that ananke seems to be in line with the merits of a quasi-state universe. Rico, G. 'Auctoritas cereum habet nasum' : Boethius, Aristotle, and the music of the spheres in the thirteenth and early fourteenth centuries. In: Citation and authority in medieval and Renaissance musical culture : learning from the learned by Suzannah Clark; Elizabeth Eva Leach. Woodbridge [UK] ; Rochester, NY : Boydell Press. 2005. ISBN: 184383166X Roguin, Cl.-F. De Les querelles d' Océanos et de Téthys: de l' Enuma elish à la cosmogonie d' Empédocle p. 377-384 In: Koryphaio Andri. Mélanges offerts à André Hurst. Édités par Antje Kolde, Alessandra Lukinovich, André-Louis Rey. (Recherches et rencontres. 22.). Genève: Droz. 2005 Ruthenberg, K. Empedokles' Naturdichtung aus chemischer Perspektive. p 7-12 In: Antike Naturwissenschaft und ihre Rezeption. Band XV. Jochen Althoff, Bernhard Herzhoff, Georg Wöhrle (Hrsgg.). Unter Mitarbeit von Sabine Föllinger. Trier: Wissenschaftlicher Verlag 2005. Schmitzer, U. Haec quoque non perstant, quae nos elementa vocamus - Die Pythagorasrede In: Ovids Metamorphosen: ein Schlüssel zum Verständnis des Werks? Didagmata - Fortbildungstagung für Lehrer der Alten Sprachen (Universität Erlangen) 8. Februar 2003. Taschner, R. Pythagoras und das Unendliche im Pentagramm. In: Das Unendliche. Mathematiker ringen um einen Begriff. Springer, Berlin. 2006. ISBN: 9783540257974

Wersinger, G. La "fete criminelle" (Empédocle, Perséphone et les Charites). p 109-132. In: La Fête. La Rencontre des Dieux et des Hommes. Actes du 2e Colloque International de Paris »La fête, la rencontre du sacré et du profane«. Organisé par les Cahiers KUBABA (Université de Paris I) et l' Institut catholique de Paris, 6 et 7 décembre 2002. Editeurs: Michel Mazoyer, Jorge Pérez Rey, Florence Malbran-Labat, René Lebrun. 2004 Collection KUBABA. Série Actes IV. Paris: L' Harmattan. Zhmud, L. Überlegungen zur pythagoreischen Frage. In: Frühgriechisches Denken. 2005. Georg Rechenauer (Hrsg.). Göttingen: Vandenhoeck & Ruprecht. p 135-151. Internetsites http://www.hti.umich.edu/g/genpub/ search: pythagoron. Title: Pythagoron; the religious, moral, and ethical teachings of Pythagoras, reconstructed and ed. by Hobart Huson. Publication Info: [San Antonio ?]: 1947. Knuth, J. Ein zahlentheoretischer Exkurs: geometrische Zahlen und das pythagoräische Zahlenfeld Universität Dortmund. Examensarbeit. 2004. Mathematik - Mathematik als Schulfach. 109 p. http://www.grin.com/de/preview/34557.html Sauer, H. Pythagoras und der Pythagoreismus Universität Wien, Institut für Musikwissenschaft. Philologisch-Kulturwissenschaftliche Fakultät. 2006. Musikethnologie – Schamanismus – Musiktherapie. 