Newsletter 15

Stichting Pythagoras Pythagoras Foundation Newsletter. No.15. December 2010.

Pythagoras Foundation Newsletter No. 15. December 2010 Website http://www.stichting‐pythagoras.nl/ E‐mailaddress 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. We may suppose that as we are given eyes to study the stars so we have ears to hear harmonic movement and that consequently a certain kinship exists between the two forms of knowledge. This is the position taken by the Pythagoreans, Glaucon, and we agree with them, don’t we? (530d) Plato, The Republic, book VII. A new translation by R.W. Stirling and W.C. Scott. 1985. ISBN 0393019721, p 224. Contents: Introduction, News from the library, Acknowledgements, Salvator Rosa; Pythagoras Emerging from the Underworld, Colophon INSTITUTO NEO-PITAGÓRICO Jay Kennedy; the Plato Code John Bremer; Plato, Pythagoras, and Stichometry Ernest G. McClain; Musical Adventures in Ancient Mythology Conferences / Symposia New books New book chapters Book reviews New journal articles Internet , Film 1 p 2 p 3 p 4 p 5 p 8 p 12 p 14 p 17 p 24

Introduction Jay Kennedy announced a ‘Plato code’ which caused a hype in the media, which is unique for such a story on research in classical antiquity! It resulted in a flood of reactions; most serious comments were given in Leiter reports, Rogueclassist and the Neoplatonism Yahoo group. A summary is given in this Newsletter. John Bremer did sent us a detailed comment. Alas the interview with Gabriele Cornelli from Brasil and information about his recent and future work did not reach us in time. For years we have good contacts with the Instituto Neo-Pitagórico, Curitiba–Parana, Brasil. Recent publications and information about this institute is given. Ernest G. McClain’s website gives his publications for free. Graham Pont and his wife Gretta did visit the Library in Naarden; we are pleased with their interest in the Foundation and we enjoyed their visit. We exchanged information. Several readers have sent us information for this Newsletter. Many thanks to all of you. We would appreciate a more active support to the Pythagoras Foundation and the Newsletter. We kindly ask you to send a donation (see next chapter), in order to cover the cost of this Newsletter. We are very proud to announce that in Newsletter 16 (June 2011) Peter Kingsley wil be our special guest / researcher. Best wishes, 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 Rabobank 1480 00 045. International Bank Account Number (IBAN): NL48 RABO 0148 0000 45 BIC: RABONL2U News from the library The internetsite has been renewed and older Newsletter contents are added. Thanks to Hans van Horssen for all the work he did concerning the website. Newsletter 12 (June 2009) was the first Newsletter being available as pdf file on the Pythagoras Foundation website. A counter on the website gives the number of visitors who do open the Newsletter. We are proud to announce there were 1500 visits to the Newsletter, of which 1000 visiting for the first time. The visitors came from 41 different countries. We are missing on countries because of language problems, there might be interest in more countries for the Newsletter? Nico Bader

Acknowledgements The Pythagoras Foundation thanks the following individuals for their contributions and generosities: John Bremer, Henrique Cairus, Dennis Clark, Harry Eighmey, Elizabeth Garzuze da Silva Araujo, Annette Huizenga, Jay Kennedy, Maria Kingsley, Ernest McClain, Jean-Claude Picot, Graham Pont, Marcel Roggemans. Salvator Rosa, Italian (1615–1673) Pythagoras Emerging from the Underworld 1662 Oil on canvas 51-5/8 x 74-3/8 in. (131.2 x 189.0 cm) Kimbell Art Museum, Fort Worth, Texas 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 (printed version)

http://www.pitagorico.org.br/index.php INSTITUTO NEO-PITAGÓRICO ESTUDO – PERSEVERANÇA – BONDADE O Instituto Neo-Pitagórico é frateria destinada ao estudo, ao desenvolvimento das faculdades superiores do Ser, ao altruísmo, inspirado nos Versos de Ouro de Pitágoras, para a Cultura, para a Verdade, para a Justiça, para a Liberdade, para a Paz, para a Fraternidade e para a Harmonia. O I.N.P. não reconhece distinções de raça, nacionalidade, fortuna e posição social, nem credo religioso, filosófico ou político. 100 ANOS - 1909 a 2009 Lista de artigos recentes Versos de Ouro de Pitágoras - Tradução Fabre d`Olivet (11/02/2010) Dario Vellozo e o Neo-Pitagorismo Contemporâneo (10/02/2010) Versos de Ouro de Pitágoras - Tradução de Luiz Antonio de ... (07/02/2010) Versos de Ouro de Pitágoras - Tradução de Dario Vellozo (31/01/2010) The Pythagoras Foundation received the following publications; these will be send on request. Dario Vellozo and Theosophy in Brazil 4 pages Word document Rosala Garzuze (ROSALA GARZUZE (1906-2009) was the second President of the Neo-Pythagorean Institute (19372009) founded by Dario Vellozo (1867-1937)) IN THE LIGHT OF THE PYTHAGOREAN METHOD 4 pages Word document Dario Vellozo (Dario Vellozo (1869-1937), fundador e primeiro Presidente do Instituto Neo-Pitagórico (1909-).)

http://www.manchester.ac.uk/aboutus/news/display/?id=5894 Science historian cracks ‘the Plato code’, 28 June 2010. A science historian at the University of Manchester has cracked ‘The Plato Code’ – the long disputed secret messages hidden in the great philosopher’s writings. Plato was the Einstein of Greece’s Golden Age and his work founded Western culture and science. Dr Jay Kennedy’s findings are set to revolutionise the history of the origins of Western thought. Dr Kennedy, whose findings are published in the leading US journal Apeiron, reveals that Plato used a regular pattern of symbols, inherited from the ancient followers of Pythagoras, to give his books a musical structure. A century earlier, Pythagoras had declared that the planets and stars made an inaudible music, a ‘harmony of the spheres’. Plato imitated this hidden music in his books. The hidden codes show that Plato anticipated the Scientific Revolution 2,000 years before Isaac Newton, discovering its most important idea – the book of nature is written in the language of mathematics. The decoded messages also open up a surprising way to unite science and religion. The awe and beauty we feel in nature, Plato says, shows that it is divine; discovering the scientific order of nature is getting closer to God. This could transform today’s culture wars between science and religion. “Plato’s books played a major role in founding Western culture but they are mysterious and end in riddles,” Dr Kennedy, at Manchester’s Faculty of Life Sciences explains. “In antiquity, many of his followers said the books contained hidden layers of meaning and secret codes, but this was rejected by modern scholars. “It is a long and exciting story, but basically I cracked the code. I have shown rigorously that the books do contain codes and symbols and that unraveling them reveals the hidden philosophy of Plato. “This is a true discovery, not simply reinterpretation.” This will transform the early history of Western thought, and especially the histories of ancient science, mathematics, music, and philosophy. Dr Kennedy spent five years studying Plato’s writing and found that in his best-known work the Republic he placed clusters of words related to music after each twelfth of the text – at one-twelfth, two-twelfths, etc. This regular pattern represented the twelve notes of a Greek musical scale. Some notes were harmonic, others dissonant. At the locations of the harmonic notes he described sounds associated with love or laughter, while the locations of dissonant notes were marked with screeching sounds or war or death. This musical code was key to cracking Plato’s entire symbolic system. Dr Kennedy, a researcher in the Centre for the History of Science, Technology and Medicine, says: “As we read his books, our emotions follow the ups and downs of a musical scale. Plato plays his readers like musical instruments.” However Plato did not design his secret patterns purely for pleasure – it was for his own safety. Plato's ideas were a dangerous threat to Greek religion. He said that mathematical laws and not the gods controlled the universe. Plato's own teacher had been executed for heresy. Secrecy was normal in ancient times, especially for esoteric and religious knowledge, but for Plato it was a matter of life and death. Encoding his ideas in secret patterns was the only way to be safe. Plato led a dramatic and fascinating life. Born four centuries before Christ, when Sparta defeated plague-ravaged Athens, he wrote 30 books and founded the world’s first university, called the Academy. He was a feminist, allowing women to study at the Academy, the first great defender of romantic love (as opposed to marriages arranged for political or financial reasons) and defended homosexuality in his books. In addition, he was captured by pirates and sold into slavery before being ransomed by friends. Dr Kennedy explains: “Plato’s importance cannot be overstated. He shifted humanity from a warrior society to a wisdom society. Today our heroes are Einstein and Shakespeare – and not knights in shining armour – because of him.” Over the years Dr Kennedy carefully peeled back layer after symbolic layer, sharing each step in lectures in Manchester and with experts in the UK and US. He recalls: “There was no Rosetta Stone. To announce a result like this I needed rigorous, independent proofs based on crystal-clear evidence. “The result was amazing – it was like opening a tomb and finding new set of gospels written by Jesus Christ himself. “Plato is smiling. He sent us a time capsule.” Dr Kennedy’s findings are not only surprising and important; they overthrow conventional wisdom on Plato. Modern historians have always denied that there were codes; now Dr Kennedy has proved otherwise.

He adds: “This is the beginning of something big. It will take a generation to work out the implications. All 2,000 pages contain undetected symbols.” Notes for editors The paper ‘Plato’s forms, Pythagorean Mathematics, and Stichometry’ is available. Dr Jay Kennedy has degrees from Princeton and Stanford. He worked at the University of Notre Dame and Cambridge University before moving to the Centre for the History of Science, Technology, and Medicine at the University of Manchester. Before becoming a teacher, he worked on the oil rigs in the Gulf of Mexico, in Tokyo as a translator, and in Baghdad at the National Computer Centre. For more information, a copy of the paper or an interview with Dr Jay Kennedy, contact Media Relations Officer Mikaela Sitford on 0161 275 2111, 07768 980942 or Mikaela.Sitford@manchester.ac.uk. Also visit http://personalpages.manchester.ac.uk/staff/jay.kennedy/ Jay Kennedy’ s new book, The Musical Structure of Plato's Dialogues, is scheduled for next Spring from Acumen Publishing. Yahoo Newsgroups; Neoplatonism: start June 30, 2010. Jay Kennedy & "The Plato Code" http://groups.yahoo.com/group/neoplatonism/message/3392 I had not heard of Jay Kennedy until just today. He is making something of a splash for his claim to have discovered objectively quantifiable musical patterns based on Pythagoreanism -- in Plato's dialogs. I have a very negative knee-jerk reaction to things like this, especially when I find out about through poorly written, poorly conceived, and overly hyped media accounts. But I took a look at Kennedy's website, especially his "Introduction for Scholars", and to my eye there appears to be something to what he is up to: http://personalpages.manchester.ac.uk/staff/jay.kennedy/#Introduction_for_Scholars His work is especially relevant to our understanding of the later Platonic school (so-called "neo-" Platonism): "The distance between 'neo-Platonism' and Platonism has been steadily diminishing since the work of Dodds. This work implies that the reports among Plato students that he was a Pythagorean in some strong sense were correct. This reaffirms the views among some neoPythagoreans and neo-Platonists. How is the history of the reception of Plato now altered?" Curt Steinmetz Hey Curt have you checked out Ernest MCclain? http://www.ernestmcclain.net/ http://www.amazon.com/gp/aw/d.html/ref=redir_mdp_mobile/186-4696601-3016669?a=08\ 92540109 He's got a Wiki page too http://en.m.wikipedia.org/wiki/Ernest_G._McClain?wasRedirected=true Scott Rhodes Hve you heard of or read McClain The Pythagorean Plato? This was a study in the 80s claiming that some key images and symbols in Plato cited Pythagorean music theory and dealt with problems in musical tuing theory as symbols for philosophical problems. Thomas Mether I haven't yet had a chance to go through Kennedy's findings in depth. However Kennedy is not the first to reason thusly, and there is a fairly mind-blowing article by John Bremer ('Some Arithmetical Patterns in Plato's Republic' Hermathena 169 (Winter 2000) 69-97) where he makes the (much more modest) claim that the Republic is structured among other things, that the dialogue is divided by the episode of the 'divided line' in such a way that the lengths of dialogue before and after this section have a phi ratio vis a vis their lengths. . . . It seems difficult to interpret this as other than a beautiful 'formal pun' (assuming that one recognises that the divided line concerns the phi ratio, as it does according to some interpretations). Bremer's interpretation goes far beyond this, and establishes pretty solidly that the Republic is structured deliberately along mathematical lines. If I find that Kennedy has not credited Bremer I shall be incensed.

There's no way to assess this new work without getting to grips with the statistics and geometric analysis and such (and control-cases must be made; contemporary works subjected to the same sort of analysis to see if they don't also yield accidental 'secret codes' of their own), but I feel that, taken alongside Bremer's (seemingly ignored) article, it deserves to be addressed properly. IF and only if it is even partially correct (e.g., if we can concretely show that Plato did have some underlying structural principles, whether related to music, esoteric numerology, simply principles of proportion and harmony in dramatic art, whatever) it would change EVERYTHING. Seriously; if it can indeed be applied to all the dialogues, it would show that there IS after all a unity to Plato's work from the beginning. It could help us with editing; In fact, we could theoretically assess emendations quantitatively (that is, as to whether they add up, literally). We would potentially have to re-approach all the data from Aristotle on Plato, and what we know of the Early Academics and their 'Pythagoreanizing'. "chronicneoplatonic" The aspect of this theory that attracts me, I must say, is that it is based on a standard ancient papyrus line of 35-36 characters- the length of an hexameter line of poetry, which prose writers would have followed, since that would have been the width of the papyrus. It would not then have been too complicated to count the lines, and with modern technology we can do so too. But the proof of the pudding.... JMD John Dillon I read the paper by Jay some time ago now, and it is certainly based, as John Dillon says, on some based principles about line-lengths and on the frequency with which [standard] lines were used as a measure in antiquity. There is some serious research that has gone into the claims that have been published, but of course by the time the academic gives his version to a journalist and the journalist has his work changed by the editors the claims tend to look a little more extreme than any academic is likely to have made. Since the article is on Jay's personal website at Manchester Uni it is available for all to read, and judge for themselves. If it all holds water, then it does have important ramifications for our understanding of the Platonic corpus, but the results *and their interpretation* need some very careful independent scrutiny before we know exactly what these ramifications are. In particular, I felt that a good case could be made for the analysis of the larger works that were probably in need of principles of composition, but the article was not using the smaller ones as case studies. I'd like to see further work from Jay himself and from others before I go overboard (with the press!), but I am looking forward to it. Even then, whether this means that we need to beef-up our ideas of 'Pythagorean influence' is unclear, since harmonics is well know to be vital in the Timaeus, and it was probably of great fascination to many of Plato's colleagues in the Academy. So alas, we need to do a little waiting before we make up our minds about things. Best, Harold Tarrant, Yes, I think the whole thing has been inevitably grossly hyped up by the press. If Jay has hit on something here, as I think he has, it would increase our appreciation of Plato¹s artistry in structuring his dialogues, and may help to point us to passages that he wished to be significant - if we had not noticed them already! - but it is all something less than a revolution in Plato studies, I think. JMD John Dillon Incidentally, Slaveva-Griffin convincingly argues for the presence of Neopythagorean numerical symbolism in Porphyry's organization of the Enneads. (Plotinus on Number, 131-140). David Gallagher See other discussions: http://rogueclassicism.com/2010/07/03/pondering-the-plato-code/ http://www.marginalrevolution.com/marginalrevolution/2010/07/are-there-hidden-codes-inplato.html http://groups.yahoo.com/group/neoplatonism/message/3392

Article submitted to the Pythagorean Foundation on 5 December 2010 by John Bremer. Plato, Pythagoras, and Stichometry §1. Introduction We know little of Plato the man and everything we need of Plato the philosopher. His name appears in the dialogues only three times, twice connected with Socrates’ trial and once with the day of his death. That is all. But to say that we know everything we need to know of Plato the philosopher is misleading because, according to Plato himself, philosophy is not to be qualified by anybody’s name. It deals with what is universal and eternal. One reason why Plato never appears as a character in his own dialogues is that he does not want to become, as it were, the subject-matter. This accords with the famous remark that Socrates can be refuted but not the logos. One thing we learn from the dialogues is that, in a certain sense, philosophy has no need of Plato, it does not belong to him, it is not his possession. But it needs us, or rather we need it if we are concerned with ‘how a man should live’. Philosophy, according to Pythagoras, who coined the term, is love of wisdom and Plato is never tired of contrasting that love with the claim of the Sophists that they have wisdom and can dispense it, as if it were a commodity that they possess and can sell—if the price is right. The ‘knowledge’ of the Sophists brings them not only wealth but also fame and prestige, which, in turn, raises their market value. Concern with ‘how a man should live’ is unfashionable these days, and a minor academic industry has been created around ‘Plato’, really around Platonism, which has nothing to do with that awkward question. Furthermore, most claimants to being Platonic scholars would deny that it was any of their concern; scholarship is not about how a man should live, but about what a philosopher said, wrote and meant—provided that it never meant that we should reflect on our lives, that we should live Socratic examined lives. But it does not deal with whether any of it is true. Of course, modern scholars exist in an institutional framework which exerts strong influence upon them. They are paid by the institution, they are promoted (or not) by it, they acquire fame through it, and, if they are institutionally successful, they create through their students academic empires, political entities which support and promote, for the most part, their own orthodoxy. They are in constant danger of living in a form of Plato’s Cave—ironically indoctrinating their version of Platonism. To take only two examples of how this distorts whatever Plato himself understood, Raphael Demos openly confesses in his book on Plato that he did not understand mathematics, and Gregory Vlastos privately wrote that he understood nothing about music. One might have thought that these confessions would disqualify them from writing about Plato since it is clear that for him they were central to an understanding, central to philosophy. But no! Nor did it seem to occur to these worthies that they might actually learn some mathematics or study some music, subjects dear to Pythagoras and described in the seventh book of the Republic. All these reflections were brought about by the appearance in the Texas academic journal, Apeiron, of an article by Jay Kennedy of the University of Manchester, with the title Plato’s Forms, Pythagorean Mathematics, and Stichometry. There are three topics requiring attention. The first is the Manchester University publicity, the second is the claim of originality, and the third is the findings of the article. Since the present author is involved in the discussion, it will be written in the third person. §2. Publicity First, the publicity announces grandly that a “science historian” has “cracked ‘The Plato Code’–the long disputed secret messages hidden in the great philosopher’s writing.” This is pure hype—or rather impure hype. There is no ‘hidden code’ except in the sense that anyone who reads anything needs to know how to read. In a certain sense all writing is encoded—that is what is meant by ‘writing’ and to deal with it one needs skill in ‘reading’. Plato hid nothing, but succeeding thinkers

