Newsletter 16

Stichting Pythagoras

Newsletter No. 16. Website E-mailaddress Editors June 2011 http://www.stichting-pythagoras.nl/ nico.bader@stichting-pythagoras.nl 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. They say Abaris arrived from Hyperborea carrying an arrow, taken by it, healing with it – then placed it in the hand of one particular person. His name was Pythagoras: the same extraordinary philosopher who played such a crucial role in seeding our western culture, in laying the foundations for this whole world we think we know. [In: Kingsley, P. A story waiting to pierce you. 2010. p 35. Contents: Introduction, News from the library, Acknowledgements, Busto di Pitagora, Napoli, Museo Archeologico Nazionale, Colophon Seminar On Pythagoreanism John Bremer; The Hero and the Philosopher Conferences / Symposia Miscellanea New books New book chapters Book reviews New journal articles 1 p 2 p 3 p 4 p 6 p 9 p 12 p 13

Introduction Thanks to all contributors to this Newsletter. Alas the interview with Peter Kingsley and information about his recent and future work could not be published in this Newsletter. There are “a number of unavoidable reasons” to give the answers to the interview questions in time. Harry Eighmey and his wife Maureen did visit the Library in Naarden; it was a most pleasant meeting and a good exchange of information and points of views. In Newsletter 12 we published Part 1 of the history of the Foundation/WUPO. A second part will be published in the next Newsletter. Although the information is not complete, we believe it is good to have it published. Our readers are asked to send us information they may have or know about this history. 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 There is some delay in activities, due to a dip in motivation. There is a danger to go down due to its own success. Dramatic changes in communication means (Internet, email, newsgroups…) ask for a different approach. From the dusty library, studying endless indexes we have come to the bright computer screen with a “one-click trial-information item” system. Our predessors had the problem of the time-consuming searching for relevant information, resulting in finding just ‘the tip of the iceberg’ and of costly spreading this information via paper mail to a limited circle of readers. We have the problem of the time-consuming processing and dealing with too much information, of tracing the important searchers and trends and of a ‘free’ emailing to a worldwide readers community. Besides this there is little response to the given information. Secondly promised information is not always given and at last information asked for does not always receive reactions. There is no clear solution yet. Please send us your opinion and suggestions how to continue. Thank you. Nico Bader

Acknowledgements The Pythagoras Foundation thanks the following individuals for their contributions and generosities: John Bremer, Harry Eighmey, Nancy J. Grayson, Leslie Greenhill, Christiane L. Joost-Gaugier, Jay Kennedy, Patrick Lee Miller, Constantinos Macris, Jean-Claude Picot, Marcel Roggemans and Sebastian Moro Tornese. Napoli, Museo Archeologico Nazionale, Busto di Pitagora, Villa dei Papiri di Ercolano 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)

On Pythagoreanism VIII International Archai SeminarIV Escola de Altos Estudos Archai/CAPES Universidade de Brasilia August 22-26, 2011 The Archai Group, from the University of Brasilia, along with the French Centre National de la Recherche Scientifique (CNRS, Paris), and the support of the Escola de Altos Estudos /CAPES, is glad to announce a seminar On Pythagoreanism to be held in Brasilia (Brazil) from 22nd to 26th August, 2011. http://www.pythagoreanism.archai.com.br/ Damon and Pythias: study for a painting (Guercino, 1606-1666 - from Bolognese School). Pen and brown ink. In Turner. Italian Baroque Drawings. British Museum Prints and Drawings Series, London, 1980, no. 45. Description: on the left Damon kneels on the ground while an executioner prepares to behead him; in the centre, seated on a throne, is the tyrant Dionysius the Younger with two attendants; he turns to his left, raising his left hand in surprise, to see Pythias at his side kneeling and gesturing to himself in an act of submission; behind Pythias stands another figure. Cf. Porphyry. Vita Pythagorae 60-61. Supporting Bodies IAPS - International Association for Presocratic Studies SBEC - Sociedade Brasileira de Estudos Clássicos CAPES - Brazilian Ministry of Education CNPq - Conselho Nacional de Pesquisa/ Brazilian Ministry of Science SBP - Sociedade Brasileira de Platonistas UnB - Universidade de Brasília

About the Seminar Controversy regarding the modern history of criticism about Pythagoras and his movement still continues. Overcoming both the dilemma between skepticism and faith in the sources and the claim to achieve a single hermeneutical key to solve the “Pythagorean question”, the Seminar aims to follow the Pythagorean traditions throughout history, as moments of a historical route resulting in a polyhedral image of one of the greatest intellectual phenomena in Western history. The seminar wishes to bring together scholars from all over the world who have dedicated themselves to studying this field in the last 30 years, in order to draw a line and define a new status quaestionis for the new wave of research on Pythagoreanism in the 21st Century. All the papers of the speakers will be available to the participants a few months before. This will allow the Seminar to be dedicated more directly to the debate of the pre-read papers: each participant will present only a 20 minute oral abstract of the written paper, and 30 minutes of discussion will follow. English will be the preferred language for the written papers. The oral abstract and the discussion could be in any other language. Confirmed Speakers Alberto Bernabé (Universidad Complutense de Madri, Spain) André Laks (Universitè de Paris-Sorbonne, France) Beatriz Bossi (Universidad Complutense de Madri, Spain) Carl Huffman (De Pauw University, Indiana, USA) Christoph Riedweg (Universität Zürich, Switzerland) Constantinos Macris (CNRS-Paris, France) Dominic O’Meara (Université de Fribourg, Switzerland) Francesc Casadesus Bordoy (Universitat de les Illes Balears, Spain) Giovanni Casertano (Università degli Studi di Napoli, Italy) Johan C. Thom (University of Stellenbosch, South Africa) Leonid Zhmud (Russian Academy of the Sciences, St. Petersburg, Russia) Livio Rossetti (Università degli Studi di Perugia, Italy) Luc Brisson (CNRS –Paris, France) Mauro Bonazzi (Università degli Studi di Milano, Italy) Omar Álvares Salas (Universidad Nacional Autónoma de México, Mexico) Richard McKirahan (Pomona College, California, USA) Sylvana Chrysakopoulou (Foundation of the Hellenic Parliament, Greece) Thomas M. Robinson (University of Toronto, Canada) Clara Acker (Universidade de Brasília, Brazil) Edrisi Fernandes (Universidade de Brasília, Brazil) Marcus Mota (Universidade de Brasília, Brazil) Miriam Campolina Peixoto (Universidade Fed. de Belo Horizonte, Brazil) Fernando Santoro (Universidade Fed. do Rio de Janeiro, Brazil) Gabriele Cornelli (Universidade de Brasília, Brazil) INVITED DISCUSSANTS: Miriam Campolina Peixoto (Universidade Fed. de Minas Gerais, Brazil) Fernando Santoro (Universidade Fed. do Rio de Janeiro, Brazil) Dennys G. Xavier (Universidade Fed. de Uberlândia, Brazil) Fernando Rey Puente ((Universidade Fed. de Minas Gerais, Brazil)

For the Pythagoras Foundation, 25 June 2011. The Hero and the Philosopher by John Bremer Institute of Philosophy, Ludlow, VT, USA The first word of Homer’s Iliad is ‘anger’, and ‘the goddess’ is invited or asked or implored or commanded to sing the anger, the anger of Achilles. She is not asked to sing about it or its consequences but to sing it. Thus, the whole epic could be understood to be a revelation of ‘anger’—what it is, as we might say, its nature. But it cannot be such a universal revelation as this suggests, for it is not just ‘anger’ but ‘the anger of Achilles’ that is to be sung. Essentially, there are no universals in Homer, only particulars—what we might call universals, but only embodied in particular heroic acts of particular heroes. Homeric language is historical or pseudo-historical narrative, not philosophical; we would search in vain for a discussion simply of ‘anger’. We—like the heroes themselves—do not enter the universe of the Iliad at its beginning. By the time we learn of the quarrel between Achilles and Agamemnon, there has been a sequence of ‘angers’. Clearly, Apollo’s priest is angry that Agamemnon will not accept the ransom for his daughter; Agamemnon is on the edge of anger, if not actually angry, in his brusque dismissal of the priest. The priest prays to Apollo who, in turn, also becomes angry at the disrespectful treatment, and punishes the Achaeans. At this point Achilles intervenes and calls an assembly. It is not stated, but it is obvious that, prior to doing so, he has consulted with the prophet Kalchas and knows full well what he is going to report—namely, that Apollo’s anger is due to Agamemnon’s refusal to give back the priest’s daughter. Achilles may well be frustrated because the fighting has stopped—because he is only there for the fighting and to win the only thing worth having, namely, glory (or to yield it to others)—but he is not yet angry. Agamemnon, on the other hand, is immediately and openly angry and for at least three reasons: first, he has been out-maneuvered by Achilles: second, he has been revealed as the cause of the Achaians’ distress: and, third, he has to give back the daughter who was his prize. He does not get angry at Apollo—nothing could be gained by that—but instead gets angry at Achilles who has, incidentally but importantly, laid bare Agamemnon’s weakness as a leader; as ‘king of men’ he has been a failure, exposed before the whole army, and all because of his touchiness and insecurity over his own pride of place. His response, as we all know, is to mollify Apollo by giving back the girl, and to take Achilles’ prize away from him, thus dishonoring him and glorifying himself. At the behest of Athena and Hera, Achilles allows this to happen, but the loss of honor, signalized by the confiscation, is what angers Achilles. Faced with Agamemnon’s claim to be the source of honor—so that he can give and take away prizes and the glory they represent—Achilles in his sorrow

and anger asks his mother, Thetis, to appeal to Zeus to vindicate him, to honor him by making the Achaians (including Agamemnon) restore his honor. Zeus agrees to do this—not, it should be noted because it is right, but because he is under an obligation to Thetis. The stage, as it were, is now set, but it must be emphasized that although the song of the Iliad is ‘the anger of Achilles’, it occurs in a complex pattern of previous feelings, characters, and actions. Humans never begin at the beginning—not even the anger of Achilles—but are always plunged into the middle of things, in medias res. Although Plato is critical of all the poets and especially of Homer, he clearly understands the philosophical problem underlying the action of the Iliad. To ask whether Agamemnon or Zeus is the greater source of honor, as Achilles does, is to ask whether honor is conventional (as Agamemnon supposes, in the keeping of the king of men) or ‘natural’ (if, in fact, the will of Zeus is accomplished and if he may be equated with nature). It is a variant of the old antithesis between custom (nomos) and nature (phusis), at least raising the question whether there is anything higher than custom. It is Plato’s Polity (or Republic, as it is usually and mistakenly called) that is the counterpart of Homer’s Iliad, and whereas Achilles seeks ‘the right manner of life’ in his actions, to go beyond the conventional heroic way, and discover in action, not thought, if ‘natural’ honor is the highest ‘good’, Socrates seeks it in the city of words, in conversation, in the realm of ideas, and in the nature of the soul itself. For Achilles, the degree of honor is measured by the value of the prizes, awarded essentially by the assembly under its ‘king of men’; but this is misleading because there isn’t anything called ‘honor’ over and above or beyond the prizes. When Agamemnon takes Achilles’ prize, he takes away his honor; whatever he had done to merit the award no longer exists and is inconsequential. To storm a city single-handed is meaningless unless Achilles has a prize, something to show for it, something extant to be seen and talked about; without a prize, something concrete, the storming of the city will not exist for long—it is a past event, not a current object-prize, and is subject to the vagaries of time and memory. Whether Achilles stormed the city will only endure if the prize for doing it can be displayed in some way, including in narrative poetry. Thus fame and reputation are critical; the deeds ‘that men do live after them’, and if they are forgotten and the prizes perish, so immortality—the only kind recognized—also disappears. For Plato’s Socrates, over and above all the individual strivings of the heroes (and also those of ordinary men), there exists an idea, a form, a universal, giving them a reality which not only persists after the war is over, but also persists for ever. It is the idea of honor, or justice, or courage that continues in existence when the deeds are all done, the heroes who performed them have all died, the words have gone silent, their written descriptions have been erased, leaving no trace. But no trace is needed, for the idea endures, and if a new race of men arose, they would find the idea of justice or courage awaiting them, as it were, if indeed they were men like us with souls like ours, with the creative power to recognize the good in all its forms, and to bring it into active being.

Of course, a new race of men is constantly arising as generations come and go, and they—each individual—find themselves in medias res. The problem seems to be how to be aware of the past without being controlled by it, as Achilles and Socrates, in different ways, tried to make it explicit, and then to examine and evaluate the past which is their present. For us, in nothing is this more evident than in the search for knowledge and what it means to know, than in learning and what it means to learn. By the time we can ask the question about what it means to learn, we have all ‘learned’ a very great deal, and, like Achilles, we find ourselves in the middle of patterns of ‘thought’ that may well be conventional and so strong that we need the excellence of an Achilles—or a Socrates—to ask whether or to what extent, if any, they are natural. This is the motive for the first half of the Polity in which Socrates guides Glaucon and his brother into recognizing what they had already ‘learned’—ironically, by criticizing and purifying it. When the soul seeks to learn, it must always remember that it is itself, the soul, that is doing the seeking, and that ultimately it must therefore know itself and what has happened to it. The old scholastic adage applies: Quiquid recipitur, ad modum recipientis recipitur, or ‘Whatever is received, is received according to the mode of the recipient’. It is customary to accord to Pythagoras the honor of first using the word ‘philosophy’ and to insist on the meaning of its two Greek parts, ‘the love’ of ‘wisdom’. Plato took this term and contrasted the lovers of wisdom, the philosophers, with those who claimed already to have it, the Sophists. It was as if the latter already possessed it, while the former were possessed by it. What is ironical is that the Sophists, by selling what they ‘knew’, brought others under their control and thus stifled their free and creative movement, their learning, while philosophers, by being controlled by their love, encouraged others to seek and learn with them. It would take too long to explore now the various meanings attached to ‘love’ and ‘wisdom’, as well as to ‘soul’, but it should be noted that Plato uses the word ‘philosophy’ and its cognates very sparingly: ‘philosophy’ (137 times), ‘philosopher’ (122 times), and ‘philosophize’ (53 times); in all the dialogues 312 times in toto—and 109 of them in the Polity. Just as Homer and his goddessmuse do not sing about the anger of Achilles, but sing the anger itself, so Plato and his Socrates do not sing about philosophy but sing philosophy itself. The dialogue, the conversation, is philosophy. That is why Plato rarely uses the word; he has no need to, because he is eternally doing what it is, what it means. And that is why he calls it ‘the greatest music’.