16 p. http://www.grin.com/de/preview/55681.html Schwender, U. Der wahre Lohn des Staatsmanns - Somnium Scipionis Uni Konstanz (Literaturwissenschaft). Seminararbeit. 2004. 14 p. http://www.grin.com/de/preview/28076.html Conferences / Presentations Institute of Classical Studies Ancient Philosophy Seminar Senate House, in Russell Square, London Room NG16. Greek Philosophy and Greek Culture December 11: Hugh Bowden (King's College London) Pythagoras and Orpheus For further information please contact Dr Peter Adamson (peter.adamson@kcl.ac.uk)

Book reviews Bollack, J. Les purifications: un projet de paix universelle / Empedocle. 2003 Reviewed by: Mansfeld, J. Mnemosyne. 2006, 59, 3, p 467-468 Chitwood, A. Death by Philosophy. The Biographical Tradition in the Life and Death of the Archaic Philosophers Empedocles, Heraclitus, and Democritus. 2004. Reviewed by: Trepanier, S. Classical review. 2006, 56, 2, p 286. Hirsch-Luipold, R. et al. Die Bildtafel des Kebes. Allegorie des Lebens. 2005. Reviewed by: Kaesser, C. Classical review. 2006, 56, 2, p 318-319. Hermann, A. To Think Like God. 2004 Reviewed by: Boys-Stones, G. Greece & Rome. 2006, 53, 1, p 129-136 Huffman (C.A.) Archytas of Tarentum. Pythagorean, Philosopher and Mathematician King. 2005. Reviewed by: O'Meara, D.J. Classical review. 2006, 56, 2, p 300. Reviewed by: Bowe, G.S. Philosophy in review. 2006, 26, 6, p 432-434. Reviewed by Byl, S. L'antiquite classique. 2006, 75, p 416-418 Joost-Gaugier, C.L. Measuring Heaven: Pythagoras and His Influence on Thought and Art in Antiquity and the Middle Ages. 2006. Reviewed by: Gavaler, C. Virginia quarterly review. 2006, 82, 4, p 267-268. Kingsley, P. Reality. 2003 Reviewed by: Gemelli Marciano, M.L. Gnomon. 2006, 8, p 657-671. Riedweg, C. Pythagoras. Leben - Lehre - Nachwirkung. Eine Einführung. 2002. Reviewed by: Haake, M. Klio. 2006, 88, 1, p 243. Riedweg, C. Pythagoras: His Life, Teaching, and Influence. 2005 Reviewed by: Boys-Stones, G. Greece & Rome. 2006, 53, 1, p 129-136 Reviewed by: Hull, A. Annals of Science. 2006, 63, 3, p 377Reviewed by: Ferrari, F. Athenaeum. 2006, 94, 1, p 354-356 Reviewed by: Steele, J.M. Annals of science. 2006, 63, 3, p 380-381. Reviewed by: McKirahan, R. Isis. 2006, 97, 2, p 345-346 Reviewed by: Busine, A. Revue Belge de philologie et d’histoire. 2005, 83, 1, p 198-199 Seddon, K. Epictetus' Handbook and the Tablet of Cebes. Guides to Stoic Living. 2005. Reviewed by: Trapp,M. http://ccat.sas.upenn.edu/bmcr/2006/2006-11-13.html Trepanier, S. Empedocles. An interpretation. 2004. Reviewed by: Schofield, M. Classical Review. 2006, 56, 1, p 12-14. Reviewed by: Lampeter, D. Journal of Hellenic studies. 2006, 126, p 209-210. Reviewed by: Destree, P. Revue philosophique de Louvain. 2005, 103, 1-2, p 194-200.

