Number Symbolism in the Mediterranean Before a.D. 1000_ a Select Bibliography

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    NUMBER SYMBOLISM IN THE

    MEDITERRANEAN BEFORE A.D. 1000: A

    SELECT BIBLIOGRAPHY

    Edited by Joel Kalvesmaki

    Updated 24 December 2004

    Part of the Theology of Arithmeticwebsite.

    The following books and articles deal with number symbolism in the ancient world (Europe, Africa, and Asiawest of the Indus River) from prehistory to the year 1000. The cutoff date is somewhat arbitrary, but it

    precludes discussion of the Kabbalah and medieval number symbolism, subjects that would require their owntreatment since authors from this period adopt and radically reconfigure ancient number symbolism.

    Nearly every study of Pythagoreanism has something to say about numbers, arithmetic, and mathematics ingeneral. I have, however, listed only those works that have advanced historical or philological argumentsconcerning Pythagoreanism, specificially its number symbolism or philosophy of number. For more general orderivative articles and books on Pythagorean numbers and their integration into Pythagoreanism as a whole,see Luis E. Navia,Pythagoras: An Annotated Bibliography(New York: Garland, 1990).

    I have not listed websites because they are ephemeral. Without doubt the attentive reader will find manyinconsistencies and typographical errors in this bibliography. I plan to correct these in future versions.

    Not all books and articles listed here are academic, or are of equal value. There are plenty of works thatpresent either foolishly naive claims, or arguments that are invalid or unsound. Caveat lector. I am slowlydeveloping this bibliography into a critical one, which, when finished, will help guide the reader. In theinterim, I have posted the text of a lecturethat provides some initial thoughts concerning the scope and valueof recent secondary literature.

    Adamson, Robert. "Pythagoras and Pythagoreanism." The Development of Greek Philosophy(1908):1728.

    1.

    Ahutin, A. V. ["The Origins of Theoretical Thinking."] Voprosy Filosofii 1 (1972): 12334.2.Aidoni, Sophia and Kritzas Charalambos B. "The Letters of the Alphabet as Numerical, Musical, orMagical Symbols [Die Buchstaben des Alphabets als Zahlzeichen, Daten und magische Symbole]." In

    Die griechische Schrift,14164. Athens: Epigraphical Museum, 2001.

    3.

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    Alfldi-Rosenbaum, Elizabeth. "The Finger Calculus in Antiquity and in the Middle Ages." In Studies inRoman Game Counters I.Frhmittelalterliche Studien 5. 1971. Pp. 119.

    4.

    Allendy, Ren Flix.Le symbolisme des nombres.Essai darithmosophie. 2d ed. Paris 1948.5.Alt, Albrecht. "Die Weisheit Solomos." Theologische Literaturzeitung76 (1951): 13944.6.Angenendt, Arnold, Thomas Braucks, and Rolf Busch. "Gezhlte Frmmigkeit." InFrhmittelalterlicheStudien, vol. 29. Berlin: De Gruyter, 1995. Pp. 171.

    7.

    Anonymous. "Table de Pythagore."Encyclopdie, ou Dictionnaire raison des scineces, des arts et desmtiers. Stuttgart: Friedrich Frommann Verlag, 1966. 13:614.

    8.

    Apatow, Robert. "The Tetraktys: The Cosmic Paradigm of the Ancient Pythagoreans."Parabola 24.3(1999): 3843.

    9.

    Appelbaum, David, ed. "Number & Symbol."Parabola24.3 (1999): 59010.Arndt, Otfried. "Zahlenmystik bei Philo : Spielerei oder Schriftauslegung?"Zeitschrift fr Religions-und Geistesgeschichte 19 no 2 (1967): 16771.

    11.

    Arpat, Atilla. "Jesus Christus und die Zahl 12 in den Dimensionen der Sergios Bakchor Kirche zuIstanbul."Ayasofya Mzesi Yay1nlar113 =Ayasofya Mzesi y1ll1 i=Ar. Sophia Museum 10 (1985):3439.

    12.

    Arx, Urs von. Studien zur Geschichte des alttestamentlichen Zwlfen symbolismus.Vol. 1:Fragen imHorizont der Amphiktyoniehypothese von Martin Noth. Europische Hochschulschriften, Reihe 23:Theologie 397. Bern: Lang, 1990.

    13.

