Nieuwsbrief 8

Newsletter No. 8. June 2007. Website http://www.stichting-pythagoras.nl/ E-mailadres nico.bader@stichting-pythagoras.nl Editors Nico Bader, Marie-Anne de Roode This semi-annual Newsletter gives articles and a summary of literature, book reviews of recent publications concerning Pythagoras and Pythagoreans. Interesting internetsites, work in progress and conferences are included. We will be very pleased to receive information of books and (journal, internet) articles to keep our lists up to date. Nico Bader - Chairman of the Pythagoras Foundation. Philosophy is a purification and perfection of human life: a purification from our irrational, material nature and the mortal form of the body, a perfection by the recovery of our proper happiness, leading to divine likeness. (The Commentary of Hierocles the Philosopher on the Pythagorean Verses. Proem. In: Schibli, H.S. Hierocles of Alexandria. 2004, p 170) Contents: Introduction by M. de Roode Pythagoras Foundation Library information by N.G. Bader Acknowledgments. Correction Colophon, copyrights APA abstracts Timaeus conference abstract Recent publications: Books Forthcoming books Chapters in books Internetsites Book reviews Letters concerning review Journal articles Work in progress / forthcoming conference Commentaries concerning Ms Wertheim article 1 p 2 p 2 p 3 p 3 p 4 p 6 p 7 p 13 p 14 p 16 p 17 p 18

Introduction We welcome the new subscribers to our newsletter. From reactions we have received, we know that our work is being much appreciated. But still more important is the development of the content. Thanks to all for sending us valuable reactions. We would like to mention the visit from Leonid Zhmud to the library. We enjoyed the conversations we had and his statement “impressive” (referring to the book collection at the library). We appreciated his critical “comments with a smile”! The next newsletter will be issued on December 2007. If you like to contribute, please do not hesitate to contact us. Best wishes for a nice summer, Marie-Anne de Roode Pythagoras Foundation Library Information. The Library collects all publications concerning Pythagoras and Pythagoreans. The library is a lending library; also copies of articles can be ordered. Copy costs and postage will be calculated. The Foundation is a non-profit organisation; our Newsletter is free of charge. Donations, also in the form of articles or books are very welcome. The Pythagoras Foundation Thorbeckelaan 46 1412 BR Naarden The Netherlands Postbank: giro 27423. International Bank Account Number (IBAN): NL84 PSTB 0000 0274 23 BIC: PSTBNL21 News from the library. May is a busy month. Time to collect, organize and compose a new Newsletter. It is amazing and surprising how much new literature has been published concerning Pythagoras and Pythagoreans. After 2500 years still so many people are fascinated by these founders of Western thought. We start realizing how much work the correction of the database takes. It is amazing to see how the founding fathers traced articles concerning Pythagoras and Pythagoreans all over the world. And they did it in that time without the help of Internet or email! We will keep you informed. Nico Bader P.S. A few (paper) copies of the article of Mr de Zwarte about the Athena temple at Paestum (zie page 22) are available.

Acknowledgements The Pythagoras Foundation thanks the following individuals for their contributions and generosities: Laura Gemelli, Katerina Ierodiakonou, Sergio Jerez, Christiane Joost-Gaugier, Kristi Jauregi Ondarra, Peter Kingsley, Peter Loptson, Tony Preus, Jacomien Prins, Albert van der Schoot, Christopher Smith, Harold Tarrant and Ruud de Zwarte. Correction The last Newsletter “Quote” on page 1 missed a word: this is the correct text: “Well known to intellectuals through the Antique texts of Plato, Aristotle, Plutarch, Cicero, Ovid, Nicomachus, Macrobius, Martianus Capella, Boethius, and many others, the image of the brilliant yet humble sage from Samos had been slowly reconstructed through medieval times, when he was admired by many influential Christian scholars from Cassiodorus to Petrarch. His admirers were to be found in Spain and England as well as France, Italy, Constantinople, and the Arab world.” From: Joost-Gaugier, C.L. Measuring heaven. 2006. p 76. Colophon Pythagoras Foundation Newsletter. Semi-annual Newsletter of the Pythagoras Foundation. Editors: Nico Bader, Marie-Anne de Roode. Address: Thorbeckelaan 46. 1412 BR Naarden. The Netherlands. E-mail : nico.bader@stichting-pythagoras.nl Website: http://www.stichting-pythagoras.nl/ Editorial Board: in progress. Advisory Board: in progress. ISSN: 1872-3241 (online version); 1872-3233 (print version). COPYRIGHT / USAGE NOTICE: PLEASE READ Contents of the Pythagoras Newslettter are copyright 2006 by the Pythagoras Foundation. The newsletter may be freely distributed in electronic or print form provided its contents are not altered and credit is given to the Pythagoras Foundation, Thorbeckelaan 46, 1412 BR Naarden, The Netherlands. If you wish to unsubscribe to this Newsletter, send an e-mail message to info@stichting-pythagoras.nl

undisputed attribution, and the tradition reflected by P.Tebt. 694 seems to be confirmed also by one of our best sources on Pythagorean musical theory, namely Boethius De institutione musica 3.9, a passage repeating very closely the operations outlined by our fragment: in this passage, the procedure described in detail by Boethius, the method of concords, is clearly attributed by him to Philolaus, and as a further confirmation of the connection to the Pythagorean milieu, the description of this procedure appears within a section of book 3 dedicated to Pythagorean musical theories. P. Tebt. 694 offers motifs of interest both for a study of the text and its reader and for its content. The use of the method of concords, a procedure otherwise known only through the indirect tradition, is thus confirmed by a witness about as old as our oldest sources, and the use of this method can be confirmed as having enjoyed a wider diffusion than could previously be demonstrated. 2006 APA (American Philological Association) Annual Meeting. Abstracts Monica SIGNORETTI P.Tebt. 694: A reader’s mark and preAristoxenian music theory P.Tebt. 694 is the only direct witness of the method of concords, a procedure for the tuning of string instruments that could also be used, as is the case here, for the measurement of the length of the intervals between notes. Yet, beyond its importance for the scholars of ancient music, P.Tebt. 694 is of great interest also for a study of the use of a text by a reader, because it may preserve one of the few marks ever left on a papyrus to demarcate a specific passage. The papyrus is remarkable for its bookhand and for the presence of a coronis on the margin of col.2, a very early example going back to the first decades after the introduction of this diacritical sign. Yet, the most interesting feature of P.Tebt. 694 is the mark on the margin of col.2, a large curved sign informally drawn in a darker ink than the rest of the text and probably made by the reader to mark a passage of particular interest, the conclusion of the demonstration carried on between col.1 and the first half of col.2. The text reflects the strong interest for one of the most technical aspects of music theory, the measurement of intervals, a topic often debated in antiquity: it gave rise to divergent views on the length of the tetrachord and of the units in which it could be divided, tone, semitone, and diesis. While the Pythagoreans believed that once a semitone was subtracted from a tone what was left was less than a semitone, a diesis, Aristoxenos supported the opposing view, that a tone was divisible into two semitones. P.Tebt. 694 contains precisely the application of the procedure consisting in the repeated subtraction of one tone from the tetrachord to determine the dimensions of the interval left after the subtraction of all whole tones, most probably with the goal of measuring the interval left. In his publication, Grenfell briefly investigated the context from which this treatise on music derived and he stressed the points of contact with Philolaus Fr.6. The elements suggesting a connection with Philolaus are undeniable: P.Tebt. 694’s technical terminology, in particular the use of terms like δι’όξειών and σνλλαβή, is paralleled in Fr.6. The closeness between this last fragment, of Harold TARRANT Proclus and Predecessors on the ‘Myth’ of Atlantis Most of the first book of Proclus In Timaeum is devoted to a discussion of Plato’s treatment of the Atlantis story and its setting (including the Phaethon myth). It is also the key source of earlier treatments, going back through Porphyry’s circle to Numenius and even Crantor. In Proclus’ own treatment the story is viewed as historical, indeed as evidence of Egyptian enthusiasm for recollecting history in order to establish the universal patterns, or periodoi, that determine past, present, and future. However, in spite of a willingness to accept literal truth in the story, Proclus cannot discard the findings of earlier Platonists who accepted only an underlying truth, reflecting ‘wars’ that constantly occur between souls, daemones, or a combination of the two. The story is indeed an account of an actual occurrence, but that occurrence’s conformity with a paradigm of ‘conflict’ within the universe (as claimed by Iamblichus) means that its use if for shedding light on a pattern of great importance for the study of the physical world, established as it is by the dyadic principle on a very high metaphysical level. Proper consideration of the Atlantis story is thus for Proclus an act of recollecting the universal and recalling the periodoi to which all peoples are subject, at the same time as considering the

relation of these periodoi to the workings of the universe. The alleged relation of an Egyptian method of using history to illuminate the universal to the Pythagorean practice of recollecting one’s earlier lives (I, 124.4ff) provides a handy link with Proclus’ insistence that the methodologies employed in the Timaeus are essentially ‘Pythagorean’, which in turn suggests dependence on images and symbols, both of which have a special place in myth. Compare the account of ‘Egyptian’ method at I, 129.23ff., where a key feature is the application of Plato’s interpretation of the Phaethon myth to the Atlantis story that it introduces. I argue that Proclus’ evidence shows what mythos as opposed historia had been for earlier interpreters (at least to Porphyry), more terms of literary genre than of truth-status, though as in Porphyry’s De Antro Nympharum the terminology of invention, plassô, plasma, had regularly been applied to mythoi. Historia was no more than a descriptive narrative based on the accounts of others. Mythos had symbolic meaning, historia a literal one. Numenius had inspired both ingenuity and debate, promoting symbolic meanings by demonstrating that literal meanings could not be taken seriously. After Numenius, no named figure resists symbolic meanings, though Longinus is behind the literalist arguments at I, 129.12-23. Iamblichus’ attempt at reconciliation is the first sign of this dichotomy being questioned, possibly at the expense of misunderstanding the terms of the debate, and replacing the contrast between genres (and the related distinction between two types of authorial meaning) with a related one between levels at which something is true. Mythos was not the same for all Neoplatonists! definitions that suggest a “political science” for Pythagoreans in Southeastern Italy during the 5th and 4th Centuries BCE. This set of terms might seem incongruous to some readers, but the Pythagorean discourse about political organization, following the amalgamation of Milesian and Eleatic philosophy with spatial geometry, developed along lines that emphasized mathematics, natural sciences, and political structures in relationships of homologia. This mode of comparative science draws the criticism of Aristotle when he refers to the “superficial definitions” of the Pythagoreans, whose attempts to establish linguistic definitions of “what exists” were culpable for their simplistic application of a single principle (numbers) to different kinds of existence: Aristotle gives as an example the confusion of the linguistic terms “two” and “double,” for not every number “doubled” will be the number “two” (Met. 987a13-28). This reference to the “Pythagoreans,” which probably refers to a sect of traditional followers of Pythagoras called the acusmatici, is contrasted with the definitions of the “so-called Pythagoreans” or mathematici, a nontraditional sect of Pythagorean philosopherpoliticians who, on the authority of Apollonius of Tyana, initiated democratic revolutions in Sybaris (ca. 453 BCE) and continued to propagate egalitarian reforms throughout citystates in Southeastern Italy (ap. Iam. VP. 25961). Prominent among these mathematici was Archytas, the famous friend of Plato and strategos of Tarentum for seven terms (most likely 367-1 BCE; D.L. VIII.79-83), whose system of analogous equality also recalls Aristotle’s censure of the “so-called Pythagoreans.” While scholars like Walter Burkert (Lore and Science in Ancient Pythagoreanism, 1972) and Carl Huffman (Archytas of Tarentum: Pythagorean, Philosopher, and Mathematician King, 2005) have examined with care the process of definition for those Pythagoreans known as the mathematici, few since Kurt von Fritz (Pythagorean Politics in Southern Italy, 1940) have seriously explored the traditions of Pythagorean politics in Southeastern Italy in relation to their philosophical theories of mathematics, which metaphorize, through categorical kinds of “likeness,” a common numerical language for many aspects of polis institution and governance. I will show that fragments of Aristotle’s Rhetoric (1412a9-17 = Huffman A12) and Problems (915a25-32 = Huffman A23a), when compared with the extant fragments of Archytas’ On Law and Justice (Stob. 4.1.135-138 pp. 82-88 He.), allow us to conceive of the ideal polis of the 2007 APA (American Philological Association) Annual Meeting. Abstracts Phillip Sidney HORKY One Must Metaphorize: Linguistic and Mathematical Analogy as Political Science among the Pythagoreans Aristotle’s Metaphysics, Problems, and Rhetoric preserve significant testimony of relationships between words and mathematical

