Hostname: page-component-74656f9884-j7cmm Total loading time: 0 Render date: 2026-11-08T07:22:33.885Z Has data issue: false hasContentIssue false
  • English
  • Français

Art and Mithāl: Reading Geometry as Visual Commentary

Published online by Cambridge University Press:  01 January 2022

Carol Bier
Carol Bier*
Affiliation:
The Textile Museum, Washington, DC, USA
*
cbier@ textilemuseum.org
Get access Rights & Permissions [Opens in a new window]

Abstract

This article seeks to develop an interpretation of ornament as geometric pattern that embodies metaphysical intent in Iranian monuments of the fifth/eleventh century. The proposed argument elucidates cultural meaning relevant to a particular time and specific place, with implications for broader application.1 Reading geometric patterns as visual commentary, this approach relates the presence of patterns in art accompanied by a Qur'anic inscription to both the practice of pattern-making and the contemporary discourse concerning mathematics, philosophy, and the Islamic sciences in Iran. Particular emphasis is placed on the use of a passage from the Qur'an (59:21–24) inscribed on the tomb towers at Kharraqān, in which the Qur'anic term, amthāl, is taken literally to refer to the patterns executed on the monuments.

Information

Type
Articles
Information
Iranian Studies , Volume 41 , Issue 4: Sciences, Crafts, and the Production of Knowledge: Iran and Eastern Islamic Lands (ca. 184–1153 AH/800–1740 CE) , September 2008 , pp. 491 - 509
Copyright
Copyright © Association For Iranian Studies, Inc 2008

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

1 An initial attempt to present these ideas appears in Bier, Carol, “Geometric Patterns and the Interpretation of Meaning: Two Monuments in Iran,” in Bridges: Mathematical Connections in Art, Music, and Science (conference proceedings), ed. by Sarhangi, Reza (Towon, MD, 2002), 67–78Google Scholar, with further development of a new paradigm presented at the College Art Association Annual Meetings in New York in February 2007 in a paper, “From Textiles to Algorithms: Revising an Islamic Aesthetic Paradigm.” The proposed paradigm is elaborated by Carol Bier, “Number, Shape, and the Nature of Space: Thinking through Islamic Art,” in Oxford Handbook for the History of Mathematics, ed. by Eleanor Robson and Jacqueline Stedall (Oxford, in press).

2 Jones, Owen, Grammar of Ornament (London, 1868 [1856])Google Scholar.

3 Trilling, James, Ornament: A Modern Perspective (Seattle and London, 2003)Google Scholar.

4 Washburn, Dorothy K. and Crowe, Donald W., Symmetries of Culture: Theory and Practice of Plane Pattern Analysis (Seattle, 1988)Google Scholar relates patterns to mathematics, and Washburn, Dorothy K. and Crowe, Donald W., eds., Symmetry Comes of Age: The Role of Pattern in Culture (Seattle and London, 2004)Google Scholar explore ways that cultural information is embedded in symmetrical patterns.

5 Bier, Carol, “Choices and Constraints: Pattern Formation in Oriental Carpets,” Forma (Journal of the Society for the Science of Form, Japan), 15/2 (2000): 127–132Google Scholar [Proceedings of the 2nd International Katachi U Symmetry Symposium (Tsukuba, 1999), Part 3].

6 Stevens, Peter S., Handbook of Regular Patterns: An Introduction to Symmetry in Two Dimensions (Cambridge, MA and London, 1981)Google Scholar.

7 Ettinghausen, Richard, “The Taming of the Horror Vacui in Islamic Art,” Proceedings of the American Philosophical Society, 123/1 (1979): 15–28Google Scholar.

8 Ettinghausen, “The Taming of the Horror Vacui in Islamic Art,” 15.

9 Golombek, Lisa, “The Draped Universe of Islam,” in Content and Context of Visual Arts in the Islamic World, ed. by Soucek, Priscilla P. (University Park, PA and London, 1988), 25–49Google Scholar.

10 Grabar, Oleg, The Mediation of Ornament, Bollingen Series XXXV, 38 (Princeton, 1992)Google Scholar.

11 Simpson, Marianna Shreve has assessed the impact of Grabar's provocative body of work in “Oleg Grabar, Intermediary Demons: Toward a Theory of Ornament,” in The A.W. Mellon Lectures in the Fine Arts: Fifty Years (Washington, DC, 2002)Google Scholar.

12 Özdural, Alpay, “Mathematics and Arts: Connections between Theory and Practice in the Medieval Islamic World,” Historia Mathematica, 27 (2000): 171–201CrossRefGoogle Scholar; see also Reza Sarhangi's article in this issue of Iranian Studies. For a contrarian view, see Saliba's, George review of Necipoglu 1995, “Artisans and Mathematicians in Medieval Islam,” Journal of the American Oriental Society, 119/4 (1999): 637–645CrossRefGoogle Scholar, in which he proposes criticism of artists' methods by mathematicians.