Compact disc Aubry, S. Die drei Urformen, Pythagoras TerrAmor. 2004, ISBN 3-935173-86-5 Audio-CD. Laufzeit ca. 40 Min. Copleston, F.C. A history of philosophy. Compact disc Princeton, NJ : Recording for the Blind & Dyslexic, 2006. Contents: Pre-Socratic philosophy: Crade of Western thought, Ionia; Pioneers, early Ionian philosophers; Pythagorean society; Word of Heraclitus; One of Parmenides and Melissus; Dialectic of Zeno; Empedocles of Akragas; Advance of Anaxsgoras; Atomists; Pre-Socratic philosophy -- Socratic period: Sophists; Some individual Sophists; Socrates; Minor Socratic schools; Democritus of Abdera -Plato: Life of Plato; Plato's works; Theory of knowledge; Doctrine of forms; Psychology of Plato; Moral theory; State; Physics of Plato; Art; Old Academy -- Aristotle: Life and writings of Aristotle; Logic of Aristotle; Metaphysics of Aristotle; Philosophy of nature and psychology; Aristotle's ethics; Politics; Aesthetics of Aristotle; Plato and Aristotle -- Post-Aristotelian philosophy: Introductory; Early Stoa; Epicureanism; Older Sceptics, the Middle and New Academies; Middle Stoa; Cynics, Eclectics, Sceptics; Neo-Pythagoreanism; Middle Platonism; Jewish-Hellenistic philosophy; Plotinian NeoPlatonism; Other Neo-Platonic schools -- Appendices: Some abbreviations used in this volume. Lesch, H. Denker des Abendlandes. Paket: Die Naturphilosophen aus Milet & Pythagoras. Teil 2 München : Komplett-Media. 2006. ISBN 3-8312-9389-9 DVD 5, Laufzeit ca. 60 Min DIE NATURPHILOSOPHEN AUS MILET Die Denker haben sich vom Götterhimmel gelöst und vertrauen nun auf die eigene Vernunft. Thales (624 - 564 v. Chr.): Seine Lehre basiert darauf, dass alles aus Wasser entstanden sei. Anaximander (611 - 546 v. Chr.): Auch er versuchte die Welt umfassend zu erklären. Im Mittelpunkt seiner Philosophie stand das "Apeiron", das Unendliche, in dem er auch den Ursprung der Dinge sah. Anaximenes (585 - 525 v. Chr.): Er war Schüler des Anaximander. In seinem Werk "Über die Natur" stellt er die Luft als das stoffliche Prinzip heraus. PYTHAGORAS (570 - 475 v. Chr.) Er versuchte Mathematik, Philosophie und Wissenschaft zusammenzubringen. "Alles ist Zahl", das ist der Satz, der seiner Philosophie zugeschrieben wird, und er verdeutlicht, dass man die Zahl als konstituierendes Element der Natur verstand. Er war der erste, der Mathematik als wissenschaftliches Instrument verwendet hat (a² + b² = c²). Lesch, H. Denker des Abendlandes. Paket: Heraklit und Parmenides & Empedokles und Philolaos. Teil 3 München : Komplett-Media. 2006. ISBN 3-8312-9390-2 DVD 5, Laufzeit ca. 60 Min. HERAKLIT UND PARMENIDES Heraklit (zwischen 540 und 535 - 475 und 480 v. Chr.) In seiner philosophischen Lehre steht das Werden, die Veränderung als Prinzip im Mittelpunkt. Die Welt ist vom Kampf der Gegensätze geprägt. Im Gegensatz zeigt sich aber auch noch eine verborgene Einheit. Im Feuer sah Heraklit den Urstoff der Welt. Parmenides (515 - ca. 445 v. Chr.) "Es gibt nur ein wahres Sein, aber kein Nichtsein" und "Denken und Sein ist dasselbe", daher ist "nicht existierendes nicht denkbar", es kann also kein "Nichts" geben. EMPEDOKLES & PHILOLAOS Empedokles (zwischen 494 und 482 - 434 und 420 v. Chr.) Ein Multitalent aus dem neuen Griechenland (Sizilien). Er brachte zum ersten Mal die vier Elemente, Feuer, Wasser, Luft und Erde in das Gedankengut ein. Werden und Vergehen gibt es für ihn durch das Zusammenspiel der vier Elemente zwischen denen die Kräfte Liebe und Hass wirken. Philolaos (470 - 390 v. Chr.) Er stammt aus Kroton (Italien) und versuchte das pythagoreische Denken in eine Philosophie zu gießen, indem er ein Werk über Welt, Natur und Seele in drei Büchern verfasste. Matteis, N. Music of the Spheres Uitgever: Berkeley : Magnatune, 2006. Contents: Ground after the Scotch humor / Niccola Matteis -- Sonata III in g minor from Sonatae unarum fidum ; Sonata IV in D major from Sonatae unarum fidum / Heinrich Schmelzer -- Sonata I in A major from 8 sonate a violino solo / Heinrich Iganz Franz von Biber -- Toccata in d minor, BWV 913 / Johann Sebastian Bach -- Passacaglia for solo violin from the Rosary sonatas / Heinrich Ignaz Franz von Biber -- Diverse bizzarrie sopra la vecchia sarabanda o pur ciaccona / Niccola Matteis -- Sonata XII "La folia" from opus 5 / Arcangelo Corelli.