Conference presentations Séminaire de la Société d’Études Platoniciennes Année universitaire 2010-2011 « Platon et ses prédécesseurs » (Université Paris Ouest), 7 janvier 2011. "Platon et la psychologie de ses prédécesseurs" Radcliffe Edmonds III. « A Lively Afterlife and Beyond: The Soul in Plato, Homer, and the Orphica » Anne-Laure Therme. « Quelles racines empédocléennes chez Platon ? » Denis O’Brien. « La connaissance et son objet : Parménide, Platon, Empédocle ». Colloque International; « Les Présocratiques dans la poésie latine » Université Paris-Sorbonne. 13 et 14 janvier 2011 Jeudi 13 janvier Matin : Lucrèce (présidence : M. Carlos Lévy) M. Francesco Montarese (Londres) : « Was Lucretius dependent on Epicurus for his critique of the Presocratics in book I ? » Mme Sabine Luciani (Grenoble) : « Lucrèce et les psychologies présocratiques » M. Thomas Baier (Würzburg) : « Lucrèce, les Présocratiques et la rhétorique » M. Alessandro Schiesaro (Rome) : « Back to the Presocratics : the Virgilian dossier » Après-midi : Empédocle (présidence : M. Aldo Brancacci) M. David Sedley (Cambridge) : « The Empedoclean allusion at Lucretius DRN 2.1081-3 » M. Jean-Christophe Jolivet (Lille) : « Présence d’Empédocle dans l’Énéide » M. Damien Nelis (Genève) : « L’amour empédocléen : how far can you go ? » Mme Jacqueline Fabre-Serris (Lille) : « Enjeux moraux et idéologiques des usages d’Empédocle au livre 15 des Métamorphoses : une réponse d’Ovide à Virgile (Enéide 6 et 8) » Vendredi 14 janvier (Maison de la Recherche, salle D.35) Matin 9h15 : Horace (présidence : Mme Sylvie Franchet d’Espèrey) M. Paolo Fedeli (Bari) : « Horace et Archytas de Tarente (Carm. 1,28) » M. Aldo Setaioli (Perugia) : « Horace et le Pythagorisme » M. Marcos Martinho (São Paulo) : « Horace et Démocrite : le poète entre l’enthousiasme et le labeur » M. Philip Hardie (Cambridge) : « Horace et Empédocle » Après-midi : Ovide (présidence : M. Aldo Setaioli) Mme Hélène Casanova-Robin (Paris) : « Reconstruire une poétique des Présocratiques : le feu chez Ovide » Mme Anne Videau (Paris) : « Les Métamorphoses d’Ovide : une cosmogonie originale » Mme Giulia Sissa (Los Angeles) : « L’ontologie fluide de l’amour (Lucrèce, Ovide et les élégiaques) Martin Dinter (Londres) : « La littérature néronienne et les Présocratiques » Myth and Literature in Ancient Philosophy. Faculty of Classics, University of Cambridge (Room G.21). 15-16 April 2011 Catherine Osborne (University of East Anglia), Literary Genres and Judgements of Taste: Aristotle on Empedocles and Plato on Science and Mythology Laetitia Monteils-Laeng (University of Caen), Destiny and Responsibility: What is Left for Human Freedom in the Myth of Er? with comments by Carol Atack (Lucy Cavendish College, Cambridge) Chiara Ferella (University of Pisa), The Proem of Empedocles' Physika: Towards a New Reconstruction with comments by Ben Harriman (Magdalene College, Cambridge)

Almagor, E. "Food for Thought: Plutarch on Animals, Humans and the Food-Chain" In: The American University of Paris. salle 29. 29 mars 2011. The ancient biographer and philosopher Plutarch was a firm believer that animals deserve moral consideration and have a status which is not inferior to humans. In the two fragments of his discourse on the eating of meat (De esu carnium) he endorses ethical vegetarianism. For the first time, Eran Almagor relates ethical views of Plutarch concerning animals in his moral treatises to the descriptions of beasts within his biographies, two worlds that have been unfortunately cut asunder in research. By employing the connotations of animal imagery to denote inner irrational passions within the soul Plutarch succeeds in harnessing his philosophical views regarding animals to literary ends, such as the characterization of the hero, which reflect, in their turn, ethical considerations. In particular, Plutarch is able to show how the carni-vorous man is what he eats. Of special interest are the scenes in which the barriers dividing humans and animals are either implied or presented as transgressed, e.g. by persons transforming into meat or flesh devoured by beasts and living creatures. The reciprocity alluded to in the similar behavior of humans and beasts in this portrayal of the food-chain may point to the fact that, for Plutarch, animals do not exist solely for the benefit of humans and that they merit better treatment. D'Ambrosio, U. FROM EA, THROUGH PYTHAGORAS, TO AVATAR: DIFFERENT SETTINGS FOR MATHEMATICS p 1-20 In: 34th Conference of the International-Group-for-the-Psychology-of-MathematicsEducation, JUL 18-23, 2010. Fed Univ Minas Gerais, Belo Horizonte, BRAZIL VOL 1 Book Series: PME Conference Proceedings. 2010 Abstract: In this paper I set two different cultural scenarios from the past (Ea in Ancient Iraq, Pythagoras in Ancient Greece) and one from the present (Avatar the movie). Ea, the god of wisdom, is a central figure in the episode of the flood, in Ancient Irk. Pythagoras is representative of the abstract and spiritual nature of Greek theoretical mathematics in Ancient Greece. Avatar, set in our days and fantasying about the future, synthesizes the most pressing social and environmental concerns of our society and, at the same time, reveals the most advanced advances of science and mathematics. In all the three different settings, we recognize theoretical mathematics, practiced by an intellectual elite, coexisting with practical mathematics, the domain of the people. Mutual exclusion in the two ancient scenarios was part of an accepted social stratification. It took many generations to reach an approximation which resulted in a cross fertilization of both the theoretical and the practical mathematics. In our days, the demands for alleviating the social stratification (inclusion) and the urgency of finding solutions to environmental disaster asks for a faster approximation of the mathematics developed in the academia and the mathematics needed and practiced by common people. A new thinking in education is necessary. Balbino Soares Pereira, A. O Conceito Pitagórico de Metempsicose In: Sociedade Brasileira de Platonistas (SBP) e o Grupo Archai promovem, mais uma vez em conjunto, o XI Simpósio Internacional da Sociedade Brasileira de Platonistas e VII Seminário Internacional Archai. O tema do encontro será o diálogo ‘Simpósio’ (Banquete) de Platão. O Evento acontecerá entre os dias 17 e 20 de maio de 2011, na Universidade Federal de Pernambuco (UFPE), em Recife. Quarta feira, 18 de Maio de 2011 Boys-Stones, G. Numénius on the soul In: La prochaine séance du sém. "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), aura lieu le 19 mai 2011. BORGES, L.N. O emprego das adverbiais no Somnium Scipionis p 47 - 52 In: Semana de Estudos Clássicos (25. : 2011: Araraquara, SP) Dionísio: travessias e transmutações: 25 anos! : anais / XXV Semana de Estudos Clássicos ; V Fórum. Acadêmico de Estudos Clássicos, Araraquara, 04-07 out. 2010 (Brasil). – Documento eletrônico. - Araraquara : Laboratório Editorial FCL - UNESP, 2011. – Modo de acesso: http://www.fclar.unesp.br/ec/anais ISBN: 978-85-87361-74-5 Cingano, E. ‘Exploring Sympotic Settings: Stesichorus, Ibycus, Simonides’ In: SYMPOTIC POETRY. A COLLOQUIUM. Oxford, March 31st - April 2nd 2011 http://www.classics.ox.ac.uk/sympoticpoetry/ Kontossi, S. Aspects of mathematics and music in ancient Greece In: MCBE'10/MCBC'10 Proceedings of the 11th WSEAS international conference on mathematics and computers in business and economics and 11th WSEAS international conference on Biology and chemistry. 2010. ISBN: 978-960-474-194-6 In this paper, through the study of the different theories concerning the calculation of intervals sizes which were developed in Ancient Greece, we are going to undertake a concise historical overview of the relationship established between music and mathematics through the Pythagorean, Euclidean and Aristoxenian tradition. Kreyszig, H. The Transmission of Pythagorean Arithmetic in the Context of the Ancient Musical Tradition from the Greek to the Latin Orbits During the Renaissance: A Computational Approach of Identifying and Analyzing the Formation of Scales in the De Harmonia Musicorum Instrumentorum Opus (Milan, 1518) of Franchino Gaffurio (1451-1522) p 392-405 In: 1st International Conference on Mathematics and Computation in Music, MAY 18-20, 2007 Berlin. Source: MATHEMATICS AND COMPUTATION IN MUSIC Book Series: Communications in Computer and Information Science. Volume: 37. 2009. Abstract: On the occasion of the three hundredth anniversary of Leonhard Euler (1707-1783) and the focus of his contribution to the mathematical explanation of scales, the quest arises to examine similar contributions of music theorists that lived prior to Euler. In this paper we selected from the trilogy (Theorica musicae, 1492; Practica musicae, 1496; De harmonia musicorum instrumentorum opus, 1518) of the eminent Renaissance scholar, musician, theorist and composer Franchino Gaffurio (1451-1522) his third work of 1518. In particular, using a modern elementary number theoretic approach, we discovered a number generating function in closed form, which we called a Gaffurio number generating Junction, that generates the tones of the Pythagorean scale. The number generating function is of the form f (n, m) = p(n) q(m), where p and q are primes, and n and m are elements of /N-0. Here, Gaffurio chooses the smallest primes p = 2 and q = 3, thereby with this ratio p / q denoting the interval of the diapente and he varies the integral exponents n and m from 0, 1, 2, 3, ... and in the process constructing a series of numbers signifying the precise placement of the tones within the gamut. His approach is in line with medieval mathematics, which focuses on elementary number theory and can be seen as a precursor to Euler's Potenzennetz (grid of proportions). This paper embeds our results in Gaffurio's oeuvre and his times and includes a concise of overview of his biography with an emphasis on his pedagogical and literary contributions.

Our approach fills a gap in research, because although Latin music theorists from the era of musical humanism frequently include mathematical approaches to the Greek systema teleion and Guidonian system, as projected onto the monochord, they do not disclose the nature and specific details of the mathematical calculations which inform the natural numbers included in both the manuscript and early printed editions. Mendonca, I. de Castro 19. Análise do emprego das formas nominais dos verbos em Somnium Scipionis, de Cícero De Re Publica, VI 9-29 p. 147 - 152 In: ANAISDA XXV SEMANA DE ESTUDOS CLÁSSICOS. V Fórum Acadêmico de Estudos Clássicos (V FAEC). DIONISO: TRAVESSIAS E TRANSMUTAÇÕES 25 anos! LABORATÓRIO EDITORIAL FCL-UNESP 2011. Rabelo, S.G. 28. O emprego dos casos latinos no Somnium Scipionis p. 214 - 219 In: ANAISDA XXV SEMANA DE ESTUDOS CLÁSSICOS. V Fórum Acadêmico de Estudos Clássicos (V FAEC). DIONISO: TRAVESSIAS E TRANSMUTAÇÕES 25 anos! LABORATÓRIO EDITORIAL FCL-UNESP 2011 Zhmud, L. « Phusis in the Pythagorean tradition » In: Séminaire de la Société d'Études Platoniciennes (etudesplatoniciennes.eu) Platon et ses prédécesseurs sous la direction de Luc Brisson, Arnaud Macé et Olivier Renaut Le vendredi 27 mai, 2011. Miscellanea Leslie Greenhill 2011 lesgreenhill@yahoo.com.au LINKING PLATO’S DESIGN FOR ATLANTIS TO THE LAYOUT OF VITRUVIAN MAN AND SPECIFICATIONS FOR ANCIENT WAR MACHINES Synopsis; Entwined Designs Vitruvian Man as rendered by Leonardo da Vinci is one of humankind’s most famous and influential images. Detailed specifications for the layout of Vitruvian Man’s body were given more than 2000 years ago by the Roman architect Vitruvius in his famous treatise The Ten Books on Architecture. The startling geometric source of the specifications has been recovered. The same geometry has a direct link to ancient images of the cosmos and the world, Plato’s famous design for the lost island of Atlantis, and remarkable material in the Histories by the Greek historian Herodotus. The histories of mathematics, architecture, design and culture are radically changed in this work. What comes to light here has no precedent. The text and illustrations in Entwined Designs are not just to be read and viewed, they are to be digested and experienced. Stephen M. Phillips News item #4 (July 5, 2010) A critique of Dr Kennedy's discovery of musical structure in Plato’s writings p 5-11 See: http://www.smphillips.8m.com/news.html This section lists (latest news first) those recent discoveries in theoretical and experimental particle physics that may have relevance to the remote-viewing of the subatomic world by the Theosophists Annie Besant and C.W. Leadbeater and to my interpretation of their observations. It also discusses other contemporary discoveries or developments that are relevant to my researches in both sacred geometries and the mathematical nature of the seven musical scales.

New books Alsina, C. La secta de los números : el teorema de Pitágoras Barcelona : RBA , 2011. mainly in their death or burials, often linked to mysterious or peculiar circumstances that now defy interpretation: Ibycus’ violent death and ‘miraculous’ vengeance by a flock of cranes, an episode which finds an echo in a Pythagorean tale and which later passed into the realm of proverb, inspiring a dramatic ballad by Schiller; Stesichorus’ complex mausoleum, a peculiar Hellenistic creation probably influenced by Pythagorean symbolism, which left traces in a motto (Panta okto) and in the traditions of medieval and modern Catania; the violation of Simonides’ grave and its punishment (also related to a proverb, “Do not move Camarina”), described by the poet himself in a Callimachean aition which, until the first half of the twentieth century, was believed to be an epigram. After Late Antiquity, the memory of these lyric poets survived for centuries preserved in anecdotal tales, random quotes and a few epigrams, evenwhen their poems, bodies and monumental graves had been destroyed by time and human impiety. Buried in papyri and in the manuscripts of epigrammatic anthologies, Ibycus, Stesichorus and Simonides would need a few more centuries to rise again from their grave as wise men Balaudé, J.F. Le savoir-vivre philosophique : Empédocle, Socrate, Platon Grasset Et Fasquelle. 2010. Collection : le college de philosophie. ISBN 9782246585817 Resume: De la connaissance à la vie, et de la vie à la connaissance : en s'installant dans cette circularité radicale, les initiateurs grecs de la philosophie ont tâché de répondre à la difficulté que résume la question lancée par Socrate à ses contemporains : "Comment doiton vivre ?". Pour ceux-là, connaître est tout sauf une activité désincarnée, et la vie humaine ne peut atteindre sa perfection propre qu'en se forgeant dans la quête d'un savoir sur soi, sur les autres et sur le monde.En ce sens, c'est un savoir-vivre fondamental qui s'élabore dans les démarches contrastées, mais à bien des égards convergentes, des trois penseurs liminaires de la réflexion éthique que sont Empédocle, Socrate et Platon.Dans cette perspective, le présent essai se donne pour objet d'explorer de multiples facettes du projet philosophique, tel qu'il s'est affirmé entre le Vème et IVème siècles, interrogeant la visée de perfection individuelle et collective, la dimension réflexive et l'exigence pratique constitutives du mode de vie poursuivi. Beer, M. Taste or Taboo: Dietary Choices in Antiquity. Totnes: Prospect Books, 2009. ISBN 9781903018637. This book looks at the way in which food was employed in Greek and Roman literature to impart identity, whether social, individual, religious or ethnic. In many instances, these markers are laid down in the way that foods were restricted, in other words, by looking at the negatives instead of the positives of what was consumed. Michael Beer looks at several aspects of food restriction in antiquity, for example: the way in which they eschewed excess and glorified the simple diet; the way in which Jewish dietary restriction identified that nation under the Empire; the way in which Pythagoreans denied themselves meat (and beans); the way in which the poor were restricted by economic reality from enjoying the full range of foods. These topics allow him to look at important aspects of Graeco-Roman social attitudes, such as republic virtue, imperial laxity, Homeric and Spartan military valour, social control through sumptuary laws, and answers to excessive drinking. He also looks closely at the inherent divide of the Roman world between the twin centres of Barbantani, S. Three Burials (Ibycus, Stesichorus, Simonides). Facts and fiction about lyric poets in Magna Graecia in the epigrams of the Greek Anthology. Edizioni dell'Orso, Alessandria 2010. Originally presented at the conference "Greek Poetry in Italy", Georgetown University, Villa LeBalze, Fiesole, June 11-12, 2007. ISBN 9788862742603 This work focuses on Hellenistic and Roman epigrams dedicated to three lyric poets who were born or died (or both) in Italy: Ibycus, Stesichorus and Simonides. Although included in the canon of the Nine Lyric Poets (AP 9.184 and AP 9.571), and frequently quoted and praised in the scholastic and rhetorical environment, these three authors did not enjoy the same popularity as their ‘colleagues’ Anacreon, Sappho and Pindar as ‘stock characters’ celebrated in epigram. For some reason epigrammatists found inspiration