13 Lu, Peter J. and Steinhardt, Paul J., “Decagonal and Quasi-Crystalline Tilings in Medieval Islamic Architecture,” Science, 315 (February 22, 2007): 1106–10CrossRefGoogle ScholarPubMed; for earlier studies treating this topic, see Bonner, Jay, “Three Traditions of Self-Similarity in Fourteenth and Fifteenth Century Islamic Geometric Ornament,” in Meeting Alhambra: ISAMA-Bridges Conference Proceedings, ed. by Barrallo, Javier et al. (Granada, 2003), 1–12Google Scholar, and Makovicky, Emil, “800-Year Old Pentagonal Tiling from Marāgha, Iran, and the New Varieties of Aperiodic Tiling It Inspired,” in Fivefold Symmetry, ed. by Hargittai, I. (Singapore, 1992), 67–86CrossRefGoogle Scholar.

14 See for example the work of artists and students at the Maryland Institute College of Art, http://mathforum.org/geometry/rugs/resources/practicums.

15 Rogers, J. M., “The 11th Century—A Turning point in the Architecture of the Mashriq?” in Islamic Civilization, 950–1150, ed. by Richards, D. S. (London, 1973), 211–249Google Scholar.

16 Ettinghausen, Elizabeth S., “Woven in Stone and Brick: Decorative Programs in Seljuk and Post-Seljuk Architecture and their Symbolic Value,” in Art Turc/Turkish Art. 10e Congres international d'art turc (Geneva, 2001)Google Scholar.

17 Baer, Eva, Islamic Ornament (New York, 1998)Google Scholar; Daneshvari, Abbas, Medieval Tomb Towers of Iran: An Iconographical Study (Lexington, KY, 1986)Google Scholar.

18 Blair, Sheila S. and Bloom, Jonathan M., Cosmophilia: Islamic Art from the David Collection, Copenhagen (Boston, 2006)Google Scholar.

19 Necipoğlu, Gulru, The Topkapi Scroll: Geometry and Ornament in Islamic Architecture (Santa Monica CA, 1995)Google Scholar; Tabbaa, Yasser, The Transformation of Islamic Art during the Sunni Revival (Seattle, 2001)Google Scholar.

20 Gombrich, E. H., The Sense of Order: A Study in the Psychology of Decorative Art (Ithaca, NY, 1984)Google Scholar.

21 Critchlow, Keith, Islamic Patterns (London, 1976)Google Scholar.

22 El-Said, Issam, Islamic Art and Architecture: The System of Geometric Design, ed. by El-Bouri, Tarek (London, 1993)Google Scholar. This work was published posthumously; El-Said's studies of the root five system still need to be brought to fruition.

23 Tabbaa, Transformation, 5, 75; see also n.24 below.

24 Akkach, Samer, Cosmology and Architecture in Premodern Islam: An Architectural Reading of Mystical Ideas (Albany, NY, 2005)Google Scholar.

25 Harris, R. Baine, ed., Neoplatonism and Indian Thought (Albany, NY, 1982)Google Scholar; see also Morewedge, Parviz, ed., Neoplatonism and Islamic Thought (Albany, NY, 1992)Google Scholar.

26 Gutas, Dimitri, Greek Thought, Arabic Culture: The Graeco-Arabic Translation Movement in Baghdad and Early ‘Abbasid Society (2nd–4th/8th–10th Centuries) (New York, 1998)CrossRefGoogle Scholar.

27 For overviews of mathematics at this time, see Joseph, George Gheverghese, The Crest of the Peacock: Non-European Roots of Mathematics (London, 1991)Google Scholar; Berggren, J. L., Episodes in the Mathematics of Medieval Islam (New York, 1986)Google Scholar, and Kennedy, E. S., “The Exact Sciences in Iran under the Saljuqs and Mongols,” in The Cambridge History of Iran, v. 5, The Saljuq and Mongol Periods, ed. by Boyle, J. A. (Cambridge, 1968)Google Scholar.

28 Sigler, L. E., trans., Fibonacci's Liber Abaci: A Translation into Modern English of Leonardo Pisano's Book of Calculation (New York, 2002)CrossRefGoogle Scholar.

29 See, for example, Fakhry, Majid, A Short Introduction to Islamic Philosophy, Theology and Mysticism (Oxford, 1997)Google Scholar; Leaman, Oliver, A Brief Introduction to Islamic Philosophy (Malden, MA and Cambridge, 1999)Google Scholar; Nasr, S. H., An Introduction to Islamic Cosmological Doctrines (Boulder, 1978)Google Scholar.

30 See Özdural, “Mathematics and Arts”; and Reza Sarhangi in this issue of Iranian Studies.

31 Bier, Carol, “Ornament and Islamic Art,” review of The Mediation of Ornament, by Grabar, Oleg (Princeton, 1992)Google Scholar, and Problems of Style: Foundations for a History of Ornament, by Riegl, Alois (Princeton, 1992)Google Scholar, Middle East Studies Association Bulletin, 28 (1994): 28–30.