Sparke, P. Music of the spheres music. Deutsche Blaserphilharmonie.; Rundfunk-Blasorchester Leipzig. Uitgever: Wembley, England : Anglo Records, 2005 Contents: The pioneers / Philip Sparke -- Largo from Winter : from The four seasons / Antonio Vivaldi ; arr. Philip Sparke -- Chorale and variations / Philip Sparke -- Jerusalem / Sir Hubert Parry ; arr. Philip Sparke -- The four truths / Philip Sparke -- Hymn to the fallen : from the motion picture Saving Private Ryan / John Williams ; arr. Philip Sparke -- Music of the spheres / Philip Sparke. Journal articles Alpers, K. Empedokles im Wiener Herodian-Palimpsest Zeitschrift für Papyrologie und Epigraphik. 2006, 156, p 27-37. Anonymus. The beautiful tapestry of King Francois. The history of Scipio Connaissance des arts. 2006, 638, p 34. Anonymus. Pythagoras en het denken Pentagram. 2006, 28, 4, p 15-22. Arguropoulou, R. La Mothe le Vayer: E Arete ton Archaion (The Virtue of the Ancients) Philosophia. 2005, 35, p 216-225 Abstract: Dans son ouvrage De la vertu des paiens, il brosse une analyse critique de la philosophie morale de l'Antiquite. Son realisme moral l'autorise a voir la vertu la ou elle est reputee absente, chez les paiens par exemple; car, il n'estime pas la foi indispensable au salut, ni une religion a la vertu. En reintegrant les peuples paiens dans la communaute humaine, il tranche un probleme que le Concile de Trente avait abandonne a l'indecision. Parmi les doctrines morales de l'Antiquite, La Mothe Le Vayer donne une place primordiale a celle de Socrate a qui il ne cesse de comparer non seulement Pythagore mais egalement Confucius, le "Socrate de Chine" comme il le qualifie. Il prefere Plato a Aristote, et se mefie de l'aristotelisme et de ses commentateurs. Il attribue des vertus a Epicure et Pythagore; mais c'est la secte sceptique qu'il considere de toutes les doctrines philosophiques, la moins contraire a la religion chretienne, et la plus appropriee a recevoir les lumieres surnaturelles de la foi. Audeguy, S. Pythagoras Nouvelle revue Francaise. 2006, 577, p 137-138. Beneitez-Prudencio, J.J. Eutopia y Polis: el lugar de la inocencia y la felicidad en la imagen de los antiguos griegos Daimon,Revista-de-Filosofia. 2005, 34, p 7-17 Abstract: Human beings have imaged ideal societies across the time, with the aim of going beyond real ones, and solving the problems emerged from common life. This article intends to remark that theorical conceptions of society frequently have a 'eutopian' counterpart, that means, a very best physical or geographical location. It can be appreciated precisely in the ancient Greek world. In order to approach to this subject, we will depart from the usual version in the polis of the golden age given by Hesiod, and we will put it together with the eutopian reformation proposed by Pythagoreans and the 'conservative' presentation found in Aristotle's Politics and Ethics. Cornish, A. Celebrity calculators Times Educational Supplement. 2006, 4667, p 27-28. Abstract: The article discusses the significance of knowing the history of mathematics, as well as the prominent mathematicians and their theorems. The author conveys that teaching origins of mathematics could encourage the students to take attention in the instruction. He added that learning mathematics is a continuous cognition. A brief history about Pythagoras of Samos and his theorems is offered Culhane, B. 'For one who first showed me Scipio's dream' Hudson review. 2006, 59, 2, p 250

Dosch, H-G. Interpretation of Musical Harmony Philosophy-in-the-Contemporary-World. 2005, 12, 1, p 75-80 Abstract: In this contribution, a scientific interpretation of musical harmony is understood as a description in an adequate frame of symbolic forms (in the sense of Cassirer), rather than as a final explanation. I describe different interpretations of musical harmony from the time of the Pythagoreans until the present times. It is noted that a symbolic interpretation of Helmholtz (in the sense of his theory of signs), which was criticized as incomplete by Ernst Mach, is recognized as adequate by Arnold Schonberg. Fabre, B. Diogenes Laertius through Marcel Schwob's reading: two philosophers' fictional biography in 'Vies Imaginaires' Revue de litterature comparee. 