(like Demos and Vlastos) forgot or never knew how to read. It would have been more significant if it had been declared that the existence and use of language is, in the old sense, a mystery, a mystery into which we must be initiated. The ability to read, especially and in this case Plato, may be illustrated from the beginning of the Republic. Its first word is ‘down-went-I’ (to the Peiraeus, it appears) which means that Socrates, who is recounting the dialogue, is now ‘back up’ (presumably in Athens). If he were still ‘down’ in the Peiraeus, he would have said ‘down-came-I’. There is no need to explore now the metaphorical significance of Athens and Peiraeus, but it is worth pointing out that the ‘down and up’ metaphor pervades the whole dialogue. The most obvious instance is the descent into the Cave (Book 7) and the laborious climb out of it. But if Socrates went ‘down’ at the beginning he comes back ‘up’ in the Myth of Er at the end of the dialogue, which explains the return. The dialogue, like all human knowledge, is circular. The second word of the dialogue is ‘yesterday’. Now, first, if Socrates is telling us of what happened ‘yesterday’ he must be telling us ‘today’, that is to say, by the use of this one word Plato makes it clear that his dialogue is in an immediate and ever-present ‘now’. It is eternally contemporary. Second, because Socrates repeats yesterday’s conversation, we are presented with a double: there was the conversation yesterday and now there is its repetition today. In other words, we are presented with a ratio of 1:2, which would immediately suggest to any ‘musical man’ that we are involved with the octave, that is, that the dialogue must be understood musically. Third, Socrates follows the rule of the Pythagoreans that the first thing to do when waking is to go over in the mind the events of the previous day. The reader or hearer is alerted to the fact that the dialogue’s spirit is Pythagorean. There is here no ‘secret code’ only a sophisticated writing and reading ability. The Republic, like any of Plato’s dialogues, invites us to learn to read (or hear) with greater understanding. It is a self-instructing lesson in language. This understanding of the first two words strongly influences the way the ensuing dialogue is understood. For example, if we understand that it is Pythagorean, we find the famous sentence in Book 1—‘This is no small thing we are discussing, but how a man should live’—more meaningful since it was well-known that to be a Pythagorean meant to have a way of life. But it also raises the question ‘How can arithmetic be a way of life?’ That needs to be pondered. §3. Originality Second, Kennedy’s claim to originality is mistaken. At least two writers had expounded the arithmetical and harmonical structure of Plato’s dialogues thirty years earlier. The story can best be told from the point of view of one of the two pioneers. In 1959 John Bremer realized that the famous Divided Line of Book 6 of Plato’s Republic, a Line divided unequally, in fact divided the dialogue. By 1960 he had by rough count of lines strengthened his suspicion that the Divided Line divided the dialogue in what we call the Golden Section. He thus was drawn to see that the Republic had within itself its own reading instructions and began to use the Divided Line as an analytical tool for understanding the dialogue itself. But a more precise way of measuring the dialogue was needed and Bremer coupled with his discovery the simple fact that in the ancient world ‘publication’ meant a reading aloud, that is, the dialogue existed, not in space as on a printed page, but through time as it was recited. It was musical. The unit of speech in time is the syllable and so Bremer laboriously counted the syllables in the Republic (and most of the other dialogues), or, in other words, he used in a new way the ancient method of stichometry. He also discovered that the Republic takes twelve hours to recount. The numbers confirmed his original intuition about the Golden Section and made it possible to identify accurately patterns and symmetries in the Republic, all based on the arithmetical counting of syllables. He never thought that the revealed patterns were simply a kind of ornamentation, a pleasurable addition to the content of the dialogue, a literary device, but rather that they were an essential, perhaps the essential, part of the dialogue. For example, the Golden Section was used

because it is the well-known principle of growth and diminution, both in geometry and biology (see d’Arcy Thompson), and was therefore a self-referring creative principle. Involved with other duties, Bremer could give little time to pursuing his discovery but by about 1980 he had prepared a book (published as On Plato’s Polity in 1984) outlining both the stichometric method and what it revealed about several of the dialogues. After the preparation, by chance in a bookstore, he came across a book that completed for him the arithmetical work that he had done. That book was The Pythagorean Plato by Ernest G. McClain and had been published in 1978. From Plato’s statements in the various dialogues and on the basis of the actual numbers quoted in them, McClain established beyond any question that “Pythagorean harmonic theory is Plato’s ‘prelude to the song itself . . . the song itself that dialectics performs.’” He showed that the later dialogues—Republic, Timaeus, Critias, Statesman and Laws—embodied a systematic treatise on harmonics, on tuning theory. To Bremer this came as an astounding revelation which opened up more possibilities for his arithmetical analysis. Through the good offices of Robert Brumbaugh (whose Plato’s Mathematical Imagination is a classic), Bremer and McClain were soon in touch and have collaborated ever since, sharing their work and thoughts. It turned out that McClain had published an earlier book The Myth of Invariance in 1976 with the intriguing and revealing subtitle of The Origin of the Gods, Mathematics and Music from the Rig Veda to Plato. This had established the use of harmonical allegories in Plato and other literatures. While Bremer could take advantage of the profound musical knowledge of McClain, McClain was no longer restricted to the numbers that Plato actually quoted but could use the syllable count to extend his analysis of the harmonic structure in the dialogues. The two complemented each other in a most fruitful way. In 1994 McClain published an introductory essay Musical Theory and Ancient Cosmology which confirmed and extended his findings about Plato. And in the issue No.169, Winter 2000 of Hermathena, A Trinity College Dublin Review, Bremer published an article introducing and extending his discoveries, Some Arithmetical patterns in Plato’s Republic. In 2002, Bremer produced a detailed arithmetical- harmonical analysis of the Republic in Plato and the Founding of the Academy, ( McClain drily observed that the Republic embodies a treatise on equal temperament). In 2005 Bremer’s study of a short dialogue the Ion appeared, with a translation and commentary; Plato’s Ion: Philosophy as Performance included a lengthy section on ‘Philosophy the Greatest Music.’ In the light of all these publications from 1976 onwards the priority for the discovery of the harmonical analysis of Plato’s dialogues must be accorded primarily to McClain, and the priority of the arithmetical and stichometric analysis to Bremer. This is not to denigrate the work of Kennedy, only to establish where the honor truly lies. A further element in this history is that one of Bremer’s students, Maya Alapin, studied at Oxford but found it very difficult to find any supervisors to oversee her work. She carefully explained to many of the scholars who might have been suitable and willing to supervise her studies that she wanted to evaluate and enlarge the findings of Bremer. Although few were willing to help her, the outline she presented got passed around, not always being taken seriously, among the academic community and undoubtedly reached Manchester with or without acknowledgement. Alapin was awarded the MPhil degree in June 2007 and her thesis The Architectonic Structure of Plato’s Republic was duly made public. In the Introduction she writes: It has been argued by John Bremer that there is a mathematical and musical structure underlying the whole text of Republic, one that is derived from the well-known Pythagorean ratios that define the musical octave and the diatonic scale. In Oxford Alapin was able to persuade Benjamin Weaver to create a software program, Panza, that would count the syllables of a Platonic text. Its uses confirmed Bremer’s hand count of the length of the Republic at 180,000 syllables.

§4. The Kennedy article First and foremost, whatever else may be said, an article analyzing the Platonic dialogues in mathematical and harmonic terms is to be welcomed and studied with great care, not least because it lies outside the conventional approaches to Plato. Furthermore this article is written by a scholar, Jay Kennedy, with some knowledge of and sympathy for both mathematics and music, unlike those mentioned in the Introduction, and therefore must be taken very seriously. The following remarks must be taken in the light of this overall commendation. The question of priority is not important and one could wish that names and personalities could be ignored—as Plato wished. It is a pity that Kennedy either did not know or chose to suppress the earlier work of McClain and Bremer—their works being available in the Bodleian—but it really does not matter. While Kennedy clearly understand something of both mathematics and music, it is not clear that he understands them as they were understood in the ancient world. For example, it is not evident that, in music, he knows that Plato worked with four different tuning systems—Just, tempered, Pythagorean, and Archytan (corresponding to the four Platonic cities of Atlantis, Callipolis, Athens, and Magnesia)—and that, in mathematics, he was concerned with what the modern world calls Diophantine approximation. Turning Greek mathematics into modern terms is dangerous and misleading, as evidenced in the work of Thomas Little Heath for he assumes that a ratio is a number (which it never was, for it was a relation between numbers), and that one is a number (rather than the origin of all numbers). Kennedy rightly emphasizes the importance of the number twelve—and certainly Plato focuses on the problem of dividing a cyclic octave into twelve equal parts, an impossible task without the use of irrationals—but he seems to ignore the significance of the number ten (so important to the Pythagoreans) and its relation to the Forms. There is in Plato a continuing ‘dialogue’, as it were, between the numbers ten and twelve which are reconciled in the number 60, the root of the Babylonian sexagesimal system. In this connection, the title of the article promises more than it delivers for it has little to say about the Platonic Forms. A connection must be made between the arithmetical and harmonical structure of the dialogues and the Forms. This Kennedy does not do—does not even allude to it. Nor does he appreciate the way in which music exists through time; he would if he saw the dialogues not as seen, as static written texts occupying space, but as heard, as dynamic sounded sequences in time; more generally as processes not products. The stated intent of Kennedy’s article is “to corroborate the view of Aristotle and other members of the early Academy that (Plato’s philosophy) was fundamentally Pythagorean.” In a purely gross and verbal sense, ‘we need no ghost come from the grave to tell us this’, but, in a more exact sense, it would have been good to know precisely what it would have meant to call Plato a Pythagorean, and if he would have accepted the description. The name of Pythagoras occurs only once in all the dialogues and the Pythagoreans are mentioned twice, all three occurrences in the Republic. This is the same number as Plato’s name appears in all the dialogues, the paucity being attributable to the reason mentioned in the Introduction. The confusion stems from the assumption that being a Pythagorean meant subscribing to an orthodoxy, whereas it actually meant following a way of life (as Plato states in the Republic, St.600b.2). Aristotle, mistakenly and for his own purposes, thinks only of a doctrine and never of the way. It is to be hoped that Kennedy will pursue his line of thought but with a more thorough search of the literature, bearing in mind that academic philosophy is a subject-matter whereas Platonic and Pythagorean philosophy is a way of life.

http://www.ernestmcclain.net/ Musical Adventures in Ancient Mythology Ernest G. McClain These occasional essays continue the author's earlier studies published in The Myth of Invariance (1976), The Pythagorean Plato (1978), and in Meditations Through the Quran (1981), correcting, updating, and extending analysis more deeply into Mesopotamian foundations and their extensive development in the Bible and (eventually) Homeric epic. October 2010 The author's First two books, The Myth of Invariance and The Pythagorean Plato are scanned here for easy downloading by interested students but the copyright restriction is still affirmed for publication. The Myth of Invariance [PDF] The Pythagorean Plato [PDF] March 2010 The author's third book, MEDITATIONS ON THE QURAN, published in 1981, is scanned here for easy downloading by interested students but the copyright restriction is still affirmed for publication. Notice, however, that a new Appendix II titled "Abraham's Children" makes very important corrections to errors made thirty years ago regarding YHWH as the "One" God of monotheism (on pp. 131, 134, and 137), and of the "chief cornerstone" on pp. 147-8, and also of the meaning of "first-born sons" (p. 151). More recent translations and publications of cuneiform mathematics now make clear that I misunderstood the greater "Marduk-Baal" matrix for "Noah's flood" as YHWH's own, and overlooked the cornerstone "unit" as eventual "Savior," and misunderstood Jacob's twelve sons as "male, odd integers" less than his death at age 147. The entire problem of ancient Egyptian and Mesopotamian mathematics is now undergoing serious reconsideration within the mathematical community, and all speculation like mine must be considered tentative perhaps for further generations. [PDF] The following titles are currently available: "Children of Abraham" (Appendix II to my book on the Quran) [PDF] [docx] [doc] "The Harmonic Series As Universal Scientific Constant," 4 pp. (orientation principles) [doc.] "Musical Theory and Ancient Cosmology," an introductory essay published in The World And I in 1994, 21 pp. "The Forgotten Harmonical Science Of The Bible," 24 pp. [doc.] "The Nine-String Akkadian Lyre Of Kilmer, Crocker, and Brown" (Essay in preparation). "Mathematical Harmonics in the Book of Jonah," 5 pp [pdf.]. My Jonah studies have been compressed and edited by the old Testament scholar, Duane L. Christensen, founder and director of Bibal Corporation (see www.bibal.net), as an Appendix to his new textbook, READING JONAH IN HEBREW, 2004, and available from: BIBAL Corporation, 845 Bodega Way, Rodeo, CA 94572, telephone 510-377-7000. Related books highly recommended. John Bremer: PLATO AND THE FOUNDING OF THE ACADEMY, University Press of America, 2002. Jay Kappraff: BEYOND MEASURE: A GUIDED TOUR THROUGH NATURE, MYTH, AND NUMBER, World Scientific, 2002.

About the author Ernest G. McClain is Professor Emeritus of Music, Brooklyn College of the City University of New York, retired since 1982 and living presently in Washington, D.C.. Clarinetist, band director, author of three books mentioned above and more than thirty related essays in various professional journals, his degrees from Oberlin, Northwestern, and Columbia are in Music Education. He chooses to make these newer essays freely accessible to anyone who finds them useful, with appropriate acknowledgement. Particular attention is given to graphics essential to understanding ancient habits of thought, for mythological narrative often proves to be verbal commentary on matrix arithmetic, and many stories are best understood as straightforward musical allegory. Questions are encouraged and will be answered periodically as time and energy permits. It should be understood that the author is neither a mathematician nor a linguist, working mainly from secondary sources available in English translation as an interested observer on current developments in other disciplines. Attention is on arithmetical details not likely to be understood except by musicologists. The interpretations offered here should be considered speculative adventures of ideas in the spirit fostered by Alfred North Whitehead in his book of that title, for they concern matters which preclude certainty about the intentions of early authors. After more than three decades of work in this area it seems plausible to propose that most of the numerology in ancient mythology÷and all theology in advanced civilizations--is musically inspired and disciplined. Thus interpretation falls into the general category of Pythagorean studies for it pursues a plausible numerical logic based on the quantification of tuning theory. Foundations appear to have been laid down in the fourth millennium BC before the invention of writing, so that for five thousand years musicians have employed essentially the same fossil science. A fairly primitive arithmetic is handled with great ingenuity, ironic humor, endless word play, and considerable arithmetical elegance. Decoding is great fun when it appears convincing, and a pocket calculator takes all the labor out of ancient multiplication, so that many of these adventures become accessible to children. And because much ancient literature has never been studied carefully from a musical perspective, this adventure is just beginning. email Ernest McClain Institute of Philosophy John Bremer A summary article of his research appeared in Hermathena (No.169) of Trinity College Dublin in 2000, Some Arithmetical Patterns in Plato’s‘Republic’. http://www.instituteofphilosophy.org/sitebuildercontent/sitebuilderfiles/plato.pdf

Conferences Elizabeth Leach, ‘Nature's Forge, Pythagoras' Smithy, and the Mechanics of Musical Invention’ EXETER MEDIEVAL SEMINAR 2005-6. May 16 http://centres.exeter.ac.uk/medievalstudies/Exeter_Medieval_Seminar0506.shtml UNIVERSITY OF EXETER: DEPARTMENT OF CLASSICS AND ANCIENT HISTORY Pagan Monotheism in the Roman Empire (1st-4th cent. AD) Conference at Exeter, 17-20 July 2006 H. Clifford: Pagan Monotheism in Philo of Alexandria The first part of this paper locates the monotheism of Philo (c.15 BC–c.AD50) within the Hellenistic Jewish tradition of assimilating the Jewish God to the God of philosophy, as seen in Ps.-Aristeas (3rd century BC), Aristobulus (2nd century BC), and Philo’s near contemporary Josephus (1st century AD). The second part outlines key aspects of Philo’s writings that suggest he would have recognised the expression ‘pagan monotheism’ (though Jewish theologians were divided on the implications of Jewish-Greek equations). These include his language for God that is generalist in character (‘first’, ‘One’, ‘Maker’, ‘Pilot’), and his creative re-use of Presocratic, Classical, Stoic and Neo-Pythagorean traditions, all of which helped commend a cosmopolitan philosophical piety. In the third and final part, Philo’s two main discussions of monotheism are mentioned (De Decalogo 52-81; De Specialibus Legibus 13-65), exegeses of the First and Second commandments, noting in particular the arguments that Philo uses to demonstrates the universal rationality of monotheism. This paper reflects the interests of an on-going project about monotheism in Philo. G.H. van Kooten: The Aniconic, Monotheistic Beginnings of Rome’s Pagan Cult, According to Varro, Plutarch, and St Paul: Romans 1.19-25 in a Roman Context In his Letter to the Romans, St Paul sketches the development of the history of pagan religion as a history of decline, drastically moving away from its original monotheistic and aniconic stance. Originally, the invisible God was visible to the eye of reason in the things he has made, but man has since long exchanged the glory of the immortal God for human and animal images (1.19-25). Implicitly, Paul acknowledges that pagan religion started off well but suffered deterioration. Although Paul’s criticism of pagan reverence for images resembles earlier Jewish criticisms, especially those contained in the first-century BC Jewish writing The Wisdom of Solomon, his argument of the degeneration of pagan religion, and his implicit acknowledgement of a originally ´pure´ pagan past of aniconic monotheism, seems to be his own. In his Letter to the Romans, Paul seems to intentionally link up with specifically Roman historiographies known from Varro and Plutarch, which speak of a ´golden´ period of 170 years following the establishment of aniconic monotheistic cults by Rome’s second, legendary king Numa (Varro, frgs 12-19 edn. Cardauns; Plutarch, Numa 8.7-8). Varro compares this original Roman practice with that of the Jews and Plutarch points at the influence of Pythagoras who, in other sources, was often closely linked with the Jews; after this golden aniconic, monotheistic age, Roman religion declined, according to both Varro and Plutarch. In this paper, I intend to explain Paul’s positive reference to a pagan monotheistic and aniconic past against the background of the relevant passages in Varro and Plutarch. B. Selter: Eadem spectamus astra. Monotheistic tendencies in the Carmina latina epigraphica. In this paper I will present the results of my research on the idea of astral immortality in the Carmina Latina Epigraphica of Rome, both pagan and christian, and dating from the 1st century to the 6th century A.D. This religious concept originates from eastern astrology and, among others, Greek pythagoreism. It would seem that the presence of verbal echo’s of astral immortality in the pagan inscriptions can only be explained by viewing them within a larger frame, i.e. the emergence of monotheistic tendencies within paganism. Moreover, it is interesting to notice the same elements of astral immortality arrising in christian epigraphic poetry, often with a very similar motivation for doing so. The source-material, a selection of epigraphic funerary poems from Rome, forms a first-hand testimony of a tumultuous period in Rome’s religious development. The inscriptions clearly illustrate the dichotomy between the philosophical ideas of intellectuals, parallel with those expressed in the literature of the era, and the beliefs of the ordinary people. Thus, the belief in astral immortality, featuring in the Carmina Latina Epigraphica, proofs to be more than a literary topos, but helps contribute to our understanding of the intellectual basis of pagan monotheism. Anne-Laure THERME, Une tragédie cosmique : l’exil amnésique des daimones d’Empédocle. In: Actes du colloque de doctorants et de jeunes chercheurs, "La rationalité tragique", Université Paris 1-Panthéon-Sorbonne et Université Paris Ouest - Nanterre-La Défense, 2-4 juin 2009. http://www.zetesis.fr/actes/spip.php?article14

Presocratics and Plato. Festschrift Symposium in Honor of Charles H. Kahn Conferences 03—07 June 2009 Delphi, Greece HYELE Institute for Comparative Studies, and Starcom AG, Parmenides Publishing, Sarah Broadie— "Fifth-Century Bugbears in the Timaeus" Lesley Brown— "Plato on not-being: some troublesome texts" Tomás Calvo— "The Method of Hypotheses and its connection to the Division and Collection Strategies" Diskin Clay— "The New Empedocles and Plato: The Metempsychosis of the Poet" Dorothea Frede— "Forms, Functions, and Structure in Plato" Arnold Hermann— "Plato's Eleatic Challenge" Carl Huffman— "Aristoxenus' Account of Pythagoras" Enrique Hülsz— "Heraclitus on the Sun" Paul Kalligas— "From being an image to being what-is-not" Vassilis Karasmanis— "Dialectic and the second part of Plato's Parmenides" Aryeh Kosman— "Self-control and self-knowledge in Plato's Charmides" Tony Long— "Slavery as philosophical metaphor in Plato and Xenophon" Susan Sauvé Meyer— "The Psychologies in Plato's Laws" Alexander P. D. Mourelatos— "The Eleaticism of the Eleatics" Satoshi Ogihara— "False Pleasures in the Philebus" Richard Patterson— "Word and Image in Platonic Myth: the Case of Laws X" Christopher J. Rowe— "Socrates in Plato's Laws" David Sedley— "Plato's Theory of Change (Phaedo 70-71)" Additional Contributors Julia Annas—"Virtue in later Plato" John Dillon—"Will the real Critias please stand up?" Richard McKirahan—"Socratic Egoism and the Happiness of Others" Daniel McLean—"Plato on Befriending Oneself" Malcolm Schofield—"Keeping Leucippus apart from Democritus" George Boys-Stones (Univ. Durham) : Numenius on the soul Le séminaire "L'âme et ses discours" dans le cadre du programme L'Héritage philosophique de l'antiquité dans la pensée byzantine et médiévale latine du Centre Léon Robin (CNRS, Paris IV-Sorbonne) reprend ses séances en novembre prochain. Voici le programme de l'année: 19 Mai 2010 Conferences 28—31 July 2010 University of Edinburgh, Scotland The Second Conference of the International Association for Presocratic Studies The second IAPS conference is taking place at the University of Edinburgh and is held in conjunction with the Celtic Conference in Classics. The HYELE Institute is co-sponsoring a Bookstore event in celebration of a new edition of A. H. Coxon's The Fragments of Parmenides (Las Vegas: Parmenides Publishing, 2009), as well as a conference Dinner in honor of A. H. Coxon, on Thursday, 29th July 2010. Speakers 40 minute papers: N. Cordero— “Gianfrancesco d'Asola, the 'creator' of Parmenides' third way” Andrew Gregory— “On Regimen I/10-12: A Hippocratic cosmological passage” Edward Hussey— “Aristotle on the Presocratics’ misunderstandings of nature” James Lesher— “Plato’s Views on Xenophanes” Laura Gemelli Marciano— “Phren, Demon, and Empedocles' Teaching” Richard McKirahan— “Philolaus' extension of the concept of number” Emese Mogyorodi— “Revelation and Reason in Parmenides” John Palmer— “On the varieties of necessity in Presocratic philosophy” Miriam Peixoto— “L'homme démocritéen: esquisses d'une anthropologie” 20 minute papers: Anna Aravantinou— “Elements and (Physical) Contraries in the Early Milesians and Anaxagoras” Scott Austin— “Heraclitus, Parmenides, and the Unity of All Things” Ran Baratz— “Parmenides on Human Error” Alberto Bernabé— “Naming the form among the Presocratics (idea, eidos, morphe, schema)” Beatriz Bossi— “Heraclitus and the Derveni Papyrus” Francesc Casadesús— “Why did Heraclitus consider Dionysus and Hades to be the same?” Sylvana Chrysakopoulou— “Doxography and Plato’s Debt to Earlier Thinkers”

