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.
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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
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4.7 Proportion and Harmony of the Cosmos ...... 43
4.8 Geometry and Moral Refinement ...... 44
Chapter 5: Conclusion ...... 46
Bibliography ...... 50
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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
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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.
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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). Form is every shape (shakl) and image (naqsh)
2. https://plato.stanford.edu/entries/form-matter/, accessed in February 12th 2018.
3. Ibid. 4
received by the substance.4 In another word, form is what unifies the substances of
matter into one single object. And it is form that makes the existing things differ from
each other. For example, both knife and sword are made of the same substance that is
metal. What makes them different from each other is their form, not their substance.
From Sufism’s point of view, the diversity of forms both temporally and spatially stem from multiplicity that is the nature of Divine creation. In another word, the state of perpetual flux is innate within this creation. Ibn ʿArabī states that the creation is Divine-
Self disclosure that undergoes fluctuation, transformation and transmutation.5 Not only in physical forms, these three natures of creation also occur in matter.
According to the Ikhwān, there are four categories of matter: matter of practical arts (hayūlā al-ṣināʿah), natural matter (hayūlā al-ṭabīʿah), universal matter (hayūlā al- kull) and original matter (hayūlā al-ūlā). The example of the first category of matter is wood for carpenters, iron for smiths, soil and water for building constructors.6 They are matter belonging to the first category with which an artist uses for his work by shaping and molding them into certain form and shape. Natural matter (hayūlā al-ṭabīʿah) is the four elements of air, water, earth and fire as mentioned before. This pertains to the world under the celestial realm (taḥta falak al-qamar) such as the plants, animals and minerals that are all made from the four principles and transmute into each other in their process of generation and corruption. The third matter, that is universal matter
(hayūlā al-kull), is the absolute body (al-jism al-muṭlaq) from which all existent things within the universe such as the orbits, the stars, the four principles of nature are composed. All of them are entities that differ from each other based on their differing
4. Ikhwān al-Ṣafāʾ wa Khullān al-Wafāʾ, Rasāʾil Ikhwān al-Ṣafāʾ wa Khullān al-Wafāʾ, Vol II, (Beirut: Dār Ṣādir,1957), 6.
5. William Chittick, The Sufi Path of Knowledge. Ibid., 96.
6. Ikhwān al-Ṣafāʾ wa Khullān al-Wafāʾ, Ibid. 5
forms. Lastly, original matter (hayūlā al-ūlā) is simple substance unperceivable by senses and can only be perceived intellectually (jawhar basīṭ maʿqūl lā yudrikuhu al-
ḥiss). It is the form of existence itself and it is no other than quiddity (huwiyyah).7 When receiving quantity, this quiddity becomes the absolute body that is associated with having three dimensions of length, breadth and depth. This absolute body then becomes more specified when it receives quality or shape such as circle, triangle and rectangle. As quality is equal to three, quantity is equal to two and quiddity is equal to one, each of them come after the other according to the sequence; quiddity comes first, quantity comes after that and quality imposed at the end.
Now it has to be mentioned that these three concepts of quality, quantity and quiddity are images perceived intellectually and that they are not sensible. If a part is left from another within this unity, one part becomes the matter and the other part the form; quality is the form for quantity and quantity is the matter for it; quantity is the form in quiddity and and quiddity is the matter for it. In the Rasāʾil, the Ikhwān give an example by tracing the origin of a shirt. A shirt is the form for yarn and yarn itself is the matter for the shirt; yarn is the form for cotton and cotton itself is the matter for the yarn; cotton is the form for plant and plant itself is the matter for cotton; plant is the form for the four elements (al-arkān al-arbaʿah) and these elements are the matter for it; these elements are forms of the corporeal body (al-jism) and this body is their matter; this corporeal body is the image for the substance (jawhar) and the substance is its matter.8 To trace other existent things works the same way and the end is the original matter (al-hayūlā
7. In his Introduction to Islamic Cosmological Doctrines, Nasr renders the word al-huwiyyah within the Epistles of the Ikhwān as foundation. Seyyed Hossein Nasr, Introduction to Islamic Cosmological Doctrines (New York: SUNY Press, 1993), 59. In some works, al-huwiyyah is translated to ‘aseity’, ‘ipseity’ or ‘it-ness’. This work in particular will use the word quiddity as its translation throughout. See Keith Critchlow, Islamic Patterns: An Analytical and Cosmological Approach (New York: Schocken Book, 1976), 70. 8. Ikhwān al-Ṣafāʾ wa Khullān al-Wafāʾ, Ibid., 7. 6
al-ūlā) that is simply the image of existence (ṣūrah al-wujūd) without quantity or quality.