belligerence. His criticism of those who prefer wealth, luxury and empire to safety, gentleness and independence with justice looks like a very sharp criticism both of the Roman empire and of where Sparta found herself in the fourth century (as Isocrates would note), and of some of his contemporaries. The picture of Numa as a philosopher king, influenced by Greeks, but failing to create the appropriate educational system to sustain his position, is therefore complex, interestingly Isocratean, and rather darker than one might at first sight think. It opens up possibilities for a surprising critique of the Roman world, and a vision of an all too brief golden age, an alternative Rome which could have ruled the world justly, but did not. Plutarch’s Pythagorean Numa remains an uncomfortable juxtaposition of Greek and Roman ideals. Pythagoreans of Southeastern Italy as one based on the same principles of mathematical equality found in Archytas’ theories of linguistic and physical analogy. We can therefore speculate, with more precision, about the structure of democratic governance employed by Pythagoreans in Tarentum, a citystate whose political influence throughout later Western Greece was overshadowed only by Syracuse. Christopher SMITH A Greek Interlude at Rome: Plutarch’s Life of Numa Plutarch’s Life of Numa is well known for its defiant belief in the relationship between Numa and Pythagoras, despite the obvious chronological impossibility. Plutarch notes this (Num. 1) but nonetheless continues to imply or state the connection (8; 14; 22). Moreover, the life is full of an array of references to Latin words which are derived from Greek (flamines from pilamenai; laena from chlaina; ancilia, for which a number of options are considered; April from Aphrodite), and he compares the Vestal fires with equivalents in Greece, and gives a very Greek twist to the story of Picus and Faunus, bound like Proteus and compared to the Idaean Dactyli. There is no doubt that Plutarch is quite deliberate in his statements here. In the comparison (Lyc. et Num. 1.5), he actually states that Numa was far more Hellenic than Lycurgus as a lawgiver. This has led some to regard Numa as embodying a fairly straightforward view of the superiority of Greek culture; so Whitmarsh writes that this passage is proof of the ‘(broadly Isocratean) presence in these writings of a “universalist” equation of Hellenism with civilization’ (Greek literature and the Roman empire: The politics of imitation, Oxford 2001, 118. In this paper I will argue that the situation is rather more complex. Numa is an outsider, not a Roman, who resists kingship, and when he accepts it, takes it in wholly different directions from Romulus, and part of his approach does not survive beyond him; as Plutarch notes, his failure to deal with the issue of education means that nothing he built survived. This is a radically different approach from that of Livy for instance, for whom Numa’s religious reforms are crucial to Rome’s development and longterm future. Yet for all Lycurgus’ focus on education, it is not all clear that Plutarch wholly admires what Spartans do with their education, any more than he relishes the return to Roman TIMAEUS CONFERENCE September 13–16, 2007 University of Illinois – Urbana Abstract: Katerina Ierodiakonou (U. Athens) "Basic and Mixed Colors in Plato's Timaeus" Modern physicists and painters both talk about basic and mixed colors, but their lists of basic colors are very different. For although they all regard basic colors as those from which mixed colors can be produced, while they themselves are not the product of mixture, the choice they make of which colors are to count as basic very much depends on the way they understand colors; namely, whether they understand them respectively as light waves or as pigments. Ancient philosophers, too, give different lists of basic colors. For instance, Empedocles postulates white and black as the only basic colors, whereas Plato lists four basic colors, namely white, black, red and bright. The question which I raise in my paper is what motivates these philosophers to choose the basic colors they do; especially in Plato's case, who undeniably is influenced in many respects by Empedocles, it is interesting to investigate what makes him introduce four, rather than two, basic colors, and in particular why he chooses these four. To try to answer this question, I look into the different way Empedocles and Plato conceive of the nature of color, their different notions of mixture, but also consider the possible influence of other disciplines, such as painting or medicine.

Recent publications. Books geometry - Hypatia of Alexandria (ca. 370- 415 C.E.): First woman of mathematics Aryabhata I (476-ca. 550 C.E.): From alphabetical numbers to the rotation of the earth - Brahmagupta (598-668 C.E.): Father of numerical analysis - Abu Jafar Muhammad ibn Musa al-Khwarizmi (800-ca.847 C.E.) - Father of algebra - Omar Khayyám (ca. 1048-1131 C.E.): Mathematician, astronomer, philosopher, and poet - Leonardo Fibonacci (ca. 1175-1250 C.E.): Hindu-Arabic numerals in Europe. Anonymus. Pensamientos de Marco Aurelio : intimidades de un emperador romano / Marco Aurelio ; Epicteto ; Cebes de Tebas Sant andreu de la barca: Círculo Latino. 2006. ISBN: 8496129942; 9788496129948 Barker, A. The science of harmonics in Classical Greece Cambridge; Cambridge University Press; New York. 2007. ISBN: 9780521879514, 0521879515 Contents: Beginnings, and the problem of measurement - Empirical harmonics before Aristoxenus - The early empiricists in their cultural and intellectual contexts - Interlude on Aristotle's account of a science and its methods – Aristoxenus - the composition of the Elementa harmonica – Aristoxenus - concepts and methods in Elementa harmonica book 1 Elementa harmonica books 2-3 - Elementa harmonica book 3 and its missing sequel Contexts and purposes of Aristoxenus' harmonics - Pythagorean harmonics in the Fifth Century - Developments in Pythagorean harmonics - Plato - Aristotle on the harmonic sciences - Systematising mathematical harmonics - Quantification under attack – Postscript - the later centuries. Candelise, A.L. Il Trono Ludovisi : tra cultura pitagorica e riti misterici : [viaggio nella cultura come fonte inesauribile di scoperte sulla percezione e sul significato della comunicazione entro la specie umana] Firenze: L'autore libri Firenze. 2006. ISBN: 8851710090; 9788851710095 Una lettura del reperto più enigmatico dell’arte greca, il famoso “Trono Ludovisi”, proveniente da Locri e forse qui realizzato, che mette in luce i valori specifici della cultura autoctona dell’estrema penisola calabrese, ove tra VI e V secolo a.C. si affermò una tra le scuole di pensiero più avanzate dell’antichità, incentrata attorno al matematico Pitagora di Samo. Del manufatto l’Autrice dà una interpretazione interdisciplinare, in linea con l’accreditata teoria che vede nella produzione artistica della Magna Grecia un “modo” affatto marginale rispetto agli sviluppi stilistici della Grecia propriamente detta, e vi ravvisa uno speciale Kunstwollen che continua a stupirci per la sorprendente qualità dell’“informazione” che proprio in essa si realizza. Il Trono Ludovisi diviene pertanto straordinario esempio di “snodo” culturale, matrice di quell’assunto per cui da Pitagora in poi il numero è alla base dell’armonia e della bellezza, non solo in arte ma persino nella poesia e nella musica. Barnes, J. The Presocratic philosophers London; Routledge. 2006. Series: Arguments of the philosophers. ISBN: 0415050790; 9780415050791 Bonazzi, M. et al (Ed). A platonic Pythagoras: platonism and pythagoreanism in the imperial age Turnhout: Brepols, 2007. Schriftenreihe: Monothéismes et Philosophie. ISBN: 978-2503-51915-9 See: Book chapters: Authors: Babut, Calabi, Donini, Gritti, Helmig, Lévy, Linguiti, O’Meara, and Steel Canes, A. Is Aristotle a follower or opponent of presocratic thought? : a study in Aristotle's use of presocratic philosophizing. Thesis (M.A. Philosophy). Catholic University of America, 2006. Bradley, M.J. The birth of mathematics: ancient times to 1300 New York: Facts on File. 2006. Series: Pioneers in mathematics. ISBN: 0816054231; 9780816054237. Contents: Thales of Miletus (ca. 652-ca. 547 B.C.E.): Earliest proofs of geometrical theorems - Pythagoras of Samos (ca. 560-ca. 480 B.C.E.): Ancient Greek proves theorem about right triangles - Euclid of Alexandria (ca. 325-ca. 270 B.C.E.): Geometer who organized mathematics - Archimedes of Syracuse (ca. 287-212 B.C.E.): Innovator of techniques in Censorinus. De die natali liber. The birthday book / Censorinus ; translated by H.N. Parker. Chicago: University of Chicago Press, 2007. ISBN: 0226099741; 9780226099743; 0226099768; 9780226099767. Contents: Happy birthday - How to honor the genius of the birthday - What is the spirit of the birthday? - Seed and conception – Pregnancy - The fetus - Growth in the womb - The origins