    Aubineau, Michel. "Les 318 serviteurs dAbraham (Gen 14:14) et le nombre des Pres au concile deNice (325)."Revue dHistoire Ecclesiastique 61 (1966), p. 543.

    14.

    Avishur, Y. "The Forms of Repetition of Numbers Indicating Wholeness (3, 7, 10) in the Bible and inAncient Semitic Literature." [In Hebrew.]Beersheva 1 (1913): 155.

    15.

    Badarau, D. "Le nombre chez les premiers Pythagoriciens."Analele Univ. dei Bucuresti 5 (1962):87101.

    16.

    Bakhouche, Batrice. "Arithmologie et cycles temporels: lhebdomade de Censorinus."Euphrosyne29(2001): 26775.

    17.

    Balch, L. "The Neo-pythagorean Moralists and the New Testament." InAufstieg und Niedergang derrmischen Welt,vol. II.26. Eds. H. Temporini and W. Haase. Berlin: De Gruyter, 1970 .

    18.

    Ballas, Kostes.Hoi Pythagoreioi. Athens: Hidryma Goulandre-Chorn, 1985.19.

    Bamford, Christopher, ed.Homage to Pythagoras: Rediscovering Sacred Science. Hudson, NY:Lindisfarne, 1994.

    20.

    Barbera, Charles Andr. The persistence of Pythagorean mathematics in ancient musical thought.Thesis (Ph. D.)University of North Carolina at Chapel Hill, 1980.

    21.

    Barbone, Steven. "El numero en Agustin."Augustinus44 (1999): 3549.22.Barker, A. D. "Sumfonoi; ajriqmoiv: A Note onRepublic531c14." Classical Philology73 (1978):33742.

    23.

    Barry, Kieren. The Greek Qabalah: Alphabetic Mysticism and Numerology in the Ancient World. YorkBeach, Me.: Samuel Weiser, 1999.

    24.

    Bauckham, R. "The 153 Fish and the Unity of the Fourth Gospel." Neotestamentica36.12 (2002):7788.

    25.

    Baudouin, Bernard.Magie et mystre des nombres. Paris: De Vecchi, 2002 (impr. en Italie).26.Bauer, Johannes B. "Drei Tage." In Scholia Biblica et patristica. Graz: Akademische Verlangsanstalt,1972.

    27.

    Bazak, Jacob. "Numerical devices in biblical poetry." Vetus Testamentum38.3 (1988): 33337.28.Beatty, H. "The Pythagoreans."Hermathena18 (?): 15874.29.Beaujouan, Guy. "Le symbolisme des nombres lpoque romane." In Cahiers de civilisationmdivale,Poitiers 4 (1961): 15969.

    30.

    Bechtle, Gerald and Dominic J. OMeara, eds.La Philosophie des Mathmatiques de lAntiquitTardive. Actes du colloque international Fribourg, Suisse (2426 septembre 1998). Fribourg: EditionsUniversitaires Fribourg Suisse, 2000.

    31.

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    Becker, Oskar.Das Mathematische Denken der Antike. Gttingen: Vandenhoeck & Ruprecht, 1957.32.Becker, Udo.Lexicon der Symbole. Freiburg: Herder, 1992.33.Bectel, E. A. "Finger-counting among the Romans in the Fourth Century." Classical Philology4 (1909):2531.

    34.

    Begey, Roger.La gomtrie sacre, ou, La magie des formes. [France]: Editions du Rocher, 1995.35.Bell, Eric T. The Magic of Numbers. London: McGraw-Hill, 1947.36.Benary, Ferdinandus and Henry Boynton Smith. "Interpretation of the number 666 (chxs) in theApocalypse (13:18) and the various reading 616 (chis)."Bibliotheca Sacra and Theological Review 1.1

    (1844): 8486.

    37.

    Bergmann, Jan. "Das Zwei-Wege-Motiv: Religions geschichtliche und exegetische Bemerkungen."Svensk Exegetisk rsbok4142 (197677): 2756.

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    Bergua, Juan B.Pitgoras. Madrid: Ediciones Ibricas, 1958.39.Bernand, E.Inscriptions mtriques de lEgypte grco-romaine. Paris, 1969.40.Berrettoni, Pierangiolo. "Numerologia e costruzione del genere: da Pitagora a Melanie Klein."AnnalidellIstituto universitario orientale di Napoli, Dipartimento di studi del mondo classico e del

    Mediterraneo antico, Sezione lingiustica19 (1997): 14776.

