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Bink Hallum Circles the Square

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We chat further about all things magical and squared with Dr Hallum. We begin with a discussion of the two surviving MSS of a magic-square text by al-Mālaqī (‘He from Malaga’) which, although problems with the text abound (see Works Cited, below), nevertheless fills in a major gap in our knowledge of the tradition, including the astrological/lettrist rationales understood to lie behind why a given square should be associated with a given planet. Al-Mālaqī gives a reverse ordering to the square/planet correspondences to that given by Ibn al-Zarqālluh: Zarq has the 3X3 square associated with Saturn, and the magnitudes of squares increasing as you approach the earth, while Mal associates the 3X3 with the moon and they get bigger as you get further away.

These are the  two main systems found throughout Islamicate and European literature (and objects) on the subject. Ibn al-Zarqālluh’s system, followed by practically the whole of Christendom, has been labelled System 1 in modern scholarship; al-Mālaqī’s, which was vastly more popular in the Islamicate world, has been called System 2. System 2 routinely, and System 1 occasionally include the 10×10 wafq associated with the fixed stars, usually called the Sphere of the Zodiac.

We then discuss the ancient talismanic statues attributed to Apollonius of Tyana in the Christian tradition – including reference to Apollonius’ famous Giant Mosquito (see Works Cited below for the references) – and the subsequent Balinas traditions in Islamicate talismanic works. We also discuss the prominent roles played by ‘Pythagoras’ and ‘Plato’ and even ‘Thales of Miletus’ in the talismanic literature.

Other topics covered:

  • We discuss the ‘amicable numbers’; what they are, what Iamblichus did with them, and what the later Islamicate tradition does with them, illustrated by Aristotle and Alexander the Great’s ‘scissors incident’.
  • Some notes on the study of Arabic scientific manuscripts and the problems with old catalogues that tend to ignore magic squares literature,
  • The case-study of Ibn Hanbālī, a sixteenth-century Syrian polymath and Sufi, whose works include a treatise on the 4X4 magic square,
  • The status quæstionis on Jewish medieval magic square texts,
  • Agrippa’s ‘Hebraicisation’ of the magic squares in a Christian-kabbalist syncretic stylee, and his importance as the man who took the squares out of the manuscripts and into print with his Three Books on Occult Philosophy,
  • The East Roman use of magic squares,
  • The extraordinary case of Johann Baptist Großschedel (5 February 1577-1630’s), who seems to have been privy, somehow, to the planetary tables from the end of Ibn Zarqālluh’s text, which otherwise seem to have been unknown in the Latinate world. Check out his unbelievable Calendarium naturale magicum perpetuum on Gallica,
  • And lots more.


Dürer’s cryptic Melencolia I, showing a 4X4 magic square, doubtless invoking Jupiter (according to the system of Ibn al-Zarqālluh) to counteract the melancholic influence of Saturn (It doesn’t seem to be working).
An early-modern, mass-produced magic-square medal, Landsmuseum Württemberg.

Many of the Islamicate scholars who made mathematical advances in the study of awfāq and wrote much of the earliest literature on the subject were astronomer-mathematicians working under royal patronage like al-Khāzinī (d. after 525/1130) the pupil of ʿUmar al-Khayyām (d. ca 517/1123), both of whom worked compiled zījes (books of tabulated astronomical data) for the Saljūq sultans and wrote lost treatises on magic squares. Here is an example from al-Khāzinī, BL, Or. 6669, fol. 123r, courtesy of Qatar Digital Library. Note that the numerical data in the tables is presented using Arabic alphanumerical notation although the text has nothing to do with lettrism or numerology.

Interview Bio:

Dr Bink Hallum is Arabic Scientific Manuscripts Curator at the British Library, and is currently doing Wellcome-Trust-funded postdoctoral research at the University of Warwick on the alchemical Twelve Books of Abū Bakr al-Rāzī. His research centres on Islamicate codicology, Græco-Arabic studies, the history of the sciences, and loads of other interesting stuff.