ISBN: 8851710333 Tre studiosi spinti dall'esigenza di scoprire l'oscuro fenomeno dell'armonia delle sfere celesti, intraprendono un viaggio verso il luogo di nascita di Pitagora, convinti che nei luoghi possa ancora permanere la magia dei riti antichi e anche la ricchezza spirituale delle anime che vi hanno vissuto. Capocolonna, Murge, Samo, Patmos e infine Pithagorion, diventano così i capitoli della loro iniziazione ai misteri sonori del pitagorismo. Protagonisti di questo romanzo a tesi, concepito in forma rapsodica (possibilità di incontro tra composizione musicale e forme letterarie), restano comunque i suoni: generati dall'anima cosmica, essi vagano come scintille di verità perduta... of astrology - The teachings of the pythagoreans - Harmony and music - Harmony in the womb - Harmony in the mind and body Harmony in the universe - Crisis years and the length of life - The praise of caerellius - Time and eternity - Ages and centuries. the Roman secular games - The great year - The year The calendar - The history of the world Months - Days - Hours. Chardak, H.E. L'énigme Pythagore : La vie et oeuvre de Pythagore et de sa femme Théano Paris: Presses de la renaissance. 2007. ISBN: 9782750901325; 2750901324 Histoire, roman, enquête, ce livre est tout cela à la fois. Pythagore y surgit, en chair et en os, du fond d'une Grèce antique plus fascinante que jamais. Héros olympique, lutteur hors du commun, élève de Thalès, ami du pharaon Amasis, géomètre, philosophe, musicien, astronome, il aimait rire, apprendre, partager. Avec lui, nous foulons le sol de Samos, d'Olympie, de Milet, de Tyr, de Saida, de Haïfa, de Jérusalem, d'Alexandrie, de Babylone, d'Héraklion... Il rêva de paix, espéra une épouse idéale... Théano combla de bonheur cet homme déjà mûr qui préférait le célibat à un mariage sans âme et sans grandeur. Épouse, mère, élève, puis maître à penser, elle ressemble à nos jeunes femmes modernes alors que ses contemporaines sont réduites à un rôle de second ordre. Le couple que forment Théano et Pythagore, et dont l'histoire n'a encore jamais été contée, innove jusqu'à l'idée de la relation entre les hommes et les femmes. L'école qu'ils fondent ensemble est celle de la tolérance et de l'ouverture sur le monde. On compara Pythagore à Apollon pour sa beauté, on compara Jésus à Pythagore pour sa bonté. Vinci, Kepler et bien d'autres furent fascinés, inspirés par sa science. Pythagore savait déjà que la terre était ronde, qu'elle tournait autour du Soleil. Enquête historique qui se lit comme un roman, L'Énigme Pythaogore est une belle leçon de bonheur et de découverte, à l'aube de notre civilisation. Farndell, A. Gardens of philosophy : Ficino on Plato. London: Shepheard-Walwyn. 2006. ISBN: 0856832405; 9780856832406. Ferwerda, R. Aarde, lucht, water en vuur Budel: Damon. Reeks: Marginalia reeks ; dl. 14. 2006. ISBN: 90-5573-729-1. Summary: Leerdicht van de Griekse filosoof Empedokles (492-432 v.Chr.) over de vier elementen waaruit alles zou zijn opgebouwd, met vertaling en toelichtingen. Gadamer, H.G. Interroger les Grecs : études sur les Présocratiques, Platon et Aristote Saint-Laurent, Québec: Fides. 2006. ISBN: 276212526X; 9782762125269 Translated from German. García del Cid, L. La sonrisa de Pitagoras : matemqaticas para diletantes Barcelona: Debate. 2006. ISBN: 8483066750; 9788483066751 Las matemáticas constituyen tanto una compleja disciplina científica como una difícil asignatura escolar que la mayoría mira con desconfianza, con miedo. Y es que uno solo puede recordar la época escolar y lo sinsabores que textos arduos y maestros sin vocación imprimían en el alma infantil o juvenil. En aquellos años, igual que en la actualidad, las matemáticas aparecen en los programas educativos bajo el rígido aspecto de una materia árida que nos exige el máximo esfuerzo intelectual y nos proporciona una mínima satisfacción. Un conocimiento fundamental al que, salvo para comprobar la subida de la hipoteca o la cuenta de un restaurante, pocos ven utilidad práctica. Sin embargo, para los seres distinguidos con el don matemático, muchos de ellos jóvenes Curti, M. La proporzione : storia di un'idea da Pitagora a Le Corbusier Roma: Gangemi. 2006. ISBN: 9788849211412; 8849211414; 8849211412 De Siena, F. Pitagora e la musica. Un viaggio sulle tracce di Pitagora alla ricerca del mistero dei suoni L'Autore Libri Firenze. 2006. Collana: Biblioteca 80. Narratori.

Darmstadt: Synergia. 2007. Kreis der Freunde um Hans Kayser, Bern. ISBN: 978-3-9810894-7-9; 3-810894-7-2 Hummels Schrift zur Harmonik von Chartres ist eine sehr wissenschaftliche Arbeit mit zahlreichen Querverbindungen. Viele Gebäudedetails sind anschaulich erklärt, die Betrachtungen werden sowohl in historischen als auch in harmonikalen Kontext gestellt. Die Poesie der Sprache vermittelt an vielen Stellen, zusätzlich zu den wissenschaftlichen Fakten und Betrachtungen, den Einklang zwischen Dichtung, Musik, Architektur und Weltharmonik. Ein Fundus für alle Chartres-Liebhaber, Harmoniker, Architekten, Mathematiker und alle die weiterforschen möchten. Umfangreiche Literaturhinweise und Amerkungen erleichtern die weitere Auseinandersetzung des Lesers mit Themen rund um die Harmonik, heilige Geometrie und speziell Chartres. llenos de imaginación, esta ciencia es prodigiosa, llena de apasionantes demostraciones y teoremas de indescriptible belleza. Partiendo de estas ideas y con el deseo de desvelar los principales misterios matemáticos, Lamberto García del Cid ha escrito un libro sorprendente, ameno e inteligente que invita a mirar en el interior de la matemática sin recelo, casi con espíritu aventurero, para descubrir -de la mano de los grandes genios, sus curiosas anécdotas y las principales teorías- los enigmas y pasadizos que encierra el arte de los números y las fórmulas. Pensado y escrito para el gran público, para cualquier que quiera iniciarse en los secretos y revelaciones de esta rama del saber, La sonrisa de Pitágoras nos abre las puertas a un universo que se hace cercano y comprensible desde la primera página. Gemelli Marciano, M.L. Die Vorsokratiker. Thales / Anaximander / Anaximenes / Pythagoras und die Pythagoreer / Xenophanes / Heraklit / 1 (Griech.-Latein.-Dtsch.) Artemis & Winkler. 2007. ISBN 3760817351; 9783760817354 Die vorsokratische Philosophie bricht mit der mythologischen Welterklärung. Man braucht die Götter nicht mehr, wenn man davon ausgeht, dass der natürliche Prozess der Weltentwicklung autonom fortschreitet, sich gesetzmäßig vollzieht und aus sich selbst erklärt werden kann. Laura Gemelli folgt Schicht um Schicht den Überlieferungssträngen und nähert sich so behutsam dem Ursprung der europäischen Philosophiegeschichte. Ianuzzi, L. Sulle tracce di Pitagora. Storie brevi Ibiskos. 2005. Collana: Il frangipane. ISBN: 8878410543 Jones, C.P. Apollonius of Tyana / Philostratus. Letters of Apollonius; Ancient testimonia Eusebius's Reply to Hierocles Cambridge, Mass.: Harvard University Press. 2006. The Loeb classical library 458. ISBN: 0-674-99617-8. Philostratus's colorful biography of Apollonius of Tyana, recounting the sayings and miracles of a Pythagorean sage, incidentally provoked a long-lasting debate between pagans and Christians. This volume, which completes the new Loeb Classical Library edition of the Life of Apollonius of Tyana, provides historical context for that much discussed third-century portrayal of a charismatic religious teacher. Here is a new translation of the surviving letters of Apollonius, augmented and illuminated by recent discoveries. These letters reveal Apollonius's personality and his religious and philosophical ideas. New for this edition is a selection of ancient reports about Apollonius from authors such as St. Jerome and St. Augustine. Philostratus's biography was quickly caught up in the religious struggles that marked the rise of Christianity. An official in Diocletian's empire named Hierocles used it as ammunition in an anti-Christian polemic, initiating a controversy that lasted well into modern times. The reply by Eusebius, the fourth-century bishop of Caesarea, was originally included in editions of the Life of Apollonius in order to serve as a spiritual antidote and to provide cover for the Ghyka, M.C. Złota liczba : rytuały i rytmy pitagorejskie w rozwoju cywilizacji zachodniej Kraków: Universitas. 2006. ISBN: 8324202854; 9788324202850 Tyt. oryg.: Le Nombre d'Or. Rites et rythmes pythagoriciens dans le développement de la civilisation occidentale. Giosue, G. La via regale da Pitagora a Wiles : storie di matematici e di problemi Pescara: Tracce, stampa 2006. Haws, C.G. The narrative function of miracles in the gospel of Mark with reference to the life of Apollonius of Tyana Jefferson City, Tenn.: Carson-Newman College. 2006. Thesis Series: Honors Project (B.A.) Hummel, C. Pythagoras und die Meister von Chartres