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    Berthelot, A.Die macht der Schrift in Glauben und Aberglauben. Abhandlungen der DeutschenAkademie der Wissenschaften zu Berlin 1948/1. Berlin: Akademie-Verlag, 1950.

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    Betz, Otto.Das Geheimnis der Zahlen. Stuttgart: Kreuz, 1989.43.

    Betz, Otto.Elementare Symbole: Zur tieferen Wahrnehmung des Lebens. 1987. Repr. Freiburg: Herder,1992.

    44.

    Bevegni, C. "I Ligure dalle sette costole." Studi Italiani di Filologia Classica2 (1984): 4051.45.Billigmeier, J. Ch. "Alphabets."Encyclopedia of Religion1:21622.46.Bindel, Ernst. "Die Zahlen in platonischer und aristotelischer Auffassung."Antaios4 (1962): 23850.47.Bindel, Ernst.Die gyptischen Pyramiden als Zeugen vergangener Mysterienweisheit. Zugleich eineallgemeinverstndliche Einfhrung in die Symbolik von Zahlen und Figuren 4. Stuttgart: FreiesGeistesleben, 1975.

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    Bindel, Ernst.Die geistigen Grundlagen der Zahlen. Die Zahl im Spiegel der Kulturen. Elemente einerspirituellen Geometrie und Arithmetik. Perspektiven der Anthroposophie. Frankfurt, 1983.

    49.

    Bischoff, Erich.Mystik und Mage der Zahlen. 1920. Repr. Wiesbaden: Fourier, 1992.50.

    Blankenburg, Walter and Willem Elders. "Zahlensymbolik." InDie Musk in Geschichte und Gegenwart,vol. 16, pp. 197178. Kassel, 1979.

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    Blazek, Vclav.Numerals : comparative-etymological analyses of numeral systems and theirimplications : Saharan, Nubian, Egyptian, Berber, Kartvelian, Uralic, Altaic and Indo-Europeanlanguages. Spisy Masarykovy univerzity v Brne, Filozofick fakulta; 322. [Brno] : Masarykovauniverzita Brne, 1999.

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    Blinn, Hansjrgen.Die Altdeutsche Exodus. Strukturuntersuchungen zur Zahlenkoposition undZahlensymbolik.Amsterdam, 1974.

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    Blumenthal, D., ed. Understanding Jewish Mysticism: a source reader.New York: Ktav, 197882.54.Bober, Harry. "In principio: creation before time." InEssays in honor of Erwin Panofsky . New York:

    New York University Press, 1961. Pp. 1.1328; 2.58.55.

    Bmer, F.Der Lateinische Neuplatonismus und Neupythagoreismus. Leipzig: Harrassowitz, 1936.56.Bond, F. B. and T. S. Lea. Gematria: A Preliminary Investigation of the Cabala Contained in theCoptic Gnostic Books and of a similar Gematira in the Greek Text of the New Testament. Oxford: BasilBlackwell, 1917. Repr., London: Research into Lost Knowledge Organization, 1977.

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    Bonnefois, J.-F. "La mystique des nombres."Revue dasctique et de mystique25 (1949): 53350, repr.Mlanges Marcel Viller, #99100.

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    Bonner, Campbell. "The Numerical Value of a Magical Formula."Journal of Egyptian Archaeology 16(1930): 69.

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    Bonnet, Hans. "Achtheit." InReallexicon der gyptischen Religionsgeschichte. Berlin: de Gruyter,1952. Pp. 56.

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    Bonnet, Hans. "Neunheit." InReallexicon der gyptischen Religionsgeschichte. Berlin: de Gruyter,1952. Pp. 52125.

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    Borchardt, L. Gegen die Zahlenmystik an der grossen Pyramide bei Gise. Berlin, 1922.62.Bouch-Leclerq. "La mdecine astrologique." Chapter 15 inLastrologie grecque, pp. 51742. Paris:Leroux, 1899.

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    Boudouris, K. I.Pythagorean philosophy. Athens: International Center for Greek Philosophy andCulture, 1992.

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    Bousquet, J. "Les confrres de la Porte Majeure et larithmologie pythagoricienne." Revue des tudes

    Grecues64 (1951): 46671.

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    Bovon, Franois. "Names and numbers in early Christianity."New Testament Studies 47.3 (2001):26788.