Works Cited in this Episode:


  • Heinrich Cornelius Agrippa von Nettesheim’s (d. 1535) discussion of the planetary awfāq in the De occulta philosophia libri tres (2nd edn, Cologne: 1533) is based on the Latin version of Ibn al-Zarqālluh’s treatise, but he added a Hebrew veneer that has remained part of the tradition of these magic squares in non-Islamicate literature until the present day: Agrippa von Nettesheim, Heinrich Cornelius, De occulta philosophia libri tres, ed. by Vittoria Perrone Compagni (Leiden/New York, NY/Köln: Brill, 1992), pp. 310–19; De occulta philosophia, facsimiles of 1510 manuscript and 1533 edn, ed. by Karl A. Nowotny (Graz: Akademische Druck-u. Verlagsanstalt, 1967), lib. 2, cap. 2.
  • The Alfonsine Astromagia: The Old Spanish translation of Ibn al-Zarqālluh’s treatise on planetary awfāq talismans produced in the latter half of the 13th century is lost, but the chapter on the wafq of Mars is preserved in the so-called Alfonsine Book of Astromagic (Libro de Astromagia; note that this title is the invention of the text’s modern editor and that in the unique and beautiful manuscript (available online through our friends at the Vatican) that preserves the text it has no title): Astromagia (Ms. Reg. lat. 1283a), ed. and trans. by Alfonso D’Agostino (Naples: Liguori Editore, 1992), pp. 246–249; Biblioteca Apostolica Vaticana, MS Reg. lat. 1283 pt. A, fol. 27rb–va.
  • al-Mālaqī: The Andalusian astronomer-mathematician al-Mālaqī ( 530/1135) wrote what may have been the first treatise on awfāq talismans that used the reverse of the system of planetary associations used by Ibn al-Zarqālluh. But the two known manuscripts of al-Mālaqī’s treatise preserve the text in different forms. The text in the older, mid-ninth/fifteenth-century manuscript is shorter, lacking the lettrist material and other details of great interest (Staatsbibliothek zu Berlin – Preussischer Kulturbesitz, Orientabteilung, Ms. or. quart. 98, fols 2r–7r) that are found in the younger, tenth/sixteenth-century manuscript (Tehran, Kitābkhāna-yi Majlis-i Shūrā-yi Islāmī, 41495, pp. 38–49).
  • Apollonius of Tyana/Balinas: For an account of the Greek sources on Apollonius’ talismanic statues, see Manuel Á. Martí-Aguilar. Talismans against Tsunamis: Apollonius of Tyana and the Stelai of the Herakleion in Gades (VA 5.5). Greek, Roman, and Byzantine Studies, 57: 968–93, 2017. On the Arabic tradition, see Manfred Ullmann. Die Natur- und Geheimwissenschaften im Islam. Brill, Leiden, 1972, pp. 378-81.
  • Großschedel: Ibn al-Zarqālluh’s treatise came with a set of tables that told practitioners when to construct the various planetary awfāq talismans. These tables are found in every Arabic manuscript of the treatise but are not found in any manuscripts of the Latin or Old Spanish versions. Inexplicably (for the time being), Ibn al-Zarqālluh’s appear in full in Johann Baptist Großschedel von Aicha’s (b. 1577) Dispositio numerorum magica ab unitate usque ad duodenarium (BL, Harley MS 3420, fols 30v–33v), which was published without the author’s consent and with the addition of numerous errors as the Calendarium naturale magicum perpetuum profundissimam rerum secretissimarum contemplationem totiusque Philosophiae cognitionem complectens, available on Gallica. On Großschedel and his Dispositio/Calendarium, see Gilly 2002.
  • Ibn al-Zarqālluh: One of the many manuscripts of the condensed Latin version of Ibn al-Zarqālluh’s treatise is transcribed and translated in Sesiano 2004.
  • Jābir ibn Ḥayyān: Mukhtār rasāʾil Jābir b. Hayyān. Essai sur l’histoire des idées scientifiques dans l’Islam, vol. 1, textes choisis, edited by Paul Kraus. Cairo: Maktabat al-Khānjī, 1935 [On magic squares in the Jābirian corpus, see Hallum 2021, pp. 78–86. On the Jābirian ‘Science of the Balance’ (ʿIlm al-Mīzān), by which the elemental properties of words can be analysed, see Nomanul Haq 1994].
  • Jewish magic squares: The earliest known appearance of a magic square in Hebrew literature is the eutocic 3×3 wafq in a magico-medical text attributed to Abraham b. Ezra (d. ca 560/1165), Sefer hanisyonot. The Book of Medical Experiences. Medical Theory, Rational and Magical Therapy. A Study in Medievalism, ed. and trans. by Joshua Otto Leibowitz and Shlomo Marcus (Jerusalem: Magnes Press, 1984), pp. 70–1 (commentary) and 238–41 (text and translation).
  • Manuel Moschopoulos’ (fl. 14th century) Greek treatise on magic squares is edited and translated in Tannery 1886 and analysed in Sesiano 1998. An East Roman Greek version of Ibn al-Zarqālluh’s treatise based on the condensed Latin version is preserved in Bodleian, MS Holkham Gr. 109, fols 7r–9v (15th century).