Greece and Rome and how it is expressed in food and its consumption. and the claim to achieve a single hermeneutical key to solve the Pythagorean question, in it searches are made throughout the history of tradition looking for an image sufficiently plural in order to understand Pythagoreanism in accordance with its irreducible articulation of bíos and theoría, not despite it. The setting of the community and its bíos is understood as central element for Pythagorean identification. An analysis of the two theories that more decisively contributed to the definition of Pythagoreanism throughout history, the transmigration of the immortal soul and the doctrine of numbers, attempts to define the conditions of possibility to assign them to the earlier Pythagoreanism and the ways in which these have contributed throughout history to the definition of Pythagoreanism as historiographical category. Presocratic sources, the platonization of Pythagoreanism, Aristotle's testimony about the "so-called" Pythagoreans, the hellenistic Pseudoepigrapha and Pythagoreanism in imperial age are understood as moments of an historical route resulting in a polyhedral image of one of the greatest intellectual phenomena in Western history. Bernabé, A. Platão e o orfismo: diálogos entre religião e filosofia. São Paulo, Annablume, 2011. Coleção Archai n. 5. ISBN 978-85-391-0239-6 O livro procura compreender o alcance das possíveis influências órficas em Platão, das quais muito se fala, mas sobre as quais não existem estudos modernos, através da análise dos textos platônicos que possam refletir idéias órficas e dos textos que conhecemos como órficos que possa ter influenciado o filósofo. Boom, G.M. van Symbols of the transcendent : the implications of infinity in Nicholas of Cusa Dominican School of Philosophy and Theology (Berkeley, Calif). 2010. Introduction – Part 1. Transmission and translation. Did Cusa know Greek? The Platonic corpus in the west : Greek into Latin. Plotinus. The Greek fathers. Proclus. Pseudo-Dionysius and the Areopagite. The Liber de causis and theology of Aristotle. The Latin Platonist tradition. Augustine. Meister Eckhart. Thomas Aquinas Part 2. Mensura and infinity. Mensura. Number and the one. Negation and the one. Geometry and mathematics. "Pythagoreanizing Platonism". Infinity -Part 3. Naming God. "The meaning of a word". Learned ignorance. The Pythagorean connection. Maximum and minimum. Coincidence of opposites. Conjecture. Notother -Conclusion. Cox, R.E. Tajemství nebeského žebř íku : posvátná vě da o nesmrtelnosti : z védských, egyptských, hebrejských a pythagorejských tradic (Secret Heavenly Ladder: Sacred Science of Immortality: the Vedic, Egyptian, and Hebrew traditions pythagorejských) V Praze : Elfa, 2010. Di Stefano, E. La Triade divina in Numenio di Apamea Un'anticipazione della teologia neoplatonica CUECM. 2010. Collana: Symbolon ISBN: 9788866000075 I frammenti teologici di Numenio, filosofo platonico pitagorizzante del II secolo d.C., che, secondo una felice espressione del Theiler, costituisce la più importante figura medioplatonica della Vorbereitung des Neuplatonismus, mostrano già chiaramente tre distinti livelli del Principio, anche se non assegnano al Primo Principio uno statuto meta-noetico. Questa di Numenio è una procedura complessa, che gerarchizzando il divino in tre distinti momenti, anticipa di certo la teologia plotiniana. Nella concezione metafisica numeniana emerge infatti, al di sopra dell’anima del mondo e dell’intelletto demiurgico, un Principio superiore che Numenio chiama “primo Dio”, o “primo Intelletto”, il quale, pur non situandosi al di là Brisson, L. Vie de Pythagore, Iamblichus Paris : Les Belles Lettres, 2011. Cornelli, G. Em busca do pitagorismo: o pitagorismo como categoria historiográfica Tese de Doutorado. Universidade de São Paulo. Faculdade de Filosofia, Letras e Ciências Humanas. 2010. Resumo em inglês: This thesis explores the definition of Pythagoreanism as historiographical category, seen as solution for the controversial general framework of modern history of criticism about Pythagoras and his movement. Overcoming both the dilemma between skepticism and faith in the sources

dell’essere e dell’intelletto, presenta tratti di trascendenza ontologica e ineffabilità epistemica, che necessariamente lo rendono affine all’Uno plotiniano. I tre Dei numeniani si presentano, peraltro, come tre differenti livelli di attività mentale, dei quali il secondo, cioè il noei`n, costituisce l’attività distintiva del secondo Dio. Anche il primo Dio può noei`n, ma solo chiedendo l’aiuto del Secondo, perché ciò che lo distingue non è il Pensiero, bensì l’Uno-Bene, che è al di sopra dell’Intelletto, cioè del noei`n. Numenio definisce il primo Dio come un’Intelligenza allo stato di quiete, perché non effettua alcun atto di pensiero, mentre definisce il secondo Dio come un’Intelligenza in atto, la cui funzione propria è appunto il pensare. In tal modo, il primo Dio pensa solo in quanto utilizza come assistente il secondo Dio, che è l’Intelletto in atto (ejn proscrhvsei tou` deutevrou noei`n). A sua volta, il secondo Dio, che per creare un mondo materiale ha bisogno dell’aiuto del terzo Dio, abbandona la novhsi~ed esercita la diavnoia, che è la caratteristica propria del terzo Dio. Handlung und das Bild, um zu erkennen, ob alles dem Sujet angemessen ist." Ralph Häfner stellt Poussins rätselhafte 'Landschaft mit Numa Pompilius und der Nymphe Egeria' (heute im Musée Condé, Chantilly) in den Kontext der intellektuellen Debatten in Rom um 1630. In seiner formalen Konzeption entfaltet das Gemälde mannigfaltige Aspekte der Bedeutung, die sich einer genaueren Allegorese erschliessen. 'Handlung' und 'Bild'Komposition sind im Sinne pythagoreischer Denkfiguren stimmig zu lesen." Heller-Roazen, D. The fifth hammer : Pythagoras and the disharmony of the world New York : Zone Books, 2011. Into the forge -- Of measured multitude -Remainders -- Disproportions -- Ciphers -Temperaments -Of measureless magnitude. Hillar, M. From logos to trinity : the evolution of religious beliefs from Pythagoras to Tertullian Cambridge ; New York : Cambridge University Press, 2011. "This book presents a critical evaluation of the doctrine of the Trinity, tracing its development and investigating the intellectual, philosophical, and theological background that shaped this influential doctrine of Christianity. Despite the centrality of Trinitarian thought to Christianity, and its importance as one of the fundamental tenets that differentiates Christianity from Judaism and Islam, the doctrine is not fully formulated in the canon of Christian scriptural texts. Instead, it evolved through the conflation of selective pieces of scripture with the philosophical and religious ideas of ancient Hellenistic milieu. Marian Hillar analyzes the development of Trinitarian thought during the formative years of Christianity from its roots in ancient Greek philosophical concepts and religious thinking in the Mediterranean region. He identifies several important sources of Trinitarian thought heretofore largely ignored by scholars, including the Greek middlePlatonic philosophical writings of Numenius and Egyptian metaphysical writings and monuments representing divinity as a triune entity" Gálvez, P. Hypatia Barcelona : Debolsillo, 2010, 2004. Hackemann,M. Orakel, Seher und Propheten. Wie die Antike in die Zukunft sah Anaconda. 2010. ISBN: 978-3-86647-321-8 Weissagung und Prophetie waren schon in der antiken Kultur tief verwurzelt: Bei wichtigen politischen Entscheidungen wurden Orakel befragt, Seher zogen durchs Land und boten ihre Dienste an. Antike Autoren wie Herodot, Platon und Plutarch befassten sich mit der Kunst, die Zukunft vorherzusagen mal als Befürworter, mal als spöttische Gegner. Dieses Buch wirft einen erhellenden Blick auf einen bisher wenig bekannten Aspekt der Antike. Besonderes Highlight ist das »Pythagoras-Orakel« des Astrampsychos, das den Leser zum Mitmachen einlädt. Häfner, R. Mysterien im Hain von Ariccia : Nicolas Poussins "Landschaft mit Numa Pompilius und der Nymphe Egeria" im intellektuellen Kontext um 1630 Paderborn : Verlag Wilhelm Fink. 2011. "Im März 1624 liess sich Nicolas Poussin (1594-1665) in Rom nieder. Für seine Auftraggeber schuf er eine Reihe von Landschaftsbildern, deren Gehalt er rätselhaft verschlüsselt hat. An den Freund Paul de Chantelou schreibt er: "Lesen Sie die Kaplan, R. Hidden harmonies : the lives and times of the Pythagorean theorem New York [etc.] : Bloomsbury Press. 2011. ISBN 978-1-596-91522-0 A squared plus b squared equals c squared. It sounds simple, doesn't it? Yet this familiar

expression is a gateway into the riotous garden of mathematics, and sends us on a journey of exploration in the company of two inspired guides, who trace the life of the Pythagorean theorem from ancient Babylon to the present, visiting along the way Leonardo da Vinci, Albert Einstein, President James Garfield, and the Freemasons--not to mention the elusive Pythagoras himself. Why does this theorem have more than two hundred proofs-or is it four thousand? And it has even more applications than proofs: Ancient Egyptians used it for surveying, and today astronomers call on it to measure the distance between stars. It works not just in two dimensions, but any number you like, up to infinity. And perhaps most intriguing of all, it opened the door to the world of irrational numbers existential anxiety; a prescription for happiness and balance, a strong mind and a healthy body, and the opportunity to catch a glimpse of that trippy realm called Ultimate Reality. Kennedy, J. B. THE MUSICAL STRUCTURE OF PLATO'S DIALOGUES Acumen Pub Ltd. 2011. ISBN-13: 9781844652679 DESCRIPTION: J. B. Kennedy argues that Plato’s dialogues have an unsuspected musical structure and use symbols to encode Pythagorean doctrines. The followers of Pythagoras famously thought that the cosmos had a hidden musical structure and that wise philosophers would be able to hear this “harmony of the spheres”. Kennedy shows that Plato gave his dialogues a similar, hidden musical structure. He divided each dialogue into twelve parts and inserted symbols at each twelfth to mark a musical note. These passages are relatively harmonious or dissonant, and so traverse the ups and downs of a known musical scale. Many of Plato’s ancient followers insisted that Plato used symbols to conceal his own views within the dialogues, but modern scholars have denied this. Kennedy, an expert in Pythagorean mathematics and music theory, now shows that Plato’s dialogues do contain a system of symbols. Scholars in the humanities, without knowledge of obsolete Greek mathematics, would not have been able to detect these musical patterns. The book begins with a concise and accessible introduction to Plato’s symbolic schemes and the role of allegory in ancient times. The following chapters then annotate the musical symbols in two of Plato’s most popular dialogues, the Symposium and Euthyphro, and show that Plato used the musical scale as an outline for structuring his narratives. CONTENTS: 1. Musical structure in the Symposium 2. An emphatic pattern in the frame 3. Making the musical structure explicit 4. Parallel structure in the Euthyphro 5. Extracting doctrine from structure 6. Some implications Held, W. Alles ist Zahl : was uns die Zahlen 1 bis 31 erzählen Stuttgart : Verl. Freies Geistesleben. 2011. ISBN 978-3-7725-2543-8 Kardaras, N. How Plato and Pythagoras Can Save Your Life: The Ancient Greek Prescription for Health and Happiness Publisher: Conari Press. 2011. ISBN-13: 978-1573244756 University professor and recovering nightclub owner Nick Kardaras presents a mind blowing, reality rocking, and life changing approach to Greek philosophy. The message of the ancient Greeks is neither irrelevant nor obscure. The truth is that they possessed the prescription for sane, happy and balanced living. After sampling both the fast-track lifestyle of the Manhattan A-list and the more effete pleasures of academia, Kardaras embarked on an amazing and transformative journey that brought him to the discovery of the practical and life-affirming teachings of Plato and Pythagoras. Their teachings led him to embrace the Pythagorean way of life: a healthy mind, body, and spirit nurtured by vigorous physical exercise, a rigorous diet, daily meditation, and contemplation. Kardaras both introduces readers to the ancient teachings and guides them through a wide array of meditative practices that will lead them into an understanding of the nature of authentic character, an exploration of the ethical choices that face each of us, and the composition of a life that is truly well lived. With clarity and enthusiasm, he brings the past fully and meaningfully into the present and demonstrates how each of us possesses the potential for extraordinary living. This is the prescription for a life unburdened by constant Martin, W. Cusanus - ein Pythagoreer und Vorläufer des Galilei : Teil II seiner Beziehungen zu St. Wendel Norderstedt : Books on Demand. 2011. ISBN 978-3-8423-6179-9 Der hier vorliegende Teil liefert Fakten und Zusammenhänge, die zuvor nicht bekannt waren oder nur ungenügend von der