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    Boyanc, P. "Note sur le tetractys."Lantiquit classique20 (1951): 42125.67.Boyanc, Pierre. "tudes philoniennes."Revue des tudes Grecques76 (1963): 64110.68.Brach, Jean- Pierre.La symbolique des nombres.Que Sais-Je?, 2898. Presses Universitaires de France:Paris 1994.

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    Brach, Jean-Pierre. "Quelques rflexions sur les fondements spculatifs de la symbolique des nombres."In:sotrisme, gnoses & imaginaire symbolique: Mlanges offerts Antoine Faivre. Ed. RichardCaron, Joscelyn Godwin, Wouter J. Hanegraaff et Jean-Louis Vieillard-Baron. Peeters: Louvain 2001,74147.

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    Bramley-Moore, A. A. The Significance of Numbers as Used in the Bible. 1917.71.Braulik, Georg. "Die Funktion von Siebenergruppierungen im Endtext des Deuteronomiums." In Gott,eine Offenbarung. Wrzburg: Echter, 1991. Pp. 3750.

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    Bravo Garca A. "Sobre un comentario annimo a la Aritmtica de Nicmaco de Gerasa y sus mss. enbibliotecas espaolas." Cuadernos de filologa clsica16 (197980): 2740.

    73.

    Brentjes, Sonja. "Untersuchungen zum Nicomachus Arabus." Centaurus 30 (1987): 21239.74.Bronowski, Jacob. "The Music of the Spheres." The Ascent of Man. Boston: Little, Brown, 1973. Pp.15587.

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    Brooke, George J. "4Q252 and the 153 fish of John 21:11." InAntikes Judentum und frhesChristentum, 25365. Berlin: Walter de Gruyter, 1999.

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    Brottier, L. "Lepisode des fleaux dEgypte (Ex 711) lu par Philon dAlexandrie et les Pres Grecs."

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    Brough, John. "The Tripartite Ideology of the Indo-Europeans: An Experiment in Method."Bulletin ofthe School of Oriental and African Studies22 (1959): 6986.

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    Bruins, Evert M. "Number of the beast."Nederlands Theologisch Tijdschrift23 (1969): 4017.79.Brul, Pierre. "Arithmologie et polythisme." In Grandes figures religieuses. Paris: Belles Lettres,1986. Pp. 3547.

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    Brumbaugh, Robert.Platos Mathematical Imagination. Bloomington, IN: Indiana University Press,1954. Reprinted, New York: Kraus 1968.

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    Bucking Scott J. "On measuring the range of Anatolian text in the Theologoumena Arithmeticae."Grazer Beitrge: Zeitschrift fr die klassische Altertumswissenschaft18 (1992): 12748.

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    Bucking, Scott J. "The excerpt format of the [Iamblichean] Theologoumena Arithmeticae and its impact

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    Buffire, F.Les Mythes dHomre et la pense grecque. Paris: CEA, 1956.84.Bullinger, E. W.Number in Scripture. Its Supernatural Design and Spritual Significance.London,1952.

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    Burkert, Walter.Lore and science in ancient Pythagoreanism. Translated by Edwin L. Minar, Jr.Cambridge, Mass.: Harvard University Press, 1972.

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    Burns, J. Patout. "Variations on a dualist theme : Augustine on the body and soul." InInterpretingtradition, 1326. Chico, Calif: Scholars Press, 1984.

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    Butler, Christopher.Number Symbolism. London: Routledge and Kegan Paul, 1970.88.

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    Cacciari Antonio. "Temi medioplatonici e neopitagorici in un frammento pseudogiustineo."Paideia 43(1988): 327.

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    Caspari, Peter. "ber pythagoreische Zahlen." Gymnasium4 (1886): 11819.95.Chaboche, Franois Xavier. Vie et mystre des nombres. Paris: Michel, 1976.96.Chrisomalis, Stephen. "The Egyptian origin of the Greek alphabetic numerals,"Antiquity77.297(September 2003): 48596.

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    Christ, W. von. Geschichte der griechischen Literatur. Vol. 2. HKAW 7.2.1. Mnchen, 1920.98.Christiansen, Irmgard.Die Technik der allegorischen Auslegungswissenschaft bei Philon von

    Alexandrien. Beitrge zur Geschichte der biblischen Hermeneutik 7. Tbingen, 1969.99.

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