2006, 317, p 37-55. Abstract: Studying the imaginary Lives of two ancient Greek philosophers writting by Marcel Schwob enables us to discover the process by which this master of the genre created it. An analysis of his borrowings from Diogenes Laertius' The Lives and Opinions of Eminent Philosophers and of the alternative he imposes upon this hypotext reveals the particular view that this end the 1911 century writer had of those two figures of history of philosophical. Seen through Schwob's imaginary vision. Empedocles and Crates illustrate the ethic of compassion the writer develops in his tales and appear to share the same ambition to singularize themselves. Fossa, J.A. On the pentagram as a Pythagorean emblem Revista brasileira de história da matemática. 2006, 6, p 127 - 137 Hladky, V. Empedocles' 'Sphairos' Filosoficky casopis. 2006, 54, 3, p 393-410. Abstract: In this article an attempt is made to open, and to critically appraise in the light of contemporary research, the rather neglected question of the character and internal structure of Sphairos. In this philosophical poem by Empedocles the mixture of the four elements, or "roots" is meant to emerge. On the basis of a detailed analysis of the preserved text the conclusion is reached that Sphairos is indeed a complex, structured, form. It is not a merely perfect, albeit quite amorphous mixture of the four primary constituents of Empedocles' cosmos, rather it has its own mutually distinguishable parts, as is clearly confirmed by some of the immediate fragments of the work of the author that are preserved. In addition to an analysis of the words of the preserved text describing Sphairos an attempt is made to base an interpretation of it on a wider presentation and analysis of Empedocles' conception of the mixing of the basic elements and the gradual emergence of ever more complex things and organisms. According to the present interpretation of Empedocles', this process should climax - in the time when the creative and synthesising Love gains ascendancy over Strife - in the emergence of a huge, internally variegated, complex and thinking "superorganism". This superorganism is at the same time identical with the whole cosmos and in it are joined and combined all the lower and simpler organisms which have emerged in the prior phases of the "zoogony". Holloway, R.R. The Tomb of the Diver (Tomba del Tuffatore at Paestum) American journal of archeology. 2006, 110, 3, p 365-388. Abstract: Dating from about 470 B.C., the frescoes of the Tomba del Tuffatore (Tomb of the Diver) at Paestum are the only example of Greek wall painting with figured scenes from the Orientalizing. Archaic, or Classical periods to survive in their entirety. Close examination of the paintings shows the working practices of the artists. Technically these are similar to those of the painters of Etruscan tombs of the period. There is a world of difference, however, between the purpose and conceptualization of Etruscan tomb painting and that revealed in the Tomb of the Diver. Furthermore. although interpretations claiming Orphic or Pythagorean significance have been advanced, reconsideration of the frescoes gives some reason to think that the program for the tomb's decoration may have been of the simplest nature and developed by the artist: themselves from prototypes in Attic vase painting available to them in Italy. Thus, although the diver may make reference to the moment of death and the symposium may have been intended to create it welcoming Scene to surround the dead man in the tomb, the creation of these frescoes may owe more to the initiative of the painters than to any complexities of philosophy. Huglo, M. The study of harmonic diagrams by Calcidius in the Middle Ages Revue de musicologie. 2005, 91, 2, p 305-319. Abstract: The diagram of "harmony, the soul of the world" elaborated by Adrastos after the Timaios of