All corporeal bodies are one genus from single substance and single matter. They are different only because of their forms. Some of them are purer than the other (aṣfā) and some are more noble than the other (ashraf). Celestial world (ʿālam al-aflāk) is purer and more noble than the terrestrial world (ʿālam al-arkān). Also the elements within terrestrial world range in their level; some are more noble, purer and softer than the other. Fire is purer and more noble than the air; air is purer and softer than the water; water is purer and more noble than the earth (or dust Ar. turāb). All of the elements mentioned are corporeal and physical bodies that transmute into each other; fire when shut off it becomes air; air when it is thick it becomes water; water when it is thick and solidified, it becomes earth; the nature of fire is that it cannot be soft and that of earth is that it cannot be solidified. However, when the elements’ parts are mixed (takawwanat), they transmute into born entities (al-muwalladāt). These entities are minerals, plants and animals. The range of level differs among these entities; some compositions are more noble than the other; ruby is purer and more noble than crystal; crystal is purer and more noble than glass; glass is purer and more noble than ceramics; so is gold purer and more noble than silver; silver is purer and more noble than copper; copper is purer and more noble than metal; metal is more noble than black lead (al-usrub or al-raṣāṣ al- aḥmar). All of them are stones made of mercury (ziʾbaq) and sulphur (al-kibrīt) whose origin is the earth, water, air and fire. Their matter is one but their forms are diverse. The degree of their purity and nobility is based on their composition and their various forms.
As minerals have one origin, so are animal and plant, and their differing level of purity and nobility based on differences of their forms.9
9. Ibid., 9.
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The Ikhwān maintain that the particular bodies (al-ajsam al-juzʾiyyah), when receiving universal form, become better and more noble than any other artless particular body. The Ikhwān give the example of copper when formed into the shape of orbit such as astrolabe or anything that has circular and rounded form. When the copper is made that way, it becomes better than when it is just an artless and simple copper.10
2.2 The Discourse Form (ṣūrah) in Islamic Philosophy and Sufism
While matter is composed of four principles of nature whose origin is simple substance (jawhar basīṭ), one shall remember that these elements only occupy the sensible realm. If compared to matter, form has higher reality of existence as it does not only partake the sensible world but also higher levels of existence within the hierarchy of beings as formulated in the concept of five divine presences by the Sufis. These levels of existence are Divine essence (aḥadiyyah/hāhūt)11, Divine nature (wāḥidiyyah/lāhūt), spiritual world (jabarūt/arwāh/ʿuqūl), Imaginal world (mithāl/barzakh/malakūt)12 and physical world (mulk).
In his Muṣannafāt, Afḍal al-Dīn al-Kashāni states:
“Creatures are of two kinds: those who receive action, which are the created, and the original beings [the archetypes], which are eternal. The place of the created beings is called the world of existence, and the place of the archetypes the world of eternity. They also call the world of created beings, the world of Nature, and the world of archetypes, the world of the Intellect; likewise, the created world is
10. Ibid.
11. To differentiate between the word dhāt and māhiyah, this work uses ‘Essence’ for the first and lower case ‘e’ for the latter.
12. This realm is between the spiritual and physical world. In addition to having a name of isthmus, this dimension is also called as ‘alam al-khayyal (mundus imaginalis) that is translated by some as Imaginal World and some as the World of Imagination. Henry Corbin is in favor to the first rendering for the reason of differentiating between unreal imagination by human and the existing level of reality of isthmus. Another scholar, Oliver Leaman, prefers the second translation arguing that the word imagination is enough to allude to this level of reality. Oliver Leaman, Islamic Aesthetics: An Introduction (Indiana: University of Notre Dame Press, 2004) 166. 8
called the particular, and the eternal world the universal. All these expressions have but one meaning, which is that there are two worlds - one, the real; the other, the symbolic. The real is the necessary, and the symbolic the particular. The beings of the world of particulars are symbol of the world of the universals. The creatures of this world subsist through the archetypes of the other; persons of this world have their existence through those of the other. The beings of the world of particulars each possess a measure and quantity, whereas the beings of the world of universals are without quantity or measure. The beings of he world of becoming are dead by themselves and alive by that which is other than themselves, while the beings of the eternal world are alive by themselves. sensible knowledge of this world, that is, the world of becoming, is a symbol of the intelligible knowledge of that world. The physical world is the symbol and image of the spiritual world.”13
The origin of form within this hierarchy of beings descends from Divine Essence
(dhāt/aḥadiyyah/hāhūt) to the level of Divine nature (wāḥidiyyah/lāhūt). These forms are intelligible (ṣuwar maʿqūlah) that are His names and qualities that are known by
God through His own essence. To the verifiers (muḥaqqīqūn), the universal forms (al-
ṣuwar al-kulliyyah) within this domain are called as essences and realities (al-māhiyāt wa al-ḥaqāʾiq). The appearance of these forms in Divine Nature (maqām of al- wāḥīdiyyah) from Divine Essence (maqām of al-aḥadiyyah), according to Ibn Arabi, is caused by the most sanctified emanation (al-fayḍ al-aqdas) through the essential love
(al-ḥubb al-dhātī) that is known only to God.14
13. Seyyed Hossein Nasr, Science and Civilization in Islam (Chicago: ABC International Group, 2001), 296.
14. The essential love is the basis of the creation of the world. This is according to a ḥadith qudsī when God says “I was a hidden treasure. Then I loved (faaḥbabtu) to be known. Therefore I created creation so that through Me they can know Me.”