second sailing – Parmenides - Socrates and Zeno - Socrates' ideas - The challenge of Parmenides - Ideas and the one - Symposium - Erotic ascent - The in-between - The genealogy of Eros, or the philosopher Possession and generation - Eros and ideas Phaedo - Safety - Soul and ideas. publishers; today it is an essential chapter in the history of Philostratus's masterpiece. Johnsen, L. Lost masters : yoga of ancient Greece Honesdale, PA: Himalayan Institute Press. 2006. ISBN: 0893892602. Contents: The light of the West - The mystery religions - Calming the savage heart - Helen's chalice - The spiritual colony - The road to reality - The private investigator - The man who stopped the wind - Atoms and the void - The man who lost a continent - Apollonius was like the sun - The priest of Delphi - From the alone to the alone - The work of enlightenment - The shepherd of men - The golden chain Extinguishing the light - The India connection Exploring our Western heritage. Mair, K E. Die fruhen und spaten Pythagoreer und ihre Mathematik im Schulbuch Innsbruck, Univ., Dipl.-Arb. 2006. Maor, E. The Pythagorean theorem : a 4,000year history Princeton: Princeton University Press. 2007. ISBN: 9780691125268; 0691125260. By any measure, the Pythagorean theorem is the most famous statement in all of mathematics, one remembered from high school geometry class by even the most mathphobic students. Well over four hundred proofs are known to exist, including ones by a twelveyear-old Einstein, a young blind girl, Leonardo da Vinci, and a future president of the United States. Here perhaps for the first time in English, is the full story of this famous theorem. Although attributed to Pythagoras, the theorem was known to the Babylonians more than a thousand years before him. He may have been the first to prove it, but his proof--if indeed he had one--is lost to us. Euclid immortalized it as Proposition 47 in his Elements, and it is from there that it has passed down to generations of students. The theorem is central to almost every branch of science, pure or applied. It has even been proposed as a means to communicate with extraterrestrial beings, if and when we discover them. And, expanded to four-dimensional space-time, it plays a pivotal role in Einstein's theory of relativity. In this book, Eli Maor brings to life many of the characters that played a role in the development of the Pythagorean theorem, providing a fascinating backdrop to perhaps our oldest enduring mathematical legacy. Laks, A. Introduction à la philosophie présocratique Paris: Presses universitaires de France. 2006. ISBN: 2130556639; 9782130556633 Les «philosophes présocratiques» ne se concevaient pas comme tels. Socrate n'était pas pour eux une référence, au mieux un cadet, voire un contemporain. Et ce n'est que sur le tard, à la dernière génération, qu'ils commencèrent à être désignés comme «philosophes». Mais si les philosophes présocratiques ne sont philosophes et présocratiques que rétroactivement, il convient de s'interroger sur la manière dont ils sont devenus tels. Pour mettre en évidence la construction, certes, mais aussi pour s'interroger sur sa possible légitimité : car il ne s'agit pas, contrairement à ce que suggère un terme aujourd'hui galvaudé, d'une simple «invention». L'importance de la question tient évidemment au fait que, quand nous parlons des philosophes présocratiques, ce sont des origines de la philosophie grecque, et par là occidentale, dont nous parlons. Leech, B. C, Geometry's great thinkers : the history of geometry New York: Rosen Publishing Group's PowerKids Press, 2007. ISBN: 1404233601; 9781404233607; 1404260730; 9781404260733. Contents: Ancient geometry -- Thales of Miletus -- Pythagoras of Samos -- Euclid of Alexandria -- René Descartes -- Grace Chisholm Young -- The pioneers of geometry Michalide s, T. Pythagoreia enklemata : mythistorema Athena: Polis. 2006. ISBN: 9604351184; 9789604351183 Morgan, K.A. Myth and philosophy from the Presocratics to Plato Cambridge; Cambridge University Press,; New York. 2006. ISBN: 0521621801; 9780521621809; 0521033284; 9780521033282. This book explores the dynamic relationship between myth and philosophy in the Linck, M..S. The ideas of Socrates London; New York: Continuum. 2007. ISBN: 082649451X; 9780826494511 Contents: Introduction - Pythagorean overture - Phaedo - Blindness - Anaxagoras - Socrates'

Greek original with Italian translation on facing page Rhees, R. In Dialogue with the Greeks Volume I. The Presocratics and Reality. Ed. D.Z. Phillips Series: Ashgate Wittgensteinian Studies Claremont Graduate University, USA and University of Wales, UK. 2004. ISBN: 0 7546 3988 6 Contents: Introduction; 'All Things'; Geometry and description; 'It is'; 'Eternal flux'; 'Indestructible roots'; Paradoxes?; Intelligence and 'original things'; Atoms; Is man the measure of all things?; Discourse and reality; Index. Presocratics, the Sophists, and in Plato - a relationship which is found to be more extensive and programmatic than has been recognized. The story of philosophy’s relationship with myth is that of its relationship with literary and social convention. The intellectuals studied here wanted to reformulate popular ideas about cultural authority and they achieved this goal by manipulating myth. Their self-conscious use of myth creates a self-reflective philosophic sensibility and draws attention to problems inherent in different modes of linguistic representation. Much of the reception of Greek philosophy stigmatizes myth as ‘irrational’. Such an approach ignores the important role played by myth in Greek philosophy, not just as a foil but as a mode of philosophical thought. The case studies in this book reveal myth deployed as a result of methodological reflection, and as a manifestation of philosophical concerns. • Focuses on myth as a form of philosophic expression • Diachronic study of an entire tradition of rigorous philosophical mythmaking • All Greek in the main text is translated Riedweg, C. Pythagoras : Leben, Lehre, Nachwirkung; eine Einführung München: Beck, 2007. Ausgabe: 2., überarb. Aufl. ISBN: 3-406-48714-9 Rühl, A. Kompositionen aus den natürlichen Zahlen : Pythagoras und seine nächste Verwandtschaft Koblenz: Rühl. 2006. ISBN: 978-3-929300-10-9; 3-929300-10-9 Sassi, M.M. La costruzione del discorso filosofico nell'età dei presocratici Pisa, Italy: Edizioni della Normale. 2006. ISBN: 8876421807; 9788876421808 Proceedings of the second Symposium praesocraticum, held at the Scuola normale superiore, Pisa, Sept. 16-18, 2004. It is well known that the category of preSocratic philosophy has been ‘invented’ by Plato and Aristotele, and it is also known how much their historiographic elaboration, combined with very fixed philosophical interests, has affected the interpretation of the pre-Socratics throughout western tradition. The essays collected in this volume propose to discuss this ancient tradition, showing the multiplicity and richness of motifs to be found in pre-Socratic philosophical research, far beyond the schemata consolidated in Platonic and Aristotelian historiographic paradigms. By assembling essays from both Italian and to a large extent non-Italian scholars, the volume offers on original contribution to a theme that has been decisive for the European xxth century, besides on the historiographic also on the philosophic level. See: Book chapters: Authors: Betegh, Huffman and Primavesi. Morishita, S. Pitagorasu no teiri hyaku no shomeiho : kika no sanpomichi. Osaka: Pureadesushuppan. 2006. ISBN: 476870879X; 9784768708798 Phelps, N. The longest struggle : animal advocacy from Pythagoras to PETA New York: Lantern Books. 2007. ISBN: 9781590561065; 1590561066. Contents: Introduction: Tearing off the cloak of invisibility - The roots of evil - The challenge of Ahimsa - The challenge comes west - Judaism crafts a compromise - Jesus vs. aristotle Secular offerings to a savage God - A few rays of enlightenment - "Pain is pain" - "Harassing the lower orders" - The great meddler - The pit of despair - Requiem for a little brown dog Ahimsa returns to the west - One step forward, twenty steps back - Heralds of change - The age of the pioneers - The sixties' last hurrah Direct action : striking back on land and sea Things fall apart - But the center takes hold Conclusion: The dream and the work. Reale, G. I Presocratici / prima traduzione integrale con testi originali a fronte delle testimonianze e dei frammenti nella raccolta di Hermann Diels e Walther Kranz. Milano: Bompiani. 2006. Series: Bompiani Il pensiero occidentale. ISBN: 8845257401; 9788845257407

Table of Contents. Pythagoras: Numbers and Symbol - Bach: Numbers and Music Hofmannsthal: Numbers and Time - Descartes: Numbers and Space - Leibniz: Numbers and Logic - Laplace: Numbers and Politics - Bohr: Numbers and Matter - Pascal: Numbers and Spirit Schuré, E. Los grandes iniciados : Rama, Krishna, Hermes, Moisés, Orfeo, Pitágoras, Platón, Jesús, Zoroastro, Buda, Jesús y los Esenios. México: Grupo Editorial Tomo. 2006. ISBN: 9706660666; 9789706660664 Taylor, T. On the mysteries of the Egyptians, Chaldeans, and Assyrians ; and, Life of Pythagoras : to which have been added ethical and political fragments of ancient Pythagorean writers / Iamblichus Whitefish, Mt.: Kessinger Pub. 2006. ISBN: 0722400810 Scully, M.O. The Demon and the Quantum : From the Pythagorean Mystics to Maxwell's Demon and Quantum Mystery Weinheim, Bergstr: Wiley-VCH. 2007. ISBN: 978-3-527-40688-3; 3-527-40688-3 Contents: this book explains the connection between Maxwell's Demon and the role of the observer and quantum eraser, showing that information science, thermodynamics and quantum physics are closely related. By focusing on entropy, information, and observation, the authors bring a unique perspective to this subject, providing an insight into the strange ways of the quantum that will fascinate scientists and lay readers alike. Valborg, H. Symbols of the eternal doctrine : from Shamballa to Paradise New York: iUniverse. 2006. ISBN: 0595421318; 9780595421312; 0595864716; 9780595864713. Contents: Shamballa -- Tetraktys -- Altar -Raven -- Sword -- Pentagram -- Owl -- Dog -Labyrinth -- Heart -- Blood -- Spiral -- Ship -Wind -- Voyage -- Dodecahedron --Mirror -Drum -- Lyre -- Cross -- Fool -- Dwarf -- Desert -- Lake -- Fish -- Dolphin -- Whale -- Paradise. Shesso, R. From the Fibonacci sequence to luna's labyrinth to golden sections and other secrets of sacred geometry San Francisco, CA: Red Wheel/Weiser. 2007. ISBN: 1578633834. Contents: The circle of creation -- Counting -The moon -- Measurements -- The days of the week -- The magical squares -- The knights tour and templar codes? -- Shapes and numbers meditation -- Pythagoras -- Fibonacci, the golden ratio, and the pentacle -- Venus pentacle -- The geometric solids -- Individual numbers -- A tale in which Gods do math -Summing up. Valta, R. Fragmentit / Filolaos. Osuuskunta Jyvas-Ainola. 2006. ISBN: 9525353249; 9789525353242. Vamvacas, C.J. Die Geburt der Philosophie. Der vorsokratische Geist als Begründer von Philosophie und Naturwissenschaften Artemis & Winkler, 11/2006. ISBN: 978-3-538-07236-7 Bestätigte die Physik des 20. Jahrhunderts die Vorstellung der antiken Atomisten? Was stimmt an den frühen Theorien zur Entstehung des Alls? Constantin J. Vamvacas vergleicht die naturwissenschaftlichen Ansätze der Vorsokratiker mit den Erkenntnissen der modernen Wissenschaften. Er lässt uns teilhaben an der Grundlegung und Entwicklung des europäischen Denkens, dessen früheste Spuren ins 7. Jahrhundert v. Chr. weisen. Im Mittelpunkt stehen Thales, Anaximander, Anaximenes, Pythagoras, Xenophanes, Heraklit, Parmenides, Empedokles, Anaxagoras und Demokrit, die die vorsokratische Philosophie begründeten. Aus dem Griechischen von Mark Michalski. Stamatellos, G. Plotinus and the presocratics : a philosophical study of presocratic influences in Plotinus' Enneads Albany: State University of New York Press. 2007. ISBN: 9780791470619; 079147061X. Contents: The origins of Plotinus's philosophy - One and unity - Intellect and being - Eternity and time - Matter and soul. Swinford, D. Through the daemon's gate : Kepler's Somnium, medieval dream narratives, and the polysemy of allegorical motifs. New York: Routledge. 2006. Series: Studies in medieval history and culture. ISBN: 0415977649; 9780415977647 Warren, J. Presocratics Berkeley: University of California Press. 2007. ISBN: 9780520253674; 0520253671; 9780520253698; 0520253698. Contents: Introduction : reading Presocratic philosophy -- Ionian beginnings -- Xenophanes Taschner, R.J. Numbers at work : a cultural perspective (Zahlen gigantische Schatten.) Wellesley, Mass.: A. K. Peters. 2007. ISBN: 9781568812908; 1568812906.