Plato, first appeared in the West in Calcidius's commentary to his Latin translation of the Timaeus. Thereafter, the diagram was added to manuscripts transmitting Macrobius's Commentary to Cicero's Dream of Scipio and the Scolica enchiriadis. The same diagram was also elaborated by Porphyrios in his Commentary of the Timaios. In the eighth century.. it was interpolated in Visigothic manuscripts with the third book of the Isidore's Etymologies, between Geometry and Music, but was never exported out of Spain. This article traces the history of this famous diagram through the thirteenth century. Ionescu, C. The mythical introduction of recollection in the Meno (81A5-E2) Journal of philosophical research. 2006, 31, p 153-170. Abstract: This essay explores the relevance of Socrates' mythical introduction of recollection in the Meno. I argue that the passage at 8 1 a5-e2 addresses different levels of understanding, a superficial and a deeper one, corresponding to a literal and a metaphorical reading respectively. The major themes addressed in this passage-the immortality of the soul, transmigration, rewards and punishments in the after-life, Hades, the kinship of all nature and anamnesis-have distinct meanings depending on whether we approach them with a Platonic or an Orphico-Pythagorean eye. The literal understanding is appealing to Meno and is offered in reply to his challenge in order to persuade him to continue the investigation of virtue. It is, however, the deeper sense that Plato's Socrates intends for a more philosophically attuned audience. Karoumi, A. OÙ EN SONT LES ZEP ? 4 Pour des zones d'exigence pédagogique - Lettre de monsieur Pythagore aux 4e C Cahiers pédagogiques. 2006, 445, p 48-49. Keyser, P.T. Numerology and text in Anatolios of Laodikaia, On the Decade Philologus. 2006, 150, 1, p 38-42 Abstract: Anatolios' Decade is rarely read despite its interest as a document of the transition from late paganism to early Christianity. Dating probably from his tenure as professor in Alexandria, it is the earliest extant work devoted to neo-pythagorean arithmology: the earlier Mathematics of Theon of Smyrna only includes a little such material, while merely fragments of the earlier Arithmetic of Nikomachos of Gerasa are pre-served, in the summary by Photios of what may be Iamblichos' work. Here I want to offer four emendations to the text of Anatollos as printed by Heiberg (1900): the text is disordered and has a lacuna in the section on 7, while in the material on 10 there is a haplography and a garble. Meletis J. Favism - From the "avoid fava beans" of Pythagoras to the present Haema. 2004, 7, 1, p 17-21. Neto, M.D. Pythagoras' celestial spheres in the context of a simple model for quantization of planetary orbits Chaos solitons & fractals. 2006, 30, 2, p 399-406. Abstract: In the present article we attempt to search for a correlation between Pythagoras and Kepler's ideas on harmony of the celestial spheres through simple quantization procedure to describe planetary orbits in our solar system. It is reasoned that starting from a Bohr-like atomic model, planetary mean radii and periods of revolution can be obtained from a set of small integers and just one input parameter given by the mean planetary radius of Mercury. It is also shown that the mean planetary distances can be calculated with the help of a Schrodinger-type equation considering the flatness of the solar system. An attempt to obtain planetary radii using both gravitational and electrostatic approaches linked by Newton's dimensionless constant of gravity is presented. Persche, G. Sturminger 'Il sogno di Scipione' Opera. 2006, 57, 7, p 806-807. Polycarpou, C.N. Eudoxean Aesthetics Philosophia. 2005, 35, p 72-84 Abstract: Far from being the first to introduce the concepts that became fundamental in Hellenistic aesthetics, Eudoxus never broke away from the Pythagorean idea that the beautiful is the result of certain numerical combinations which are manifested under the aspect of proportions. In our opinion, Eudoxus might have exerted influence upon Aristotle, who asserted that the main species of beauty are orderly arrangement, proportion and definiteness. On the other hand, we consider that for