Matthew Cosgrove— “What are ‘True’ doxai worth to Parmenides?” Aryeh Finkelberg— “Aristotle on the identity of knowledge and sensation in the Presocratics” Enrique Hülsz— “Heraclitus, Plato and the philosophic dogs” Claire Louguet— “Sur les fragments 6 et 7 de Parménide” Constantin Macris— “The mysterious Petron of Himera and his mathematically constructed multiverse” , Nie Minli— “A Notable Passage in Plato’s Theaetetus 152D-E Concerning Our Understanding of Thales’ Thought” Marcus Mota— “Performative and antiperformative arguments in Heraclitus” Serge Mouravieff— “Stoicheion : Platon, Empédocle ou Héraclite ?” Mourelatos, Alex— “The light of day by night (nukti phaos): the Moon in Parmenides B14” Marco Antonio Santamaría— “Ananke in Parmenides, Empedocles, and the Orphic Theogonies” Andreas Schwab— “Thales and the Aristotelian Commentators” Lucia Saudelli— “Heraclitus’ River-Fragments” Anne Gabrielle Wersinger— “Empedocles: Nestis-Persephone and the Charites” Rosemary Wright— “Ethics in an atomic theory” Robert Zaborowski— “Courage in the presocratics' Prado dos Santos, E.C. A voz pitagórica nas Metamorfoses de Ovídio: o discurso de Pitágoras XXI Simposio Nacional de Estudios Clásicos Santa Fe, 21 al 24 de septiembre de 2010. FHUC – UNL Correa Pabón, G.L. El De Musica de San Agustín y la Tradición Pitagórico-platónica. XXI Simposio Nacional de Estudios Clásicos Santa Fe, 21 al 24 de septiembre de 2010. FHUC – UNL Prado dos Santos, E.C. O DISCURSO DO “PITÁGORAS OVIDIANO” NAS METAMORFOSES . SEMINÁRIO DO GEL. 2010, 58. Programação... São Carlos (SP): GEL, 2010. Disponível em: <http://www.gel.org.br/?resumo=6250-10>. Acesso em Jay Kennedy The Musical Structure of Plato's Dialogues University of Manchester. Classics Department Research Seminar October 27th 2010 Thomas A. Szlezák (Univ. de Tübingen, Alemanha): Aristotle´s testimonies on the relationship between Plato and the Pythagoreans. I Simpósio Internacional. "As Doutrinas não escritas de Platão" De 24 a 26 de Novembro de 2010 Instituto de Filosofia e Ciências Sociais (IFCS/UFRJ) www.simposionaoescritas.nefa.pro.br Chiara Cremonesi Lingue, performance e identità nella Vita di Apollonio di Tyana. Colloque "Langage des hommes, langage des démons, langage des dieux", Institut protestant de Théologie, Paris les 25 et 26 novembre 2010 Abstract: Nella Vita di Apollonio di Tyana di Filostrato le lingue degli uomini, dei demoni e degli dei sembrano rincorrersi in un processo di continua metamorfosi. Esse vengono tra-dotte dal sapiente che le rende efficaci sulla scena di un teatro permanente, quel viaggio che attraversa lo spazio e il tempo, il mito e la storia, la Grecità e la barbarie, ridefinendo l'identità stessa della lingua sacra. Danny Praet (Gent): In praise of long hair. The use of Homer, Euripides and second sophistic rhetoric in the Life of Apollonius of Tyana by Flavius Philostratus international conference QUATTUOR LUSTRA, 3-4 December 2010 in Tartu, Estonia. Department of Classical Philology of the University of Tartu, Estonia. http://www.fl.ut.ee/quattuor_lustra/ Leonid Zhmud (Saint Petersburg): A Pythagorean number doctrine in the Academy international conference QUATTUOR LUSTRA, 3-4 December 2010 in Tartu, Estonia. Department of Classical Philology of the University of Tartu, Estonia. For more information see http://www.fl.ut.ee/quattuor_lustra/

New books Agnello, N. Empedocles. Frammenti. traduzione, introduzione e commento. Cosenza : L. Pellegrini. 2008. Series 1: Filosofia teoretica; 6. Electronic ed. avail. at the URL: http://digital.casalini.it/9788881015214. ISBN/ISSN: 978-88-8101-521-4 INDICE; Introduzione - La poesia di Empedocle - Frammenti di Empedocle - L’Empedocle di Strasburgo - SCHEDA BIOGRAFICA - SCHEDA BIBLIOGRAFICA traduzione italiana inedita, corredata di note puntuali e introdotta da uno studio sui problemi legati all’identificazione del suo autore e alla classificazione della sua dottrina. Barth, V.C. A IDEOLOGIA NEOPLATÔNICA NAS VIDAS DE PORFÍRIO Caderno de resumos em formato digital. 2010. URL: http://www.fclar.unesp.br/25sec/ V Fórum Acadêmico de Estudos Clássicos (V FAEC). DIONISO: TRAVESSIAS E TRANSMUTAÇÕES 25 anos! Resumo: O cenário político e social da Roma do século terceiro (d.C.) engloba duas correntes filosófico-religiosas principais: o Cristianismo e o Neoplatonismo. É um período de grande rivalidade entre os dois pólos, já que as duas crenças buscam novos adeptos em meio à fragilidade moral do cidadão romano nessa época de crise imperial. Nesse contexto, embora a literatura e a produção artística estivessem fragilizadas, a biografia assume um papel de relevância em meio à sociedade por se tornar campo de discussão entre as doutrinas. Porfírio, discípulo do conhecido filósofo neoplatônico Plotino, coloca-se em posição oposta ao Cristianismo de maneira declarada. Suas Vidas apresentam personalidades biografadas que sintetizam os valores platônicos que seriam introduzidos aos novos alunos, ao mesmo tempo em que constituem parte da “publicidade” frente aos rivais cristãos. Tendo em vista esse contexto, o interesse deste trabalho é a discussão dos modos como Porfírio se apropria da forma da prosa biográfica em favor da promoção de sua doutrina, usando de personalidades de bastante prestígio – Plotino e Pitágoras – que seriam capazes de rivalizar com a figura do próprio Jesus Cristo. Consideraremos os modos como a tradição biográfica está presente neste autor, portanto, fazendo referência a outras biografias, e também considerando as diferenças entre os dois textos de Porfírio: a Vida de Plotino e a Vida de Pitágoras. Ahmadi-Nezhad, R. 'An Architext's Mind'. The effect of philosophers on architecture Heleh Publications. 2010. Summary: Pythagoras's ideas was influenced the construction of Pantheon, as Saint Agustin's thought was effective on the formation of Cathedrals during the middle ages. The book "Archtect's Mind" is an attempt to survey these effective thoughts on architecture from ancient times up to the beginning of Post-modern era. "This book explores the thoughts of all influential philosophers to make a survey of their mind and their marks on architecture." Barbone A. La tavola di Cebete. Testo greco a fronte La Scuola di Pitagora. Collana: Pythagorea. Studi e testi. 2010. ISBN-13: 9788865420126 Opera di un anonimo autore eclettico vissuto tra il I e il II secolo d. C., scritta in una lingua così semplice da guadagnarle il titolo di “classico” nell’insegnamento del greco dal Rinascimento fino a tutto l’Ottocento, la Tavola di Cebete segue gli itinerari dell’uomo virtuoso nella vita, dacché nasce fino al conseguimento della felicità, mostrando da un lato le fatiche di un’esistenza spesa alla ricerca della sapienza e della virtù, dall’altro i fallimenti e le disillusioni di coloro che si lasciano ammaliare dalla fortuna e dai vizi. Il nome di Cebete rimanda alla veneranda tradizione pitagorica, cui la Tavola non appartiene per contenuti, giacché la sua dottrina si inserisce pienamente nell’ambito della morale ellenistica, variamente influenzata dal platonismo, dal cinismo e dallo stoicismo. Tanto ammirata da umanisti del calibro del Giraldi e del Gronovio, e ricordata da Vico, Campanella e Leopardi, la Tavola di Cebete è caduta nell’oblio da quando l’interesse per la sua dottrina morale non ha più stimolato letterati e filosofi, insegnanti e studenti. L’edizione della Tavola di Cebete curata da Alessandro Barbone ripropone il testo greco dell’edizione teubneriana con una Brodersen, K. Briefe einer antiken Philosophin : Griechisch/Deutsch / Theano. Stuttgart : Reclam. 2010. Reclams UniversalBibliothek ; Nr. 18787 ISBN: 978-3-15-018787-6 Einfuhrung - Christoph Martin Wieland: Die Pythagorischen Frauen - Quellen zu den antiken Philosophinnen - Texte der antiken Philosophinnen - Briefe der Theano Sinnspruche der Theano - Texte weiterer

Philosophinnen - Quellen- und Literaturhinweise. periodical press, and in particular, on the influence of medical thinking and the science of the mind on the writing of James Hogg (1770-1835). Charrue, J.M. De l'être et du monde. Ammonius, Plotin, Proclus Klincksieck. 2010. Études et commentaires 110. ISBN 978-2-252-03666-2 Description: Le néoplatonisme a été cette découverte du monde, depuis Ammonius, le maître de Plotin, où l'âme se révèle d'une autre nature que le corps, dont Origène le chrétien fut l’élève probable. Pourquoi le monde est-il ce qu’il est, si ce n’est l’effet d’une Providence, qui se révèlera thème majeur, et ce, jusqu’à Proclus, et les trois Opuscules, là où comme chez le précédent elle doit rencontrer cette liberté humaine, si fortement présente. L’horizon mystique n’en marquait qu’une sortie provisoire, mais Plotin voit le monde à travers les regards que Parménide, Socrate, Épicure, ou encore le stoïcisme, avaient jeté sur lui, dans un langage où l’image devient l’un des modes d’expression nouveau et privilégié, fasciné déjà par le désir, comme le sera A. Camus, à ses débuts. C’est à travers ces treize chapitres que l’on pourra avoir l’ un des meilleurs accès à la pensée néoplatonicienne. Cusimano, A. Importance of Medieval Numerology and the Effects Upon Meaning in the Works of the Gawain-Poet Thesis. University of New Orleans, May 2010 An examination of the influence of medieval numerology and number theory upon the works of the Gawain poet, this essay seeks to connect the importance of numbers to the construction of the four poems. By examining such number theories as the Divine Proportion and marriage numbers, as well as Pythagorean number concepts of masculine and feminine numbers, a clear connection between the literature and the number can be found. The poet not only seeks to use numbers to impart important Christian doctrine to his readers in a subconscious way, he also demonstrates an extreme pre-planning of every line and layout of each poem upon the page. Continuing in current critical traditions of examining this manuscript as whole, "Pearl, " "Patience, " "Cleanness, " and "Sir Gawain and the Green Knight" are shown to join together in an interweaving of connectivity through number pattern and the repetition of important numerological concepts. Correa Pabón, G.L. Numerus-Proportio en el de música De San Agustín (Libros I y Vi) Tesis y disertaciones académicas. Universidad de Salamanca (España) 2010. Resumen: (English) This research develops the concept of numerus / proportio in the dialogue of music libri sex of St. Augustine, in the context of matemáticopitagórica tradition of ancient and medieval philosophy, and in light of the Greco-Latin music theory. The work makes a careful reading of the text following argumentative sequence, highlights and modulates the central elements of the Pythagorean tradition and ancient musical thought, which makes a broad philological analysis. These concepts, often omitted or treated as incidental by critics and interpretation of the work of the philosopher of Hippo, appear here with a new vitality, as fundamental elements, not only the Treaty but also of the Augustinian conception of the universe and the aesthetics of proportion and symmetry. Des Places, E. Vie de Pythagore : lettre `a Marcella / Porphyre. Paris : Les Belles Lettres, 2010. Collection des Universités de France ; Sér. Grecque. ISBN: 2-251-00361-4 Diels, H. Griechische Philosophie : Vorlesungsmitschrift aus dem Wintersemester 1897/98. Hrsg. von Johannes Saltzwedel Stuttgart : Steiner, 2010. Schriftenreihe: Philosophie ISBN: 978-3-515-09609-6 Ehlers, W.W. Reuchlin, Johannes: Sämtliche Werke. Stuttgart- Bad Cannstatt : FrommannHolzboog. Teil: Bd. 2.; 1., De arte cabalistica libri tres. 2010. ISBN: 978-3-7728-1773-1 Reuchlin: Sämtliche Werke Bd 2 - De arte cabalistica libri tres (1517) : Lateinischer Text, deutsche Übersetzung, Stellennachweis, Register, editorische Beigaben Summary: Reuchlins ›Kunst der Kabbala‹ erschien 1517 in Hagenau bei Anshelm und ist Papst Leo X. gewidmet. Reuchlin zog hierin die Summe seines Forschens und Denkens über die jüdische Geheimlehre der Kabbala. Coyer, M.J. The Ettrick Shepherd and the Modern Pythagorean: science and imagination in romantic Scotland PhD thesis, University of Glasgow. (2010) Abstract: This thesis focuses on predisciplinary dialogue in the Romantic

Das Werk setzt frühere Gedanken aus ›De verbo mirifico‹ fort. Es ist ebenfalls als Dialog gestaltet, aufgeteilt in drei Bücher, von denen das erste und dritte den Fragen der Kabbala gewidmet sind, während sich das zweite Buch mit dem pythagoreischen Denksystem befaßt. Die Schrift wurde in ihrer Zeit mehr bewundert oder auch abgelehnt als von den Gelehrten angemessen verstanden. Gleichwohl dürfte in ihr ein wichtiger Schlüssel zu Reuchlins Denken und seiner Weltvorstellung enthalten sein. Das nicht leicht verständliche Werk wird im textkritisch bearbeiteten lateinischen Original und mit einer neuhochdeutschen Übersetzung herausgegeben, der sich ein umfangreicher, interdisziplinär zu erarbeitender Kommentar anschließen wird. Chapter Four returns to Empedocles’ use of language to express his intent. Since controlling the world can be a dangerous lesson, Empedocles uses ambiguity and the model of initiation into a mystery intentionally to conceal the lessons from hoi polloi. The audience must decode Empedocles’ message before they can make further observations of the world on their way to meeting their goal. Following the model for initiation, the readers will come to the ultimate revelation on their own. Finally, Chapter Five focuses on what can be determined from Empedocles verses: the readers must learn how to emulate the actions of Love and Strife since they are the active agents of change in the world. By learning about how the world works from Empedocles’ verses and their own observation, his students, as gods themselves, will also influence the fabric of the universe to achieve whatever they wish. Galsworthy, C. Language and Intent in Empedocles’Cosmic Cycle Dissertation University of Cincinnati. 2010. The University of Western Ontario (Canada), May 2010 Abstract: In this dissertation, I analyze how Empedocles uses language to present himself andhis intent. Although Empedocles’ contemporaries and more modern readers present himas a scientist or magician, he portrays himself as a god and claims that he will teachothers to become a god like him in order to manipulate the universe. In Chapter One, Iexamine the concept of science from an Aristotelian bias and from the standpoint ofmodern expectations of science to show that, despite verses that describe how the worldworks, Empedocles does not follow the patterns of active conversation with otherthinkers that are available. His stated intent (fragment 111) is to teach others how to control the universe – cure disease and old age, affect the weather, and raise the dead – rather than learn about it theoretically. In Chapter Two, I will show that although the claims that he makes link him to magicians, he does not present himself as one. Magicians act as intermediaries between men and the gods (at least in the time contemporary with Empedocles); the gods do as the magicians ask them because the magicians have built up a successful relationship through sacrifices and incantations. Empedocles, on the other hand, accomplishes these feats on his own as a god. Chapter Three sets out what sort of god Empedocles is: he is a mortal, long-lived god in contrast with the immortal gods – Love, Strife, and the four roots (fire, water, air, and earth). Anyone can become a god, as I illustrate, as long as one is pure enough and wise enough. Gangi, G. I presocratici : l'anteprima filosofico. Marina di Massa (Massa Carrara) : Edizioni clandestine. 2010. ISBN/ISSN: 978-88-95720-53-1 Indice. Introduzione. 1. Dal mito alla filosofia. 2. II problema "Presocratici". 3. La Scuola ionica: Talete, Anassimandro, Anassimene, Senofane. 4. Pitagora e la Scuola pitagorica. 5. La Scuola eleatica: Parmenide, Zenone, Melisso. 6. Eraclito di Efeso e la dottrina del divenire. 7. Pluralisti: Empedocle di Agrigento e Anassagora di Clazomene. 8. La Scuola atomistica: Leucippo e Democrito. 9. La poesia tragica e la problematica morale. Conclusione. Indicazioni bibliografiche. Gusmão, C. Sampaio de Harmonics in greek antiquity ; A harmônica na antiguidade grega Dissertação de Mestrado. Unidade da USP. Faculdade de Filosofia, Letras e Ciências Humanas. 2010 Resumo em inglês This work presents the central ideas related to two main theories about musical sound in greek Antiquity between the end of VI century and the beginning of III B.C. First, the historical and material contexts that lead to the development of greek musical theory, called Harmonics, are investigated, and its relationship with the musical practice of the period. The first theory analyzed comes from the pythagorean school, in which cosmology is the framework of a world view that expands connecting all areas of thought and one of its