Deel 1 De kosmologie die ten grondslag ligt aan de traditie van de harmonie der sferen: Robert van Gent, Harmonie als sleutel tot het universum van de Oudheid tot en met de Renaissance Deel 2 Hemelse harmonie in de Middeleeuwen: Marike Teeuwen, Hemelse harmonie in de vroege Middeleeuwen: visies op antieke tradities José van der Helm, Harmonie der sferen in Dantes Divina Commedia Eddie Vetter, Hildegard van Bingen en de harmonie der sferen Deel 3 Hemelse harmonie in de Renaissance: Willem Elders, Symbolische partituren: de notie van ‘musica celestis’ in composities uit de Renaissance Jacomien Prins, Marsilio Ficino over Plato’s Timaeus. Kosmische harmonie en de lever Deel 4 Hemelse harmonie in de zeventiende eeuw: Natascha Fabbri, Een debat over kosmologie en harmonie in de zeventiende eeuw tussen Kepler en Mersenne Koen Ottenheym, Harmonie en getal in de Hollandse bouwkunst van de zeventiende eeuw Deel 5 De receptie van de traditie van de harmonie der sferen in de negentiende en twintigste eeuw: Jeroen Stumpel, Over harmonie der sferen en de receptie van de ‘School van Athene’ in de negentiende en twintigste eeuw Joscelyn Godwin, De herleving van speculatieve muziek: van Albert Freiherr von Thimus via Rudolf Steiner naar hedendaagse ideeën over harmonie der sferen -- The riddles of Heraclitus -- Parmenides -Reactions to Parmenides -- Anaxagoras -Empedocles -- Leucippus and Democritus. Forthcoming books Forthcoming books: Aristoteles. Werke in deutscher Übersetzung 20/II. Über die Lehrmeinung der Pythagoreer Verlag: Akademie Verlag GmbH. Juni 2008. ISBN: 3050037342 Inhalt: Gemeinsam mit den Fragmenten aus Philolaos und Archytas bilden die Nachrichten des Aristoteles das Fundament für die Rekonstruktion des älteren Pythagoreismus. Während andere Überlieferungen einem eher vorsokratischen Wissenschaftsbegriff verpflichtet sind, decken die Berichte des Aristoteles die ganze Skala von der Pythagoraslegende über die urtümliche Lehre der Akusmata und Zahlensymbolik bis zur Astronomie des Philolaischen Systems ab. Spätestens seit Andronikos von Rhodos (1. Jh. v. Chr.) wurden die beiden speziellen Aristotelischen Abhandlungen unter dem Titel "Über die Lehrmeinung der Pythagoreer" zu einer Pragmatie in zwei Büchern vereinigt. Die erhaltenen Fragmente daraus werden hier in deutscher Übersetzung vorgelegt und kommentiert. Gemelli, L., Die Vorsokratiker, I-III, hrsg. und übers., Sammlung Tusculum, Artemis & Winkler, Düsseldorf/Zürich 2006-2007 Band 1: Thales / Anaximander / Anaximenes / Pythagoras und die Pythagoreer / Xenophanes / Heraklit, erschienen 2007. Band 2: Parmenides / Zenon / Empedokles, erscheint 2007. Band 3: Anaxagoras / Melissos / Diogenes / Die Atomisten, erscheint 2007. Ferguson, K. The Music Of Pythagoras. How An Ancient Brotherhood Cracked The Code Of The Universe And Lit The Path From Antiquity To Outer Space Walker & Company. Available Dec 2007. ISBN 978-0-8027-1631-6 Harmonisch Labyrint. Redactie Prins, J. / Teeuwen, M. Verloren, b.v., 2007. ISBN 9789065509741 Verwachte verschijningsdatum: juni 2007 Inleiding. De traditie van de harmonie der sferen: een harmonisch labyrint

Chapters in books Donini, P. Tra Academia e pitagorismo. Il platonismo nel De genio Socratis di Plutarco In: Bonazzi, M. et al (Ed). A platonic Pythagoras : platonism and pythagoreanism in the imperial age Turnhout: Brepols, 2007. Schriftenreihe: Monothéismes et Philosophie. ISBN: 978-2-503-51915-9 Babut, D. L’unité de l’Académie selon Plutarque. Notes en marge d’un débat ancien et toujours actuel In: Bonazzi, M. et al (Ed). A platonic Pythagoras: platonism and pythagoreanism in the imperial age Turnhout: Brepols, 2007. Schriftenreihe: Monothéismes et Philosophie. ISBN: 978-2-503-51915-9 Förster, N. Some observations on Josephus' description of the Essenian morning prayer p 245-253 In: Josephus and Jewish history in Flavian Rome and beyond. Papers from a conf titled "Josephus between Jerusalem and Rome" held at the Pontifical Biblical Inst and the Pontifical Gregorian Univ, Rome, 21-24 Sept 2003. Leiden; Boston : Brill, 2005 Subjects: Josephus, Flavius; Essenes; Pythagoras and Pythagorean school; Jews Historiography; Jews in Hellenistic literature; Jewish prayers; Judaism, Hellenistic Baulig, A. Die Welt des Pythagoras : FolieSonst. In: Muster & Strukturen: Gesetzmäßigkeiten. Seelze-Velber: Kallmeyer, 2006 Schriftenreihe: Grundschule Mathematik. Betegh, G. Eschatology and Cosmology: Models and Problems p 27-50 In: Sassi, M.M. La costruzione del discorso filosofico nell'età dei presocratici Pisa, Italy : Edizioni della Normale. 2006. ISBN: 8876421807; 9788876421808 Proceedings of the second Symposium praesocraticum, held at the Scuola normale superiore, Pisa, Sept. 16-18, 2004. Gest, K. L. Pythagoras, mystery schools, and freemasonry. Chapter 5. In: Secrets of Solomon's Temple : discover the hidden truth that lies at the heart of freemasonry Gloucester, MA : Fair Winds Press. 2007. ISBN: 9781592332540; 1592332544 Boehme, H. Mathematik der Pythagoreer. P 41-53 In: Wanderschaft in der Mathematik. Augsburg. 2006. (Algorismus; 53). Calabi, F. Filone di Alessandria e Ecfanto. Un confronto possible In: Bonazzi, M. et al (Ed). A platonic Pythagoras : platonism and pythagoreanism in the imperial age Turnhout: Brepols, 2007. Schriftenreihe: Monothéismes et Philosophie. ISBN: 978-2-503-51915-9 Gritti, E. Insegnamento pitagorico e metodo dialettico in Proclo In: Bonazzi, M. et al (Ed). A platonic Pythagoras : platonism and pythagoreanism in the imperial age Turnhout: Brepols, 2007. Schriftenreihe: Monothéismes et Philosophie. ISBN: 978-2-503-51915-9 Censorinus. The Teachings of the Pythagoreans. Chapter 9 In: Censorinus. De die natali liber. The birthday book / ; translated by Holt N. Parker Chicago : University of Chicago Press, 2007. ISBN: 0226099741; 9780226099743; 0226099768; 9780226099767. Helmig, C. The Relationship Between Forms and Numbers in Nicomachus’ Introduction to Arithmetic In: Bonazzi, M. et al (Ed). A platonic Pythagoras : platonism and pythagoreanism in the imperial age Turnhout: Brepols, 2007. Schriftenreihe: Monothéismes et Philosophie. ISBN: 978-2-503-51915-9 Cotter, W. Miracle Stories: The God Asclepius, the Pythagorean Philosophers, and the Roman Rulers. p 166-178. In: The Historical Jesus in Context. Amy-Jill Levine, Dale C. Allison Jr., and John Dominic Crossan, Editors. (Princeton Readings in Religions). Princeton and Oxford: Princeton University Press. 2006.

Mourelatos,A.P.D. The Concept of the Universal in Some Later Pre-Platonic Cosmologists. P 56-76 In: A Companion to Ancient Philosophy: Blackwell Companions to Philosophy, Gill, Mary Louise (ed), Blackwell-Publishing: Malden MA, 2006. Abstract: Empedocles and Philolaus make thematic use of the token/type and type/type distinctions in their respective philosophies. Moreover, In Democritus, we find: (1) welldeveloped typologies of atomic shapes; (2) deployment of the token/type distinction for the purpose of proclaiming (a) infinity of types of atomic shape, and (b) infinity of token-atoms for every type of shape; (3) two contexts (frr. B124 and B165) which, properly interpreted, offer reflective comments on the token/type distinction. Aristotle's use of the alphabet example (Metaphysics. XIII.10) to illustrate that distinction may have its origin in Democritus' use of the term stoicheion, "letter," to refer to atoms. Huffman, C. Aristoxenus’ Pythagorean Precepts: A Rational Pythagorean Ethics p 103-122 In: Sassi, M.M. La costruzione del discorso filosofico nell'età dei presocratici Pisa, Italy : Edizioni della Normale. 2006. ISBN: 8876421807; 9788876421808 Proceedings of the second Symposium praesocraticum, held at the Scuola normale superiore, Pisa, Sept. 16-18, 2004. Ireton, S.M. Holderlin : dialectical death and ontological guilt - The problem of unification and dialectics - Dialectal death in hyperion The death of Empedocles : genesis and drafts - Nietzsche : the deaths of Empedocles and Zarathustra - Empedocles and the problem of tragedy - The existential function of death in Thus spoke Zarathustra and other writings. In: An ontological study of death : from Hegel to Heidegger. Pittsburgh, Pa.: Duquesne University Press. 2007. ISBN: 9780820703961; 0820703966; 9780820703978; 0820703974. O'Brien, D. Life beyond the stars: Aristotle, Plato and Empedocles (De Caelo I.9 279a1122). p 49-102. In: Common to body and soul. Philosophical approaches to explaining living behaviour in Greco-Roman antiquity. R. A. H. King (Ed.). Berlin / New York: de Gruyter. 2006. Jones, C.P. Apollonius of Tyana in late antiquity In: Johnson, S.F. Greek literature in late antiquity : dynamism, didacticism, classicism. Aldershot, England ; Ashgate Pub.,; Burlington, VT. 2006. ISBN: 0754656837; 9780754656838. O’Meara, D. Hearing the Harmony of the Spheres in Late Antiquity In: Bonazzi, M. et al (Ed). A platonic Pythagoras : platonism and pythagoreanism in the imperial age Turnhout: Brepols, 2007. Schriftenreihe: Monothéismes et Philosophie. ISBN: 978-2-503-51915-9 Lévy, C. La question de la dyade chez Philon d’Alexandrie In: Bonazzi, M. et al (Ed). A platonic Pythagoras : platonism and pythagoreanism in the imperial age Turnhout: Brepols, 2007. Schriftenreihe: Monothéismes et Philosophie. ISBN: 978-2-503-51915-9 Primavesi, O. Apollo and Other Gods in Empedocles p 51-80 In: Sassi, M.M. La costruzione del discorso filosofico nell'età dei presocratici Pisa, Italy : Edizioni della Normale. 2006. ISBN: 8876421807; 9788876421808 Proceedings of the second Symposium praesocraticum, held at the Scuola normale superiore, Pisa, Sept. 16-18, 2004. Linguiti, A. Prospettiva pitagorica e prospettiva platonica nella filosofia della natura di Proclo. In: Bonazzi, M. et al (Ed). A platonic Pythagoras : platonism and pythagoreanism in the imperial age Turnhout: Brepols, 2007. Schriftenreihe: Monothéismes et Philosophie. ISBN: 978-2-503-51915-9 Scott, C. E. Pythagoras, Indifference, and the Beautiful Soul. Chapter 3. In: Living with indifference. Bloomington: Indiana University Press. 2007. Series: Studies in continental thought ISBN: 0253348560; 0253219000; 9780253348562; 9780253219008. Mastrocinque, A. Creating one’s own religion: Intellectual and professional choices (neoPythagorism etc.) Chapter 26 In: A companion to Roman religion / edited by Jorg Rupke. 2007. Malden, MA: Blackwell Pub.2007. ISBN: 1405129433; 9781405129435.