Eudoxus the so-called Pythagorean equilateral triangle, which had a great deal to do with the construction of the so-called Pythagorean pentagram, was the symbol of the beautiful. Rhee K.B. Early Greek medicine and Plato's cosmology. Uisahak. 2004, 13,1, p 81-93 . The purpose of this paper is to show the influence of early greek medicine on Plato's Cosmology. Alcmaeon holds that health depends on proportion (equality; isonomia) or proportioned mixture of opposing factors. This notion dominated nearly all greek medicine, and also influenced Plato's cosmology greatly. Generally each greek doctor believed that man consisted of opposing factors, though these are designated differently. Alcmaeon takes powers - hot and dry, cold and hot, vitter, sweet and the rest as those factors. On the other hand, Philistion of Locri adopts the four element theory of Empedocles. He conceives that human body as a mixture of the four elements, and health consists in proportion of these opposing four element, basically as Alcmaeon. This notion is accepted by Plato. Only Plato differs from Philistion in that he doesn't consider the four elements as the ultimate factors.In Timaeus Plato explain that the Demiourgos constructed the four elements through introducing 'proportion' into the primitive materials (the oppositives) by means of shapes and numbers. And Plato thinks that the cosmic body and soul was constructed basically in the same way as the four elements. This is true of the human body and soul. Also Plato explicates diseases from standpoint of proportion or symmetry. Moreover according to Philebus, the good states (i.e. 'health', 'music', 'season' etc) in the cosmos arises out of the right mixture of the limit and the unlimited. In the other word this mixture is proportioned mixture of the oppositives by aid of ratios.In short Plato believes that both the cosmos itself and the good states as proportioned mixture of the oppositives. Thus Plato' cosmology is fundamentally based upon Alcmaeon's or Philistion's concept of Health. . Rossi, A. Introduction: Ennius and the traditions of epic Arethusa. 2006, 39, 3, p 397Samalavicius, A. Architecture and Sound in Antiquity (in Lithuanian) Logos. 2005, 41, p 27-33 Abstract: The article deals with the relation of antique cosmology and its impact upon the architectural structures of antiquity. Metaphysical beliefs shared by Orphics and eventually Pythagoreans who adopted the doctrines of their predecessors were strongly associated with mathematical analogies between the structure of cosmos and music. Correspondences between sound, mathematics and architecture, expressed in this ancient esoteric thinking, gave an impetus to their practical application in architecture. The treatise of Vitruvius in which he contemplates the concept of harmony designed by the Greeks, demonstrates that harmonics, as a branch of science, entered Roman architectural theory and practice as something that was taken as a dogma that was taken for granted and held beyond dispute. (edited) Schedler, U. Brunelleschi's cathedral dome, Pythagoras and Fibonacci. Architectura. 2005, 35, 2, p 148-167. Abstract: Up to now it is not understood, how the Cupola of Florence cathedral was surveyed while construction was in progress. This thesis postulates that Brunelleschi used mathematical procedures according to Pythagoras and above all Fibonacci. His surveying instruments were a chain-star hung across the cupola to converge at the centre, a pivot Joint fastened to this central point with three ropes leading to the course of brick being laid and stretched taut there, as well as plumb lines and templates pushed upwards along the ribs on the outside of the cupola. The ropes were made to describe a circle at the uppermost course of brick, thus creating in effect a rotation cupolas. Similar triangles were generated with ropes and plumb lines, by which means the essential measurements could be monitored: the 36-metre radius of the quinto acuto, the geometric figure prescribed in 1367, and, therefore, the increase in the angle of inclination of both rising shells as well as the radial alignment of the building elements and their downwards tilt. Schipper, H.G. Nietzsche en Empedokles Hermeneus. 2006, 78, 3, p 223-229. Schmitzer, U. Reserare oracula mentis. Abermals zur Funktion der Pythagoras-Rede in Ovids Metamorphosen. Studi italiani di filologia classica. 2006, 99, p 32-56..