departure point is mathematical Harmonics. Afterwards, I discuss the demonstrations that are done from the calculations of proportional medias and their relations with the octave harmonic cohesion principle. In the second chapter, its exposed the acoustic theories of Antiquity which originated from the musical ratios and had developed in the branch of natural sciences, deepening by the Aristotelian Philosophy. In the third chapter, I presented the most important issues concerning the differences between the aristoxenian current, which belongs to the aristotelian epistemological framework, against the pythagoreans. In this new way of thought, Harmonics is studied as a tékne that has a particular range of specialized terms and a specific object, the mélos. The concept of aisthésis assumes relevance and to put it into practice, the idea of dynamis becomes central. At last, the persistency of the pythagorean conception it is presented in the calculations of the musical intervals in the division of the canon. participants with a less stigmatizing view of the mentally ill did not exhibit a golden section pattern in rating all diagnostic labels, despite what was hypothesized. Participants with a stigmatizing view of the mentally ill did not exhibit a reverse golden section pattern in rating psychiatric labels as expected either. The results of the current study did show, however, that people who have more contact with the mentally ill also have a less stigmatizing view of the mentally ill. Hudry, F. Le livre des vingt-quatre philosophes: résurgence d'un texte du IVe siècle. Histoire des doctrines de l'antiquité classique 39. Paris: Librairie Philosophique J. Vrin, 2009. ISBN 9782711619566. Huizenga, A. Biblical Studies "What's a Woman To Do?: Training Women to Virtue in the Pastoral Epistles and Texts by Pythagorean Women." Dissertation. 2005-2006. University of Chicago Divinity School Abstract: Who is a virtuous woman? How could she develop such goodness? This dissertation examines the moral-philosophical curriculum for women by comparing two epistolary corpora: the letters attributed to Pythagorean women and the New Testament Pastoral Letters. The investigation is organized around four elements necessary for this educational program: textual resources, teachers and learners, instructional strategies, and subject matter. I provide a text history of each collection and suggest how the letters function as teaching resources. My conclusions are: (1) that the authors identify older women in particular as the appropriate teachers for younger women; (2) that the argumentation of the letters relies heavily on antithetical reasoning and examples; and (3) that the various elements of the topos of “the good woman” limit a woman’s demonstration of her virtue to her domestic relationships and activities. The author of the Pastorals has taken up nearly all of the “pagan” aspects of this curriculum, but has supplemented these with theological justifications drawn from the Pauline literature and traditions. Hagel, S. Ancient Greek Music: A New Technical History Cambridge University Press, 2009. ISBN 9780521517645 Offers a fundamental reworking of the history of Greek music from the classical period to Roman times. It explains anew the development of ancient melodic notation, embedding it in a context of professional music-making, in a musical culture determined mainly by the dominant instruments, the lyre and the aulos. Harasym, M.T. The golden section and attitudes towards mental illness: how does stigma influence golden section ratings? Thesis. University of New York. 2008. Abstract: Studies have shown that when people are asked to make judgments about others using a list of bipolar adjective pairs, they consistently produce ratings that are approximately 62% positive and 38% negative. The precise proportion of 61.8:38.2, known as the golden section, stems from Pythagorean principles that explain how people organize and make sense of the world around them. The current study examined how a stigmatized view of the mentally ill can affect golden section ratings of various diagnostic labels. One hundred and eighteen participants were tested on: (1) their view of the mentally ill (level of stigma), (2) how much contact they have had with the mentally ill, and (3) their golden section ratings of various medical and psychiatric labels. Results indicated that Journee, G. « Rien ne saurait naître de rien ». L’émergence du problème de l’être dans la philosophie préplatonicienne. Thèse Universite Charles de Gaulle. Lille. 2007 D’après Aristote, que rien ne naît du non étant constituerait l’opinion commune des

physiciens, sans restriction apparente, affirmation qui vient recroiser la thèse selon laquelle tous les anciens physiciens, de Thalès à Démocrite, ont renoncé à la génération proprement dite. Une bonne partie de l’interprétation moderne reconnaît cependant dans le principe l’œuvre de Parménide, qui l’aurait énoncé pour la première fois, dans son Poème, s’en servant pour abolir précisément la génération. Cette conception a contribué à changer profondément l’approche moderne concernant les penseurs venant avant Parménide, en particulier les Milésiens. Peuton toutefois refuser à ceux-ci le respect au moins implicite du principe ? Et si tel n’est pas le cas, peut-on encore maintenir que le principe rien ne naît du non étant constitue immédiatement un principe de non devenir ? La thèse s’interroge sur les schèmes relevant de la causalité naturelle mis en avant par les Milésiens, et sur leurs rapports avec le problème classique de la conservation, et donc de l’absence de génération à proprement parler. Repartant d’Aristote, elle s’interroge ensuite sur les conceptions raisonnablement attribuables aux Milésiens, avant d’étudier les occurrences du principe chez Parménide, et chez les physiciens du Vème siècle, Anaxagore, Empédocle et Démocrite. they perceived as the most consonant. Results of the study revealed an overall preference for equal temperament in contradiction to coincidence theory. Several additional areas for research are suggested to further investigate the results of this study. Longfellow, K. Flow down like silver : Hypatia of Alexandria ; a novel Belvedere, Calif. : Eio Books, 2009. ISBN: 978-0-9759255-9-1 Loupiac, A. Virgile. La lettre et l'esprit Peeters, coll. "Bibliothèque d'Études Classiques" Louvain, 2008. ISBN 978-90-429-2019-4 434 Présentation de l'éditeur: En dépit de la formation épicurienne de Virgile et des emprunts lexicaux et poétiques à la lettre de Lucrèce, présents dans toute son oeuvre, sa volonté d'engagement, son rejet des passions et de la Vénus érotique, sa conception d'un univers régi par la mens, son idéal apollinien de labor moral et poétique, de justice et d'harmonie manifestent un esprit plus proche de Pythagore que d'Epicure. Il fait surtout de la poésie une fin en soi, non plus moyen mais création et forme parfaite à l'image du cosmos et du nombre qui le régit. Un idéal si haut est malheureusement inaccessible: l'inachèvement de l'Enéide et la réception de l'oeuvre par les Elégiaques et Lucain consacrent à la fois la suprématie du Prince des Poètes et la faillite de ses aspirations. Kaplan, R. Hidden harmonies : the lives and times of the Pythagorean theorem New York : Bloomsbury Press, 2010. ISBN: 978-1-596-91522-0 Inhaltsverzeichnis: The mathematician as demigod -- Desert virtuosi -- Through the veil -Rebuilding the cosmos -- Touching the bronze sky -- Exuberant life -- Number emerges from shape -- Living at the limit -- The deep point of the dream -- Magic casements. Memminger, A. Das Erbe der Druiden : die Geschichte der Geheimbünde ; über die Kelten, Druiden, Pythagoräer, Essäer, Heilige, Barden und Freimaurer Leipzig : Bohmeier, 2010. ISBN: 978-3-89094-647-4 Long, D.R. Coincidence theory: Seeking a perceptual preference for just intonation, equal temperament, and Pythagorean intonation in excerpts for wind instruments Thesis. University of Southern Mississippi. 2008. Abstract ; [Unedited] Coincidence theory states that when the components of harmony are in enhanced alignment the sound will be more consonant to the human auditory system. An objective method of examining the components of harmony is by investigating alignment of the mathematics of a particular sound or harmony. The study examined preference responses to excerpts tuned in just intonation, Pythagorean intonation, and equal temperament. Musical excerpts were presented in pairs and study subjects simply picked one version from the pair that Miller, F.P. Empedocles Alphascript Publishing. 2010. ISBN-13: 9786130776473 Empedocles was a Greek pre-Socratic philosopher and a citizen of Agrigentum, a Greek city in Sicily. Empedocles' philosophy is best known for being the origin of the cosmogenic theory of the four Classical elements. He also proposed powers called Love and Strife which would act as forces to bring about the mixture and separation of the elements. These physical speculations were part of a history of the universe which also dealt with the origin and development of life. Influenced by the Pythagoreans, he supported the doctrine of reincarnation. Empedocles is generally considered the last Greek philosopher to record his ideas in verse. Some

of his work still survives today, more so than in the case of any other Presocratic philosopher. Empedocles' death was mythologized by ancient writers, and has been the subject of a number of literary treatments. Milano : Lampi di stampa. 2009. Series 1: Tutti autori. ISBN/ISSN: 978-88-488-0935-1 Introduzione 9 1. La Teoria delle proporzioni p 15-86 2. Il concetto matematico di … p 87-136 3. L'uso di termini appartenenti alla teoria delle proporzioni nell'etica aristotelica p 137-176 4. Il pensiero analogico nell'Organon p 177-206 Appendice. Bibliografia Naether, F. Die Sortes Astrampsychi : Problemlösungsstrategien durch Orakel im römischen Ägypten. Tübingen : Mohr Siebeck, 2010. Schriftenreihe: Orientalische Religionen in der Antike ; 3. ISBN: 978-3-16-150250-7 Hochschulschrift: Zugl.: Leipzig, Univ., Diss. 2009 "Du wirst deine Geliebte heiraten, aber es wird dir leid tun"; "Du wirst von deiner Frau erben, aber nicht als Alleinerbe". So spricht ein dem Pythagoras zugeschriebenes Orakel, das schon Alexander zur Weltherrschaft verholfen haben soll. Das Losbuch "Sortes Astrampsychi" ist auf römerzeitlichen Papyri und mittelalterlichen Handschriften in griechischer Sprache überliefert. Mit 92 vorformulierten Fragen und 1030 Antworten aus fast allen Lebensbereichen liegt eine ergiebige Quelle zur Sozialgeschichte Ägyptens vor - vom Überleben von Krankheiten über Geschäftsbeteiligungen hin zu Verhandlungstaktiken vor Gericht. Wichtige Fragestellungen dieses Kommentars zu den Sortes Astrampsychi zielen auf den Anwendungskontext und die Einordnung des Werks innerhalb der religiösen, divinatorischen und magischen Praktiken Ägyptens unter besonderer Berücksichtigung der "TicketOrakel" in demotischer, griechischer und koptischer Sprache. Palù, C. Philosophie et écriture : analyse des débuts de la tradition ancienne Thèse de doctorat : Philosophie : Lille 3 : 2004. Resume: La thèse se propose d'analyser la question du rapport entre philosophie et écriture chez les premiers philosophes. Elle se présente sous forme d'un recueil de textes avec commentaire et elle se partage en deux parties : dans la première partie, titrée "les philosophes qui n'ont pas écrit", sont répertoriés les témoignages sur la production écrite de Thalès et de Pythagore ; dans la deuxième partie, titrée "la prose hilosophique", ceux sur Phérécyde, l'école de Milet, Héraclite. La thèse esaie de réfuter la thèse qu'Havelock avait été amené à formuler sur les penseurs présocratiques, qu'il devait situer, en vertu de sa thèse générale, dans la tradition orale. On a montré, au contraire, que, si l'on ne néglige pas les notices dont nous disposons, on retrouve les traces d'une sorte de réflexion présocratique sur l'écriture qui n'exclut pas un certain emploi, à l'époque archäique, du texte écrit. En outre, m^eme lorsque les philosophes, ainsi que dans le cas de Pythagore, décident d'abandonner de l'écriture, on ne peut pas parler, comme le fait Havelock, de simple oralité. Narongrit, Symphony of the Spheres Symphony of the Spheres is inspired by the Greek music theory and philosophy of Pythagoras and Boethius. This 25-minute-long symphony consists of 3 movements which based on Boethius’s “De institutione musica” (The Principle of Music). These movements are 1.) Musica Mundana, referring to music of the spheres, 2.) Musica Humana, referring to the ways harmonics relations are imprinted in the soul and body of man, 3.) Musica Instrumentalis, referring to audible music produced by instruments. http://hdl.handle.net/123456789/7836 Narongrit.pdf 16423Kb Adobe PDF View/Open (Chula only) (CUIR Chulalongkorn University Intellectual Repository) Pieri, S. Tetraktys : numero e filosofia tra il I e II secolo d. C. Firenze : Ermes, 2005. Philosophia perennis ; 2. ISBN - 88-900851-7-7 Ritter, J. Vorlesungen zur Philosophischen Ästhetik Göttingen : Wallstein-Verl., 2010. Schriftenreihe: Marbacher Schriften ; N.F., 6 ISBN: 978-3-8353-0744-5 Schreiber, A. Die Leier des Pythagoras : Gedichte aus mathematischen Gründen Wiesbaden : Vieweg+Teubner Verlag / GWV Fachverlage GmbH, 2010 ISBN: 978-3-8348-9352-9 [Elektronische Ressource] Elektron. Referenz: http://dx.doi.org/10.1007/978-3-8348-9352-9 Notargiacomo, S. Medietà e proporzione : due concetti matematici e il loro uso da parte di Aristotele.

Stroppini, G. Virgile et l'amour : Les bucoliques. Paris : Orizons. 2010. Series 1: Universitésdomaine littéraire ISBN/ISSN: 978-2-296-08752-1 THEON DE SMYRNE, Lire Platon. Le Recours au savoir scientifique : Arithmétique, Musique, Astronomie. Texte présenté, annoté et traduit du grec par Joelle Delattre Biencourt. Préface de Luc Brisson. Postface de Rudolf Bkouche, Anacharsis Editions, Toulouse 2010, ISBN : 978-2-914777-704. Philosophe et mathematicien du IIeme siecle notre ere, Theon de Smyrne s’inscrit dans les courants remuants et contradictoires de la pensee hellenisee autour de la Mediterranee. Sa demarche de Recours au savoir scientifique pour lire Platon se presente comme la quête de systemes d'equilibre et d'harmonie numerique dans la nature – d’origine pythagoricienne.A partir d'une arithmologie, à la fois theorique et procedurale, plutôt que d'une arithmetique proprement dite, il s'attache à agencer, progressivement et avec minutie, les elements d'une theorie medioplatonicienne des savoirs musicaux et des savoirs astronomiques. L'ouvrage offre au lecteur curieux un etat interessant des savoirs scientifiques et philosophiques du IIeme siecle, juste avant les ecrits de Ptolemee. Il est donne ici dans sa premiere traduction complete depuis 1892, precede d'une dense presentation et d'un sommaire detaille. Une centaine de pages d'annexes explicatives et un index thematique completent l'ensemble. has yet to be definitively answered. Some people believe that the human mind is the creator of mathematics, like a painter or poet, is a maker of patterns. [N, p. 2027] Others believe that mathematics exists independently of the human mind and therefore was discovered. This thesis will support the position that mathematics was discovered, not invented. When making a discovery, we are obtaining knowledge about something that already previously existed, just hadn’t been found yet. This paper will develop the ideas of previous philosophers and mathematicians to support my own mathematically philosophical based theory. It will take basic elements and prove they exist by showing their constructability. Then proceed to show that every branch of math is based on these constructible elements by the use of deductive reasoning. With constructability, comes existence, and with existence, comes discoveries. The following is a list of the basic elements this paper will use as the foundation of mathematics; a point, a line, a line segment, a surface, a plane surface, addition, commutative property of addition, associative property of addition, multiplication, commutative property of multiplication, associative property of multiplication, distributive property for multiplication over addition, subtraction, division, square roots, the natural numbers, the integers, the rational numbers, the 5 irrational numbers, the real numbers, pi, Euclid’s 5 axioms, Euclid’s 5 propositions, area of a rectangle, area of a triangle, area of a parallelogram, area of a trapezoid, area of a circle, volume of a 3-dimensional object, perpendicular lines, parallel lines, proportionality, similar triangles, bisection of an angle, bisection of a finite line, angle-sum theorem, right triangles, equilateral triangles, the Pythagorean theorem, inscribing a regular polygon in a given circle, circumscribing a regular polygon about a given circle, the coordinate plane, coordinate space, fundamental theorem of arithmetic, Euclidean algorithm, a prime number, Euclid’s lemma, divisibility, the division theorem, sets, and infinity. Urbano, S. Peripatetikon : itinerario esoterico tra massoneria e pitagorismo. Roma : Atanòr. 2010. Series 1: Vitriol. Esoterismo. ISBN/ISSN: 88-7169-252-7 INDICE: C'era una volta un re - Prologo Protocapitolo PRIMA PARTE ALLA GLORIA DELL'ETERNA ESSENZA DELL'ESSERE Argomenti Spirituali in Chiave Pitagorica SECONDA PARTE OPUS LATOMORUM Tavole Architettoniche Massoniche viste in Prospettiva Pitagorica TERZA PARTE DELL'EPOCA POSTMODERNA Breviario per un Tempo di Apocalisse Considerazioni di un Pitagorico su Argomenti di Attualità Yi, Sŏn-yŏng Ch'ŏnnyŏn-ŭi ch'immuk : Yi Sŏn-yŏng changp'yŏn sosŏl = The last pythagorean P'aju : Kimyŏngsa, 2010. ISBN: 978-89-3493707-4 Wiggins , C. Mathematics was Discovered Thesis. Central Connecticut State University New Britain, Ct. 2010. Abstract: “Was mathematics invented or discovered?” This is an age old question that

Book chapters Abdounur , O.J. Razones, proporciones y pensamiento proporcional en la música pitagórica: un abordaje histórico-didáctico, p 61-86 In: La proporción : arte y matemáticas. coord., Joaquín Giménez. Graó, 2009. Series 1: Biblioteca de uno. Didáctica de las matemáticas; 266 ISBN/ISSN: 978-84-7827-777-3 9 Les origines radicales du christianisme. Saint Paul contre les livres de magie - Les livres de Porphyre contre les chrétiens - Les textes des gnostiques - L'hétérodoxie des premières années - L'assassinat d'Hypatie p 123 -129 In: Histoire universelle de la destruction des livres : des tablettes sumériennes à la guerre d'Irak. Paris : Fayard. 2008. ISBN/ISSN: 978-2-213-63484-5 Allione, L. 3. Il medioplatonismo e il neopitagorismo p 66-73 In: Dall'atarassia alla fuga dal mondo : i greci, i latini e la filosofia nell'età ellenistica e nell'età imperiale. 2009. ISBN/ISSN: 978-88-6129-408-0 Balbino, A. A questão das fontes para o estudo do pitagorismo In: SOBRE AS ORIGENS DA FILOSOFIA: PRIMEIROS ENSAIOS (Gabriele Cornelli & Mariana L. Belchior ORGS). Coleção Archai Supplementa. Archai/Etcetera Editora, São Paulo, 2010. Alvares, J.R. Por que é necessário falar de religiosidade no pitagorismo In: (Gabriele Cornelli & Mariana L. Belchior ORGS). Coleção Archai Supplementa. Archai/Etcetera Editora, São Paulo, 2010. Baldi, D. Milone di Crotone p 57-60, Empedocle p 190-193 In: Morti favolose degli antichi. Macerata : Quodlibet. 2010. Series 1: Compagnia extra; 20 LC Classification: PQ ISBN/ISSN: 978-88-7462-337-2 Amenábar, A. Un viaje a la historia y los tiempos de Hipatia de Alejandría p 11-57 In; Ágora : el viaje al Mundo Antiguo de Alejandro Amenábar. Barcelona : Libros Cúpula : Timun Mas. 2009. ISBN/ISSN: 978-84-480-4878-5 Bar-Kochva, B. Jewish Influence on Pythagoras according to Hermippus of Smyrna p In: The image of the Jews in Greek literature : the Hellenistic Period Berkeley [u.a.] : Univ. of California Press, 2010. Schriftenreihe: Hellenistic Culture and Society ; 51. ISBN: 978-0-520-25336-0 Andolfo, M. Il medioplatonismo e il neopitagorismo p 102-115, Numenio e gli Oracoli Caldaici p 116-127 In: L'uno e il tutto : la sapienza egizia presso i greci. Milano : Ares. 2008. Series 1: Origini; 9 ISBN/ISSN: 978-88-8155-443-0 Beagon, M. Ordering Wonderland: Ovid's Pythagoras and the Augustan Vision. p 288-309. In: Paradox and the Marvellous in Augustan Literature and Culture. Ed. by Philip Hardie. Oxford: Oxford University Press. 2009 ISBN 9780199231249. Arocena, N. Torres-García - Pitágoras – Platáo. Um Diálogo Geométrico ou a Visao p 80-93 In: A intuição e a estrutura : de Torres-García a Vieira da Silva 1929 - 1949 ; [Museu Cleccão Berardo 04.12.2008 - 25.01.2009, IVAM 24.02.2009 - 19.04.2009] = La intuición y la estructura / [comisario, Conseulo Císcar Casabán... Valencia : IVAM, 2009. ISBN: 978-84-482-5105-5 Borlik, T.A. Reincarnating Pythagoras: anima mundi and Renaissance gaia theory In: Ecocriticism and early modern English literature : green pastures New York : Routledge, 2010. Routledge studies in Renaissance literature and culture ; 16, Originally presented as author's thesis (doctoral)--University of Washington, 2008, under title: Green pastures : ecocriticism and early modern English literature. ISBN: 978-0-415-87861-6 Baez, F. 3. La Grèce. Entre ruines et fragments - La destruction des poèmes d'Empédocle - Censure contre Protagoras Platon aussi a brûlé des livres - La destruction du temple d'Artémis Un médecin grec de l'Antiquité - Deux biblioclastes