der beiden Gedichte - Rückblick In: Die Geburt der Philosophie : der vorsokratische Geist als Begrunder von Philosophie und Naturwissenschaften Dusseldorf : Artemis & Winkler. 2006. ISBN 978-3-538-07236-7, ISBN 3-538-07236-1 Simmans, G. French connection: Pythagoras Ch 13. In: Jesus after the Crucifixion : from Jerusalem to Rennes-le-Cha teau Rochester, Vt. : Bear & Co.,2007. ISBN: 9781591430711; 1591430712. Staab, G. Pythagoras und der frühe Pythagoreismus In: Musik in der antiken Philosophie / Eine Einführung KÖnigshausen & Neumann. 2007. ISBN: 3826033930 Internetsites http://www.priory.com/homol/empedocles.htm EMPEDOCLES’ BIO-MEDICAL COMMENTS: A PRECURSOR OF MODERN SCIENCE N.P. Stathakou,MD, G.P. Stathakou,MD, S.G. Damianaki,MD, Published April 2007 ABSTRACT: Empedocles, born in 490 ΒC (Diogenis Laertius), lived in Agrigento, Sicily. He died in 440 BC and was considered a physician and a philosopher. About 450 verses have been saved from his work, some of them have biomedical references. He observed that plants and animals, including man, are created from four basic elements, which he called «ριζ?µατα» (roots or elements). When combined in different ways, these succeed in producing all the varieties of vegetal and animal species on earth. Concrete mixtures of these four elements describe each organ or part of our body, thus proposing a genetic and hereditary biology based on the mixture of the four «ριζ?µατα». He had treated an endemic disease from Selinounta a nearby city,by opening a canal and emptying stagnating water to the sea. It has also been reported that he had cured plague from the city of Athens by using fire. He did the same at his birthplace with the method of disinfection by smoke: “δι’ αψεως πυρων καιυποκαπνισµων”. Overall, his insight seen through his biomedical comments reveal an admirable precursor of modern medicine. Steel, C. Proclus on Divine Figures. An Essay on Pythagorean-Platonic Theology In: Bonazzi, M. et al (Ed). A platonic Pythagoras : platonism and pythagoreanism in the imperial age Turnhout: Brepols, 2007. Schriftenreihe: Monothéismes et Philosophie. ISBN: 978-2-503-51915-9 Stoltzfus, P.E. Pythagoras and Orpheus as premodern theological resources. P 19-58 In: Theology as performance : music, aesthetics, and God in western thought. New York : T & T Clark International. 2006. ISBN: 0567029212; 9780567029218. Stuart, T. Pythagoras and the sages of India p 39-60 In: The bloodless revolution : a cultural history of vegetarianism from 1600 to modern times / Tristram Stuart. New York : W.W. Norton & Company, 2007. Vamvacas, C.J. PYTHAGORAS VON SAMOS: Persönlichkeit - Leben Lebensweise Akusmatiker - Mathematiker - Akoúsmata, Symbota - Unsterblichkeit der Seele Homogenität - Reinigung - Harmonie der Seele - Ethik - Gemeinwesen - Erziehung - Theologie - Philosophie - Mathematik - Arithmetik Geometrie - Asymmetrie - Geometrische Algebra - Musik - Harmonie - Gegensätze Zahl - Kosmogonie - Kosmologie - Rückblick Physik - Philosophie - Holismus In: Die Geburt der Philosophie : der vorsokratische Geist als Begrunder von Philosophie und Naturwissenschaften Dusseldorf : Artemis & Winkler. 2006. ISBN 978-3-538-07236-7, ISBN 3-538-07236-1 http://www.princeton.edu/~pswpc/papers/date/ date/2007.html Martin, R.P. Golden Verses: Voice and Authority in the Tablets Stanford University Abstract: This paper attempts to read the gold “Orphic” tablets found in tombs from Thessaly to Sicily against the background of Homeric epic. It introduces the notion of “speech typescene” and draws conclusions, from the deployment of formulae and pragmatic situations, about the “voice” one is supposed to hear behind the tablet texts. It was originally Vamvacas, C.J. EMPEDOKLES VON AKRAGAS: Persönlichkeit - Werk Physikalische Welt - Wurzelstoffe - Werden Kräfte - Kosmischer Zyklus - Kosmogonie Kosmologie - Entstehung der Lebewesen Erkenntnistheorie - Reinigungen - Verhältnis

http://www.mlahanas.de/Greeks/Archytas.htm Archytas und das unendliche Universum Michael Lahanas delivered as a paper at the Ohio State University conference Ritual Texts for the Afterlife (April 2006), organized by Fritz Graf and Sarah Iles-Johnston. Book reviews Huffman (C.A.) Archytas of Tarentum. Pythagorean, Philosopher and Mathematician King. 2005. Reviewed by: Dillon, J. Bryn Mawr Classical Review. 2007. 03.34 Reviewed by: Rousseau, P. Review of Metaphysics. 2006, 60, 2, p 406-408 Reviewed by: Stuckelberger, A. Museum Helveticum, 2006, 63, p 215-216 Reviewed by: Taub, L.C. The American journal of philology. 2007, 128, 1, p 133-136 Jones, C.P. (ed., trans.) Philostratus I. Apollonius of Tyana. Books I-IV. (Loeb Classical Library 16.) University Press, 2005. Reviewed by: Hodkinson, O. The classical review. 2006, 56, 2, p 324 Reviewed by: Wyles, M.R. The expository times. 2007, 118, 5, p 253 Joost-Gaugier, C.L. Measuring Heaven: Pythagoras and His Influence on Thought and Art in Antiquity and the Middle Ages. 2006. Reviewed by: Browning, E.A. Bryn Mawr Classical Review. 2007. 02.43 Reviewed by: Bussanich, J Choice. 2006, 44, 1, p 94 Reviewed by: Trapp, M. The Times Literary Supplement. 2006, 5400, p 28-29 (Sep 29) Kahn, C. Pythagoras and the Pythagoreans. 2001. Reviewed by: Burnyeat, M.R. The London review of books. 2007, 29, 4, p 3 Karamanides, D. Pythagoras: Pioneering Mathematician and Musical Theorist of Ancient Greece. 2006. Reviewed by: Thompson, J.S. School Library Journal. 2006, 52, 9, p 228-230 Rhees, R. In Dialogue with the Greeks, Volume I: The Presocratics and Reality; Volume II: Plato and Dialectic, edited by D. Z. Phillips, Ashgate Publishing Company, 2004 Reviewed by: Northwood, H. Philosophical investigations. 2006, 29, 4, p 369-382 Reviewed by: Sayre, P. Notre Dame Philosophical Reviews, 2005, March 8. Riedweg, C. Pythagoras: His Life, Teaching, and Influence. 2005 Reviewed by: Blanchard, A. Revue des Etudes Grecques, 2006, 119, p 797. Reviewed by: Burnyeat, M.R. The London review of books. 2007, 29, 4, p 3. Reviewed by: Motte, A. Kernos, 19, p 489-492 Reviewed by: Pinheiro, S. Euphrosyne, 34, 2006, p 430-431 Staab, G. Pythagoras in der Spätantike. Studien zu De vita pythagorica des Iamblichos von Chalkis, 2002. Reviewed by: Mansfeld, J. Mnemosyne, 2006, 59, 4, p 633-634 Taylor, J. Pythagoreans and Essenes: Structural Parallels. 2004. Reviewed by: Brooke, G. J. Journal for the Study of the Old Testament. 2006, 3, 5, p187-188 Reviewed by: Gusella, L. Journal for the Study of Judaism. 2006, 37, 3, p 500-503

Burnyeat, M.F. Other Lives. London Review of Books. 2007, 29, 4 (22 February 2007) Reviews: Pythagoras: His Life, Teaching and Influence by Christoph Riedweg trans. Steven Rendall. 2005, and Pythagoras and the Pythagoreans: A Brief History by Charles Kahn · Hackett, 193 pp. 2000. London Review of Books. 2007, 29, 8, p 5 (26 April 2007) Letters (concerning this review) analogous to the soul-body distinction we later find in Plato, who also believed in transmigration. In due course, the history of philosophy would reach the dualist mind-body distinction in the Meditations of Descartes, who most certainly did not believe in transmigration. And the mind-body distinction is still being argued over today. One difficulty for this Whiggish approach is posed by the philosopher-poet Empedocles of Acragas, c.495-435 BC, the founder of the long-lived theory of the four elements, earth, air, fire and water, to which he added the motive forces Love and Strife in order to explain the repeated formation and dissolution of the cosmos as we know it. He too believed in transmigration: ‘I have already been once a boy and a girl, a bush and a bird and a leaping journeying fish.’ He described Pythagoras as having a memory that spanned back over twenty generations. Yet Empedocles’ account of knowledge and thought sounds as physicalist as a theory could be: ‘With earth do we see earth, with water water, with air bright air, with fire consuming fire; with Love do we see Love, Strife with dread Strife.’ Or again: ‘The blood around men’s hearts is their thought.’ To suppose that a believer in transmigration must be a soul-body dualist in the way Plato was later, and must think of thought as enabling its possessor to transcend their body, is to miss out on one of the challenges that accurate history of philosophy can put before us and our students. Plato is again the lure for Loptson’s second Whiggish proposal: Pythagoras as the first to introduce philosophy to ideas of abstract entities like numbers and triangles. Certainly, Plato did go in for philosophical discussion of the nature and reality of mathematical entities like numbers and triangles. So did Aristotle and numerous later ancient philosophers from the fourth century BC onwards. But not the great mathematician Euclid, who flourished around 300 BC: his famous Elements is a magnificent achievement, but there is not one ounce of philosophy to be found in it. He talks about numbers and triangles, subjects them to From: Peter Loptson Unfair to Pythagoras M.F. Burnyeat sets out to show that the notion that Pythagoras was the original architect of mathematical demonstration, or even a practitioner, is without basis or warrant (LRB, 22 February). Nowhere, though, does Burnyeat directly address, still less refute, what many students of pre-Socratic philosophy attribute to Pythagoras, and regard as his primary importance in the history of philosophy, namely his introduction of the idea of abstract entities and some type of psychophysical dualism. We don’t know how selfconsciously he held these ideas, what precise form they took, or what theoretical ramifications he thought they had, but there is good reason to believe that it is because of Pythagoras, the early Pythagoreans and their influence, that later philosophers – Plato among them – have worried about the nature and reality of numbers and triangles (and things like them), and what it is about thought which seems to enable its possessors to be independent of this or that body, perhaps of any body at all. Burnyeat acknowledges that mathematical objects and transmigrating souls were central parts of Pythagoras’ philosophical views, but doesn’t appear to see the significance of these views in later philosophy. Obviously enough, people before Pythagoras believed in numbers and in the transmigration of souls; but Pythagoras seems to have been the first to make such ideas matter in philosophy. Peter Loptson University of Guelph, Ontario Reply from M.F. Burnyeat Peter Loptson’s letter invites discussion of two ideas or issues which, he claims, Pythagoras is widely agreed to have contributed to the history of philosophy. Let me start with ‘psycho-physical dualist theory’. The idea is that Pythagoras, a believer in the transmigration of souls from one life to another, must have accepted a distinction between the psyche or soul and the physical body