32 Martin Davis, personal communication; see also Stillwell, John, Mathematics and Its History, 2nd ed. (New York, 2002), 82CrossRefGoogle Scholar.

33 Fārābī, quoted by Martin Levey and Marvin Petruck in Kushyar ibn Labban, Principles of Hindu Reckoning, Kitāb fī uūl isāb al-Hind (Madison, WI and Milwaukee, 1965), x.

34 Tabbaa, Transformation.

35 Dodd, Erica Cruikshank and Khairallah, Shereen, The Image of the Word (Beirut, 1981)Google Scholar.

36 Begley, Wayne, “The Myth of the Taj Mahal and a New Theory of Its Symbolic Meaning,” The Art Bulletin, lxi/1 (1979): 7–37CrossRefGoogle Scholar. More recently, Maria E. Subtelny contributes an interpretation of the polyvalence of symbolism in the Taj Mahal, based as she argues on Persian garden design, situated within the pragmatic needs of agriculture and the imaginal realm: Le monde est un jardin: aspects de l'histoire culturelle de l'Iran médiéval (Paris, 2002).

37 Most recently, Oleg Grabar, The Dome of the Rock (Cambridge, 2006); see also Dodd and Khairallah, The Image of the Word, 19–26.

38 Shani, Raya, A Monumental Manifestation of the Shi'ite Faith in Late Twelfth-Century Iran: The Case of the Gunbad-i ‘Alawiyan, Hamadan, Oxford Studies in Islamic Art, XI (Oxford, 1996)Google Scholar.

39 Khwārizmī, , The Algebra of Mohammed ben Musa, trans. by Rosen, Frederic (London, 1831)Google Scholar. The following discussion appears in Bier, Carol, “Pattern Power: Textiles and the Transmission of Mathematical Knowledge,” Appropriation, Acculturation, Transformation: Proceedings of the 9th Biennial Symposium of the Textile Society of America (Madison, WI, 2004)Google Scholar.

40 See Bier, “Pattern Power.”

41 Bier, “Pattern Power”; see Bier, Carol, “Patterns in Time and Space: Technologies of Transfer and the Cultural Transmission of Mathematical Knowledge across the Indian Ocean,” Ars Orientalis, 34 (2007): 174–196Google Scholar.

42 Mahdi, Muhsin, trans., “Alfarabi: The Attainment of Happiness,” in Medieval Political Philosophy: A Sourcebook, ed. by Lerner, Ralph and Mahdi, Muhsin (Ithaca, NY, 1993), 59–82Google Scholar.

43 Mahdi, “Alfarabi,” 62.

44 Al-Fārābī, , Al-Farabi on The Perfect State: Abu Nasr al-Farabi's Mabādī Ārā' Ahl al-Madīna al-Fāila, trans. by Walzer, Richard (Oxford, 1985), 109Google Scholar. I am indebted to Najm al-Din Yousefi for drawing my attention to this reference.

45 Netton, Ian Richard, Muslim Neoplatonists: An Introduction to the Thought of the Brethren of Purity (Ikhwān al-afā) (London, 1982), 34Google Scholar (emphasis added).

46 For the earliest recording of these monuments, see Stronach, David and Jr.Young, T. C., “Three Seljuk Tomb Towers,” Iran, 4 (1966): 1–20CrossRefGoogle Scholar. A selection of color photographs from a collection held in its entirety in the archives of the Freer Gallery of Art is published in Seherr-Thoss, S. P. and Seherr-Thoss, H. C., Design and Color in Islamic Architecture (Washington, DC, 1968)Google Scholar, pls. 17–26.

47 For discussion relating Avicenna's commentary on the Light Verse and the play of light at Kharraqān, see Bier, “Geometric Patterns and the Interpretation of Meaning,” 9.

48 Corbin, Henri, Mundus Imaginalis or the Imaginary and the Imaginal (London, 1976)Google Scholar; see also Rahman, Fazlur, “Dream, Imagination, and ‘Alam al-Mithal,” Islamic Studies: Journal of the Central Institute of Islamic Research, Karachi, 3/2 (1964): 167–180Google Scholar.

49 Corbin, Mundus Imaginalis, 8.

50 Corbin, Mundus Imaginalis, 10.

51 Corbin, Mundus Imaginalis, 9.

52 Fakhry, Majid, Islamic Occasionalism and its Critique by Averroes and Aquinas (London, 1958), 9Google Scholar.

53 Roshdi Rashed situates these mathematical developments between algebra and arithmetic, and between algebra and geometry; see Rashed, Roshdi, The Development of Arabic Mathematics: Between Arithmetic and Algebra, trans. by Armstrong, A. F. W. (Dordrecht and Boston, c.1994), 3CrossRefGoogle Scholar.

54 See Corbin, Mundus Imaginalis.