Bougearel, A. Tarocchi e Neopitagorismo In: Il castello dei tarocchi. a cura di Andrea Vitali Torino : Lo scarabeo. 2010. ISBN 978-88-6527-003-5 La struttura numerologica dei Tarocchi e la sua derivazione dall’aritmologia pitagorica. Castaldo, D. Aspetti della cultura musicale a Taranto nell'età di Archita p 137-145 In: Per una storia dei popoli senza note : atti dell'Atelier del Dottorato di ricerca in musicologia e beni musicali F. A. Gallo, Ravenna, 15-17 ottobre 2007. a cura di Paola Dessì Bologna : CLUEB. 2010. Series 1: Heuresis. Sez. 13.: Arti, musica, spettacolo; 9 ISBN/ISSN: 978-88-491-3199-4 Brambilla, S. Antonio Brucioli traduttore del Somnium Scipionis :origini efortuna di un volgarizzamento ciceroniano nel Cinquecento e oltre p 99-130 In: Antonio Brucioli, humanisme et évangélisme entre Réforme et Contre-Réforme : actes du colloque de Tours, 20-21 mai 2005. dirigé par Elise Boillet Paris : H. Champion. 2008. Series 1: Le savoir de Mantice; 15 ISBN/ISSN: 978-2-7453-1824-4 Centrone, B. Confraternite pitagoriche e neopitagoriche p 77-103 In: Storia d'Italia : annali. Torino : G. Einaudi. 2010. Volume description: 25. : Esoterismo / a cura di Gian Mario Cazzaniga. ISBN/ISSN: 978-88-06-19035-4 Chiaradonna, R. Autour d’Eudore: Les débuts de l’exégèse des Catégories dans le Moyen Platonisme . . . . . . . . . . 89-112 In: Mauro Bonazzi, Jan Opsomer (ed.), The Origins of the Platonic System: Platonisms of the Early Empire and their Philosophical Contexts. Collection d'Études Classiques 23. Louvain/Namur/Paris/Walpole, MA: Éditions Peeters; Société des Études Classiques, 2009. ISBN 9789042921825 Bresch, C. Wozu brauchte Aristoteles die Zähne des Empedokles? Historisches zum Evolutionsgedanken p 7-22 In: Evolution : was bleibt von Gott? Stuttgart : Schattauer. 2010. Wissen & Leben. ISBN: 978-3-7945-2757-1 Cabada C.M. LA PREVALENCIA DEL INFINITO EN PRESOCRÁTICOS Y ATOMISTAS p 73- 105 In: Recuperar la infinitud : en torno al debate histórico-filosófico sobre la limitación o ilimitación de la realidad. 2008. Series 1: Biblioteca Comillas. Filosofía; 1 ISBN/ISSN: 978-84-8468-243-1 Contu, F. "Una mujer de cultura sin frontras entre cristianismo y paganismo: Hipatia de Alejandría de Egipto" p 77-94 In: De lo sagrado y lo profano : mujeres tras/ entre/sin fronteras. editoras Mercedes Arriaga Flórez ... [et al.] Sevilla : ArCiBel. 2008. ISBN/ISSN: 978-84-96980-26-6 Carena, T.C. Pitagora e Piatone, gli antichi pelasgici p 127-132 In: La pneumatologia teologico-estetica di Vincenzo Gioberti Milano [etc.] : Mimesis, 2009. Schriftenreihe: Filosofie. ISBN: 978-88-8483-977-0 Cornelli,, G. Una città dentro le città: la politica pitagorica tra i lógoi di Pitagora e le rivolte Antipitagoriche p 21-39 In: Pensare la città antica : categorie e rappresentazioni. a cura di Gabriele Cornelli, Giovanni Casertano Casoria (Napoli) : Loffredo. 2010. Series 1: Philosophica; 1 Notes: Papers presented to the seminar held in Brasília (BR), June 2-6, 2008. ISBN/ISSN: 978-88-7564-398-0 Casertano, G. I Pitagorici e il potere p 9-21 In: Pensare la città antica : categorie e rappresentazioni. a cura di Gabriele Cornelli, Giovanni Casertano Casoria (Napoli) : Loffredo. 2010. Series 1: Philosophica; 1 Notes: Papers presented to the seminar held in Brasília (BR), June 2-6, 2008. ISBN/ISSN: 978-88-7564-398-0 Cornelli, G. Sulla vita filosofica in comune: koinonía e philía pitagoriche. In: Il V secolo. Studi in onore di Livio Rossetti Aguaplano—Officina del Libro, Perugia 2010 Cassinelli, A. Pitagora p 29-33, Le terne pitagoriche p 33-37 In: Contro la matematica : la scienza inesatta. Roma : A. Gaffi. 2009. Series 1: Pamphlet ISBN/ISSN: 978-88-6165-055-8 Cremonesi, C. Apollonius of Tyana or the spectacle of wisdom

In: Guru: The Spiritual Master in Eastern and Western Traditions--Authority and Charisma. Edited by Antonio Rigopoulos, D K Printworld. 2007, ISBN : 81-246-0390-1 Diehl, L. PYTHAGOREER. Wer sind die Pythagoreer? Die pythagoreischen Gemeinschaften der Grunderzeit - Die Pythagoreer der Folgezeit - L'Ordre Occultiste d'Hermès Tétramégiste (O::H::T::M::) - Der Orden der Goldenen Rose (ORA) - Einfuhrende Stufen; Initiationsstufen; Unterweisungen p 195-200 In: Initiatenorden und Mysterienschulen. Teil: Bd. 2., Die Orden und Gemeinschaften. Schalksmühle : Pomaska-Brand. 2010. ISBN: 978-3-935937-72-6 Cristiani, M. Dal sensibile all'intellegibile : la musica nell'enciclopedia del sapere tra antichità e medioevo p 15-56 In: « Harmonia mundi » : musica mondana e musica celeste fra antichità e medioevo : atti del convegno internazionale di studi : (Roma, 14-15 dicembre 2005) / a cura di Marta Cristiani, Cecilia Panti e Graziano Perillo Tavarnuzze : SISMEL-Ed. del Galluzzo, 2007. Micrologus' library ; 19 Résumé : Statuto disciplinare della musica tra le arti liberali nel « De ordine » di Agostino e nel « De nuptiis » di Marziano Capella, nell'àmbito del dibattito di 4° e 5° s. d.C. sulle differenti prospettive dottrinali del platonismo cristiano di Agostino e di quello pagano di Capella ; Macrobio nel commento al « Somnium Scipionis » conduce una strenua difesa della cultura pagana da un punto di vista privilegiato De Marco, M. Archita. Oriente di Tarante (Lecce) " p 563-603 In: Giuseppe Libertini : patriota e fondatore delle Logge massoniche in Terra d'Otranto : testi e documenti. Lecce : Edizioni del Grifo. 2009. ISBN: 8872613612 Dijk, G.J. van The odyssey of Apollonius: an intertextual paradigm In: Bowie, E. Philostratus. Greek Culture in the Roman World. Cambridge: Cambridge University Press, 2009. De Santis, L. La basilica neopitagorica p 160-163 In: I segreti di Roma sotterranea : alla scoperta di un mondo misterioso e sommerso dove passato e presente si fondono fino a diventare una cosa sola. Roma : Newton Compton. 2008. Series 1: Tradizioni italiane; 58 ISBN/ISSN: 978-88-541-1234-6 Dollo, C. I modelli neoterici e l'Empedocle redivivus di G.B. Hodierna » p 219 - 272 In: La contea di Modica : secoli XIV-XVII : atti del settimo centenario. a cura di Giuseppe Barone Acireale (Catania) [etc.] : Bonanno. 2008. ISBN/ISSN: 978-88-7796-590-5 Delattre, J. « Álogon, eúlogon, analogôs » chez deux philosophes médio-platoniciens : Plutarque et Théon de Smyrne p 115-126 In: En deçà et au-delà de la « ratio » : actes de la journée d'étude, université de Lille 3, 28 et 29 septembre 2001 / Valérie Naas éd. Villeneuve-d'Asq : Université Charles-deGaulle-Lille III, 2004 Collection UL3. Résumé : Dans les commentaires de Plutarque et de Théon de Smyrne au « Timée » de Platon, l'étude des termes formés sur λόγος montre que la relation de proportionnalité joue un rôle important en tant que solution raisonnable contre l'irrationnel Fabbri, N. L'armonia delle sfere da Pitagora a Kircher p 269-277 In: Galileo : immagini dell'universo dall'antichità al telescopio. Statement of responsibility: a cura di Paolo Galluzzi Firenze [etc.] : Giunti. 2009. Series 1: Gamm, Giunti arte mostre musei ISBN/ISSN: 978-88-09-74232-1 Farinelli, G. Filolao e l'armonia del numero. Il numero come pari e dispari, - . Il numero

come mediazione, - Il numero come armonia, In: Simone Weil e la paideia greca. Perugia : Morlacchi. 2008. Series 1: Università. Pedagogia. ISBN/ISSN: 978-88-6074-261-2 In: La seconda nascita. Bergamo : Moretti & Vitali. 2010. Series 1: Narrazioni della conoscenza ISBN/ISSN: 978-88-7186-455-6 Geymonat, L. Pitagora e Zenone p 18-29, Anassagora, Democrito, Eudosso p 29-41 In: Storia e filosofia dell'analisi infinitesimale: introduzione di Gabriele Lolli Torino : Bollati Boringhieri. 2008. Series 1: Universale Bollati Boringhieri; 573 ISBN/ISSN: 978-88-339-1947-8 Favrod, J. LES GRECS À L'HEURE DE LA SICILE ET DE L'ITALIE DU SUD. Les Sybarites - Empédocle, philosophe d'Agrigente - Tyrans siciliens - Denys l'Ancien, tyran de Syracuse - Denys le Jeune, tyran de Syracuse - Archytas, philosophe et politicien p 82 - 85 In: La Grèce et Rome par les anecdotes. Gollion (CH) : Infolio. 2008. Series 1: Testimonia. ISBN/ISSN: 978-288474-080-7 Gottschlich, M. Die „pythagoreischen" Intervalle als das schönheitsfähige Material p 132-158 In: Auf der Suche nach dem Logos der Musik : eine Kritik der Tonalitätsbegründung bei Ansermet Würzburg : Königshausen & Neumann. 2010. Hochschulschrift: Zugl.: Wien, Univ., Diss., 2004 u.d.T.: Gottschlich, Max: Das Problem der Begründung tonaler Syntax in Ansermets "Die Grundlagen der Musik im menschlichen Bewußtsein" und dessen systematische Auflösung mit Hegel. ISBN: 978-3-8260-4398-7 Feo, G. Numi e numeri di Pitagora p 41-49 In: Il tempio di Voltumna : [alla scoperta del sacrario dei dodici popoli etruschi]. Viterbo : Stampa alternativa/Nuovi equilibri. 2010. Series 1: Eretica speciale ISBN/ISSN: 978-88-6222-117-7 Frédéric B. Protée et Pythagore dans la Vie d'Apollonios de Tyane de Philostrate p 263-283 In: Protée en trompe-l'oeil : genèse et survivances d'un mythe, d'Homère à Bouchardon. dirigé par Anne Rolet Rennes : Presses universitaires de Rennes. 2010. Series 1: Interférences ISBN/ISSN: 978-2-7535-0981-8 Guarradno, V. Pitagora p 243-251 In: Lirici greci tradotti da poeti italiani contemporanei ; a cura di Vincenzo Guarracino Milano : Bompiani. 2009. Series 1: Tascabili Bompiani. Poesia; 549-550. ISBN/ISSN: 978-88-452-6330-9 Frova, A. Pitagora, Aristotele ed Eratostene p 68-77, LAntiterra e il quadrato magico p 78-85, Eudosso, il genio delle sfere p 110-115 In: Il cosmo e il buondio : dialogo su astronomia, evoluzione e mito. Milano : Biblioteca universale Rizzoli. 2009. Series 1: BUR. Saggi ISBN/ISSN: 978-88-17-02743-4 Hajdas, G. Die pythagoreische Zahl; die „Dyas" bei Schelling und das angedachte „Böse" p 281-285 In: Adam Mickiewicz - die Bedeutung der Sprache für die polnische Nation Marburg : Tectum-Verl. 2010. Wissenschaftliche Beiträge aus dem TectumVerlag, Reihe Politikwissenschaften ; Bd. 28. (Hochschulschrift: Zugl.: Duisburg, Essen, Univ., Diss., 2009 u.d.T.: Hajdas, Georg: Die Bedeutung der Sprache bei der Konstruktion der polnischen Nation im Werk von Adam Mickiewicz) ISBN: 978-3-8288-2354-9 Gaona, B.S. Pythagorean and Platonic Roots p 38-47 In: Through the lens of freemasonry: the influence of ancient esoteric thought on Beethoven’s late works Dissertation. Submitted in partial fulfillment of the requirements for the degree of Doctor of Musical Arts in Music with a concentration in Performance and Literature in the Graduate College of the University of Illinois at Urbana-Champaign, 2010 Haustein, H.D. Antike bis zur Kaiserzeit Pythagoras und seine Schule - Von Eudoxos bis Euklid - Die Rechenpraxis der Römer Formeln der Periode 720 v - 90 u. Z. p 68-92 In: Kulturgeschichte der Formel : vom Mondkalender der Vorgeschichte bis zur Aktienkapitalformel . München : AVM, 2009. Gargani, A.G. Pitagora e le colline della Sicilia

ISBN: 978-3-89975-933-4*kart. Huizenga, A.B. Sophrosyne for women in Pythagorean texts In: Women and gender in ancient religions : interdisciplinary approaches. Wissenschaftliche Untersuchungen zum Neuen Testament, 263. Tübingen : Mohr Siebeck, 2010. ISBN: 978-3-16-150579-9 Hildebrandt, D. Morgenröte oder Die Griechen erfinden den Kosmos. Wir denken immer noch antik - Die ersten Philosophen in ihrem Element - Pythagoras und seine Schule Piatons großes Kino - Aristoteles geht aufs Ganze p 45-85 In: Die Sonne : Biographie unseres Sterns München : Dt. Taschenbuch-Verl. 2010. dtv ; 34651. ISBN: 978-3-423-34651-1 Ibáñez Orts, V. ¿ Hay un pitagórico detrás de las taulas de Menorca? p 561-576 In: La historia de la ciencia y de la técnica : un arma cargada de futuro : ensayos en homenaje a Mariano Hormigón. coords.: María Ángeles Velamazán ... [et al.] Cádiz : Diputación de Cádiz. 2008. ISBN/ISSN: 978-84-96583-82-5 Horky, P.S. “Aristotle’s Description of Mathematical Pythagoreanism in the 4th Century BCE” In: The City-State Commensurate: Plato and Pythagorean Political Philosophy Stanford University. May 2010 http://www.princeton.edu/~pswpc/papers/autho rAL/horky/horky.html Abstract: Scholars of the history of ancient philosophy have been hesitant to attribute particular characteristics to those Pythagoreans called “mathematical” by Aristotle. Aristotle himself, to be sure, not only felt it important to distinguish this type of Pythagorean from the more traditional “acousmatic” type, but he also invested in this distinction the basic tenets of his own philosophical methodology regarding the pursuit of knowledge from first principles. In this chapter, I describe the philosophical system (pragmateia) of the mathematical Pythagoreans by analyzing and comparing the accounts of Pythagoreanism in both the surviving treatises of Aristotle (especially Metaphysics) and the fragmentary works on the Pythagoreans preserved in Iamblichus’ On the General Mathematical Science and On the Pythagorean Way of Life. This is the newest version of the first chapter of a book-length study in which I describe the philosophical and political history of the mathematical Pythagoreans and their influence on Plato’s later thought. Idotta, F. Tra Sole e Mare. Con Pitagora e Auden. Nòstos e fuga. p 49-56 In: Rotte mediterranee : dal mare sopraggiunge l'altro, messaggero di novità... Reggio Calabria : Città del sole. 2009. ISBN/ISSN: 978-88-7351-277-6 Jaquet, C. La panosmie d'Empédocle p 339-350 In: Philosophie de l'odorat. Paris : PUF. 2010. ISBN/ISSN: 978-2-13-057914-4 Kamphausen, G. Der Pythagoräer und die Sucht p 164-169 In: Unwerter Genuss : zur Dekulturation der Lebensführung von Opiumkonsumenten Bielefeld : Transcript. 2009. Körperkulturen. ISBN: 978-3-8376-1271-4 Kiehl, R. Der ,vollkommene Bildungsroman' Analyse von C (1794): ,Die Lebensweisheit des Archytas' p 87-124 In: Das Experiment des aufgeklärten Bildungsromans : ein Vergleich der Fassungen von Christoph Martin Wielands "Geschichte des Agathon" Würzburg : Königshausen & Neumann. 2008. Epistemata, Reihe Literaturwissenschaft ; Bd. 647. Hochschulschrift: Zugl.: Saarbrücken, Univ., Diss., 2007. ISBN: 978-3-8260-3886-0 Huizenga, A.B. Advice to the Bride: Moral Exhortation for Young Wives in Two Ancient Letters In: "Jewish and Christian scripture as artifact and canon" eds. Craig A. Evans and H. Daniel Zacharias. London ; New York : T & T Clark, 2009. Studies in scripture in early Judaism and Christianity ; v. 13. Library of Second Temple studies ; 70. T & T Clark library of biblical studies. ISBN 9780567584854 Kobbert, M.J. Spiel - nur ein Zeitvertreib? Die Klapper des Archytas. Senet - ein Brettspiel im alten Ägypten p 11-32 In: Kulturgut Spiel / Max J. Kobbert. Mit einem Vorw. Von Bernward Thole Münster : Daedalus, 2010. ISBN: 978-3-89126-252-8

Köhler, P. Pythagoras um 570-um 497 v. Chr. In: Religionen : Glaubenslehrer von Abraham bis Zarathustra / Hildesheim : Gerstenberg, 2010. Schriftenreihe: 50 Klassiker ISBN: 978-3-8369-2617-1 ISBN/ISSN: 88-7588-028-X Mazzara, G. Aspetti gorgiani e pitagorici nel socratico Antistene. In: Il V secolo. Studi in onore di Livio Rossetti Aguaplano—Officina del Libro, Perugia 2010 Menn, S. The 'Timaeus' and the Critique of Presocratic Vortices p 141-150. In: One Book: The Whole Universe: Plato's 'Timaeus' Today, Mohr, Richard D (ed); Sattler, Barbara M (ed) Parmenides Publishing. 2010. ISBN 978-1-930972-32-2 Summary: Stephen Menn's essay “The Timaeus and the Critique of Presocratic Vortices” views the development of Presocratic philosophy not as a smooth arc of ideas rising either toward Plato's Timaeus or Aristotle's Physics, but as a series of oppositional moves launched by later philosophers against earlier. Plato's critiques of earlier writers can be marshaled into five types, of which Menn's essay addresses two: the earlier writers' resort to narrative at the expense of demonstration and their failure to give teleological explanations. The bulk of the essay tracks the latter line of critique. Specifically, Menn contends Plato tacitly holds the view that Anaxagoras' reason-initiated centrifugal separations of physical kinds cannot give an adequate account of animal life. The criticism is shown to echo the earlier critique of Anaxagoras by Empedocles, a critique which is generalized by Plato into his attack on all the Presocratics. So while Plato's account of vortex explanations might initially seem to be incidental in the Phaedo and Timaeus, it is actually the starting point of his criticism of Presocratic physics and thus the starting point of his own physical project in the Timaeus. Kouremenos, T. Eudoxus' theory of homocentric sphères and Aristotle's Metaph. A 8 33 p 33-50 In: Heavenly stuff : the constitution of the celestial objects and the theory of homocentric spheres in Aristotle’s cosmology Stuttgart : Steiner. 2010. Palingenesia ; Bd. 96; Klassische Philologie ISBN: 978-3-515-09733-8 Lucchetta, G. A. Pitagorici p 199-202 Empedocle p 219-223 In: Metafisica I : la sophia degli antichi. Lanciano (Chieti) : R. Carabba. 2009. Series 1: Nuove prospettive sulla cultura dell'anima; 1 : Vailati traduce Aristotele. ISBN/ISSN: 978-88-95078-60 Lucchetta, G.A. Parmenide tra I physiologoi. - Mappe e genealogie - Parmenide GliEleati - I Pitagorici - Eraclito p 161-207 Teorie fisiche dei componenti minimi. - Democrito - Anassagora - Empedocle p 208-222 In: Vailati traduce Aristotele. Lanciano : Carabba, 2009. Metafisica I, la sophia degli antichi. Vol. 1 Nuove prospettive sulla cultura dell'anima ; 1. ISBN: 978-88-950786-0-1 Mansfeld, J. Plato, Pythagoras, Aristotle, the Peripatetics, the Stoics, and Thales and his Followers "On Causes". p 375-414. In: Aëtiana. The Method and Intellectual Context of a Doxographer. Volume Three. Studies in the Doxographical Traditions of Ancient Philosophy. By J. Mansfeld and D. T. Runia. (Philosophia Antiqua. A Series of Studies on Ancient Philosophy. Volume 118.). Leiden / Boston: Brill. 2010 ISBN 978 90 04 18041 3 Menu, M. « On recherche toujours son semblable » : fortune du proverbe dans le théâtre grec p 555-568 In: Φιλευριπίδης = Phileuripidès : mélanges offerts à François Jouan / textes réunis par Danièle Auger et Jocelyne Peigney Nanterre : Presses Universitaires de Paris 10, 2008 ISBN 978-2-84016-029-8 Résumé : Dans la tragédie et la comédie, mais aussi chez d'autres auteurs, notamment Empédocle (fr. 22, 62 et 90 DK), Platon (Prt. 337c-d, Grg. 510b, Ly. 214a, Phd. 240c), Lysias (24, 27) et Théophraste (Char. 29, 6). Le proverbe acquiert ainsi la force et l'autorité d'un argument de persuasion Manuli, P. ALCMEONE p 41-49, FILOLAO e lo schema biologico tripartito p 120-127 In: Cuore, sangue e cervello : biologia e antropologia nel pensiero antico. Paola Manuli, Mario Vegetti ; in appendice Galeno e l'antropologia platonica Pistoia : Petite plaisance. 2009. Series 1: Il giogo; 22

