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The Significance of Geometry (Al-Handasah) in the Treatises of the Brethren of Purity (Rasāʾil Ikhwān Al-Ṣafāʾ Wa Khullān Al-Wafāʾ)

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The Significance of Geometry (Al-Handasah) in the Treatises of the Brethren of Purity (Rasāʾil Ikhwān Al-Ṣafāʾ Wa Khullān Al-Wafāʾ) The Philosophy of Art of Geometry: The Significance of Geometry (al-handasah) in The Treatises of the Brethren of Purity (Rasāʾil Ikhwān al-Ṣafāʾ wa Khullān al-Wafāʾ) by Halim Miftahul Khoiri B.A. in Islamic Philosophy and Religion, August 2014, Paramadina University A Thesis Submitted to The Faculty of The Columbian College of Arts and Sciences of The George Washington University in partial fulfillment of the requirements for the degree of Master of Arts May 20, 2018 Thesis directed by Mohammad Faghfoory Professorial Lecturer and Director of Graduate Program in Islamic Studies © Copyright 2018 by Halim Miftahul Khoiri All rights reserved. ii Table of Contents Chapter 1: Introduction ................................................................................. 1 1.1 Introduction ............................................................................................................ 1 1.2 Primary Questions .................................................................................................. 2 1.3 Subsidiary Issues ..................................................................................................... 2 1.4 1.4 Methodologies ................................................................................................... 3 Chapter 2: The Origin of Form and Matter and Spiritual Realization through Forms of Art in Islam ................................................................................... 4 2.1 Matter in Hylomorphism; the Beginning Philosophical Discussion of Matter and Form ................................................................................................................................. 4 2.2 The Discourse Form (ṣūrah) in Islamic Philosophy and Sufism .............................. 8 2.3 Symbolism in Islamic Forms of Art ......................................................................... 13 2.4 Forms of Islamic Arts and Spiritual Realization; Returning to The Origin (ta’wil) 17 Chapter 3: The Historical and Essential Origin of Geometry and Its Relation with The Science of Numbers and Letters ................................................... 21 3.1 Geometry in the Traditional Curriculum ................................................................. 21 3.2 Geometry and The Correspondence between The Science of Numbers and Letters 22 Chapter 4: Geometry and Its Relation with the Divinity, Cosmos and Soul within The Epistles of the Brethren of Purity ............................................. 28 4.1 The Source of Geometry in The Epistle of the Brethren .......................................... 28 4.2 Geometry, Number and Music ................................................................................. 29 4.3 Geometry in the Epistles of Brethren of Purity ....................................................... 34 4.4 Geometry and The Perfected Wisdom (itqān al-ḥikmah) in Animal ..................... 36 4.5 Divine Wisdom in Human Collaboration (al-ḥikmah al-ilāhiyya fī al-taʿāwun) . 37 4.6 Proportion and Its Effect upon the Soul and Body .................................................. 39 iii 4.7 Proportion and Harmony of the Cosmos ................................................................. 43 4.8 Geometry and Moral Refinement ............................................................................ 44 Chapter 5: Conclusion ................................................................................ 46 Bibliography .............................................................................................. 50 iv Chapter 1: Introduction 1.1 Introduction The Latin proverb “art without science is nothing” (ars sine scientia nihil est) precisely describes the art within Islamic tradition. Whether sonoral or plastic, Islamic art carries within it a scientific aspect drawn from the understanding of the universe. At once, Islamic art also carries mystical dimension that through its appearances, one is led to remembrance of the Divine. Geometry is the most apparent pattern in Islamic plastic art. It replaces the position of the Icon in Christianity and Idols in Hinduism. Beginning with its setting as one of seven liberal arts (Artes Liberales) Muslims inherited from the ancient sciences (al-ʿulūm al-awāʾil), geometry is apparent as basis for understanding the nature of form and shapes. Through understanding geometry, one is able to build or form an edifice. It is then also developed as a form of Islamic arts as can be seen in various mosques in many parts of the Islamic world. Ikhwān al-Safāʾ wa Khullān al-Wafāʾ or The Brethren of Purity are known to be one of the first