Aristotle repeatedly complains that the Pythagoreans failed to distinguish abstract mathematical entities from corporeal bodies: ‘They construct the whole universe out of numbers – only not numbers consisting of abstract units; they suppose the units to have spatial magnitude.’ There is much to puzzle over in this report, but it clearly runs counter to Loptson’s claim that Pythagoras was the first to bring ideas of abstract entities into the history of philosophy. M.F. Burnyeat precise mathematical definition in order to prove important, unobvious theorems about them, without for one moment raising philosophical questions about, as Loptson puts it, ‘the nature and reality’ of such things. And to return from the sublime to the ridiculous, there is no evidence that Pythagorean dicta such as ‘Marriage is five’ ever led to philosophy. Or will Loptson accept ‘Seven is Athena,’ another Pythagorean example discussed in my review, as a contribution to the philosophy of mathematics on the grounds that it speaks to the nature and reality of the number seven? Journal articles Brooke, G.J. Pythagoreans and Essenes: structural parallels Journal for the Study of the Old Testament. 2006, 30, 5, p 187-188. Anonymus. The Music of the Spheres. Wilson Quarterly. 2006, 30, 4, p82-83 Abstract: An excerpt from the articles "The Geometry of Musical Chords," by Dmitri Tymoczko and "Exploring Musical Space," by Julian Hook in the July 7, 2006 issue of "Science" is presented. Caleon, I.S. From Pythagoras to Sauveur : tracing the history of ideas about the nature of sound Physics education. 2007, 42, 2, p 173-179 Barker, A. "Archytas Unbound,": A Discussion of Carl A. Huffman, Archytas of Tarentum Oxford Studies in Ancient Philosophy. 2006, 31, p 297–321 Costanza, S. Una Syntaxis Mantica Pitagorica Byzantinische Zeitschrift. 2005, 98, 1, p 5-22 Crowley, T.J. "On the Use of Stoicheion in the Sense of 'Element'" Oxford Studies in Ancient Philosophy. 2005, 29, p 367-394 Bangu, S. Pythagorean Heuristics in Physics Perspectives on science : historical, philosophical, social. 2006, 14, 4, p 387-416 Abstract: Some of the great physicists' belief in the existence of a connection between the aesthetical features of a theory (such as beauty and simplicity) and its truth is still one of the most intriguing issues in the aesthetics of science. In this paper I explore the philosophical credibility of a version of this thesis, focusing on the connection between the mathematical beauty and simplicity of a theory and its truth. I discuss a heuristic interpretation of this thesis, attempting to clarify where the appeal of this Pythagorean view comes from and what are the arguments favoring its acceptance or rejection. Along the way, I sketch the historical context in which this heuristic interpretation gained credibility (the quantum crisis in physics in the 1920s), as well as the more general implications of this thesis for physicists' metaphysical outlook. Evans, T.V. Valedictory 'eppwao in Zenon Archive Letters from Hierokles Zeitschrift für Papyrologie und Epigraphik. 2005, 153, p 155-158 Di Meo, P. Eccentric Italies - The Pythagorean fairytale Quinzaine Litteraire. 2007, 939, p 6. Fermani, A. Il concetto di limite nella filosofia antica La-Societa-degli-Individui. 2005, 23, 2, p 5-17 Abstract: La filosofia nasce e si fonda sul concetto di limite. Il termine stesso 'filo-sofia', infatti, sembra essere stato inventato da Pitagora per indicare l'impossibilita dell'essere umano di avere accesso alla sapienza, cioe ad un possesso pieno del sapere che, in quanto tale, e proprio solo degli dei. Il saggio si propone di ripercorrere questa originaria coappartenenza della filosofia e del 'limite attraverso le sue articolazioni principali (soffermandosi, in particolare, su alcuni snodi Bordoni, C. FUORI QUOTA - Ma i Presocratici sono di destra o di sinistra? Il ponte : rivista mensile di politica e letteratura. 2007, 63, 1, p 13-14

the Middle Ages, especially by William of Ockham. It begins by tracing the "official history" according to which Empedocles' original suggestion of natural selection lay dead at the hands of Aristotle, Aquinas, and Giles of Rome. It then supplies the "missing history" in which the idea lives on, gaining momentum from John Philoponus to Averroes to Ockham. Ockham was critical of Aristotle's teleology. In challenging Aristotle's argument against Empedocles and in promoting nominalism, Ockham lays important groundwork for Darwin's revolutionary theory. del pensiero platonico e aristotelico) e nelle sue ricadute sul versante gnoseologico, etico e politico. Ferwerda, R. De Papyrus van Strootsburg : een nieuw fragment van Empedokles Hermeneus. 2007, 79, 1, p 23-30 Giovannozzi, D. Studi e ricerche - Paignion dia tou katoptrou. Lo specchio di Pitagora tra prestigio e leggenda Giornale critico della filosofia Italiana. 2006, 26, 3, p 458-468 Kihc, C. The Metaphysics of Numbers from "One" to "Ten" (in Turkish) Felsefe-Dunyasi. 2006, 43, 1, p 31-55 Abstract: Studies on abstract numbers and the efforts for the founding of the existence of thought over mathematics have been carried out by Pythagoras and the followers in Greek thought. Consequently, they believe that all of the universe comes into those numbers and a ratio of it while loading religious characteristics to numbers that were created by God. At the same time the universe - from physical events and stars to things on earth - is administered by numbers. The verbs of "commander of the universe is a number", "numbers are administering the universe" belong to Pythagoras. According to Pythagoras, the universe cannot be perceived and learnt without numbers. For these reasons the origin of everything is numbers and there is no wisdom except without them. Namely, these numbers are God himself. There is a Pythagorean philosophy on the basis of interest in the ontological features of numbers in the ancient tradition of Judaism, Christianity, and Islamic thought. (edited) Goodrich, P. The Pythagoras Complex : respondeo etsi mutabor - I respond even though I have to change Juridikum.2006, 4, p 216 -223 Guardo, A.A. Los Prenostica Pitagorice consideracionis : un libro de suertes medieval. Estudio introductorio Studi medievali. 2006, 47, 2, p 839-854 Gusset, D. Music of the spheres Strad. 2006, 117, 1400, p 48-52 Summary: The article discusses forms of creating Cremonese stringed instruments. Cremonese violin making began with the Amati family in Cremona, Italy during the 16th century, but eventually disintegrated by the 18th century with the Stradivari family. Researchers have found that the Cremonese design system was based on the geometric principles of Pythagoras. Certain geometric relationships can be traced to its centers, but researchers are puzzled as to how they are connected to soundpost location Hicks, B. tes.co.uk/staffroom Times Educational Supplement. 2006, 4670, p 2-3 Summary: The article discusses various topics that might be of interest to online forum participants of the Times Educational Supplement. The author describes that compelling topics include: 1) Canadian teachers in London; 2) Modern Foreign Language teachers who don't have their own classroom; and 3) Student teachers and mentor teachers arguing about Pythagoras nationality Loukas M, et al The cardiovascular system in the preHippocratic era. Int J Cardiol. 2007. Feb 19. Although Hippocrates has been traditionally recognized as the father of medicine and one of the major early writers regarding the cardiovascular system, very little is known of about the knowledge of the cardiovascular system in the pre-Hippocratic period. We reviewed the literature and examined available references regarding the cardiovascular system in the pre-Hippocratic era of the Chinese, Indians, Egyptians, and Ancient Greeks including Asclepios, Alcmaeon, Empedocles and Diogenes. All pre-Hippocratic civilizations attributed the illnesses and the structures of the human body to divine powers. Pre-Hippocratic medicine was largely based on Kaye, S.M. Was There No Evolutionary Thought in the Middle Ages? The Case of William of Ockham British Journal for the History of Philosophy. 2006, 14, 2, p 225-244 Abstract: This paper shows how the concept of evolution was preserved and advanced in