Montevecchi, F. Empedocle d'Agrigento. Napoli : Liguori. 2010. Series 1: Profili. Biografie; 9 ISBN/ISSN: 978-88-207-5043-5 eine heidnische Version der Auferstehung Jesu und seiner wunderbaren Erscheinung gelesen werden konnte. Muñoz Redón, J. Empédocles p 107 -110, Hipatia p 116 – 119 In: La piedra filosofal : [cómo morir y no perecer en el intento]. Barcelona : Ariel. 2009. ISBN/ISSN: 978-84-344-8825-0 Moreno Sanz, J. Ética del pensamiento, religión de la luz y pitagorismo encarnado.... La penumbra tocada de alegría: la ironía zambraniana. - De lo cómico y lo sublime: del romanticismo alemán a Pirandello yjankélévich. Ironía, piedad y penumbras: teoríay ética. p 9-51 Segundo interludio, exclusivamente nietzscheano: danza de estrellas en la raíz del pensar La estrella pitagórica y las incitaciones de la IIIntempestiva. Suena la música callada de la soledad. La tensión vertical entre alturas y abismos. Entre sospechas, congojas y éxtasis esperando la llegada de nuevos amigos. p 51-102 In: El logos oscuro : tragedia, mística y filosofía en María Zambrano : el eje ... Madrid : Verbum. 2009. Series 1: Mayor. Serie crítica. Vol 2 ISBN/ISSN: 978-84-7962-445-3 Nannicini, M.P. Il numero come principio dell'universo: Pitagora p 92-97 In: Il cammino della matematica nella storia. Maria Paola Nannicini, Stefano Beccastrini Roma : Armando. 2008. Series 1: Matematica per gli insegnanti e per la classe; 2 ISBN/ISSN: 978-88-6081-406-7 Niola, M. II vegetarianesimo, ovvero il teorema di Pitagora p 69-73 In: Si fa presto a dire cotto : un antropologo in cucina. Bologna : Il mulino. 2009. Series 1: Intersezioni; 345. ISBN/ISSN: 978-88-15-13159-1 Mratschek, S. Identitätsstiftung aus der Vergangenheit : zum Diskurs über die trajanische Bildungskultur im Kreis des Sidonius Apollinaris p 363-380 In: Die christlich-philosophischen Diskurse der Spätantike: Texte, Personen, Institutionen : Akten der Tagung vom 22.-25. Februar 2006 am Zentrum für Antike und Moderne der Albert-Ludwigs-Universität Freiburg / hrsg. von Therese Fuhrer Stuttgart : Steiner, 2008. Philosophie der Antike ; 28. Résumé : Die geistige Welt, in die sich Sidonius und seine Freunde versenkten, suchte ihre Anregungen im Rückblick auf die frühere lateinische Literatur bis zur trajanischen Epoche. Hinter diesen traditionellen Mustern römischen Lebens und hinter einer scheinbar statischen kulturellen Atmosphäre vollzog sich ein unmerklicher Wandel, in dessen Verlauf viele der Rituale eines kultivierten Privatlebens stufenweise in ein christliches Religionssystem integriert und neu interpretiert wurden. So liess sich Euergetismus in christliches Almosen umdeuten und fortführen. Talentierte Dichter wie Constantius und Sidonius entwarfen als Priester und Bischöfe um die Wette Versinschriften für die neu erbaute Basilika des Hl. Justus in Lyon. Sidonius empfand keine Skrupel, die asketische Lebensweise von Eurichs Berater mit der Vita des Apollonius von Tyana zu vergleichen, die als Odifreddi, P. In nome di Pitagora, di Archimede e di Newton p 129-133 In: Perché Dio non esiste. Claudio Sabelli Fioretti intervista Piergiorgio Odifreddi Reggio Emilia : Aliberti. 2010. ISBN/ISSN: 978-88-7424-419-5 Olivieri , O. La geografia mitica delle imprese di Alcmeone dalla poesia epica alla tragedia p 299-315 In: Tra panellenismo e tradizioni locali : generi poetici e storiografia. a cura di Ettore Cingano Alessandria : Edizioni dell'Orso. 2010. Series 1: Hellenica; 34 Notes: Papers presented to the meeting held in Venice, Italy, Sept. 21-22, 2006, now revised. ISBN/ISSN: 978-88-6274-206-1 Oliveira Leão, E. De Empédocles de Acragas e o orfismo In: SOBRE AS ORIGENS DA FILOSOFIA: PRIMEIROS ENSAIOS (Gabriele Cornelli & Mariana L. Belchior ORGS). Coleção Archai Supplementa. Archai/Etcetera Editora, São Paulo, 2010. Opsomer, J. M. Annius Ammonius, a Philosophical Profile . . 123-186 In: Mauro Bonazzi, Jan Opsomer (ed.), The Origins of the Platonic System: Platonisms of the Early Empire and their Philosophical Contexts. Collection d'Études Classiques 23.

Louvain/Namur/Paris/Walpole, MA: Éditions Peeters; Société des Études Classiques, 2009. ISBN 9789042921825 In: Eduard Zeller : Philosophie- und Wissenschaftsgeschichte im 19. Jahrhundert Berlin ; New York, NY : de Gruyter. 2010. ISBN: 978-3-11-020857-3 Parenti, S. La tradizione liturgica dell'eucologio di Archimede Pitagorico p 129-145 In: A Oriente e Occidente di Costantinopoli : temi e problemi liturgici di ieri e di oggi. Città del Vaticano : Libreria editrice vaticana. 2010. Series 1: Monumenta studia instrumenta liturgica; 54. ISBN/ISSN: 978-88-209-8201-0 Ravenna, G. Pythagoricus et magus: Nigidio Figulo rivisitato. p 1-16. In: Esoterismi e Costruzione dei Saperi. Atti del Convegno Padova, 3 - 4 Maggio 2007. A cura di Paolo Scarpi, Michela Zago. (Università degli Studi di Padova. Dipartimento di Scienze del Mondo Antico). Padova: S.A.R.G.O.N. Editrice e Libreria. 2009. Peiretti, F. Pitagora. La matematica con i sassi. La vita di Pitagora - Il teorema « di Pitagora » - L'aritmogeometria in riva al mare - Problemi per gioco - Risposte Appendice Per saperne di più p 31-52 In: Il matematico si diverte : duecento giochi ed enigmi che hanno fatto la storia della matematica. prefazione di Piergiorgio Odifreddi Milano : Longanesi. 2010. ISBN/ISSN: 97888-304-2739-6 Reale, G. III. Pitagora e la Scuola pitagorica p 75 - 88 In: Storia della filosofia dalle origini a oggi. Giovanni Reale, Dario Antiseri ; con la collaborazione di Vincenzo Cicero Milano : Bompiani. 2009. ISBN/ISSN: 978-88-452-6347-7 Revel, J.F. Vom Logos zum Atom (5. Jahrhundert) p 47-70 In: Geschichte der westlichen Philosophie : von Thales bis Kant Berlin ; Münster : Lit. 2010. Philosophie: Forschung und Wissenschaft ; [30] Einheitssachtitel: Histoire de la philosophie occidentale ISBN: 978-3-8258-1168-6 Pisano, F. I Severi, le loro donne, i loro amici neopitagorici seguaci di Apollonio di Tiana e l'emblema del delfino nella tholos p 42-43 Il possibile "zampino" dei Neopitagorici nella costruzione della tholos. E riguardo alla tholos più resto del Macelluml Gli incredibili esiti di una inedita lettura p 43-50 In: Hic sunt delphini : la singolare propagazione del simbolo del delfino nei Campi Flegrei in età antica Napoli : A. Pisano, 2008. Nuovi tasselli ; 1. ISBN: 978-88-959380-0-4 Ricoveri, G. Empedocle e i quattro elementi p 33-39 In: Beni comuni vs merci. Milano : Jaca book. 2010. Series 1: Terra terra. Series 2: Di fronte e attraverso; 951 ISBN/ISSN: 978-88-16-40951-4 Platt, V. Virtual visions: 'phantasia' and the perception of the divine in 'The Life of Apollonius of Tyana' In: Bowie, E. Philostratus. Greek Culture in the Roman World. Cambridge: Cambridge University Press, 2009. Rosario, H. Epistemology of the Exact Science(s): Mathematical Knowledge vis-à-vis Spiritual Knowledge p 11-19 In: Science and Spiritual Quest 2008 Department of Mathematical Sciences. University of Puerto Rico, Puerto Rico Abstract: This manuscript explores epistemologies of mathematical and spiritual knowledge. It embodies a critique of the categorical error in mathematics that logical truth is absolute in its inferred unification of mind and spirit. I validate trans-rational approaches toward spiritual truth as distinct from the truth statements of mathematical logic. Pòrtulas, J. Els Creofileus, entre Licurg i Pitágoras p 416-421 La crítica homérica de Teágenes de Región 490-496 In: Introducció a la Ilíada : Homer, entre la història i la llegenda Barcelona : Alpha, 2009. Escriptors grecs. ISBN: 978-84-98591-35-4 Primavesi, O. Aristoteles oder Empedokles? Charles Darwin und Eduard Zeller uber einen antiken Ansatz zur Evolutionstheorie

Sauron, G. INSPIRATIONS PYTHAGORICIENNES Une chambre hivernale dans la villa «de Poppée» à Oplontis/Torre Annunziata - La zone de la porta Maggiore à l'époque d'Auguste : aqueducs, tombes et jardins - L'hypogée de la Porte Majeure : la crypte de la tombe de T. StatiliusTaurus, le consul de 37 et 26 avant J.C? _ - L'hypogée de la Porte Majeure : un monument du pythagorisme romain - La redistribution ornementale des thèmes de l'abside : l'apothéose deTaurus dans le Verseau p 33 - 62 In: Les décors privés des Romains : dans l'intimité des maîtres du monde. Paris : Picard. 2009. Series 1: Antiqua; 11. ISBN/ISSN: 978-27084-0837-1 In: Musik in der antiken Philosophie : eine Einführung Würzburg : Königshausen & Neumann. 2010. ISBN: 978-3-8260-3393-3 Teixeira, C. P Crotona no Satyricon de Petrónio: uma distopia pitagórica? p 163-173 In: Utopias & distopias. coordenação, Maria da Fátima Silva. Coimbra : Universidade de Coimbra. 2009. Series 1: Documentos Notes: Papers presented to the meeting, Coimbra, 2008. ISBN/ISSN: 978-989-8074-74-4 Thadeutz, F. Getreu seine Zahlen. Der Mathematiker Pythagoras stilisierte sich als Sektenfuhrer zur Kultfigur p 110-135 In: Saltzwedel, J. Götter, Helden, Denker : die Ursprünge der europäischen Kultur im antiken Griechenland München : Goldmann ; Hamburg : SpiegelBuchverl., 2010. Schriftenreihe: Goldmann ; 10227. ISBN: 978-3-442-10227-3 Schlesak, D. Pythagoras und Keplers Musik p 29-44 In: Der Tod ist nicht bei Trost : Liebes- und Todesgedichte München : Allitera-Verl. 2010. Lyrik-Edition 2000. ISBN: 978-3-86906-117-7 Therme, A.L. « Une tragédie cosmique : l’exil amnésique des daimones d’Empédocle. » In: Rationalité tragique, S. Alexandre et O. Renaut (ed.), Zetesis - Actes des colloques de l’association [En ligne], n°1, 2010, pp. 129, URL: http://www.zetesis.fr/actes/spip.php?article14 Signore, G. La Magna Grecia - Pitagora e la sua dieta p 10-13 In: Storia delle abitudini alimentari : dalla preistoria ai fast food. Milano : Tecniche nuove. 2010. ISBN/ISSN: 978-88-481-2428-7 Spengler, O. Pitagora, Maometto, Cromwell . . . . p 1036-1131 In: Il tramonto dell'Occidente : lineamenti di una morfologia della storia mondiale. edizione a cura di Rita Calabrese Conte, Margherita Cottone, Furio Jesi ; traduzione di Julius Evola ; introduzione di Stefano Zecchi Nuova ed. I marmi. Milano : Longanesi. Series 1: I marmi; 185 Notes: Orig. title: Der Untergang ... - 1st publ. 1957, now revised. ISBN/ISSN: 978-88-304-2558-3 Todescan, F. LA FILOSOFIA PRESOCRATICA:IONICI, ELEATI E PITAGORICI p 15-27 In: Compendio di storia della filosofia del diritto. Padova : CEDAM. 2009. Series 1: Biblioteca di Lex naturalis; 7 ISBN/ISSN: 978-88-13-29197-6 Staab, G. Pythagoras und der fruhe Pythagoreismus - Die „pythagoreische Frage" - Kurzbiographie - Philosophie und Kunst Pythagoreisches „Weltbild" - Philosophie als vorrationale Theoria - Kunst und Musik - Die Musik als Beweis und Mittel pythagoreischer Weltbetrachtung - Harmonie und Zahl Sphärenharmonie und Seelenharmonie Ethische Bedeutung der Musik - Damon aus Athen und die pythagoreische Musiklehre Rezeption - Bibliographie - Literatur p 103-122 Tonelli, A. Parmenide, Eraclito, Empedocle: la parola come iniziazione p 50-80 In: Sulle tracce della sapienza : per una rifondazione etica della contemporaneità.

Bergamo : Moretti & Vitali. 2009. Series 1: Il tridente. Saggi; 56. ISBN/ISSN: 978-88-7186-428-0 Résumé : The κλίσις χρείας-exercise was part of the « progymnasmata » or preliminary exercises in rhetoric, intended for students who had completed their secondary education and prepared themselves for declamation. Several manuals containing such preparatory material have been preserved. The most important are those by Aelius Theon of Alexandria, Hermogenes, Aphthonius, and Nicolaus of Myre. Such inflexion excercises are, on the one hand, a (more complex) continuation of the morphological paradigms studied in the class of the γραµµατικός, while, on the other hand, they imply some training in elementary syntax. Three student notebooks on papyrus inform about the daily practice of the κλίσις χρείας in the 3rd-4th c. AD (Oxford, Bodleian Libr., Gk. Inscr. 3019 ; London, BM, Add. MS 37533 and 37516). Trainito, M. Pitagora e il magico numero sette per tre p 113-121 In: Il codice D'Arrigo : dall'Orca alla placenta : Hatshepsut. Villorba (Treviso) : Anordest. 2010. ISBN/ISSN: 978-88-96742-06-8 Varsamis, S, Spatial Palindromes. Classical Philosophy - Orpheus - Pythagoras - Vitruvius - Vitruvius’ Ten Books on Architecture as a Temple - Temple as an Expression of Words p 73-132 In: Varsamis, S. Spatial palindromes/palindromic spaces: spatial devices in Vitruvius, Mallarmé, Polieri, Perec and Libeskind. Doctoral thesis, UCL (University College London). 2010. http://eprints.ucl.ac.uk/20479/1/20479.pdf Zacchini, S. La genesi deiVepisteme nel contesto pitagorico e il logos deduttivo "cosiddetti" Pitagorici - Il concetto di numero: proporzioni e armonia - La fondazione deduttiva della conoscenza Dimostrazione e assiomatizzazione: l'eredità greca. p 33-61 In: La collana di Armonia : Kant, Poincaré, Feyerabend e la crisi dell'episteme. Milano : F. Angeli. 2010. Series 1: Filosofia storia scienze sociali / Dipartimento di studi storico-sociali e filosofici, Facoltà di lettere e filosofia (Arezzo), Università di Siena; 19 ISBN/ISSN: 978-88-568-2241-0 Vial, H. Ambiguïté du discours de Pythagore (XV, 75-478) p 73-77 In: La métamorphose dans les Métamorphoses d'Ovide : [étude sur l'art de la variation]. Paris : Les belles lettres. 2010. Series 1: Collection d'études anciennes. Série latine; 70 ISBN/ISSN: 978-2-251-32879-9 Wismann, H. Der Begriff des Gesetzes bei Hesiod und den Vorsokratikern p 1-10 In: Gesetz und Gesetzlichkeit in den Wissenschaften / Wolfgang Bock (Hrsg.) Darmstadt : Wissenschaftliche Buchgesellschaft, 2006. Résumé : Hesiod beschreibt in seiner « Theogonie » Themis als Titanin der ersten Generation der Götter und Nomos als die Verteilung der göttlichen Rechtsansprüche durch Zeus, die verhindert, dass eine Gottheit ihre Grenze überschreitet. Parmenides und Empedokles ordnen das Sein selbst der Themis zu, während die verteilte, sichtbare Wirklichkeit, die im Gegensatz zur Themis nicht einheitlich ist, dem Nomos zugeordnet wird. Yribarren, M. La gamme de Pythagore de sept notes p 54 - 56 Le cycle des quintes et la gamme de Pythagore de douze notes p 56 – 60 Proximité harmonique des échelles de Pythagore et de Zarlino p 82 – 84 In: Échelles musicales et proximité des harmoniques, ou Comment la gamme chromatique également tempérée, base universelle de toutes les musiques d'aujourd'hui, trouve sa justification dans la proximité des harmoniques naturels. Bourg-la-Reine : ich. 2009. Series 1: Les carnets de Sonatine. ISBN/ISSN: 978-2-87750-123-1 Wouters, A. Between the grammarian and the rhetorician : the κλίσις χρείας p 137-154 In: Festschrift für Gerhard Petersmann zum 65. Geburtstag / hrsg. von Veronika Coroleu Oberparleiter, Ingrid Hohenwallner, Ruth Elisabeth Kritzer Publication : Horn : Berger, 2007. Collection(s) : Grazer Beiträge. Supplementband ; 11. Zellini, P. Cristo e Pitagora p 166- 178 In: Numero e logos. Milano : Adelphi. 2010. Series 1: Biblioteca scientifica; 47 ISBN/ISSN: 978-88-459-2516-0