Forschung berücksichtigt wurden. Er legt dar, wie Cusanus in den Besitz der St. Wendeler Pfründe kam, wie lange er sie besaß, und warum diese Gegebenheit bisher vernachlässigt worden ist.Er macht auf Ornamente in St. Wendel aufmerksam, die auf Cusanus als Pythagoreer hinweisen. Zudem charakterisieren die Darlegungen mit seiner Erkenntnis der Messbarkeit Cusanus als Vorläufer des Galilei.Weiter zeigt der Teil Indizien auf, denen zufolge Cusanus aufgrund genauer Beobachtung des variablen Sonnenstandes mit seinem Torquetum die Bedingungen für eine programmierte Schattenbildung nach dem Umbau der Kirche erzielte. Diese Schattenbildung zeigt einerseits die Uhrzeit an und veranschaulicht andererseits das in seiner „belehrten Unwissenheit“ als grundlegend erkannte Dreier-Prinzip.Mutmaßlich ermunterte das so gelungene Experiment Cusanus dazu, auch den Zeitpunkt des Endgerichts zu berechnen. Wie es ebenfalls als Vorarbeit diente für die Einrichtung der Schattenbildung durch Papst Pius II. zur Tag- und Nachtgleiche in dessen Stadtplanung für Pienza. in their own right, a full understanding of the Greek mathematical corpus cannot be bereft of systematic studies of the Conics. However, recent scholarship on Archimedes has revealed that the role of secondary commentaries is also important. In this thesis, I provide a translation of Eutocius' commentary on the Conics, demonstrating the interplay between the two works and their authors as what I call conjugate. I also give a treatment on the duplication problem and on compound ratios, topics which are tightly linked to the Conics and the rest of the Greek mathematical corpus. My discussion of the duplication problem also includes two computer programs useful for visualizing Archytas' and Eratosthenes' solutions. Miller, P.L. Becoming God. Pure Reason in Early Greek Philosophy A lucid presentation of the first and most influential attempts to weave together philosophical thought on God, reason and happiness. Continuum 2011. Series: Continuum Studies in Ancient Philosophy. ISBN: 9781847061645 Description: Becoming god was an ideal of many ancient Greek philosophers, as was the life of reason, which they equated with divinity. This book argues that their rival accounts of this equation depended on their divergent attitudes toward time. Affirming it, Heraclitus developed a paradoxical style of reasoning— chiasmus—that was the activity of his becoming god. Denying it as contradictory, Parmenides sought to purify thinking of all contradiction, offering eternity to those who would follow him. Plato did, fusing this pure style of reasoning—consistency—with a Pythagorean program of purification and divinization that would then influence philosophers from Aristotle to Kant. Those interested in Greek philosophical and religious thought will find fresh interpretations of its early figures, as well as a lucid presentation of the first and most influential attempts to link together divinity, rationality, and selfhood. Table of Contents: 1. Introduction \ 2. Heraclitus \ 3. Parmenides and Pythagoreans \ 4. Plato \ Conclusion \ Bibliography \ Index. Bust of Pythagoras of Samos in the Capitoline Museums, Rome McKinney, C.B.P. Conjugate diameters : Apollonius of Perga and Eutocius of Ascalon Iowa City, Iowa : University of Iowa, 2010 The Conics of Apollonius remains a central work of Greek mathematics to this day. Despite this, much recent scholarship has neglected the Conics in favor of works of Archimedes. While these are no less important Mohr, R.D. One book, the whole universe : Plato's Timaeus today / edited by Richard D. Mohr and Barbara M. Sattler. Las Vegas : Parmenides Pub., 2010. ISBN 9781930972322.

The much-anticipated volume of essays by philosophers, classicists, physicists, and architects revealing the meaning and assessing the impact of one of the most profound and influential works of Western letters: Plato's Timaeus a work which comes as close as any to giving a comprehensive account of life, the universe, and everything! Table of Contents Plato’s Cosmic Manual: Introduction, Reader’s Guide, and Acknowledgments. Richard D. Mohr I. The Big Questions 1. Plato’s Timaeus: Some Resonances in Modern Physics and Cosmology. Anthony J. Leggett II. God and Related Matters 2. Cosmic Craftsmanship in Plato and Stoicism. Anthony A. Long 3. Philosopher-Kings and Craftsman-Gods. Allan Silverman 4. The Place of Cosmology in Plato’s Later Dialogues. Charles H. Kahn 5. Maker or Father? The Demiurge from Plutarch to Plotinus. Matthias Vorwerk 6. Plato on (just about) Everything: Some Observations on the Timaeus and Other Dialogues Thomas M. Robinson III. Space, Place, and Motion: The Receptacle of Becoming 7. Visualizing Platonic Space. Donald Zeyl 8. The Receptacle and the Primary Bodies: Something from Nothing? 131 Verity Harte 9. The Timaeus and the Critique of Presocratic Vortices 141 Stephen Menn 10. What’s the Matter? Some Neo-Platonist Answers, Ian Mueller 11. Derrida’s Khôra, or Unnaming the Timaean Receptacle, Zina Giannopoulou IV. Aristotle’s Timaeus 12. Should Aristotle Have Recognized Final Causes in Plato’s Timaeus? Thomas K. Johansen 13. Aristotle on Plato on Weight. Alan Code V. Reason and Myth 14. What Makes a Myth eikôs? Remarks Inspired by Myles Burnyeat’s EIKÔS MYTHOS Gábor Betegh 15. The Epistemological Section (29b–d) of the Proem in Timaeus’ Speech: M. F. Burnyeat on eikôs mythos, and comparison with Xenophanes B34 and B35 225. Alexander P. D. Mourelatos VI. Time, Narrative, and Myth 16. A Time for Learning and for Counting: Egyptians, Greeks, and Empirical Processes in Plato’s Timaeus. Barbara M. Sattler 17. Narrative Orders in the Timaeus and Critias. Kathryn A. Morgan 18. Timaeus in Tinseltown: Atlantis in Film. Jon Solomon VII. Timaean Architecture: Timber Framing the Universe and Building Today 19. The Atlantis Effect: The Lost Origins of Architecture. Anthony Vidler 20. Plato’s Timaeus and the Aesthetics of “Animate Form”. Ann Bergren VIII. Ever After, Ever Before 21. Time and Change in an Eternal Universe. Sean M. Carroll Moneti Codignola, M. Ipazia muore Milano : La tartaruga, 2010. Montepaone, C. Pitagoriche : scritti femminili di età ellenistica. Bari : Edipuglia. 2011. Series 1: Documenti e studi / Dipartimento di scienze dell'antichità dell'Università di Bari, Sezione storica; 46. ISBN/ISSN: 978-88-7228-620-3 INDICE Prefazione 7 Introduzione. Le filosofe pitagoriche nella prospettiva di genere 9 Avvertenza 19 1. Le Pitagoriche. Il catalogo di Gianiblico 21 2. Theano 23 3. Myia 59 4. Aisara / Aresa 65 5. Arìgnote 71 6. Deino, Damo, Bitale 75 7. Melissa 81 8. Periktione ( 85 9. Phintys 95 Appendice. Themistokleia 103 Bibliografia 105 Indice dei nomi 119 Indice dei termini notevoli i 123 Moro, S. Music and Philosophy in the Neo-Platonic tradition Thesis. Royal Holloway, University of London. 2010. "My thesis examines philosophical questions about music according to Neoplatonism: what is music and what is the place of music in the structure of reality. I focus my examination of Neoplatonic music on the philosopher Proclus. For Proclus, music is something much richer than the phenomenon usually called music. My thesis studies this wide notion of music: music as art and as science, and furthermore music as a principle of order and harmony in the universe. Accordingly, music is intimately

related to metaphysical principles: the WorldSoul and the Intellect. In Chapter I, I concentrate on the explanation of the mathematical proportions that are the basis for the musical scale of the Timaeus of Plato, according to Proclus’ commentary on this dialogue. Secondly, in Chapters II and III, I study Proclus’ metaphysical interpretation of the scale, understood as a symbol of the hierarchy of levels in Neoplatonism. In Chapter IV, I study what is the value of music for human life, in Proclus’ commentary on the Republic. Neoplatonism is a philosophy of Unity, and in this context, music and harmony are a way of returning to Unity from multiplicity and division. I study how music can guide the human soul to come back to the origin of reality, with the help of musician gods such as Hermes, the Muses and Apollo. My dissertation shows the connection between philosophy, mathematics, art and mythology. Music is a privileged art because it is related by an essential kinship to the soul. I have applied the Boethian classification of music to the inner logic of my thesis in order to show that in Neoplatonism all these aspects are organized in a complex conception of music. Neoplatonic music is consequently understood as an encompassing phenomenon, which mirrors the encompassing nature of Neoplatonic philosophy." El Sueno De Hipatia / The Hypatia Dream. Debolsillo 2010. Prado, L.A.G. Matemática, física e música no renascimento: uma abordagem histórico-epistemológica para um ensino interdisciplinar Dissertação de Mestrado. Unidade da São Paulo. Faculdade de Educação. 2010. Resumo em inglês During the Renaissance there is a resumption of the rational thought in which classical knowledge is revisited and rearranged by man. There is a contestation that challenges the Pythagorean intervals. Vincenzo Galilei opposed the way that Pythagoras listed the musical intervals by ratios of natural numbers. It was then established a revolution of scientific ideas that influenced music. Vincenzo Galilei breaks the Pythagorean view and starts to test experimentally musical relationships that were supposedly correct and begins to write a new music theory based on experimental foundations. His son Galileo, in turn, puts physics within a practical an experimental approach. Due to this new approach, the Pythagorean concept of music is threatened. The relationships between physics, mathematics and music are intensified and the study of music at this time has a particularly interesting character from an interdisciplinary point of view. Through a historical and epistemological approach, this work studies the importance of interdisciplinary education in general, especially in mathematics, physics and music, and aims at suggesting some interdisciplinary workshops such that these three disciplines can somehow be present. Learning involving more than one subject through an interdisciplinary activity is not always easy and may represent an epistemological obstacle since we go out of our comfort zone. These workshops therefore also aim at instigating the students as well as inviting them to take a reflective and critical approach, and realize how challenging is to see and study phenomena through different points of view. It is hoped in this way to enrich the learning potential through a complementation of the education process, traditionally done by separate subjects, by the inclusion of interdisciplinary activities whenever possible. Petta, A. Ipazia : vita e sogni di una scienziata del IV secolo Roma : La lepre, 2010. Phillips, S.M. The Mathematical Connection between Religion and Science Printed by Antony Rowe, Publishing (UK), 2009. Summary: This profusely illustrated book reveals for the first time the common mathematical blueprint determining superstrings, the DNA molecule and the human skeleton and how it is embodied in the sacred geometries of the world's religions. It also proves that these sacred geometries are equivalent representations of the map of the physical and superphysical levels of reality and that they encode in analogous ways the structure and dynamics of superstrings. The composition of intervals between the notes in the seven musical scales known as the church modes is shown to conform to the same universal pattern as that embodied in sacred geometries and physically manifested in the superstring. 500 pages (50 pages in colour). Poyato, J.C. Rahm, J. Science and fiction in Dialogue concerning the two chief world systems and Somnium : Galileo's and Kepler's literary techniques for discussing scientific theories

Scriptie/Proefschrift : Manuscript Archiefmateriaal Uitgever: 2010. Ruiz, N.E.L. Heraclitus and the Work of Awakening Dissertation Stony Brook University. 2007 http://gradworks.umi.com/3334944.pdf Reale, G. Pitagorici antichi : testimonianze e frammenti. Statement of responsibility: a cura di Maria Timpanaro Cardini ; presentazione di Giovanni Reale ; realizzazione editoriale, aggiornamento bibliografico e indici di Giuseppe Girgenti Edition: 1. ed. Bompiani Il pensiero occidentale. Milano : Bompiani. 2010. Series 1: Il pensiero occidentale ISBN-13: 9788845266331 Sachs, E. ie fünf Platonischen Körper : zur Geschichte der Mathematik und der Elementenlehre Platons und der Pythagoreer Nachdruck der Orig.-Ausg. Berlin, Weidmann, 1917 Hamburg : Severus-Verl. 2010. ISBN 978-3-86347-009-8 Schiel, C. Earth's rotation on trial is Theon of Alexandria the better fact witness after all? München Schiel 2011. Reville, A. Apollonius of Tyana, the pagan christ of the third century : an essay. General Books, 2010 Schroeder, L. Von Pythagoras und die Inder : Eine Untersuchung über Herkunft und Abstammung der pythagoreischen Lehren Bremen : Salzwasser-Verlag in Europäischer Hochschulverlag. 2011. ISBN 978-3-86195-640-2 (Repr. d. Ausg. v. 1884.) THEON DE SMYRNE, Lire Platon. Le Recours au savoir scientifique : Arithmétique, Musique, Astronomie. Texte présenté, annoté et traduit du grec par Joelle Delattre Biencourt. Anacharsis Editions, Toulouse 2010, ISBN : 978-2-914777-704. Philosophe et mathematicien du IIeme siècle 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 saviors 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. APOLLONIUS OF TYANA (?). BUST IN THE CAPITOLINE MUSEUM, ROME. Roberts, J.M. Apollonius of Tyana, identified as the Christian Jesus : a wonderful communication explaining... General Books, 2010 Ronchey, S. Ipazia : la vera storia Milano : Rizzoli, 2010.

Book chapters Acerbi, F. Miti storiografici - Pitagora matematico e la matematica pitagorica - Le notizie biografiche su Archimede - Erone il «meccanico» Ipazia matematico p 149-170 In: Il silenzio delle sirene : la matematica greca antica. Roma : Carocci. 2010. Series 1: Saggi; 59. ISBN 9788843055791 In: Protée en trompe-l'oeil : genèse et survivances d'un mythe, d'Homère à Bouchardon. Rennes : Presses universitaires de Rennes. 2010. Series 1: Interférences ISBN/ISSN: 978-2-7535-0981-8 Burkert, W. VI MYSTERIEN UND ASKESE 1 Mysterienheiligtumer p 413- 431 Allgemeines - Gentil- und Stammesmysterien Kabiren und Samothrake - Eleusis 2 Bakchika und Orphika p 432-448 Bakchische Mysterien - Bakchische Jenseitshoffnung - Orpheus und Pythagoras VII PHILOSOPHISCHE RELIGION 1 Der Neuansatz: Das Seiende und das Göttliche p 455-464 2 Die Krise: Sophisten und Atheisten p 464-472 3 Neue Grundlegung: Kosmosreligion und Metaphysik p 473-492 Vorsokratische Ansätze - Piaton: Das Gute und die Seele - Platon: Kosmos und sichtbare Götter - Aristoteles und Xenokrates: Geistgott und Dämonen 4 Philosophische Religion und Polisreligion: Piatons „Gesetze" p 493-498 In: Griechische Religion der archaischen und klassischen Epoche Stuttgart : Kohlhammer. 2011. Gesamttitel: Die Religionen der Menschheit ; Bd. 15 ISBN 978-3-17-021312-8 Anonymus. Pitágoras arquitectos. In: Lisboa : Caleidoscópio. 2010. Series 1: Arquitecturas. ISBN 9789896580681 Anonymus Open Building Research. Museo di Pitagora Crotone p 80-88 In: Progetti di giovani architetti italiani. Torino : UTET scienze tecniche. 2011. Series 1: Linea GiArch ISBN/ISSN: 978-88-598-0596-0 Athanassiadi, P. Épilogue. Pourquoi la tétractys ? p 237-242 In: La lutte pour l'orthodoxie dans le platonisme tardif : de Numénius à Damascius. Paris : Les belles lettres. 2006. Series 1: L'âne d'or; 25. ISBN 9782251420288 BAYÓN, D. Sebastián 85: un pitagórico moderno. p 55-63 In: Sebastian Escultor. Statement of responsibility: [ed., Héctor Tajonar] Barcelona : Turner. 2010. ISBN-13: 978847506899 Bychkov, O.V. Philostratus : from Life of Apollonius of Tyana, Pictures preface p 167-170 In: Greek and Roman aesthetics New York, NY : Cambridge University Press, 2010. ISBN 9780521547925 Beneduci, L. Il «noviziato pitagorico» sinisgalliano: la geometria e il furore dei sensi p 46-59 In: Bestiario sinisgalliano : studio dell'immaginario zoomorfo nelle opere di Leonardo Sinisgalli. Roma : Aracne. 2011. Series 1: Scienze dell'antichità, filologicoletterarie e storico-artistiche; 732 ISBN/ISSN: 978-88-548-4021-8 Cabezas, L. El origen poliédrico de las especies de Arturo Soria y Mata. Ciencia, pitagorismo y pensamiento estético p 15-48 In: Hernández Rojo, F. / L. La Rubià, eds.: Arte y geometría. 2010 . Granada : Universidad de Granada. 2010. ISBN 9788433851680 Blay, F. XI — Protée et Pythagore dans la Vie d'Apollonios de Tyane de Philostrate