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There are two types of emanation (al-fayḍ); first is the most sanctified emanation
(al-aqdas) which through the oneness of Divine Essence,15 the immutable entities and their original preparedness (al-istiʿdād al-aṣlī) appears within Divine Knowledge and the second is the sanctified emanation (al-fayḍ al-muqaddas) through which the archetypes within Divine Knowledge manifest in the outer or lower domain within the hierarchy of beings. These two emanations depict how the inner reality becomes externalized. The primary dimension or the unmanifest (al-bāṭin) belongs to the intelligible existence (al- wujūd al-ʿilmī) while the latter or the manifest (al-ẓāhir) belongs to the external existence (al-wujūd al-ʿainī). These two modes of existence are related to each other as cause and effect; things do not exist in entity unless they take existential precedence within the Divine Knowledge.16
These forms within Divine Intellect have their own existence within the unmanifest and independence from the manifest, therefore these forms are intelligible beings (wujūdāt ʿilmiyyah) that cannot be attributed with existence of entity (al-wujūd al-ʿainī). Hence, these forms cannot be felt or comprehended by people of reasoning for there is no door for reason to enter. It is only through the niche of prophecy and sainthood (mishkāt al-nubuwwah wa al-wilāyah) and faith in them that one can access these forms.17
The essences (al-māhiyāt) are all particular beings (wujūdāt khāṣṣah) in reality either in the form of entity or mental form. If they are mental forms (al-māhiyāt al- dhihniyyāt), they are called as the immutable entities (al-aʿyān al-thābitah) that exist thanks to the unity within Divine Essence (maujūdah bi al-waḥdah al-aḥadiyyah), and
15. Dāwud al-Qayṣarī, Sharḥ Fuṣūṣ al-Ḥikam (Qom: Maṭbaʾah Maktab al-Iʾlām al-Islāmī, 1962), 90.
16. Ibid., 81-82.
17. Ibid., 83. 10
within the domain of humanity they are named as intellectual forms (ṣuwar ʿilmiyyah) that are the shadow corresponding those entities.18
In the form of entity (ʿainiyyah), these essences are united within existence as intact particular form (ittiḥad al-amr al-ʿainī). These essences within particular existent things are intellectual forms that can be seen from two viewpoints. Firstly, they are the locus of manifestation of the immutable entities and second, these essences are related to intellectual forms within human being; that is to say the divine knowledge corresponds to the external entity and vice versa. If the Truth is the mirror of humanity, therefore the knowledge of human beings necessarily corresponds to the archetypes without any mediation, or else it corresponds to them through a mediator.19
Essences are intellectual beings for they are not in the external domain. It is obvious that something either exists in the external world or it does not exist. When something exists in the external world, it is then a necessary being (wājib al-wujūd) and that which does not partake existence in the external world is non-existent (al-maʿdūm).
Therefore, the essences are only within the intellect and every form within the intellect emanates from the Truth. The emanation of external things from something else is preceded by knowing it in the first place and this knowing is immutable within Divine knowledge. Divine knowledge is His own Being for it is His essence.20
Being manifests with attributes and It appears particularized in form and distinct from other entity. Therefore, that being becomes a reality from realities of Divine Names.
The form of this reality is the knowledge of God that is named as essence (al-māhiyah)
18. Ibid., 90.
19. Ibid., 90.
20. Ibid., 91. 11
or the immutable entity (al-ʿayn al-thābitah). This reality has external existence21 within the domain of the spiritual or intellectual world (ʿālam al-arwāh; ʿālam al-ʿuqūl; ʿālam al-jabarūt). Then this reality has external existence in the imaginal world (ʿālam al- mithāl; ʿālam al-barzakh) within which this reality appears in the bodily form (ṣūrah jasadiyyah). This reality is called as hurqalya by Ishraqi scholars, a realm that contains the forms of physical bodies without beings in specific place.22 Lastly, this reality partakes in the sensible world which in turn becomes intellectual existence within human’s mind (wujūd ʿilmī fī adhhāninā).23
Based on the appearance of the light of existence with its perfections in its loci of manifestation, the essences and their necessary properties appear in the mind and also in the external world. This appearance becomes intense or weak based on the proximity and distance from the light, the large and few number of the medium, the purity and turbidity of the preparedness. This is why all the necessary perfections of the reality can be seen clearly by some people but not to some others.24 The Images of these essences within our mind are the shadow of those intellectual images within Divine presence that reaches us through the way of reversal from the high principles (al-mabādiʾ al-ʿāliyah).