  • Bligh Bond, Frederick and Lea, Thomas Simcox. Gematria. Research into Lost Knowledge Organization; Distributed by Thorsons, London/Wellingborough, 1st ed. reprinted with new notes by Anne Macauley and new foreword by Keith Critchlow, 1977.
  • Carlos Gilly. The Rediscovery of the Original of Großschedel’s Calendarium Naturale Magicum Perpetuum. In Carlos Gilly and Cis van Heertum, editors, Magia, alchimia, scienza dal ’400 al ’700: L’influsso di Ermete Trismegisto/Magic, Alchemy and Science, 15th–18th Centuries, pages 310–15. Centro Di, Firenze, 2002.
  • Jacques Sesiano: see below.

Recommended Reading:

  • Coulon, Jean-Charles. La magie islamique et le « corpus bunianum » au Moyen Âge, (unpublished doctoral dissertation, Université Paris IV – Sorbonne, 2013).
  • Hallum, Bink. “New Light on Early Arabic Awfāq Literature”. In Liana Saif, Francesca Leoni, Matthew Melvin-Koushki, and Farouk Yahya, editors, Islamicate Occult Sciences in Theory and Practice, number 140 in Handbuch der Orientalistik, pages 57–161. Brill, Leiden/Boston, MA, 2020.
  • Hummel, Siegbert. “The sMe-ba-dgu, the Magic Square of the Tibetans.” East and West 19, no. 1/2 (1969): 139–46.
  • Martí-Aguilar, Manuel Á. “Talismans against Tsunamis: Apollonius of Tyana and the Stelai of the Herakleion in Gades (VA 5.5).” Greek, Roman, and Byzantine Studies 57 (2017): 968–93.
  • Nomanul Haq, Syed. Names, Natures and Things: The Alchemist Jābir bin Ḥayyān and his Kitāb al-Aḥjār (Book of Stones), Boston Studies in the Philosophy of Science 158 (Dordrecht/Boston, MA/London: Kluwer Academic Publishers, 1994).
  • Nowotny, Karl A., ‘Zur Geschichte der astrologischen Medaillen’, Numismatische Zeitschrift, 74 (1951), 100–104 and pl. III.
  • Rashed, Roshdi and Christian Houzel, ‘Théorie des nombres amiables’, in Thābit ibn Qurra. Science and Philosophy in Ninth-Century Baghdad, ed. by Roshdi Rashed (Berlin: De Gruyter, 2009), pp. 77–151
  • Roberts, Alexandre M. “Being a Sabian at Court in Tenth-Century Baghdad.” Journal of the American Oriental Society 137, no. 2 (2017): 253–77.
  • Sesiano, Jacques, “Les Carrés magiques de Manuel Moschopoulos.” Archive for History of Exact Sciences 53, no. 5 (1998): 377–97.
  • Idem, “Magic Squares for Daily Life.” In Studies in the History of Exact Sciences in Honour of David Pingree, edited by Charles Burnett et al., 715–34. Leiden/Boston, MA: Brill, 2004.
  • Tannery, Paul. “Le Traité de Manuel Moschopoulos sur les carrés magiques. Texte grec et traduction.” Annuaire de l’Association pour l’encouragement des études grecques en France 20 (1886): 88–118; reprinted in Tannery, Paul. Mémoires scientifiques, vol. 4, 27–60. Toulouse–Paris: Edouard Privat, Gauthier-Villars, 1920.