Cantarano, G. La vita contemplativa: i Pitagorici p 29-34 In: Le lacrime dei filosofi : l'idea di salvezza in Occidente. Genova [etc.] : Marietti 1820. 2011. Series 1: Collana di saggistica; 125 ISBN/ISSN: 978-88-211-7550-3 In: Geschichte der musikalischen Bildung : eine Kultur-, Sozial- und Ideengeschichte in 40 Stationen ; von den antiken Hochkulturen bis zur Gegenwart Darmstadt : Wiss. Buchges. 2010. ISBN 978-3-534-24413-3 García-Carril Puy, N. ¿Por qué la música para el pitagorismo no es geométrica sino harmónica? p 185-208 In: Hernández Rojo, F. / L. La Rubià, eds.: Arte y geometría. 2010 . Granada : Universidad de Granada. 2010. ISBN 9788433851680 Cascio, M. Pitagora e Platone p 37-45 In: La massoneria è il suo segreto : [una questione di metodo]. Foggia : Bastogi. 2011. Series 1: Biblioteca massonica. ISBN/ISSN: 978-88-6273-321-2 Gaspari, G. Pitagorismo e numerologia a Milano nel primo Seicento, p 66-80 In: Libertinismo erudito : cultura lombarda tra Cinque e Seicento. Milano : F. Angeli. 2011. Series 1: Rassegna gallaratese di storia e d'arte; 131 Proceedings of the meeting held in Somma Lombardo, Italy, Oct. 15-16, 2009. ISBN/ISSN: 978-88-568-3667-7 Clauss, M. IV.PHILOSOPHEN p 90-113 Pythagoras: a2 + b2 = c1 Platon: Drei vergebliche Reisen Hypatia: Der höchsten Weisheit reiner Stern In: Große Gestalten der Antike Berlin : Rowohlt. 2010. ISBN 978-3-87134-673-6 Cunha, R.S. Afinidades. Pitagorismo e radioactividade: o comentàrio dejoaquim Domingues. Pintura, história p 51-59 In: Filosofia do ritmo portuguesa. Sintra : Zéfiro. 2010. Series 1: Nova águia. ISBN 9789896770419 Geck, M. Concordia discors. Bachs Kontrapunkt gegen die Pythagoreer unter seinen Liebhabern verteidigt p 5-21 In: Philosophie des Kontrapunkts / hrsg. von Ulrich Tadday München : Ed. Text + Kritik. 2010. Gesamttitel: Musik-Konzepte, Sonderband ; N.F., 2010 ISBN 978-3-86916-088-7 Ehrenforth, K.H. STATION 6 Die Welt als Zahl und Proportion: Pythagoras – Vom Mythos zum Logos - Die PythagorasLegende – Harmonikale Kosmologie - MusikeErziehung als Weg zur Harmonie der Welt p 55-60 STATION 7 Musik in der Welt der Ideen: Platon - Von Pythagoras zu Piaton - Piatons Ideenlehre: Das Höhlengleichnis - Musik - Abbild der Abbilder? - Böse und gute Musik? Pythagoreische Spätspuren p 60-67 STATION 8 Musik zwischen Idee und Wirklichkeit: Aristoteles - Die realistische Wende - Chancen und Grenzen der Musikerziehung Kathartische Wirkungen der Musik? p 67-78 STATION 9 Hellenismus und Rom - Musik in den Septem artes liberales - Der Aufstieg der Rhetorik - Der Mann im Hintergrund: Isokrates - Auf der Brucke ins Römische Weltreich: Varro 81 - Der Traum des Scipio: Cicero - Der lange Schatten der Antike: Quintilian - Capella - Boethius p 78-96 Giaquinta, M. Capitolo 1. Il Periodo Ellenico: Le origini Talete e Pitagora: una stona inventata, ma verosimile - Numeri, rapporti di grandezze e processi infiniti - Da Pitagora ad Euclide Platone ed Aristotele - Linguaggio comune e linguaggio matematico p 1-68 In: La forma delle cose : idee e metodi in matematica tra storia e filosofia. Teil: 1: Da Talete a Galileo e un po' oltre Giaquinta, Mariano. Roma : Ed. di Storia e Letteratura, 2010. Schriftenreihe: Temi e testi ; 80 ISBN: 978-88-637-2178-2 Grandinetti, P. Cultualità, pitagorismo e prestigio sociale: il ruolo delle donne a Locri Epizefirii p 477-492 In: Lo spazio ionico e le comunità della Grecia nord-occidentale : territorio, società e istituzioni : atti del convegno internazionale, Venezia, 7-9 gennaio 2010.

Pisa : ETS. 2010. Series 1: Diabaseis; 1. ISBN-13: 9788846728494 Hume, D.A. 5. Iamblichus' "On the Pythagorean Way of Life" p 68-76 In: The Early Christian Community : a narrative analysis of Acts 2:41-47 and 4:32-35 Tübingen : Mohr Siebeck. 2011. Wissenschaftliche Untersuchungen zum Neuen Testament : Reihe 2 ; 298. ISBN 978-3-16-150729-8 Guicciardini, N. Newton e Pitagora p 119-127 In: Newton. Roma : Carocci. 2011. Series 1: Pensatori; 20. ISBN/ISSN: 978-88-430-5796-2 Ito, J.P. On music, mathematics, and theology : Pythagoras, the mind, and human agency In: Resonant witness : conversations between music and theology. Grand Rapids, Mich. : W.B. Eerdmans Pub. Co., 2011. Hackemann, M. Zum Mitmachen: Das antike PythagorasOrakel in vollständiger Übersetzung p 114-118 In: Orakel, Seher und Propheten : wie die Antike in die Zukunft sah Köln : Anaconda.2010. ISBN 978-3-86647-321-8 Heyman, I.W. Alcmaeon and Empedocles p 24-28 In: Melissus on pain Austin, Tex. : Dissertation, University of Texas, 2010. Hopkins, D. Ch. 9: “Translation, Metempsychosis, and the Flux of Nature: Dryden’s ‘Of the Pythagorean Philosophy.’” In: Conversing with Antiquity: English Poets and the Classics, from Shakespeare to Pope. Classical Presences. Oxford/New York: Oxford University Press, 2010. ISBN 9780199560349. Abstract: From 2001, this chapter considers Dryden’s translation of the Pythagorean excursus in Met. 15. 60-478. Hopkins takes very seriously Dryden’s engagement with Pythagoreanism on the political, personal, and even religious levels, which may be further than some readers will want to go, at least in the terms raised. But this is one of the more interesting essays in the volume. Klein, Y. Part II: Philosophy. The Theoretician's Laboratory In: Musical Instruments as Objects of Meaning in Classical Arabic Poetry and Philosophy Dissertation Harvard University. Cambridge, Massachusetts. 2009., http://gradworks.umi.com/3385552.pdf Abstract: Part 2 analyzes discussions of musical instruments by al-Kindi (d. c. 256/870), the Ikhwan al-S[dotbelow]afa` (c. 4th /mid-10th century) and al-Farabi (d. 339/950). Arab philosophers regarded musical instruments as products of scientific speculation--as laboratories, in which nature's laws could be tested as well as demonstrated. Al-Kindi and the Ikhwan evinced strong Pythagorean influence in their understanding of music. They regarded music as the audible manifestation of the order of the universe expressed in mathematical ratios, and musical instruments as scientific devices constructed primarily for the purpose of displaying these mathematical Hume, D.A. 4. The Use of Friendship Maxims in Three Biographies by Diogenes Laertius p 62-67 A. Diogenes Laertius' Life of Bion B. Diogenes Laertius' Life of Pythagoras C. Diogenes Laertius' Life of Epicurus In: The Early Christian Community : a narrative analysis of Acts 2:41-47 and 4:32-35 Tübingen : Mohr Siebeck. 2011. Wissenschaftliche Untersuchungen zum Neuen Testament : Reihe 2 ; 298. ISBN 978-3-16-150729-8

proportions and the interconnectedness the of the micro- and macro-cosmos. Al-Farabi's understanding of the nature of music, and consequently, musical instruments, was radically different from that of his ArabPythagorean predecessors. He played down Pythagorean ideas in favor of Aristoxenian and Ptolemaic concepts. Music for him was a human project developed in a historical context and not representative of any superordinate mathematical order beyond music. Instruments, in turn, were scientific tools with which to think music: to gather musical data and experiment with various hypotheses. series of numbers signifying the precise placement of the tones within the gamut. His approach is in line with medieval mathematics, which focuses on elementary number theory and can be seen as a precursor to Euler's Potenzennetz (grid of proportions). This paper embeds our results in Gaffurio's oeuvre and his times and includes a a concise of overview of his biography with an emphasis on his pedagogical and literary contributions. Our approach fills a gap in research, because although Latin music theorists from the era of musical humanism frequently include mathematical approaches to the Greek systema teleion and Guidonian system, as projected onto the monochord, they do not disclose the nature and specific details of the mathematical calculations which inform the natural numbers included in both the manuscript and early printed editions. Krantz, S.G. The mystical mathematics of Hypatia In: An episodic history of mathematics : mathematical culture through problem solving. Washington, DC : Mathematical Association of America, 2010. Künne, T. Die himmlischen Klänge der Planeten. - Eine Zeitreise von Pythagoras bis zu Cousto - Die uberirdisch harmonische Ordnung der Sphärenmusik - ..was die Welt im Innersten zusammenhält - Alles auf einen Blick: Übersicht der Planetenfrequenzen p 77-103 In: Die Schwingung der Archetypen : die Resonanz der Planetentöne in Astrologie, Mythologie und Klangarbeit Battweiler : Traumzeit, Verl. der Neuen Klangkultur. 2010. ISBN 978-3-933825-87-2 Kreyszig, H. The Transmission of Pythagorean Arithmetic in the Context of the Ancient Musical Tradition from the Greek to the Latin Orbits During the Renaissance: A Computational Approach of Identifying and Analyzing the Formation of Scales in the De Harmonia Musicorum Instrumentorum Opus (Milan, 1518) of Franchino Gaffurio (1451-1522) In: MATHEMATICS AND COMPUTATION IN MUSIC Book Series: Communications in Computer and Information Science Volume: 37 Pages: 392-405 Published: 2009 Abstract: On the occasion of the three hundredth anniversary of Leonhard Euler (1707-1783) and the focus of his contribution to the mathematical explanation of scales, the quest arises to examine similar contributions of music theorists that lived prior to Euler. In this paper we selected from the trilogy (Theorica musicae, 1492; Practica musicae, 1496; De harmonia musicorum instrumentorum opus, 1518) of the eminent Renaissance scholar, musician, theorist and composer Franchino Gaffurio (1451-1522) his third work of 1518. In particular, using a modern elementary number theoretic approach, we discovered a number generating function in closed form, which we called a Gaffurio number generating Junction, that generates the tones of the Pythagorean scale. The number generating function is of the form f (n, m) = p(n) q(m), where p and q are primes, and n and m are elements of /N-0. Here, Gaffurio chooses the smallest primes p = 2 and q = 3, thereby with this ratio p / q denoting the interval of the diapente and he varies the integral exponents n and m from 0, 1, 2, 3, ... and in the process constructing a Lake, O.O. Hypatia's pearls : democracy ancient and modern In: Uprisings for the earth : reconnecting culture with nature Ashland, Or. : White Cloud Press, 2010. Lanzi, C. Piccola considerazione metafisica d'ordine pitagorico p 182-186 In: Intelletto d'amore : la metafisica dell'eros. Roma : Simmetria. 2010. Series 1: Simmetria. ISBN 9788887615630 Lombardo, G. Chapitre II : L’esthétique préplatonicienne 8. De quand date l’émergence d’un conflit entre la poésie et la vérité ? Et comment l’exigence d’une « poétique de la vérité » se développe-telle ? 9. Quel est l’apport de la pensée pythagoricienne au débat esthétique préplatonicien ? 10. Quels sont les origines mythiques et les débuts historiques de l’éloquence ? Et quel est le rôle joué par les