Book reviews Deakin, M.A.B. Hypatia of Alexandria: Mathematician and Martyr. 2007. Reviewed by: Bowman, E. http://mathdl.maa.org/mathDL/ Reviewed by: Lamborn Wilson, P. http://www.sevenpillarshouse.org/reviews/ Reviewed by: Rauff, J.V. Mathematics & Computer Education, 2009 Reviewed by: Berghout, B. Gazette of the Australian Mathematical Society, 2008 Demoen, K. Theios Sophistes: Essays on Flavius Philostratus'. Leiden. Brill 2009. Reviewed by: Anonymus Listy filologické. 2010, 133, 1-2, p 183-185 Reviewed by: Kemezis, D.M. http://bmcr.brynmawr.edu/2009/2009-10-40.html Reviewed by: Elsner, J. Classical Review. 2009, 60, p 77-79 Ferguson, K. The Music of Pythagoras: How an Ancient Brotherhood Cracked the Code of the Universe and Lit the Path from Antiquity to Outer Space. 2008. Reviewed by: Anonymus Isquared. 2008, 4. Reviewed by: Kaplan, G. Loci. 2010, April Reviewed by: Traveler, J. http://www.helium.com/channels/899-Ancient-History Reviewed by: Ziauddin Sardar The Independent. 2010, 8 Oct. Gemelli Marciano, M.L. Die Vorsokratiker. Band I: Thales, Anaximander, Anaximenes, Pythagoras und die Pythagoreer, Xenophanes, Heraklit. Griechisch-lateinisch-deutsch. Auswahl der Fragmente und Zeugnisse. Düsseldorf 2007. Reviewed by: Bergemann, L. Ancient Philosophy. 2010, 30, 1, p 167-171 Hermann, A. To think like god : Pythagoras and Parmenides, the origins of philosophy. Las Vegas (Nev.) : Parmenides Publ., 2004. Reviewed by: Mansfeld, J. Phronesis. 2005, 50, 4, p 340 Huffman, C.A. Archytas of Tarentum : Pythagorean, philosopher, and mathematician king. Cambridge ; New York : Cambridge University Pr., 2005. Reviewed by: Centrone, B. Exemplaria classica. 2007, 11, p 285-289 Reviewed by: Schofield, M. Philosophical Review. 2009, 118, 1, p 108-112 Megino Rodríguez, C. Orfeo y el Orfismo en la poesía de Empédocles : influencias y paralelismos. Madrid : Universidad Autónoma de Madrid, 2005. Reviewed by: Long, A.A. Phronesis. 2008, 53, 3, p 299 Riedweg, C. Pythagoras: His Life, Teaching, and Influence. 2005 Reviewed by: Imhoof, S. Revue de theologie et de philosophie. 2009. 141, 1, p 73-74. Reviewed by: Rognon, F. Revue d’histoire et de philosophie religieuses. 2009, 87, p 86 Sassi, M.M. La costruzione del discorso filosofico nell'età dei Presocratici = The construction of philosophical discourse in the age of the Presocratics / a cura di Pisa : Ed. della Normale, 2006. Reviewed by: Iribarren, L. Philosophie antique. 2007, 7, p 262-265 Reviewed by: Long, A.A. Phronesis. 2008, 53, 3, p 301-301 Reviewed by: Bonazzi, M. Rivista di storia della filosofia. 2008, 63, 2, 381-382 Stamatellos, G. Plotinus and the presocratics: a philosophical study of presocratic influences in Plotinus' Enneads. 2007 Reviewed by: Gurtler, G.M. Ancient Philosophy. 2010, 30, 1, p 203-207 Zaborowski, R. Sur le sentiment chez les Présocratiques : contribution psychologique à la philosophie des sentiments. 2008. Reviewed by: Boys-Stones, G. Greece and Rome. 2010, 56, p 127

Journal articles Adorjáni, Z. Pindarus allegoricus zur Deutung der 2. und 3. olympischen Ode Acta Antiqua Academiae Scientiarum Hungaricae. 2009, 48, 3-4, p 305-338 Summary: In this paper I analyse two Pindaric poems in order to detect similarities in the imagery. The central motifs turn out to be strong optical metaphors that cluster around the extremes of light and darkness. Furthermore, these motifs support the same poetic message in both poems: The notion of victory bringing about harmony and equilibrium in the life of the victor. The artistic expression of this is the equinox in the Second, the newmoon ( synodos ) in the Third Olympian Ode. Therefore, the much controverted question of pythagorean-orphic influence in the Second seems to be futile, since the underlying system does not obey the rules of philosophy, but of poetry. Its meaningfulness is provided not by philosophic concepts, but by poetic vision. en la « Historia eclesiástica » de Teodoreto de Cirro Gerión. 2008, 26, 1, p 453-490 Résumé : Se repasan los distintos episodios de violencia cristiana relatados por Sócrates de Constantinopla en su « Historia eclesiástica ». Sócrates relata, entre otros, los sucesos acaecidos en Alejandría en el año 412 (HE 7, 6) con ocasión de la elección de Cirilo ; luchas con ocasión de la elección de otros obispos ; persecuciones ; enfrentamientos entre los obispos ; la revuelta de los esclavos (HE 7, 33) ; la violencia contra los arrianos, contra los judíos, contra los sasánidas, el asesinato de Hipatia, etc. Teodoreto, por su parte, describe sin tapujos en su « Historia eclesiástica », entre otros casos de violencia religiosa, las luchas feroces que ocasionó el arrianismo. Caldini Montanari, R. Tra « scogli » e « macchie » : l'immagine delle οἰκούµεναι nel « Somnium Scipionis » e un passo del Περι κόσµου attribuito ad Aristotele Pallas. 2006, 72, p 83-96 Résumé : Dans le « Somnium Scipionis », Cicéron définit les οἰκούµεναι vues d'en haut « quasi maculae », terme dont on considère communément qu'il correspond à σπίλοι, utilisé à propos des οἰκούµεναι dans le Περι κόσµου attribué à Aristote. Ici cependant il ne s'agit pas du terme courant ὁ σπίλος, « tache », mais de son homographe très rarement attesté ἡ σπίλος, « roche, écueil ». Les οἰκούµεναι se trouvent en fait sur les saillies de la terre, qui émergent de l'eau. Le terme cicéronien « maculae » doit donc être considéré comme une méprise, due à la confusion entre les deux σπίλοι. On en déduit l'utilisation du Περι κόσµου comme source du « De republica » de Cicéron, où figurent d'autres thématiques communes, et l'opportunité de mener un enquête sur la fortune d'un traité grec chez les auteurs latins. Anonymus. Three translations of the Golden Verses of the Pythagoreans The Meadow. A journal of Philosophy, Religion, Mysticism and allied arts. Year?, 3. 5 pages. http://www.prometheustrust.co.uk/html/the_gol den_verses.html Azzarello, G. P.Oxy. XVI 2039 e la nascita della « domus gloriosa » degli Apioni Zeitschrift fur Papyrologie und Epigraphik. 2006, 155, p 207-228 Résumé : Il papiro riporta un rendiconto relativo allo svolgimento della funzione di riparios (ufficiale di polizia) spettante originariamente alla casata di Theon, ma, a causa della sua estinzione, ripartita in misura diversa tra le famiglie aristocratiche ossirinchite. Tra queste, l'ἔνδοξος οἶκος degli Apioni è quella cui tocca la parte maggiore. Con edizione e commento. Appendice : Osservazioni a P.Iand. 8, 155 e a due testi dell' archivio degli Apioni (P.Oxy. 16, 2019 e P.Lond. 3, 777) Cardigni, J. El comentario como género de la memoria : « Commentarii in somnium Scipionis » de Macrobio (1.3.17-20) Habis. 2008, 39, p 275-283 Résumé : El comentario es un género literario apropiado para presentar nuevas doctrinas en el contexto de una tradición literaria recurrente que les confiere « auctoritas », de ahí que fuera ampliamente cultivado en una época de transformaciones como la Antigüedad Tardía. Por medio del citado pasaje se ejemplifica cómo Macrobio rememora, reescribe y Bisaccia C. The nature of water: Excerpts from Pythagoras, Xenophanes, Heraclitus and Parmenides Journal of Nephrology. 2009, 22, SUPPL. 14, p 103-S107 Blázquez Martínez, J.M. La violencia religiosa cristiana en la « Historia eclesiástica » de Sócrates durante el gobierno de Teodosio II y

transforma el pasado para darle continuidad en el presente. νους (Plotin) . Retour à une pensée du cogito, du Dieu vérace, mais qui, à l’inverse doit prouver l’existence de la matière( Descartes), puis au siècle de l’Encyclopédie à cette matière d’un monde scientifique naissant. Le monde contemporain séduit expliquera celleci, à travers un matérialisme instruit (Bachelard) de la science. Mais le spiritualisme chrétien résiste. La matière et l’esprit n’étaient qu’ensemble, et à eux deux, ce qui devait expliquer l’être et le monde. Cardigni, J. Apropiación y traducción en un texto tardoantiguo: Comentario al sueño de Escipión de Macrobio. Circe clás. mod. [online]. 2008, 12, p 77-86 Abstract: El presente trabajo estudia los Commentarii in Somnium Scipionis de Macrobio, escritos en el siglo V, desde el punto de vista de la apropiación y traducción de la tradición literaria que se opera en la exegesis macrobiana, operación por medio de la cual el sujeto se constituye al leer y reformular discursivamente un pensamiento anterior. Este tipo de práctica exegética resulta especialmente importante en el tardoantiguo, momento en el que se buscaba implementar un método de interpretación del pasado que permitiera insertarse en la tradición y construir al mismo tiempo una nueva identidad cultural. Clark, S. "I knew him by his voice". Can animals be our friends? Philosophy Now. 2008, 67, p 13-16 Abstract: Examines how far Aristotle's concept of friendship could apply to animals; the title is a quotation from Pythagoras, who was referring to a dog which was being beaten. Considers the differences and similarities between animals like dogs, cats and pigs on one side, and humans on the other; the concepts of speciation; and the many relationships between animals - even invertebrates - which bear some resemblance to friendship. While animals do not plan and reflect in the way that humans do, this does not preclude them enjoying human and each other's company in the same sorts of way that humans enjoy friendship. Concludes that, in view of the above, and also since many humans lack the linguistic and rational facilities which are traditionally held to justify human uniqueness, there is no reason to exclude animals from moral concerns. INTERFOTO PRESSEBILDAGENTUR / ALAMY Clemente, P.G. El debate acerca del presunto influjo del Pseudo-Empedocles en el pensamiento de Ibn Massarra de Cordoba. Revista Espanola de Filosofia Medieval. 2009. 16, p 23-33. Since Asin Palacios first published his pioneering study on the Andalusian thinker Ibn Masarra, based on indirect sources, there has been an intense debate on some of his conjectures: he proposed that Ibn Masarra was influenced by the writings of the so-called Pseudo-Empedocles and he introduced philosophy (in particular Neoplatonism) in alAndalus. The discovery of two unknown works by the author provided a new framework for discussion. The present article examines Asin's “reconstruction” of Ibn Masarra's thought, analysing the theory of the PseudoEmpedocles influence, as well as a text by Ibn 'Arabi which inspired the association of the image of the five pillars attributed to Ibn Masarra with the five principles of the PseudoEmpedocles. Arab astronomers study the heavens in this print from a commentary on Cicero’s Somnium Scipionis, whose central character ranges through the celestial spheres that surround the Earth, and carry the planets and the stars. Caruso, V. Empedocle. ‘ figura di frontiera” Vichiana. 2010, 4, 12, p 99-114 Charrue, J.M. « La matière et l’esprit » Le Portique. 2006. 2 http://leportique.revues.org/index859.html Une théorie de la matière se trouve développée, pour la première fois par les physiciens ioniens, puis par Empédocle et Héraclite, coïncidant, le plus souvent avec les quatre éléments, dont l’un ou l’autre prédominait, auquel Empédocle avait joint, l’Amour et la Haine. Mais comme celle-ci se révèle insuffisante, pour expliquer le monde, dans son entier on y adjoint, le νους ou l’esprit, ainsi, Anaxagore. Tentative d’explication du monde par la matière (Epicure), puis par le

Clucas, S. Pythagorean Number Symbolism, Alchemy, and the Disciplina Noua of John Dee's Monas Hieroglyphica Aries: Journal for the Study of Western Esotericism. 2010, 10, 2, p 149-167 poems written by Spanish poet Antonio Machado. It addresses Machado's concept of universal harmony and intersubjective reconciliation. Machado's portrayal of Jesus Christ and Buddha is examined. The article also examines the use of Greek philosopher Pythagoras' dictum in the beginning of the poem. Correa Pabón, G.L. "Teoría de la Proporción Pitagórica" . Colombia Escritos. 2006, 14, 33, p 600 - 617 Gencarella, S. O. Purifying Rhetoric: Empedocles and the Myth of Rhetorical Theory. Quarterly journal of speech. 2010, 96, 3, p 231-257 Correa Pabón, G.L. "Harmonía y Analogía en el contexto pitagórico" . Colombia Escritos. 2006, 13, 30, p 358-387 Correa Pabón, G.L. "LA ARMONÍA DE LAS ESFERAS" . Colombia Escritos. 2005, 13, 31, p 675-697 Granger, H. The theologian Pherecydes of Syros and the early days of natural philosophy Harvard studies in classical philology. 2007, 103, p 135-163 Résumé : Pherecydes of Syros is more relevant than scholars generally think to understanding the intellectual milieu that fostered cosmology and led to philosophy as we have come to appreciate it. That milieu was primarily theological, and, accordingly, Pherecydes' contribution may be appreciated as more theological than physical. Pherecydes makes advances in the Greek conception of the divine nature. Once the shared interest in theology of the new intellectuals of the 6th cent. is recognized, diverse thinkers such as Pherecydes, the Orphic poets, Pythagoras, and others may be appreciated as forming a more unified group than is usually acknowledged, through their efforts to reform or break with the theological tradition embodied in the poetry of Hesiod. Corrigan, J.M. The Metempsychotic Mind: Emerson and Consciousness Journal of the History of Ideas. 2010, 71, 3, p 433-455 Abstract:This article argues that Ralph Waldo Emerson employs metempsychosis (reincarnation or the transmigration of the soul into successive bodies) as a figurative template for human consciousness. Mapping various traditions from Hinduism, Pythagoreanism, Platonism, and Neoplatonism onto the vastness of the geological and biological records, Emerson translates metaphysics for modernity: he depicts the soul's journey through the chronological sequence of history as a poetic process that culminates in a tenuous form of selfknowledge. Fernandez, A.G. La monada pitagorica y el cosmos de Platon. Cuadernos de Ontologia. 2009, 9, p 155-163. Abstract: The interpretation of the Platonic cosmogony presents one of its more controversial aspects in the appreciation of the meaning of the creational act. The interpretations given so far clash “creationist” ; and the “mathematics”; with passages that show the inadequacies of both approaches. Our work will analyse the different arguments concerning: (1) the status of the numbers; (2) the role of the limited, unlimited and the sperm; (3) the biological model of the Platonic cosmology. Green, S.J. Save our cows ? : Augustan discourse and animal sacrifice in Ovid's « Fasti » Greece and Rome. 2008, 2, 55, p 39-54 Résumé : Building more boldly upon earlier sentiments in the « Metamorphoses », the « Fasti » sets up a contemporary debate on animal sacrifice that centers around two opposing viewpoints : a traditional, « Augustan » viewpoint that highlights the practice as a solemn tradition in Roman religion ; and a « Pythagorean » viewpoint that invites sympathy for the animal victims by inviting us to break down barriers between human and animal experiences. Fernandez-Medina, N. Pythagoras, Buddha and Christ: Antonio Machado's Poem lxv of 'Proverbios y cantares' (Nuevas canciones). Bulletin of Spanish Studies. 2010, 87, 5, p 613-624 Summary: The article offers poetry criticism of the poem "lxv" of the "Proverbios y cantares" Heller-Roazen, D. Into the Forge Qui Parle: Critical Humanities and Social Sciences. 2010, 19, 1, p 1-8 In lieu of an abstract, here is a preview of the article.

Pythagoras knew not to trust his ears. Sage and scientist, he understood that such organs of perception might well reveal the truth. But he was also aware that they might lead him into error. As Boethius relates in Institutions of Music, Pythagoras "put no credence in them," since the ears, being bodily parts like all others, are subject to incessant change. 1 Sometimes they vary on account of external and accidental circumstances; sometimes they begin to differ by necessity, as when they age. Pythagoras could hardly have expected more from acoustical devices made by men. Musical instruments were, for him, "sources of much variability and inconstancy" ("FM," 18; TM, 46– 47). More than once, he had studied the nature of strings. Their tones may change for reasons almost too numerous to enumerate. Depending on their matter, depending on their length and width, depending on the air about them and the force with which one plucks them, cords will inevitably produce different noises. Pythagoras had observed that other instruments are of a like nature. The sole certainty about them is that, sooner or later, they must abandon "the state of their previous stability" ("FM," 17), causing their tones to change perceptibly. In awareness of the implications of these facts, Pythagoras had resolved to liberate himself and his investigations, as much as he could, from the troubling consequences of sensible things. He would study the laws of sound without needing to encounter them in bodily form, and he would acquire knowledge of the properties of audible things by the aid of reason alone. The project was boldly conceived, but it was never to reach completion. As Pythagoras decided on the course his inquiry must take, he was suddenly distracted. "As if impelled by a kind of divine will," the thinker found himself led from the place of his customary calculations out Holm, A. Wisdom From Ancient Greece: Music, Sculpture, and Architecture. Sculpture Review. 2008, 57, 4, p 8-11 Abstract: Vitruvius, writing for his patron Caesar Augustus in the first century, set forth the necessity for an architect to have knowledge of music. Had he included sculptors or painters, he would likely have required of them to have a a similar understanding of music. Two thousand years of scholarship have continued to ponder this idea. In the fifteenth and sixteenth centuries, architects like Palladio wondered why ….. what pleases the ear pleases the eye, …. and Pythagoras may have provided the clue to the answer. Johnston, L. The Music of the Spheres The Meadow. A journal of Philosophy, Religion, Mysticism and allied arts. Year?, 3. 5 pages. http://www.prometheustrust.co.uk/html/music_ of_the_spheres.html Hu, Peng Origins of music theory: Theory of the Pythagorean school. I [Yinyue lilun de qiyuan: Bidagelasi xuepai de lilun (shang)] Yinyue yishu: Shanghai Yinyue Xueyuan xuebao/Art of music: Journal of the Shanghai Conservatory of Music. 2009, 3, p 75-80 Abstract: [Unedited] An introduction to the major scholars of Pythagorean School in Ancient Greece leads to the exploration of the process of how music theory came to be established and developed. Junqua, F. « « Les oreilles dans les pieds » » Agone. 2007, 37 http://revueagone.revues.org/373 Resume: La vie, aurait répondu Pythagore au tyran de Phlionte, est comme une panégyrie : il y a ceux qui s’y rendent pour remporter des couronnes et acquérir la gloire, ceux qui viennent pour faire du commerce et gagner de l’argent, et une troisième catégorie, la plus noble et la plus sensée : celle des spectateurs, qui viennent là pour observer ce qui se passe. « Philosophes » est le nom que l’on donne à ceux qui appartiennent à cette troisième catégorie. Est-ce aussi simple ? Car la figure

du philosophe conseiller du prince est courante dans l’Antiquité. Cet article évoque trois figures significatives et contemporaines qui nous paraissent incarner trois postures représentatives des relations entre les philosophes antiques et le pouvoir. de pensée traditionnels ? L’article étudie sous ce rapport deux cas célèbres : la description fantastique que donne Parménide de son voyage chez la Déesse dans le proème de son poème et l’autoportrait d’Empédocle en « magicien » dans un de ses fragments, pour suggérer, contre certaines tendances récentes de l’interprétation, qu’ils répondent tous deux à la seconde hypothèse. Kingsley, P. The Spiritual Tradition at the Roots of Western Civilization AntiMatters. 2007, 1, p 111-141. Excerpts from In the Dark Places of Wisdom and Reality by Peter Kingsley1 A compilation by Ulrich Mohrhoff Lami, A. Un'argomentazione di Filolao Filologia antica e moderna. 2007-2008, 18-20, p 5-17 Résumé : Per Filolao il costituente essenziale dell'uomo è il caldo, poiché sia l'elemento che lo produce (il seme maschile), sia l'ambiente che accoglie quest'ultimo (l'utero femminile) sono caratterizzati dal calore Kotschy, J. Mikrotonalität: Eine Zeiterscheinung? Österreichische Musikzeitschrift. 2008, 63, 7, p.8-15 Abstract: Die Mikrotonalität findet sich sowohl in der traditionellen Volksmusik innerhalb Europas als auch in den meisten außereuropäischen Tonsystemen. Im Aufsatz werden drei Personen vorgestellt, die für die mikrotonale Musik von großer Bedeutung waren: Archytas von Tarent, Ramos de Pareja und Jörg Mager. Obwohl bereits in der Antike asymmetrische MikrotonTeilungen bekannt waren, setzte sich das symmetrische Prinzip durch, das auf den Grundlagen des Pythagoras beruhte. Erst um 1480 geriet dieses System durch die Einführung der Naturterz und aufgrund arabischer Einflüsse ins Wanken. Zu Beginn des 20. Jahrhunderts nahm das Interesse an Mikrotonsystemen zu und setzte sich an der Wende zum 21. Jahrhundert fort. Die Fülle an vorhandenen Mikrotönen wartet darauf, von Komponisten verantwortungsbewusst und phantasievoll eingesetzt zu werden. Lowry, S. Todd Pythagorean mathematical idealism and the framing of economic and political theory Advances in mathematical economics. 2010, 13, S. 177-199 MacGregor, A.P. Was Manilius really a Stoic ? Illinois Classical Studies. 2005, 30, p 41-65 Résumé : It is commonly assumed that Manilius is a « Stoic » poet . Consideration of a number of passages (e.g., 1, 456-531 ; 1, 774777 ; 2, 583-588 ; and 5, 734-745), and also of presuppositions that run through the poem, disproves this hypothesis. Time and again Manilius contradicts or ignores the central tenets and prejudices peculiar to Stoicism. For the most part, he embodies an idealistic Pythagoreanism and Platonism. Meyer, M.F. Der Wandel des Psyche-Begriffs im frühgriechischen Denken von Homer bis Heraklit Archiv fur Begriffsgeschichte. 2008, 50, p 9-28 Résumé : Bei Homer hatte « Psyche » ursprünglich rein substitutive Funktion (Ersatz für einen bestimmten gestorbenen Menschen). In der archaischen Lyrik wurde der Begriff zum Synonym für « Leben ». Bei den milesischen Naturphilosophen galt « Psyche » als (stoffliches) Bewegungsprinzip. Ein Paradigmenwechsel vollzog sich bei Pythagoras und den Pythagoreern : « Psyche » wurde zu dem, was fortan als « Seele » oder Bewusstsein im weitesten Sinne begriffen wurde. Heraklit verstand schliesslich unter « Psyche » den sich wandelnden Logos. Laks, A. « Phénomènes et références : Eléments pour une réflexion sur la rationalisation de l’irrationnel » Methodos 2003. http://methodos.revues.org/205 Le terme de « rationalisation », qui renvoie à un processus menant de l’« irrationnel » au « rationnel », prend deux valeurs opposées, selon que le processus en question est considéré comme objectif ou subjectif, légitime ou non. Le développement d’une nouvelle forme de rationalité en Grèce ancienne (la philosophie) et son historiographie postérieure présentent souvent des tensions intéressantes entre les deux options. Avons-nous affaire au « phénomèn » originel, dont la raison, malgré qu’elle en ait, doit s’accommoder, ou déjà à des utilisations et transpositions, qui font « référence » à des prétentions ou des types