expositors of the science of geometry within Islamic tradition deriving it from Euclid’s Elements (Stoekheia; kitāb uqlīdis fi al-uṣūl). It is elaborated in two parts within their Epistles (Rasāʾil Ikhwān al-Ṣafāʾ wa Khullān al-Wafāʾ). The first is the second epistle on geometry and its essence “The Second Epistle on The Branch of Mathematics Named as Geometry: In the Science of Measurement and the Exposition of Its Essence” (al-risālah al-thāniyah min al-qism al-riyāḍī al-mausūmah bijūmaṭriyā; fi al-handasah wa bayāni māhiyatihā) and the second is their elaboration that geometry along with arithmetic can function as the tool to discipline the soul and 1 beautify human’s behavior (al-risālah al-sādisah min al-qism al-riyāḍī; fi al-nisbah al- ʿadadiyyah wa al-handasiyyah fī tahdhībi al-nafs wa iṣlāḥ al-akhlāq). The Ikhwān relate geometry with other sciences such as music and number. This relationship is the basis of the creation of the universe. In addition to that, they also relate geometry with human soul and theology. This thesis will focus more into esoteric philosophical values of geometry as exposed by the Ikhwān within their Epistles. 1.2 Primary Questions What is the origin of form? What is its significance, especially that of geometry, within Islamic tradition? What is the relation between geometry as a branch of mathematics with other sciences such as science of numbers, that of letters and music? What is the relation between geometry and human soul within the scope of Rasāʾil? 1.3 Subsidiary Issues This work discusses the philosophy of Islamic art. It will allow us to understand the importance of visual form, especially geometry, within Islamic tradition. This discussion will prove that Islamic art is not just an art but it is based on science and at the same time carries mystical symbolism in its very meaning, that is to unite (Lat. symballein). The explanation of geometry in the Epistles comprises of its quantitative and qualitative nature. The quantitative nature of geometry discusses the regulation of order and construction of forms. The qualitative aspect of it talks about the proportion of forms in relation with visual representation of the truth. This thesis will focus on the latter.1 1. Loai M. Dabbour, Geometric Proportions: The Underlying Structure of Design Process for Islamic Geometric Patterns, Frontiers of Architectural Research (2012) 1, 380-391, 381. 2 1.4 1.4 Methodologies This thesis in an analytical study on the philosophy of art. Firstly, the explanation of the importance of visual form within Islam will be given to give the sense of the need to discuss form (ṣūrah or morphe) and its relation with spiritual realization. The analysis is then turned to the discussion of geometry both from its historical and essential origin. Lastly, the focus will be oriented to exposition of geometry within the Epistles. All of these discourses will be drawn from primary sources by the Ikhwān. In explaining the nature of forms and the relation between geometry and the science of letters, we will also cite some explanation from Sufi sources such as Ibn ʿArabī and Abd al-Karīm al-Jīlī. Lastly, we will use the help from Ibn Miskawayh through his book in understanding Ikhwān’s exposition that geometry can be used in disciplining the soul and beautifying moral. 3 Chapter 2: The Origin of Form and Matter and Spiritual Realization through Forms of Art in Islam 2.1 Matter in Hylomorphism; the Beginning Philosophical Discussion of Matter and Form Before delving into the discussion of form in general and form of art in particular within Islam, it is best to open the discourse of form that can be found within Aristotle’s theory of hylomorphism. This theory is contained within his physics concerning things (or substances) that change accidentally or substantially. This change occurs in physical objects composed of matter (Gr. hulê, Ar. hayūlā) and form (Gr. eidos or morphê, Ar. ṣūrah). Hylomorphism is an intellectual attempt to trace the origin of matter in the physical reality. That is to say, it is a way to understand how substance turns to existence while everything must come from something and that there is nothing comes from nothing.2 All sensible things comprise of matter and form. A matter itself can be divided into matter and form. For example, a ball has the form of being round and the matter foundation of rubber. The rubber itself has its own matter and form and if this analysis is continued, one will arrive at the four elements; earth, air, fire and water. Aristotle agrees with Empedocles that all sensible things are made of different ratios of these elements. However, ancient thinkers differ in pinpointing the prime matter between the these elements.3 The discussion of traditional physics, according to Ikhwān al-Ṣafāʾ, is begun with understanding five things; matter, form, movement, time and space. Matter (hayūlā) is all substance that accepts form (ṣūrah).
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