Sophistes (et surtout par Gorgias) dans l’esthétique grecque ? 11. Pourquoi Les Grenouilles d’Aristophane sont-elles un texte fondamental afin de comprendre l’ancienne opposition entre moralisme et hédonisme ? In: L'esthétique antique. Éditeur : Klincksieck. 2011. Collection : 50 questions. 57. ISBN 978-2-252-03794-2 Miller, P.L. Greek philosophical dualism p 107-44. In: Light against Darkness : dualism in Ancient Mediterranean Religion and the Contemporary World Göttingen : Vandenhoeck & Ruprecht, 2011. Serie: Journal of ancient Judaism / Supplements, 2. ISBN 9783525550168 Martínez Nieto, R.B. Novedades en los estudios de transmisión textual de Empédocles: Los comentarios de Simplicio p 721-731 In: Dialéctica histórica y compromiso social : homenaje a Domingo Plácido. Zaragoza : Libros Pórtico. 2010. ISBN 9788479560676 Monaci Castagno, A. CAPITOLO TERZO. 1. La critica epicurea degli uomini divini: la Vita di Demonatte e Alessandro il falso profeta di Luciano di Samosata, - La Vita di Apollonio di Tiana fra taumaturgia e filosofia, - Porfirio biografo: la Vita di Pitagora e la Vita di Piotino, - La Vita pitagorica di Giamblico, - La critica cristiana deH"'uomo divino": il Contro Ierocte di Eusebio di Cesarea, - Biografie eusebiane: Origene e Costantino, p 93- 122 In: L'agiografia cristiana antica : testi, contesti, pubblico. Brescia : Morcelliana. 2010. Series 1: Letteratura cristiana antica. Nuova serie; 23 ISBN 9788837224417 Megino, C. Capítulo 10. El origen del hombre según Empédocles p 263-296 In: Mitos sobre el origen del hombre. Madrid : Círculo de Bellas Artes : Universidad Carlos III. 2011. ISBN-13: 9788487619823 Mikalson, J.D. 2. Prayer, Sacrifice, Festivals, Dedications, and Priests in `Service to the Gods' p 43-110 In: Greek Popular Religion in Greek Philosophy. 2010. Oxford Scholarship Online Monographs ISBN 978-0-19-957783-5 Abstract: Most Greek philosophers accepted and even promoted prayer, sacrifice, festivals, and dedications, but with modifications and restrictions. The Socratic argument that prayers should be made only for what is good, not for specific things, and that this required philosophical knowledge of what is good was widely accepted in the philosophic tradition. Sacrifices are to be made to honour the gods, establish a relationship of reciprocal favours (charis) with them, and to acquire good things. Humble and regular sacrifices by good people are better received than expensive sacrifices by evil people. Pythagoras, Empedocles, and Theophrastus opposed both the popular and philosophical traditions by excluding animal sacrifice. Festivals honour the gods and provide opportunities for relaxation and education. Dedications also honour the gods but are subject to restrictions of objects and expense. Priests are given a relatively low political status and have a limited role in prayer and sacrifice. The chapter concludes with a survey of other religious officials. Montepaone, C. Théanô la pythagoricienne In: Nicole Loraux; La Grèce au feminine Les Belles Lettres: La Grèce au feminine. 2009. ISBN 978-2-251-32665-8 Morlok, E. 2.4 Pythagorean and Neoplatonic Background to Gikatilla's Hermeneutics p 77-83 3.3.3 Ginnat 'Egoz - Siman as Heshbon and its Pythagorean Background p 222-226 3.3.4 Pythagorean Symbol as Entry-Token p 226-228 In: Rabbi Joseph Gikatilla’s hermeneutics. Tübingen : Mohr Siebeck. 2011. Gesamttitel: Texts and studies in medieval and early modern Judaism ; 25. Hochschulschrift: Zugl. rev. Fassung von: Jerusalem, Hebr. Univ., Diss., 2008 ISBN 978-3-16-150203-3 Odifreddi, P. IV L'irrazionale scende in campo. Pitagora Ipse dixit, - II quadrato costruito sull'ipotcnusa, - Si può fare di meglio, - La divina proporzione, La diabolica proporzione, - Unità di crisi al Pentagono, - Invito a nozze, p 68-91 XI Le cose da una nuova angolazione. Aristarco, Ipparco e Tolomeo Le proporzioni dell'universo, - Riscopriamo l'America, Equilibrismi sulle corde, - Lezione di anatomia

femminile, - Quanti gradi ci sono oggi?, - La Somma Summa, - Operazioni al seno, - La prima tangente edilizia, p 233-256 In: C'è spazio per tutti : il grande racconto della geometria. Milano : Mondadori. 2010. Series 1: Saggi. ISBN 9788804603313 Roecklein, R.J. Parmenides' influence on Empedocles and Anaxagoras In: Plato versus Parmenides : the debate over coming-into-being in Greek philosophy Lanham, Md. : Lexington Books, 2011. ISBN 978-0-7391-5077-1 Roullier, P.H. Du sage au disciple : autorité charismatique, domination romaine et identité grecque dans la Vie d’Apollonios de Tyane de Philostrate p 359-378 In: Glyptique romaine : Le public et son miroir : Varia. door Hélène Guiraud; et al Toulouse : Presses universitaires du Mirail, 2010. O’Neill, J.F. Chapter 3: The Greek Experience of Transcendence p 125-195 In: TOWARD A NEW MYSTICAL POETICS OF GOD IN THE POST-MORTEM AGE: FROM GOD AS THE SUPREME BEING TO GOD AS THE ONE-AND-ONLY BEING Dissertation. University at Albany, State University of New York. 2009 SKARSOULI, P. « ‘Confiner le monde par des mots’. Réflexions sur la cosmologie (et la) poétique d'Empédocle : le terme πεῖραρ », p 231-244. In : Texte du monde - Monde du texte. Isabelle Milliat-Pilot (dir.) Grenoble : J. Millon, 2010. Collection Horos. ISBN: 978-2-84137-252-2 Platt, V.J. 7. The apologetics of representation in Philostratus' Life of Apollonius of Tyana In: Facing the gods : epiphany and representation in Graeco-Roman art, literature, and religion Cambridge ; New York : Cambridge University Press, 2011. Series: Greek Culture in the Roman World ISBN: 9780521861717 Talamo, C. Pitagora e la trufhv p 141-157 In: Contributi sui Greci d'Asia. Pisa : ETS. 2010. Series 1: Quaderni del Dipartimento di scienze dell'antichità / Università degli studi di Salerno; 36. ISBN 9788846726506 Primavesi, O. Zu Brechts Empedokles p 25-37 In: Der Philosoph Bertolt Brecht Würzburg : Königshausen & Neumann. 2011. Gesamttitel: Der neue Brecht ; Bd. 8 ISBN 978-3-8260-4552-3 Urbano, S. Capitolo III I Versi Aurei di Pitagora p 65-114 In: Peripatetikon : itinerario esoterico tra massoneria e pitagorismo. Roma : Atanòr. 2010. Series 1: Vitriol. Esoterismo. ISBN-13: 9788871692524 Rausch, S. Pythagoras - Alles besteht aus Harmonie und Zahl p 62-66 Empedokles - Die Erfindung der vier Elemente p 106-112 In: Griechische Antike : die bedeutendsten Persönlichkeiten von Homer bis Kleopatra Hildesheim : Gerstenberg. 2011. Gesamttitel: 50 Klassiker. ISBN 978-3-8369-2579-2 Waibl, E. PYTHAGORAS UND DER PYTHAGOREISMUS p 35-42 In: Ästhetik und Kunst von Pythagoras bis Freud Verlag: Facultas Universitätsverlag. 2009. ISBN: 978-3-8252-3304-4 Sammlung: UTB Uni-Taschenbücher Bd.3304 Reale, G. GRUPPO DEI FILOSOFI PRESOCRATICI ISPIRATI ALL'ORFISMO p 23-48 Pitagora con un gruppo di ascoltatori - II filosofo Empedocle - Il giovane in abito bianco e il suo significato - II filosofo - Eraclito nelle sembianze di Michelangelo Buonarroti In: Raffaello : la Stanza della segnatura. Statement of responsibility: Govanni Reale, Elisabetta Sgarbi Milano : Bompiani. 2010. ISBN 9788845264573

Reviews Balaudé, J.F. Le savoir-vivre philosophique : Empédocle, Socrate, Platon. 2010. Reviewed by: Ponchon, P. http://cahiersphilosophiques.hypotheses.org/589 Bonazzi, M. A Platonic Pythagoras : Platonism and Pythagoreanism in the Imperial Age. Brepols, 2007. Reviewed by: Pradeau, J.F. BULLETIN PLATONICIEN. 2009, 8, p 237-239 Bowie, E., Elsner, J. (edd.) Philostratus. Cambridge: Cambridge University Press, 2009. Reviewed by: Etherington, P. The Classical Review. 2010, 60, 2, p 397-400 Curd, P. Graham, D.W. (edd.) The Oxford Handbook of Presocratic Philosophy. 2008. Reviewed by: Bryan, J. The Classical Review. 2010, 60, 2, p 366-368 Deakin, M.A.B. Hypatia of Alexandria: Mathematician and Martyr. Prometheus Books, 2007 Reviewed by: Morpeth, N. EUROPEAN LEGACY. 2010, 15, 7, p 928-929 Demoen, K. Praet, D. (edd.) Theios Sophistes. Essays on Flavius Philostratus’ Vita Apollonii. (Mnemosyne Supplementum 305.). Brill, 2009. Reviewed by: Robiano, P. L'Antiquité Classique. 2010, 79, p 422-425 Drozdek, A. In the beginning was the apeiron. Infinity in Greek philosophy. 2008. Reviewed by: Marcinkowska-Rosół, M. Gnomon. 2011, 1, p 10-14 Reviewed by: Therme, A.L. Revue des eudes grecques. 2010, 123, p 458-460 Joost-Gaugier, C.L. Pythagoras and Renaissance Europe: Finding Heaven. Cambridge: 2009 Reviewed by: Bell, R. History: Reviews of New Books. 2011, 39, 2, p 53-54 Reviewed by: Gordian, M. http://www.h-net.org/reviews/showrev.php?id=33289 Reviewed by: Knobloch, E. ISIS. 2010, 101, 4, p 869-869 Reviewed by: Smith C. Journal of the Society of Architectural Historians. 2011, 70, 1, p 118Kardaras, N. How Plato and Pythagoras Can Save Your Life: The Ancient Greek Prescription for Health and Happiness. Conari Press. 2011. Reviewed by: Anonymus Publishers weekly. 2011, 258, 9, p 49Reviewed by: Bigelow, D. Library journal. 2011, 136, 1, p 114Kingsley, P. Story Waiting to Pierce You: Mongolia, Tibet and the Destiny of the Western World. The Golden Sufi Center, 2010 Reviewed by: Fox, M. http://www.tikkun.org/nextgen/ecstatic‐origins‐of‐the‐western‐soul Reviewed by: Moore, T. PARABOLA 2010. Reviewed by: Ruiz, N.L. http://www.sacredweb.com/online_articles/sw26_kingsley_review.pdf Reviewed by: Steinberg, M. http://killingthebuddha.com/mag/exegesis/only-a-god-can-save-us/ Reviewed by: Tick, E. http://www.sevenpillarshouse.org/reviews/arrow_to_the_soul/ Primavesi, O. Empedokles "Physika" I Eine Rekonstruktion des zentralen Gedankengangs. 2008. Reviewed by: Clay, J.S. Religious Studies Review. 2011, 37, 1, p 52 Reviewed by: Janko, R. Ancient philosophy. 2008, 30, 2, p 407-411 Wersinger, A.G. La sphère et l’intervalle, Le schème de l’Harmonie dans la pensée des anciens Grecs d’Homère à Platon. Grenoble, Millon, 2008. Reviewed by: Macé, A. BULLETIN PLATONICIEN. 2009, 8, p 205-216 Reviewed by: Perrot, S. Aestimatio. 2009, 6. p 212-221 Zaborowski, R. Sur le sentiment chez les Présocratiques. Contribution psychologique à la philosophie des sentiments. 2008. Varsovie, Stakroos. Reviewed by: Cursaru, G. Revue de metaphysique et de morale. 2011, 1, p 82-84

Journal articles Adamo, A. Connecting Art and Science for Education: Learning through an Advanced Virtual Theater with "Talking Heads.". Leonardo. 2010, 43, 5, p 442-448 The authors present an innovative virtual theater in which the language of performance joins advanced technologies for educational goals. On the stage of this pioneering theatrical environment human actors interact with 3D faces ("talking heads") on a wide screen. These synthetic characters are endowed with emotional expressions and voices and resemble famous personalities such as Pythagoras and Einstein. The performance aims at the exposition of difficult subjects in various fields and making learning enjoyable and entertaining. Classical Philology, Vol. 105, No. 4, Special Issue: Beauty, Harmony, and the Good. II Musical Harmony and Mathematical Proportion This special issue of Classical Philology consists of papers and responses presented at a conference on “Beauty, Harmony, and the Good” that was sponsored by the Chicago Area Colloquium on Ancient Greek and Roman Philosophy in October 2008. Barker, A. Mathematical Beauty Made Audible: Musical Aesthetics in Ptolemy’s Harmonics (pp. 403-420) Huffman, C. Response to Barker (pp. 420425) Netz, R. What Did Greek Mathematicians Find Beautiful? (pp. 426-444) Lee, A. Response to Netz(pp. 444-449) In his paper “Mathematical Beauty Made Audible: Musical Aesthetics in Ptolemy’s Harmonics,” Barker suggests that what many Greek writers admired most about music was not the melodies that they heard, but the formal structure of the composition. At this level, “musical and mathematical perfection coincide.” To illustrate the connection, Barker analyzes Ptolemy’s preference for simple proportions in his Harmonics. In his response, Huffman adds further insights about the Pythagoreans and notes that Plato opted for complexity rather than simplicity in at least some cases. Netz (“What Did Greek Mathematicians Find Beautiful?”) offers a two-pronged approach: on the one hand, there is something beautiful in the telling of mathematics, that is, the telling of a story that reveals a surprising result; on the other hand, there is a beauty that resides in the simplicity of the proportions, which differ from those of Pythagorean musical theory. Building on Netz’s interpretation, Lee argues that in the third division (dianoia) of Plato’s divided line, visible diagrams are configured in such a way as to point to an invisible structure in the same way as mathematical diagrams indicate an underlying structure. Aggarwal, A. PYTHAGORAS TREE: A FRACTAL PATCH ANTENNA FOR MULTI-FREQUENCY AND ULTRA-WIDE BANDWIDTH OPERATIONS Progress In Electromagnetics Research C. 2011, 16, p 25-35 Atilano, D. Pitágoras: número, música y proporción Revista UCSAR. 2009, 1, 2, p 9-28 Ban, D. The Methods of Western Medicine in On Ancient Medicine KOREAN JOURNAL OF MEDICAL HISTORY. 2010, 19, 1, p 119-135 Abstract: The treatise On Ancient Medicine attests that questions of method were being debated both in medicine and in philosophy and is important evidence of cross-discipline methodological controversy. The treatise On Ancient Medicine is the first attempt in the history of Greek thought to provide a detailed account of the development of a science from a starting point in observation and experience. The author of it criticizes philosophical physicians who attempt to systematized medicine by reducing it to the interaction of one or more of the opposites hot, cold, wet, and dry, factors. He regards the theory of his opponents as hypothesis(hypothesis). Medicine has long been in possession of both an arche and a hodos, a principle and a method, which have enabled it to make discoveries over a long period of time. As far as method is concerned, the traditional science of medicine attained the knowledge of the visible by starting from observation and experience, but it recommended the use of