influenced by the "barbarian" hyperborean wisdom. religious beliefs and not in scientific observations. Interestingly, despite these erroneous methods, the pre-Hippocratics were able to identify pipes carrying air into the body and name the air carriers (arteries). Unfortunately, the arteries were not associated with blood but rather with air, however, this ancient word still remains in use in our days. This paper reviews the evolution of thinking and discovery regarding the different aspects of the cardiovascular system in the preHippocratic era. Primavesi, O. Die Suda über die Werke des Empedokles Zeitschrift für Papyrologie und Epigraphik. 2006, 158, p 61-75 Primavesi, O. Empedokles in Florentiner Aristoteles-Scholien Zeitschrift für Papyrologie und Epigraphik. 2006, 157, p 27-40 Redondo Reyes, P. Pitágoras en la herrería : variaciones sobre un episodio legendario Prometheus. 2005, 31, 3, p 193-215. MacWilliam, S. Pythagoras's screen Parallax. 2006, 12, 4, p. 4-12. Martín Morillas, A.M. El diálogo de Heidegger con los filósofos presocráticos Pensamiento. 2007, 63, 235, p 35-58 Stam, H.J. Pythagoreanism, meaning and the appeal to number New Ideas in Psychology. 2006, 24, 3, p 240-251 Abstract: The threat of Pythagoreanism hovers over the appeal to quantification, despite Yanchar's and Westerman's calls for a liberal, interpretive view of numbers. I discuss their articles by agreeing that the distinction between qualitative and quantitative methods is of limited utility, by noting various versions of interpretation in their articles, and by pressing the need to address questions of measurement. Without a coherent measurement strategy, the use of numbers remains at best ambiguous and at worst arbitrary. Although disagreeing with a number of issues in their respective positions, I welcome this opportunity to consider the broader question of measurement and its place in psychology. Messina,G. Una nuova lettura di Empedocle 100 DK Giornale-di-Metafisica. 2005, 27, 3, p 777-787 Montgomery, W. Susan Howe's Renaissance period: Metamorphosis and representation in 'Pythagorean Silence' and 'Defenestration of Prague' Journal of American Studies. 2006, 40, 3, p 615-633 Summary: The article discusses the metamorphosis and representation of ideas in the poetry of Susan Howe. The reflection focuses on the motifs drawn from the literature of the Renaissance. The poems include "Pythagorean Silence" and "Defenestration of Prague" which were published at the beginning of the 1980s. It is stated that her version of the metamorphosis is a passing-into-statis that retains spirit within a physical universe Ulliana, S. Giordano Bruno: E il problema della modernita Cosmos-and-History. 2005, 1, 1, p 146-176 Abstract: The arguments that have been presented in this essay have managed to rise the deepest and most important core of the true foundation of Giordano Bruno's speculative thinking, the active presence of a triadic theological-political concept of the Father, the Son and the Spirit of Christian tradition. However, this triad has also been reformulated through the revolutionary overturning of this tradition and realized through a creative and dialectical concept of the infinite. Problems that have been apparently solved and codified in the Platonic and Aristotelian thought are reversed back to the Presocratic way of thinking (Parmenides, Heraclitus and Empedocles). Naddaf, G. DISCUSSION - What Is Presocratic Philosophy? Ancient philosophy. 2006, 26, 1, p 161-179 Pogorilovschi, I. Comparative Temptations in Philosophy (III) Zamolxis - Sokrate - (Plato) (in Romanian) Revista-de-Filosofie-(Romania). 2005, 52, 5-6, p 953-971 Abstract: The final part of the present study (the first being a comparative approach of Zamolxis and Thales, and the second being focussed on Pythagoras) extends the comparative analysis to the Platonic thought and to the Socratic one, at the same time. Plato's dialogue Charmides where Socrates acts the core part represents the ancient text in which Greek philosophical thought is most

existence of standardized Greek measures of length. Vitek, T. Newly Recovered Empedoclean Verses (in Czech) Reflexe. 2005, 27, p 75-94 Abstract: The article discusses the texts recovered on the papyrus Strasburghiensis and edited by Martin and Primavesi. The present author concludes that, first, the text of the papyrus is very uncertain and contributes little to our knowledge; second, the Martin-Primavesi restoration of Empedocles's verses is far too speculative and distorted by the controversial philosophical position of the editors: for instance, the reading--metha in aI, 6, ail, 17 and c3, and M-P's presentation of Empedoclean demonology are demonstrably incorrect. Work in Progress M. Laura Gemelli Marciano, Titularprofessorin für Klassische Philologie Klassisch-Philologisches Seminar der Universität Zürich Laufende Forschungsprojekte Die Vorsokratiker. Ausgabe von ausgewählten Texten mit Einleitung, Übersetzung und Kommentar, Artemis-Verlag, Reihe "Tusculum". Antike Atomisten. (Gesamtprojekt: Die Vorsokratiker. Texte zu ihrer Überlieferung, De Gruyter, Berlin). http://www.klphs.uzh.ch/Personen/Gemelli.php Vinel, N. La naissance oubliée du concept de zéro chez Jamblique de Chalcis (IIIe-IVe s.) Les études classiques. 2006, 74, 1, p 49-68. Zwarte, R.de Greek temple design reconsidered: the temple of Athena at Paestum and its monumental stepped altar. With a digression on methodology in Greek metrology Talanta, Proceedings of the Dutch archeological and historical society. 20042005, 36-37, p 11-47. Abstract: The dimensions of the outlying altar of the temple of Athena at Paestum show that the Greek architect used his imagination to create a safe building – i.e. protected from evil spirits – by means of ‘applied magic’. It follows that aesthetic matters seem to be of secondary importance. The work as a whole was fully designed before construction began (ca. 510 BC). The altar provides the clue to a full understanding of the cella dimensions. Although the cella is not well preserved, an analysis of its metric dimensions gives striking results. The plan’s features lean on a fixed foot-standard of Athenian origin. The characteristic measure of hundred feets was composed of the lowest number of three successive Pythagorean number triples beginning with a prime number. These number triples emerge in the series immediately after the well-known 3/4/5 triple. Our analysis shows once more the. ISNS sessions at the American Academy of Religion meeting in November 17-20, 2007 in San Diego. Platonism and Neoplatonism Group 1) Foundations of Neoplatonism -- Papers are invited to explore the sources of classical neoplatonic theory and practice. These sources may include but are not limited to Platonic, Pythagorean, Aristotelian, Stoic, Gnostic, and Hermetic writings. The question to be addressed is how these traditions are given expression by neoplatonic authors and what distinguishes them as neoplatonic. Are there distinctly neoplatonic principles and, if so, what are they? 2) Expressions of New Age Neoplatonism -- It has been argued that Neoplatonism has been a primary influence on New Age authors from Helena Blavatsky to contemporary Wiccans. In what senses are New Age beliefs and practices neoplatonic? Is Neoplatonism today being given authentic expression and new life or have contemporary authors and practitioners misappropriated and/or misunderstood classical neoplatonic literature?

Commentary in Science Section of NYTIMES, Tuesday, October 3, 2006 Numbers Are Male, Said Pythagoras, and the Idea Persists, by Margaret Wertheim. A letter not published by the NY Times, by Christiane L. Joost-Gaugier Contrary to what commentator Margaret Wertheim said in her otherwise very interesting feature on Women in Physics, there is no evidence known to me that supports the stunning headline, "Numbers are Male, Said Pythagoras." While I, as the first person who brought a class action on behalf of women in academe (which became the precedent setting case in academia), sympathasize with and appreciate the other things that she said in her article concerning the humiliation still suffered by women in Physics and other sciences, I find her comments on Pythagoras superficial and incorrect. As the author of a new book that studies the reputation of Pythagoras and Pythagoreanism (MEASURING HEAVEN: PYTHAGORAS AND HIS INFLUENCE ON CULTURE AND ART IN ANTIQUITY AND THE MIDDLE AGES), I would say that the facts known to us are quite the contrary of what she says. Pythagoras himself said nothing (that we know of) about numbers and sex. However, his followers, in later times, especially in the lst - 3rd centuries (AD) maintained that some numbers are male and others are female. Also, to set the record straight, according to the testimony of his followers, Pythagoras was the first scholar of antiquity to educate female students. His wife Theana and daughter Damo were both reputed to be scholars who protected his cherished secrets. Pythagoras should, indeed, be regarded as a hero to women in the sciences. Professor Christiane L. Joost-Gaugier Ph.D., Harvard Discussion in the Yahoo Newsgroup Pythagorean-L (Pythagorean-L@yahoogroups.com) Concerning NYTIMES article, Tuesday, October 3, 2006 Numbers Are Male, Said Pythagoras, and the Idea Persists, by Margaret Wertheim. Sergio Jerez jerez_sergio@yahoo.com 3 oktober 2006 I don't know the sources Ms Wertheim has searched. But her opinion is quite strange . Theano of Crotona, for example, Pythagoras' wife, seems to have been very active among the academy students. The concept of the "golden section" is attributed to her. Here is a list of important Pythagorean women: Abrotelia, the daughter of Abroteles of Tarentum Babelyma of Argos Bryo of Argos Byndacis, the sister of Ocellus and Occillus, of Lucania Cratesiclea the Lacedaemonian, the wife of Cleanor the Lacedaemonian Cleaechmas, the sister of Autocharidas the Lacedaemonian Chilonis, the daughter of Chilon, the Lacedaemonian Echecratia of Phlius Lasithenia the Arcadian Mya, the wife of Milon the Crotonian Nisileadusa the Lacedaemonian Philtis, the daughter of Theophrius the Crotonian Pisirrhonde of Tarentum Theano the wife of Brontinus of Metapontum Timycha, the wife of Myllias the Crotonian Tyrsenis of Sybaris Maior rory12001@yahoo.com 3 oktober 2006 this article is absolutely wrong. I'd use a stronger word if I didn't follow the mean. Pythagoras said he was taught by Themistocleia the oracle of Delphi. He took women as students on an equal basis as men. He thought men and women different but morally equal. His wife Theano

wrote treatises & his daughters continued his school at his death. There are many eminient women pythagoreans who were mathematicians and philosophers. Additionally, 2 - the dyad is regarded as female. Please read Diogenes Laertius on Pythagoras, he doesn't get it completely but he's good. Then read Iamblichus 'On the Pythagorean Life' he and Suda have a list of Pythagoras's female students. Two good articles on the internet are Greek women: "Mathematicians and Philosophers" http://www.mlahanas.de/Greeks/Women/Philosopher.htm There is a lot more material on Pythagoras. Here's a small mention of the great Pythagorean women [ Hipparchia, Hypatia, Axiothea aren't stricltly Pythagorean but these are true women philosophers: Themistokleia Theano of THurii Damo of Crotona Arignote of Samos Myia Deino Eloris of Samos Melissa Tymicha Ptolemais of Cyrene Cleobulina of Rhodes Okkelo & Ekkelo of Lucania Cheilonis Kratesikleia Lasthenia of Arcadia Habroteleia Echekrateia of Phlius Tyrsenis of Sybaris Ryndako Peisirhode of Tarentum Theadousa Boio from Argos Vavelyca of Argos Diotima Vitale Periktione Lasthenia Aesara of Lucania Axiothea of Philesia Nikarete of Corinthos Hipparchia the Cynic Arete of Cyrene Pythais Hypatia Asclepigenia of Athens & a course description http://www.macalester.edu/~warren/courses/In5Pythagoreans.htm I also can assure you that Pythagoras advocated vegetarianism. Nigidius Figulus & Vatinus in Rome were noted neo-pythagoreans & another philosopher, I believe Seneca flirted with pythagoreanism, he followed a vegetarian diet in Rome. Another, Plutarch I beleive was buried with Pythagorean rites. I belong to a Sodalitas of Nova Roma devoted to Hellenism & the name I use is Ptolemais to commemorate this woman mathematician!! Pythagoras was pro-women & pro-vegetarian. (Margaret Wertheim did not give a response to these comments. NB)