Stakhov, A. The golden section, secrets of the Egyptian civilization and harmony mathematics Chaos, Solitons & Fractals. 2006, 30, 2, p 490-505 Abstract: The main goal of the present article is to consider the harmony mathematics from the point of view of the sacral geometry and to show how it can be used in this field. We also consider some secrets of the Egyptian civilization that have relation to the golden section and platonic solids. Briefly, this is considered to be the main concepts involved in harmony mathematics and its application to the sacral geometry. Todoua, M. I Littérature grecque - Empédocle : Empêche-vents ou Dompteur de mauvais génies ? Bulletin de l'Association Guillaume Budé. 2005, 1, p 49-81. Vinel, N. The hidden Judaism of the Pompeiian SATOR square Revue de l’histoire des religions. 2006, 223, 2, p 173-194. Abstract: A recent discovery in the Pythagorean mathematical field leads to the deciphering of the SATOR square, the earliest examples of which are in Pompeii. It hides another Latin inscription, in full, which shows that it's a Jewish cryptogram, based on the bronze altar in Ex 27 and the bronze serpent in Nb 21, as an identification mark and a symbol of salvation for the Diaspora. Furthermore, the word "SAUTRAN" below the SATOR in Pompeii doesn't mean the greeting from someone called Sautran(us) : before the letter N, symbol of the serpent according to the Judeo-Christian epigraphy, SAUTRA transcribes an imperative of the hebrew root str "to hide", the infinitive absolute of which is SATOR. Vitek, T. The seven wise men and their statements. Filosoficky casopis. 2006, 54, 3, p 363-380. Abstract: In Greece, from the earliest times, various anonymous sayings circulated, expressing the life-experience of observant and reflective people. These made up a part of the unwritten ethical, legislative and religious rules. Some of them were formulated in such a concise and general way that they were pertinent in many different fields. These maxims were inscribed on the Delphic temple sometimes during 6(th) B.C. It was Plato who linked a trinity of delphic statements with the seven wise men. He saw Apollo as the patron of the seven and in their wisdom he discerned SocraticPlatonic doctrines. Plato also provided the mythical seven wise sons of Apollo-Helius with the names of the wise men of archaic times whose lives and works were known only in a very sketchy way, but whose wisdom was famous (mainly thanks to Herodotus). Subsequently Aristotle and his pupils ascribed to the seven wise men other statements in addition to the delphic, which, in part, they took from former tradition and, in part, they themselves created according to their own ethical principles on the basis of older aristocratic values. In the second half of the fourth century the statements started to be published in collections which gave voice to the interests and aims of various groups. This led to variations of form and content. Some authors emphasised the ethico-religious character of the statements and formulated them as sacred laws arising from Delphus (the Sosiad tradition), others conceived them as the fruits of philosophical discussion (at the symposium) and distributed them to individual wise men (the Demetrios tradition). In Hellenism and in late-antiquity, the statements were understood as the general code of behaviour, and an expression of national character, and children were taught them in school. They do not however pertain to presocratic philosophy, nor do they have any philosophical significance, even if philosophers gave them form and sometimes used them in their own doctrines. Wolfe, J. Spenser, Homer, and the mythography of strife Renaissance quarterly. 2005, 58, 4, p 1220-1299. Abstract: This article examines a central narrative and ethical motif of Edmund Spenser's Faerie Queene - the golden chain - in the context of Spenser's broader debts to Homeric epic. While largely neglected in favor of more immediate sources, such as Virgil's Aeneid and Tasso's Gernsalemme Liberata, the influence of Homer's Iliad and Odyssey is profoundly felt in Spenser's mythography of strife. In its representation of the consequences of cosmological and spiritual strife, The Faerie Queene realizes the classical and late antique allegorical tradition of interpreting Homeric epic as illustrative of the doctrines of pre-Socratic philosophers such as Heraclitus and Empedocles. Its moral landscape structured according to the oppositional yet complementary forces of love and strife, Spenser's epic enacts the Homeric-Empedoclean epic of the allegorists so as to offer its own etiology of discord, one sympathetic with, but also distinct from, that of Homer.