reasoning and analogies with familiar objects as a means of learning about the invisible. It also utilized inference from the visible to the visible(epilogismos) and inference from the visible to the invisible(analogismos). The use of analogy as a means of learning about the obscure was also part of the common heritage of early philosophy and medicine. But the author's use of the analogical method distinguishes it from Empedocles' well-known analogy comparisons of the eye to a lantern and the process of respiration to the operations of a clepsydra. According to the author, traditional science of medicine used functional analogy like wine example and cheese example to know the function of humors within the body and utilized structured analogy like a tube example and a cupping instrument example to acknowledge an organ or structure within the body. But the author didn't distinguish between the claim that medicine has a systematic method of making discoveries and very different claim that it has a systematic method of treatment. The reason for this is that he thought that discoveries are the end point of the method of investigation and the starting point of the procedures used in treatment. understands them, could conceive cognitive processes only as "alterations," i.e. at a merely physical level of description, which made them unable to account for the difference between truth and error: by this failure, Aristotle argues in Met. G 5, they unwittingly prepared the way for Protagorean relativism. This reconstruction will permit us also to have a more coherent understanding of some of Aristotle's criticisms of Parmenides and Melissus; finally, I will shortly point out some analogies and differences between Aristotle's theory of cognition and functionalist theories in contemporary philosophy of mind. Bredlow, L.A. Cosmología, cosmogonía y teogonía en el poema de Parménides Emerita. 2010, 78, 2, p .. Resumen: El propósito de este artículo es ofrecer una nueva reconstrucción del sistema del mundo físico de Parménides, distinguiendo debidamente los momentos cosmológicos, cosmogónicos y teogónicos de la teoría, cuya confusión ha sido fuente principal de malentendidos en las interpretaciones anteriores. En particular, el sistema de coronas o anillos de B 12 y A 37 no representa el orden actual del universo, sino la estructura general de la materia, así como el estado inicial de la cosmogonía (sección 1), según puede inferirse también de la lectura de los fragmentos por Simplicio (sección 2). Esa distinción permitirá una reconstrucción tentativa de la cosmogonía (sección 3) y la cosmología de Parménides, cuyo rasgo más llamativo es la ubicación de las estrellas fijas por debajo del Sol y de la Luna, sostenida asimismo por Anaximandro y —como trataré de mostrar— en la cosmología del papiro órfico de Derveni (sección 4). Barker, A. Mathematical Beauty Made Audible: Musical Aesthetics in Ptolemy’s Harmonics See: Classical Philology, Special Issue; p 28 Belenkiy, A. An astronomical murder? ASTRONOMY & GEOPHYSICS. 2010, 51, 2, p 9-13 Abstract: Ari Belenkiy examines the murder of Hypatia of Alexandria, wondering whether problems with astronomical observations and the date of Easter led to her becoming a casualty of fifth-century political intrigue. CAMILLE, A. Soul searching. U.S. catholic. 2010, 75, 11, p 44-46 The article examines where souls go after departing from the earthly lives. The author refers to several explanations from the Scriptures on what happens after death but do not contain exact details and man's belief on resurrection of the body. It explores the Hebrew perception of life after death and how the Pythagorean and Platonists view the soul. Several other beliefs from philosophers such as Tertullian, Thomas Aquinas and Alphonsus Liguori are also noted. Bredlow, L.A, Aristotle on pre-Platonic theories of senseperception and knowledge FILOSOFIA UNISINOS. 2010, 11, 3, p 204-224 Abstract: This paper is an attempt to make sense of Aristotle's polemic -and, if taken at face value, quite evidently wrong-contention that the ancient thinkers globally failed to distinguish thought and knowledge from sensation. As I will try to show, what these thinkers missed, in Aristotle's view, was his own concept of intellect (nous) as a distinct mental faculty correlative to forms (eide). Lacking a concept of "forms" (formal and final causes), pre-Platonic thinkers, as Aristotle Castro, D.H. Aeneas' commitment. Virtue and radical democracy after the dialectic of Enlightenment

ISEGORIA. 2009, 41, p 137-162 Abstract: The aporia resulting from Horkheimer and Adorno's critique of the Dialectic of Enlightenment has been raised after the hermeneutic turn of the tradition started by Nietzsche and Heidegger. Essentially it proposes a new Western philosophy beginning, starting from the ontological duality established by the presocratics and maintained by Aristotle against the monological reason of Plato's teachings. Starting from a new point of view on the Nicomachean and Eudemian ethics, the author puts forward a critique of modern views on Aristotle's virtue theory, including MacIntyre, in order to propose a new approach to connect the practice of virtue to radical democracy. De Santo, N.G. Where philosophy meets clinical science HEMODIALYSIS INTERNATIONAL. 2011, 15, 2, p 178-182 Abstract: Nowadays, there is a renewed interest in bone changes in experimental and clinical nephrology. However, the need for understanding the peculiarity of bone can be traced back to the 5th century BC, when Empedocles of Acragas put forward a theory of a world made of air, water, fire, and earth governed by love and hate. By observing the various body tissues, he strove to demonstrate that they consisted of 4 elements assembled with different mathematical ratios (logos). Blood is considered the most perfect tissue, because the ratio between elements is one. Bone is a very unusual tissue because it is made of 2 parts of earth, 2 parts of water, and 4 parts of fire. This kind of reasoning could be considered the first cry in the birth of quantitative chemistry. Coelho, R.F. History of robotic surgery Journal of Robotic Surgery. 2010, 4, 3, p 141-147 Dušanic, S. Plato’s Projects for a Confederate Sicily and the Constitutional Patterns in the Third Book of the “Laws” Aevum. 2010, 84, 1, p 61-68 Cohen-Skalli, A. À propos de l'anecdote pythagoricienne de Phintias et Damon : extrait du PseudoMaxime, un nouveau témoin d'un fragment de Diodore Revue des études grecques. 2010, 123, 12, p 543-585 ELIOPOULOS, P. ARS VITAE IN IAMBLICHUS AND IN THE STOIC SENECA ΣΧΟΛΗ. ANCIENT PHILOSOPHY AND THE CLASSICAL TRADITION. 2010, 4, 2, p 210–219 ABSTRACT. Seneca expounds a theory of therapy and teaching with the ultimate goal of self knowledge and wisdom. Some of his techniques are based on Pythagorean principles or derive ideas from them, among them the focused and constant ascesis of self control. Iamblichus in De Vita Pythagorica exhibits great interest on the fact that man’s inherent abilities along with the aid of proper education suffice for his attainment of wisdom. For both thinkers, knowledge through practice is considered to be one of the major philosophical demands in the perspective of an “ars vitae”. The human being has to canalize himself into the modeling of a new way of living, an “art of living” which will contribute decisively to the fulfillment of his teleology, to his perpetual eudaimonia (bene vivere). The admittance of individual differences in people’s ability to reform themselves only signifies the more intense effort of the teacher towards a purification of their intellect and greater engagement of the individuals’ volition but not their inability for correction. COULOUBARITSIS, L. ÉMERGENCE DE L’INDIVIDUALITÉ DANS LA PRATIQUE ARCHAÏCHE DU MYTHE D’HOMÈRE À EMPÉDOCLE HYPNOS. 2010, 24, p. 1-23 Abstract: The article aims to explain the emergence of the concept of individuality from Homer and Hesiod on; the concept is difficult to capture from other mythical texts which use a different structure of thought. It is shown that subsequently in Heraclitus, Parmenides and Empedocles this concept becomes more complex and that in Plato and Aristotle there is a polysemy in its logos that transgresses myth in part and combines with the field of metaphysics so that it is thought of as an “individual substance” governed by the idea of “simplification”. DAVIES, M. FROM RAGS TO RICHES: DEMOCEDES OF CROTON AND THE CREDIBILITY OF HERODOTUS Bulletin of the Institute of Classical Studies. 2010, 53, 2 p 19-44

Festini, H. Petric and Acastos, Sequel One FILOZOFSKA ISTRAZIVANJA. 2010, 30, 3, p 451-456 Abstract: The author established on the occasion of the previous presentation "Petric and Acastos" given at the symposium Petric and Renaissance Philosophical Traditions, held in 2008, that Petric was closest to the Platonist-Neoplatonist-Pythagorean original, but also that he contributed to the disintegration of classical ethical virtue (by some utilitarian interventions in particular) and that there were two more comparative models he came close to - that of Acastos I (in connection with the view that artistic creation contains all religion and morality) and to some extent that of Acastos II (only in connection with justice). Retaining the three models, the author now deals with the comparison in relation to poetic art as it is outlined in the fifteen selected (translated) Petric's texts in the book by Ljerka Schiffler entitled Frane Petric o pjesnickom umijecu (Frane Petric on Poetic Art, Zagreb: Institut za filozofiju, 2007). The author will look into the degree to which the mentioned comparison revealed connections with previous conclusions. Needless to say, the author will along the way try to determine whether Petric's poetics presents merely a defence of Plato's attitude or it contains some elements of Aristotelianism, which would connect Petric with not only Baroque and Mannerism but also modernist aesthetics. Platonic doctrine about general terms, to the extent that a commentator such as Simplicius works to reduce the dissonance between Archytas' and Aristotle's words. This paper has three aims: to restore the general grid that Simplicius uses for reading and commenting on Archytas through Aristotle; to identify the exegetical strategies aimed at a doctrinal reconciliation; to consider a specific case, provided by the doctrine of weight, which engenders a new physical theory by Simplicius. Gencarella, S.O. Purifying Rhetoric: Empedocles and the Myth of Rhetorical Theory QUARTERLY JOURNAL OF SPEECH. 2010, 96, 3, p 231-256 Abstract: 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. García Quintela, M.V. La destrucción de Síbaris y la política pitagórica Athenaeum, Studi di Letteratura e Storia dell’Antichità. 2010, p 365-388 Gavray,M.A. Archytas lu par Simplicius. Un art de la conciliation* International Journal of the Platonic Tradition, 2011, 5, 1, p 85-158 Abstract: Intent upon harmonizing doctrines of their predecessors, some Neoplatonic commentators are faced with a problem of resolving doctrinal discrepancies so as to restore the συµφωνία in the history of philosophy. This article considers a particular example of this attempt ats harmonization: how Simplicius reconciles Aristotle's Categories with the Neopythagorean doctrine of the Pseudo-Archytas. The chronological inversion introduced by the counterfeiter produces remarkable effects on the late Harrán, D. An Early Modern Hebrew Poem on Music in Its Beginnings and at the End of Time Journal of the American Musicological Society. 2011, 64, 1, p 3-50 Abstract: One of the mainstays of this Journal is the history of music. But its readers are unlikely to envision a history told from a biblical and rabbinical point of view. Such an account is encapsulated in a Hebrew sonnet written by the learned Paduan scholar and rabbi Samuel Archivolti (d. 1611) and included in a treatise published in 1602. The poem is introduced there, in a chapter on Hebrew metrical schemes, by a lengthy inscription that summarizes its themes and refers to questions

of prosody. Using Hebrew sources, Archivolti details an unconventional history, in the poem itself, that begins with the sounds of the planets, then continues on earth after divine inspiration with the invention of music by Jubal and, after the Flood, its reinvention by Pythagoras. He signals the major role played by David and his kinnor (lyre) in the Temple, then augurs a future history of music, no less fictitious, in the time of the Messiah (when David's seven-string kinnor will expand to eight strings) and the world to come (when it will expand to ten). Beyond discussing the poem for its singularity, I will identify its contents for their Hebrew and comparable non-Hebrew sources and trace its origins to the one source that, in a surprising bibliographical turn of events, seems to have prompted Archivolti to write it in the first place. The concluding section turns on its broader implications. une représentation symbolique du cosmos. Cette interprétation pythagoricienne ou pythagorisante pourrait avoir été la conséquence de l’adoption de la forme circulaire du Comitium, dont le mundus finit par traduire la dimension cosmique. Le mundus et le Comitium sont donc devenus, entre la fin du IVe et le milieu du IIIe siècles, les centres symboliques de l’espace de la cité, et leur interprétation pythagoricienne (ou pythagorisante) en fit des représentations cosmiques de l’univers, auquel les nouvelles institutions, adoptées vers la fin du IVe siècle, tâchaient de se conformer. Kainzinger, A. The mathematics in the structures of Stonehenge ARCHIVE FOR HISTORY OF EXACT SCIENCES. 2011, 65, 1, p 67-97 Abstract The development of ancient civilizations and their achievements in sciences such as mathematics and astronomy are well researched for script-using civilizations. On the basis of oral tradition and mnemonic artifacts illiterate ancient civilizations were able to attain an adequate level of knowledge. The Neolithic and Bronze Age earthworks and circles are such mnemonic artifacts. Explanatory models are given for the shape of the stone formations and the ditch of Stonehenge reflecting the circular and specific non-circular shapes of these structures. The basic mathematical concepts are Pythagorean triangles, thus adopting the construction procedures of the Neolithic circular ditches of Central Europe in the fifth Millennium bc and later earthworks and stone circles in Britain and Brittany. This knowledge was extended with new elliptical concepts. Approximations for the values of π and the square root of 2 are encoded in the henge. All constructions were performed using a standardized “Babylonian” metrology that shows a remarkable consistency and comprehensible development over some 14 centuries. Hasler, J.F.W. Fragmento anonimo sobre los pitagoricos, preservado por Focio (s. IX). IDEAS Y VALORES. 2010, 142, p 161-167 Abstract: After a brief historical context of the work and its sources -- notably its possible origin in the compilation "miriobiblion" by Photius of Constantinople (ca. 810-ca. 893), Hasler (professor at the Universidad de Antioquia, Colombia) presents the full Spanish translation of Kenneth Sylvan Guthrie's English translation (from the original Greek) of the pseudo-Aristotelian "On the Pythagoreans". The first part focuses on Pythagoras and his teachings, mentioning his influence on Plato. The second part compares and contrasts the doctrines of the Pythagoreans, Plato and Aristotle, while the final part is a systematic, quite Aristotelian classification of nature and the human senses. Huffman, C. Response to Barker See: Classical Philology, Special Issue; p 28 Humm, M. Le mundus et le Comitium : représentations symboliques de l'espace de la cité Histoire urbaine. 2004, 2, 10, p. 43-61. Le mundus et le Comitium sont deux monuments symboliques placés au cœur de la Cité, à Rome : alors que le Comitium est le lieu de réunion symbolique des assemblées du peuple, le mundus est un monument qui évoque la fondation de la Cité ainsi que la communication de celle-ci avec ses dieux. Mais le mundus romain aurait reçu, entre la fin du IVe et le milieu du IIIe siècle, une interprétation pythagoricienne qui l’assimila à Knobloch, E. Nomos und physis Alexander von Humboldt und die Tradition antiker Denkweisen und Vorstellungen HiN. Internationale Zeitschrift für Humboldt Studien. 2010, 21, p 45-55 Abstract: Alexander von Humboldt’s world view, philosophy of science, and scientific practice were dominated by the notions of measure and harmony. This matter of fact