Nabielek, M. Silenus' Song (Virgil Ecl. 6.2786) -- A Source for Ovid's Pythagoreanism in the Metamorphoses?. Topicos: Revista de Filosofia (Mexico). 2007, 33, p 97-118. Abstract: Pythagorean ideas in Silenus's song in Virgil's Eclogue 6 are set out. The role of music in ordering a transcendent, stable world and changing cosmos and in accessing the transcendent world is shown to be stressed by Virgil. A modern-philosophical account of musical transcendence is provided, as well as an explanation of its continued attractiveness for poets and philosophers who ponder the notion of immortality. The same ideas are then shown to be emphasised in Ovid's Metamorphoses. The conclusion is drawn that the Metamorphoses owe their philosophical dimension to Virgil's Pythagoreanism in Eclogue 6. Poseidonia. A historical overview of Poseidonia is presented which includes information on who built the city, a description of the city's three surviving temples, and several photographs of the temples. Polycarpou, C.N. Archytas' ontology Parnassos. 2007, 49, p 89-108 Résumé : Archytas s'intéresse notamment à l'application des principes mathématiques et mécaniques dans le domaine de la métaphysique. Il examine les λογιστικά dans le cadre de l'étude du mouvement et des forces qui l'affectent. En considérant la δύναµις comme la principale propriété définissant les ὄντα et en se démarquant ainsi du monisme, il contribue à la transition entre pythagorisme et philosophie platonicienne. Sans rompre avec les pythagoriciens, il s'interroge sur la façon dont les nombres étaient considérés par eux comme la base de toute réalité O’ Brien, C. The philosophy of Apollonius of Tyana: an attempt at reconstruction Dionysius. 2009, 27, p 17-32. Polycarpou, C.N. An addition to Archytas' ontology Parnassos. 2008, 50, p 59-64 Olbrys Gencarella, S. Purifying Rhetoric: Empedocles and the Myth of Rhetorical Theory Quarterly Journal of Speech. 2010, 96, 3, p 231-256 Summary: The polymath Empedocles has not been considered a prominent figure in the history of rhetorical studies nor contemporary appropriations of antiquity, despite the reported attribution of his invention of rhetoric by Aristotle. This neglect is understandable, as the surviving fragments of Empedocles' work provide no significant reference to rhetoric per se. Attention to the folklore surrounding Empedocles (including legends of his deeds as a physician and politician, and his association with Pythagoras, Gorgias, and the god Apollo) is noteworthy, however, as it helps explain ways the ancient Greeks conceptualized rhetoric as a potentially healing discourse. Analysis of the Empedoclean tradition discloses a call to redress any human penchant for violence and to resist tyranny, themes relevant for critical rhetorical studies today. These contributions further demonstrate an affinity between Empedocles and Kenneth Burke's concern with the purification of war, and temper the recent interest in an Isocratean development of citizens by advancing a more ecumenical perspective on humanity. Rocha, R. UMA INTRODUÇÃO À TEORIA MUSICAL NA ANTIGUIDADE CLÁSSICA AN INTRODUCTION TO MUSICAL THEORY OF THE CLASSICAL ANTIQUITY Revista Eletrônica Via Litterae. 2009, 1, 1, p 138-164 [www.unucseh.ueg.br/vialitterae] RESUMO: Este texto apresenta uma introdução à teoria musical desenvolvida pelos antigos gregos. Apresento e explico os principais conceitos como mousike, harmonia, tonos, systema etc. Ao final, trato também dos principais instrumentos musicais, explicitando quais eram suas características e sua importância dentro da cultura grega antiga. Roullier, P.H. Du sage au discipline: autorite charismatique, domination romaine et identite grecque dans la "Vie d'Apollonios de Tyane" de Philostrate Pallas. 2010, 83, p 359-378 Scully, M. The Demon and the Quantum: From the Pythagorean Mystics to Maxwells Demon and Quantum Mystery Physics Today. 2008, 61, 11, p 57 Stuckrad, K. Rewriting the Book of Nature: Kabbalah and the Metaphors of Contemporary Life Sciences Journal for the Study of Religion, Nature and Culture. 2008, 2, 4, p 419-442 Summary: At the beginning of the twenty-first century, it seems as if biology, genetics, and Patel, S.S. Rediscovering Paestum. Archaeology. 2010, 63, 4, p 44-48 The article discusses the forgotten Greek temples of Paestum in southern Italy, which are the ruins of an ancient Greek colony called

the ‘life sciences’ are in normative control of cultural discourses regarding nature, the body, and the cosmos. This article addresses religious and esoteric semantics that underlie modern biology. The ‘deciphering’ of the human genetic ‘code’—a metaphor introduced to the ‘life sciences’ by Erwin Schrödinger in 1944—rests on Pythagorean and kabbalistic notions about letters and numbers as the building blocks of the cosmos. The progress of ‘genetic engineering’ and related techniques puts the human being into the position of universal creator of life. The philosophical interest in natura naturans returns in modern science in an unambiguously religious and metaphysical way. Looking at the kabbalistic tradition and its ‘ontologization’ of language and letters reveals the genealogy of conceptual frameworks that are still operative today. Résumé : La aparición fugaz y brillante de la figura del Fénix en el libro 15 de las « Metamorfosis » de Ovidio parece comportar, por el hecho mismo de que interviene en el seno del discurso de Pitágoras, una dimensión filosófica. Asimismo está cargada de una significación política, la « pietas » del joven Fénix ante el cuerpo de su padre es una evidente alusión a la virtud restablecida por Augusto y atribuida a Eneas, ancestro de la « gens Iulia ». Se analizan estos dos niveles de interpretación, examinándose asimismo la hipótesis según la cual el ave mítica representa al poeta-narrador que domina, no sin ironía, la palabra del filósofo y la puesta en escena del príncipe. Sühring, P. Was vermögen Philosophie, Kunst und Religion inmitten von Natur, Technik und Kapital? : Empedokles - Hölderlin - Marx / Musik & Ästhetik. 2010, 14, S. 51-73 Wang, K. Plato's Poetic Wisdom in the Myth of Er. Frontiers of Philosophy in China. 2009, 4, 2, p 282-293. Abstract: The interlink between myth and wisdom in Hellenic heritage is characteristically embodied in the Platonic philosophizing as regards the education and enculturation of the human psyche. As is read in the end of The Republic, the myth of Er turns out to be a philosophical rewriting of poetry to a large degree. For it engagingly reveals Plato's moral inculcation, philosophical instruction and poetic wisdom in particular, all of which are intended to guide human conduct along the right track for the bliss of the postmortem cycle, and put philosophy learning into first priority for the choice of the future life. Moreover, the transmigrate experience in the mystic overtone of “the Orphic-Pythagorean conglomerate”; is discussed with a intercultural reference to the Buddhist doctrines of samsara and karma. Vitek, T. Le sphairos d’ Empedocle et son substrat mythologique Elenchos. 2010, 31, 1, p 21-49 Varela Machado, O.L. Continuidad y discontinuidad en la filosofía de la naturaleza de la antiguedad clásica Ontology Studies 9, 2009 189-197 One of the current debates in nature philosophy focuses on the continuous or discontinuous structure of the world. This invites us to look -- as part of a basic assumption -- at the origin of an old and interesting debate which will open a sincere and profound discussion. It departs from the Pythagorean School passing by Parmenides including Zeno and Aristotle as the main thinkers, revealing the ”rupture” between the real and the apparent. Conclusion: the debate in science continues to be in force. Velardi, R. La testimonianza di Aristotele sulle origini della retorica Annali dell’ Instituto Universitario Orientale di Napoli (AION) (filol). 2008, 30, p 99-113 Résumé : Ricostruzione del punto di vista aristotelico sulle origini della retorica, attraverso l'esame delle testimonianze di autori successivi, di SE. 183b, 15-36 e di Rh. 3, 1, 1403b, 35-36, con particolare attenzione per il ruolo attribuito dal filosofo ad Empedocle e a Tisia Williams, G. Friends in high places Mathematical Spectrum 2010, 42, 2, p. 54–58. The article discusses number mysticism, which steams from the belief of the Pythagoreans that natural numbers hold the secret of the universe. The development of the number theory, the recognition of even, odd , prime and composite numbers can be traced back to number mysticism. Thabit ibn Qurra, an Arab polymath, is considered as the first serious contributor in the field of amicable numbers but it was the emergence of Euler in 1737 changed the scene of the field when he was able to discover a total of 62 amicable numbers. Vial, H. « Poète est le nom du sujet qui se brise et renaît de ses cendres » : le phénix dans les « Métamorphoses » d'Ovide (XV, Euphrosyne. 2008, 36, p 119-133

Wiśniewski , R. Si fama non fallit fidem: les druides dans la littérature latine de l’Antiquité tardive Antiquité Tardive. 2009, 17, 1, p 307-315 Summary: This paper deals with the reasons of intense, though short-lived, interest that a few Latin writers of the late 4<SUP>th</sup> century, namely Ammianus, Ausonius and the author of the Historia Augusta, had in the druids. In older scholarship it was commonly believed that the druidic passages in these authors testified to the revival of indigenous Gallic priesthood in the 3<SUP>rd</sup> century, and its survival in the 4<SUP>th</sup> century. Nowadays scholars are more cautious about the actual renaissance of the druidism. However, even if this revival was only a literary phenomenon, the question rises about its sources.I suggest that there were three reasons of the popularity of the druids. The first was the interest of the late ancient intelligentsia in one’s own people and family history: the druids were attractive both as a subject of research and as forefathers. The second was their philosophical profession, they were viewed as Gallic representatives of Pythagoreanism. The third was the fact that they were teachers, and so proper role models for Ausonius and his fellow-professors. The re-disappearance of the druids from the literature should be linked to the disappearance of Gallic pagan intellectuals. Zhmud, L. Mathematics vs philosophy : an alleged fragment of Aristotle in Iamblichus Hyperboreus. 2007, 13, 1-2, p 77-88 Résumé : Iamblich's Comm. Math. 25, p. 78, 818 Festa relies as much on Nicomachus and Ptolemy as on Aristotle and therefore cannot be considered as a fragment of Aristotle. Furthermore, its significance lies not in referring to Pythagorean optics, but in repeating the argument about the unique ability of mathematics to produce irrefutable proofs. But unlike Ptolemy, whose attitude to µαθήµατα was quite conscious and consistent, Iamblichus does not seem to draw any important conclusions from the words he repeats in passing. In a good Platonic fashion Iamblichus identifies mathematical objects as intermediary between immaterial being and the material world, so that for him µαθήµατα are the second best choice, not the first, as they were for Nicomachus. Woolerton, E. The roots of Lucretius' treeman, <i>De Rerum Natura</i> 2.702-3. Classical Quarterly. 2010, 60, 1, p 255-257 Abstract: Lucretius gives us four types of impossible portent, of which three are very familiar to us from myth: centaurs, chimaeras and conecti terrestria membra marinis, which is generally taken to be a reference to Scylla. The fourth portent, altos ramos egigni corpore uiuo, that is, a part plant, part mammal hybrid, does not appear to correspond to a specific mythological figure. Woolerton suggests that Lucretius' reference to tree-mammal hybrids is designed to engage with and discredit a now lost passage to Empedocles, who raised the possibility of such hybrids. This fits well with Lucretius' argumentative and poetic strategy throughout his treatment of atomic shape, and furnishes us with an origin for his otherwise mysterious tree-man. Zago, G. Porfirio, de abst. 1,10,2-3 (Ermarco, fr. 34 Longo Auricchio). Rheinisches Museum. 2009, 152, P 409-410 The Monument of Pythagoras of Samos at the Yacht Harbor in Pythagorion Samos

Internet http://ancienthistory.about.com/od/grecoromanmyth1/a/110910-Damon-And-Pythias.htm?nl=1 Damon and Pythias James Baldwin (1841-1925) wrote a collection of 50 stories he thought children of his day should know. He wrote them at the turn of the 20th century, but there is no reason to think the historical and legendary stories he told, transmitted from ancient times and the Renaissance to the era of Napoleon, should be forgotten. One of the stories is known as Damon and Pythias. http://classicpersuasion.org/pw/diogenes/dlpythagoras.htm THE LIVES AND OPINIONS OF EMINENT PHILOSOPHERS BY DIOGENES LAERTIUS, TRANSLATED BY C.D. YONGE LIFE OF PYTHAGORAS http://numenius-of-apamea.com/index.html Numenius of Apamea: Text, Translation and Commentary The contents of this website are taken from a doctoral dissertation that was completed in 1993 at the University of California, Santa Barbara. The dissertation was composed using a now obsolete DOS based program and printed out on a dot-matrix printer. Though the text is in obvious need of revision, I have found neither the leisure nor the will to re-type it into a modern graphics based word processor so that it might easily be altered. If there is an OCR option that is up to the task it has escaped me, however the advent of low cost scanning devices has made it a simple matter to produce graphic PDF files of recalcitrant text. So at the urging of several friends I have set it out here in the hope that even in its outdated form it might prove useful to those working in the fields of Middle Platonism and Plotinian studies. http://sites.google.com/site/empedoclesacragas/bibliography-a-z ᾿Εµπεδοκλῆς EMPEDOCLES - Empedocle - Empédocle - Empedokles - Empedoklés - Empédocles Bibliographie présentée par Tomáš Vítek, avec la collaboration de J.-C. Picot Tomáš Vítek met à jour régulièrement la bibliographie d'Empédocle parue dans son Empedoklés : II (2006). Installée désormais sur le web, elle est présentée au plus grand nombre. Pour s'informer des nouveautés concernant les études empédocléennes : http://sites.google.com/site/empedoclesacragas/home Pour connaître rapidement la bibliographie attachée à un fragment donné : http://sites.google.com/site/empedoclesacragas/bibliography-to-b-fragments Jean-Claude Picot Dernière mise à jour : 24 / 10 / 2010 Contact : empedocles.acragas@gmail.com Empedocles - Bibliography This bibliography includes all books and articles somehow devoted to Empedocles from 1500 until nowadays. It excludes most reviews, translations of modern works, and some more general works of reference. Simply, it was not possible to involve exhaustively all encyclopaedias, histories and surveys of Greek, European and World philosophy. I add to some titles very concise annotation or the discussed fragments and testimonies (in numbering of D-K). This bibliography is a work in progress. It is not quite completed and is not rid of all lacks and errors. I could personally verify only ca 70 % items, the other data were acquired from different sources. The list of bibliographies: (1) General bibliography (without Nr. 2); (2) Works of arts and art-historical articles; (3) 1500 - 1804; (4) 2002 - nowadays. Tomáš Vítek

Yahoo Newsgroups; Neoplatonism: start Jun 30, 2010 Jay Kennedy & "The Plato Code" http://groups.yahoo.com/group/neoplatonism/message/3392 Yahoo Newsgroups; Neoplatonism: Jul 29, 2010 Timaeus 32A http://groups.yahoo.com/group/neoplatonism/message/3468 Yahoo Newsgroups; Neoplatonism: Sep 9, 2010 Re: Philoponus on Nicomachus http://groups.yahoo.com/group/neoplatonism/message/3543 Yahoo Newsgroups; Neoplatonism: start Oct 26, 2010 One and Two as numbers or not http://groups.yahoo.com/group/neoplatonism/message/3613 Yahoo Newsgroups; Neoplatonism: start Oct 26, 2010 Moderatus on Number http://groups.yahoo.com/group/neoplatonism/message/3811 Yahoo Newsgroups; Neoplatonism: start Oct 28, 2010 Re: Moderatus and Theon on Number http://groups.yahoo.com/group/neoplatonism/message/3831 Film. Michelangelo Frammartino The Four Times. Le Quattro Volte Country: Italy, Germany, Switzerland. 2010. Language: Italian Producer: Susanne Marian, Philippe Bober, Gabriella Manfré, Andres Pfaeffli Executive Producer: Gregorio Paoness, Marta Donzelli, Gabriella Manfé Screenplay: Michelangelo Frammartino. Runtime: 88 Summary: Said to be inspired by Pythagoras’s belief in four-fold transmigration – by which the soul is passed from human to animal to vegetable to mineral, until completely purified – The Four Times is a genre-defying work of cinematic transcendence. The film, which delves into a world of tantalizing philosophy, unfolds in a gorgeous sequence of long takes, shot with vitality and imagination. While the film focuses initially on the perspective of an old shepherd – who will later become a baby goat, a giant tree and, hilariously, a lump of coal – the heart of Michelangelo Frammartino’s (The Gift) majestic sophomore feature lies in its exploration of the tangible versus the metaphysical. Frammartino captures the nebulous space between seeming and being, delighting his viewers with a lyrical approach to a topic that’s as magical as it is bizarre. Coasting across the countryside around an isolated Calabrian village, Frammartino’s spirited film showcases rural life in its various renditions, shifting from the everyday to the exceptional. Humour, pathos and dazzling camerawork inflect seemingly random sequences, evincing Frammartino’s deft sense of timing. He shows off his comic chops when a herd of goats runs haywire through the village and invades the shepherd’s home just moments before he departs for the netherworld. An homage, on one hand, to the physical beauty of life, this fantastical film is anything but earthbound. Frammartino’s ability to meld the prosaic with the sublime is a mark of extraordinary cinematic dexterity. His camera is always positioned at just the right angle, appearing to anticipate life instead of simply following it around. The Four Times embodies a certain candour, as authentic at times as any documentary, but Frammartino’s playful layering of style and theme make for an explosively original film. Dimitri Eipides