does not leave any doubt about Humboldt’s Pythagoreanism. Already the choice of the title of his Kosmos was led by Pythagorean thought. In 1846 he explicitly wrote to Jacobi that the whole first book is based on the idea that the first Hellenic seeds to all further progresses of mathematical natural knowledge are owed to the Pythagoreans and their emphasis on measure, number, and weight. The paper consists of four parts. The first part deals with Humboldt’s acquaintance with the fragments of the Pythagorean Philolaus. The second part compares the Aristotelean tradition with Philolaus’s informations on Pythagoreanism. The third part relying on the two foregoing parts explains Humboldt’s philosophy of science as a tranformation of Pythagoreanism. The last part discusses three examples taken from Humboldt’s scientific practice in order to illustrate the results deduced up to then. Lévi, N. Le De Rervm Natvra de Lucrèce, ou la subversion épicurienne de la révélation pythagoricienne des Annales d’Ennius Revue de philologie, de littérature et d'histoire anciennes. 2011, 1, p 113-132 Au livre I du De rerum natura (v. 112-126), Lucrèce fait allusion au prologue des Annales d’Ennius, où ce dernier faisait le récit d’un songe oraculaire au cours duquel l’ombre d’Homère lui apparaissait pour lui faire une révélation de nature pythagoricienne sur les secrets de l’âme et de l’univers. Cet article se propose de montrer que l’évocation qu’en fait Lucrèce, placée sous le double signe du rejet doctrinal et de l’admiration poétique, est le point de départ d’une dynamique qui traverse l’ensemble du De rerum natura : en effet, le poème philosophique de Lucrèce, tout en condamnant le pythagorisme sur la question de l’âme, subvertit son symbolisme religieux en le transposant vers la seule « révélation » authentique – celle de l’épicurisme – et vers le vrai dieu – Épicure. Lee, A. Response to Netz See: Classical Philology, Special Issue; p 28 Mack, J. The Tree in Pythagoras' Garden Australian Senior Mathematics Journal. 2010, 24, 2, p 58-63 This geometrical account of primitive Pythagorean triples was stimulated by a remark of Douglas Rogers on a recent paper by Roger Alperin (Alperin, 2005). Rogers, in commenting on this paper, noted that Fermat in the 17th century had posed a challenge problem on Pythagorean triples that suggested he knew how to construct a sequence of them, possibly via a geometrical method (Fermat, 1643). Rogers himself gave an expanded version of such a method and from this has come the present investigation. In this article, the authors discuss Pythagoras' theorem and describe Fermat's challenge to his correspondents, which was to find six "Primitive Pythagorean Triples" (PPTs) in which the two legs differed in value by 1. The authors show that given any right-angled triangle with sides forming a PPT, they can associate with each side a new right-angled triangle, likewise with sides forming a PPT. (Contains 3 figures.) Lee, J.S. Iannis Xenakis and the Presocratic Foundations of a New Music Journal of Modern Greek Studies. 2011, 29, 1, p 73-82 Abstract: Paradoxes abound in the music of Iannis Xenakis (1922–2001), a music almost paradigmatically "difficult," recalcitrant to traditional modes of musical and aesthetic analysis, and yet shockingly direct in its aural richness and in its impact on listeners. In his theoretical writings, Xenakis makes repeated references to Presocratic philosophers—in particular, to Heraclitus and Parmenides— using these archaic texts to help make a case for his own "stochastic music." Xenakis's interest here is in finding ways to integrate the stasis characteristic of Parmenides's account of the real with the constant flux of the real that Heraclitus describes. Xenakis goes further, however, to develop an account of listening as "experimental" on the basis of his distinctive reading of the Presocratic tradition. Thalleïn, a composition for large chamber ensemble, provides a vivid illustration and test case both for Xenakis's interpretation of the Presocratics and for his approach to listening as experiment. Marcinkowska-Rosół, M. Empedocles B 105 and the Definition of Human Mind. Eranos. 2008-2009, 105, p 118–123 Leikola, A. Darwinista kohti Empedoklesta Tieteessä tapahtuu. 2010, 28, p 55-57 Michell, J. Qualitative research meets the ghost of Pythagoras.

Theory & Psychology. 2011, 21, 241–259. Abstract: The issue of qualitative versus quantitative methods is rooted first and foremost in the character of the phenomena investigated and not in an investigator’s methodological preferences. If the phenomenon under investigation is nonquantitative, then it cannot be studied successfully by attempting to use quantitative methods because trying to impose quantitative concepts upon qualitative phenomena misrepresents them. If the target articles provide any guide, these truths are ignored as much by psychologists wanting to mix quantitative with qualitative methods as by mainstream quantitative researchers. These articles display both the power of the modernist fantasy that measurement is always a discretionary choice of any investigator and the power of the persistent delusion that psychological attributes must be measurable. In psychology, as ever, the ghost of Pythagoras rules. Abstract: As the outcome of an internet search in full digital versions of German texts from the 18th century, this contribution provides new information concerning the formation of substantive verbs in the domain of esotericism: the concept of an “esotericist” (Esoteriker) appears for the first time in 1770, followed by the abstractum “esotericism” (Esoterik) in 1792. This development took place within the historical context of scholarly discussion about Pythagoras and his school in the works of Christoph Meiners (1747-1810) and Johann Philipp Gabler (1753-1826). The standard view in the study of esotericism, according to which the term esotericism first appeared in Jacques Matter's study of gnosticism of 1828, must therefore be revised: the concept Esoterik was born in the Late Enlightenment, not in the 19th century. After this, however, it takes a long time for the concept to be established as a lemma in German lexicons and dictionaries: here, the decisive shift takes place only in the theosophical / anthroposophical movement and its popularization in the “New Age” context around 1970. Most, G.W. Pi omicron lambda epsilon mu omicron sigma pi alpha nu tau omega nu pi alpha tau eta rho THE PRESOCRATICS IN THE RESEARCH OF THE 1920s ETUDES PHILOSOPHIQUES. 2010, 2, p 235- Nicolau, S.N. Lectia lui Pythagoras sau introducere in filosofie. Analele Universitatii din Craiova, Seria: Filosofie. 2009. 24, 2, p 137-151. AB En partant de la regle du silence et de la discipline dans la vieille ecole pythagoricienne, l'article s'efforce d'eclaircir la signification plus profonde des ces gestes de commencement, s'appuyant, d'une part, sur des raisons historiques detachees des sources antiques et, d'autre part, sur des raisons etymologiques de la langue grecque. Müller, G.F. LA DOCTRINA DE LOS TRES DIOSES DE NUMENIO Revista Archai. 2010, 5, p 29-36 ABSTRACT: This paper will focus on what is perhaps the most characteristic doctrine of Numenius: that which taking into account what is said in the Second Letter attributed to Plato (312 e 1-3), affirms the existence of three gods. By analyzing some preserved fragments, I try to offer an overview of numenian theology to thereby specify the particularity of Numenius’ thought in the context of Platonism of his time, fact that makes him one of the most relevant predecessors of Plotinus’s system. Oliveira, A.R.E. ARCHIMEDEAN SCIENCE AND THE SCIENTIFIC REVOLUTION History of Mechanism and Machine Science. 2011, 11, p 377-386 Conference Information: International Conference on Genius of Archimedes (23 Centuries of Influence on the Fields of Mathematics, Science, and Engineering), JUN 08-10, 2010 Syracuse, ITALY Abstract: According to Richard Westfall (Westfall, 1977) the Scientific Revolution of the seventeenth century was dominated by two themes: the Platonic-pythagorean tradition "which looked on nature in geometric terms" and mechanical philosophy "which conceived of nature as a huge machine". This paper is an attempt to study the appropriation of Archimedean science in the Scientific Revolution in Western Europe. Netz, R. What Did Greek Mathematicians Find Beautiful? See: Classical Philology, Special Issue; p 28 Neugebauer-Wölk, M. Der Esoteriker und die Esoterik: Wie das Esoterische im 18. Jahrhundert zum Begriff wird und seinen Weg in die Moderne findet Aries. 2010, 10, 2, p 217-231

Padmanabhan, T. Dawn of science: 2. The Athens factor Resonance. 2010, 15, 7, p 590-594 Keywords: Pythagoras, Kepler, Plato, Academy at Athens. Peláez del Rosal, J. Espacio, tiempo y adversidad en los relatos de milagro del Evangelio de Marcos y de la Vida de Apolonio de Tiana , de Flavio Filóstrato Fortunatae. 2009, 20, p 101-126 Papathanassiou, M.K. Reflections on the antikythera mechanism inscriptions ADVANCES IN SPACE RESEARCH. 2010, 46, 4, p 545-551 Abstract: A close look at the fragmentary inscriptions of the Antikythera Mechanism published by Freeth et al. [Freeth, T., Bitsakis, Y., Moussas, X., Seiradakis, J.H., Tselikas, A., Magkou, E., Zafeiropoulou, M., Hadland, R., Bate, D., Ramsey, A., Allen, M., Crawley, A., Hockley, P., Malzbender, T., Gelb, D., Ambrisco, W., Edmunds, M.G. Decoding the Antikythera mechanism: investigation of an ancient astronomical calculator. Nature 444 (7119), 587-591, 2006] reveals some elements, which could help to decode its function and use. The Back Door Inscription seems to give a detailed description of some external parts of the instrument and the related instructions for their use. We especially refer to the term "ecliptic" as compared to that in Ars Eudoxi and other papyri and inscriptions. The Back Plate Inscription seems to give instructions for the proper orientation and use of the instrument. The Front Door Inscription refers to the stationary points of planetary motion, but only two planetary names have been read, that of Venus and Mercury, as far as we know. After a study of the works of Alexandrian scholars Ptolemy, Theon, Paulus and Heliodorus regarding the stationary points of planetary motion, we arrive at the following conclusion: it seems very likely that the Antikythera Mechanism has been constructed apart from other uses (a) for the observation of the Sun, the Moon and the stars; (b) to simulate the longitudinal motion of the Sun, the Moon and the planets, and (c) in the case of Mercury and Venus the instrument could also show their stationary points and the retrograde arc between them; here we present additional arguments to support the view that this is also true for the three outer planets. As far as the technical knowledge underlying the construction of Mechanism's gear trains is concerned, the last (eighth) book of Pappus's Collection, includes the basic notions and theorems for such constructions, known from the earlier works of Archimedes. Pesic, P. The History of Hearing the Irrational Music and the Development of the Modern Concept of Number Isis. 2010, 101, p 501–530 ABSTRACT: Because the modern concept of number emerged within a quadrivium that included music alongside arithmetic, geometry, and astronomy, musical considerations affected mathematical developments. Michael Stifel embedded the then-paradoxical term “irrational numbers” (numerici irrationales) in a musical context (1544), though his philosophical aversion to the “cloud of infinity” surrounding such numbers finally outweighed his musical arguments in their favor. Girolamo Cardano gave the same status to irrational and rational quantities in his algebra (1545), for which his contemporaneous work on music suggested parallels and empirical examples. Nicola Vicentino’s attempt to revive ancient “enharmonic” music (1555) required and hence defended the use of “irrational proportions” ( proportiones inrationales) as if they were numbers. These developments emerged in richly interactive social and cultural milieus whose participants interwove musical and mathematical interests so closely that their intense controversies about ancient Greek music had repercussions for mathematics as well. The musical interests of Stifel, Cardano, and Vicentino influenced their respective treatments of “irrational numbers.” Practical as well as theoretical music both invited and opened the way for the recognition of a radically new concept of number, even in the teeth of paradox. Petrucci, F. Se per Platone 9/8 non è un rapporto epimore. Su una curiosa esegesi tecnica del Timeo (Theon. Smyrn. exp. 74, 15-75, 25) » p 319-330 Abstract: The classification cf 9/8 as epimoric ratio is not only a basic arithmectical notion, but also an important technical ground for Pythagorean-Platonic musical theory. Why then does Theon of Smyrna avoid this point? The common explanation, which refers to Theon's inadequate technical knowledge, is unsatisfactory and aprioristic. A better solution can be found in the exegetical nature af the Expositio. Thcon's

technical perspective is inspired by a distinctive understanding of the "musical theory" of the Timaeus. cosmic cycle as a fourfold continuous process is deeply inadequate. Redfield, J. The Philosophers and the Many History of Religions. 2010, 50, 1, p 43-53 Pontiggia, E. Tra Piatone e Pitagora: la concezione del tempo nel Ritorno all'ordine in Europa (19191930) Rivista dell'Istituto per la storia dell'arte lombarda. 2010, 1, 1, p 75-85 Rossi, K. THE HYPATIA OF ALEXANDRIA BY ALEJANDRO AMENABAR film director, has works published PONTE. 2010, 66, 9, p 89-93 Porubjak, M. Presocratic Socratics on the Care of the Self FILOZOFIA. 2010, 65, 3, p 214-226 Abstract: The aim of the article is to show that epimeleia heautou (the care of the self) one of the key issues of ancient Greek philosophy can be found in a tradition which is older than the Socratic one. First, the author outlines modem paradigmatic interpretations of the history of philosophy (Platonic and Aristotelian) and tries to offer an alternative interpretation based on Hellenistic tradition influenced by Socrates. Then he explores the texts of archaic lyrics the elegies of Theognis of Megara. Resulting from the analysis of the problem of Theognis' seal, and the parallels between Theognis and archaic lawgivers is the author's conviction, that the Theognidean poetry as a whole represents a coherent sociopolitical discourse based on the care of the polis. In conclusion the author traces three basic Socratic issues in Theognidean poetry: political action, pedagogy, and love between a men and a boy. Schacht, U. The Hubble View of Heraclitus To let out a new Edition of the Presocratics MERKUR-DEUTSCHE ZEITSCHRIFT FUR EUROPAISCHES DENKEN. 2011, 65, 3, p 259SKARSOULI, P. DES PAPYRI GRECS EN CONTEXTE FUNÉRAIRE. L'EXEMPLE DE < L'EMPÉDOCLE DE STRASBOURG> Metis. 2010, 8, p 167-187 Somers, V. Thesaurus Sententiarum Sexti. Textus auctus una cum Sententiis Clitarchi, Sententiis Pythagoricorum et Translatione Latina Rufini Aguileiensis. REVUE D HISTOIRE ECCLESIASTIQUE. 2010, 105, 1, p 168-170 Szlezak, T.A. PLATON IN SYRAKUS: Politik, Philosophie, Eros Perspiven der Philosophie. 2010, 36, p 185-210 Die Verwicklung Platons in die Politik von Sizilien von seinem ersten Besuch 388/87 bis zum gewaltsamen Tod Dions 355 wird verfolgt unter Berucksichtigung der persönlichen Beziehungen und der Charaktere und Intentionen nicht nur der Hauptakteure (Platon, Dion, Dionysios II), sondern auch einiger Nebenfiguren (Speusippos, Kallippos, Herakleidas, Archytas), so weit die Quellen das zulassen. Die Angaben des Siebten Briefes werden wegen ihrer Konsistenz und hohen inneren Wahrscheinlichkeit als verläßlich betrachtet, wobei es keinen großen Unterschied macht. ob wir sie fur authentisch platonisch halten oder “einem engen Schuler Platons" (W. Burkert) zuweisen. Im Anhang werden drei neuerdings formulierte “Verdachtsmomente" gegen die Echtheit des Briefes einer kritischen Prufung unterzogen. Rashed, M. La zoogonie de la Haine selon Empédocle: retour sur l'ensemble `d' du papyrus d'Akhmim* Phronesis. 2011, 56, 1, p 33-57 Abstract: This article aims at reconstructing the most damaged part of the Strasbourg papyrus of Empedocles (fragment f-d), by taking into account all the parameters at our disposal: palaeography, metre and, of course, content. According to this attempt, Empedocles would be describing the very moment in the phase of increasing Strife when the whole-natured creatures (the ολοφυ) were split into male and female beings. Thus, the first part of the fragment becomes very similar, in its content, to fr. 62 D.-K. and to Plato's parody of Empedocles in Aristophanes' myth in the Symposium, while its second part emerges as containing new details of the process by which double creatures were split into two. If this reconstruction is accepted, its implication will be that Aetius' presentation of Empedocles'