They become clear within us according to our portion from that presence. This is why
‘knowing things of things as they are’ (al-ʿilm biḥaqāiq al-ashyāʾ ʿalā mā hiya ʿalaihi) is hard to gain except to the man whose heart is enlightened with the divine light.25 One
21. From divine point of view, realities within the spiritual world is external since it is its locus of manifestation.
22. Mian Mohammad Sharif. A History of Muslim Philosophy, Vol II (Kempten: Pakistan Philosophical Congress, 1966) 920.
23. Dāwud al-Qayṣarī, Sharḥ Fuṣūṣ al-Ḥikam. Ibid., 92.
24. Ibid., 91. 25. Ibid., 92-3.
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should note that according to Qayṣarī, this knowing is given and is no other than divine wisdom alluded to in the Quran 2: 269.
2.3 Symbolism in Islamic Forms of Art
The discussion of form encompasses the very basic of epistemological foundation of human understanding. This is expressed in the Rasāʾil in one of its sub-chapters on the fact “That Everything is Forms and Entities” (faṣl fī anna al-ashyāʾ kullahā ṣuwar wa aʿyān). All things in their totality are forms and entities emanated from God to the
Active Intellect that is simple substance (jawhar basīṭ). From this Intellect, the emanation then continues to the universal astral soul (al-nafs al-kulliyyah al- falakiyyah) that is no other than the universe itself (al-ʿālam). This universe encompasses both the small universe (al-ʿālam al-ṣaghīr) that is human being and the great universe (al-ʿālam al-kabīr). From this universe, then the emanation goes to the prime matter (al-hayūlā al-ūlā). From this point, then the emanation goes to particular human soul in his thoughts (al-nafs al-juzʾiyyah al-bashariyyah) through his perception of the sensible matter.26 This is the gate where the sensible art penetrate into the soul of human being.
Since everything is basically form, the definition of knowledge (al-ʿilm) as exposed by the Ikhwān pertains to this. Knowledge is the form (or image) of the known in the soul of the knower (ṣūrah al-maʿlūm fī nafs al-ʿālim). It is the opposite of ignorance (al-jahl) that is the absence of that image from the soul. The souls of intellectuals know in actuality while to the souls of learners know in potentiality.
26. Ikhwān al-Ṣafāʾ wa Khullān al-Wafāʾ, Rasāʾil. Vol I, (Beirut: Dār Ṣādir, 1957), 398. 13
Learning (taʿallum) and teaching (taʿlīm) are but the process of externalizing what is in potentiality or possibility toward actuality or existence.27
The ultimate form, as discussed earlier, lies within the Divine Nature as the locus of manifestation of Divine Essence. The form in the Divine Nature is named as the immutable entities and is manifested into the spiritual world as spiritual forms. These spiritual forms are then manifested into the imaginal world as imaginal forms possessing the bodily form (ṣūrah jasadiyyah) that later manifest in the physical world as physical forms that define the existence of matters (al-hayūlā). The lower level of a reality is the locus of manifestation (maẓhar)28 of its direct higher level reality.
It has to be noted that most of the Sufis say that forms that one perceives in reality can be deceptive to him from knowing the Truth. The reason for this is what appears to humanity is in fact the Divine Reality. Meanwhile the phenomena that one sees, even though one can say that it comes into existence, is just a metaphor. What is apparent to human is but One Being colored by the properties of possible things that are nonexistent. However, the Sufis also say that in some manner these forms can also function as symbolism that reveal the Divine Reality.29
Just as ordinary language conveys partial knowledge attained by reason, the language of symbolism utters the knowledge acquired through gnosis (maʿrifah). That which is the lowest reflects that is the highest. Therefore, the lowest level of reality that is the material world, reflects the spiritual world. Whether one could comprehend this language or not, symbolism is there and it functions to transform the soul.30
27. Ibid., 262.
28. The word maẓhar is first introduced by Ibn ʿArabī for explaining the nature of existence. William Chittick, The Sufi Path of Knowledge, Ibid., 89.
29. Ibid.
30. Nader Ardalan and Laleh Bakhtiar, The Sense of Unity (Chicago: The University of Chicago Press, 1973) 5. 14
The word ‘symbolism’ has its closest meaning to the word āyah in the Islamic tradition, if not equal. It is derived from the word symballein that carries the meaning of
‘to unite’ and is the opposite of the word diabolism that is taken from diaballein which means ‘to divide’.31 In a sense, the symbols are sent down from heaven to the world that is full of multiplicity of form in order to return the consciousness of human being back into the One. The word āyah itself – often taken for granted with the meaning of verse – actually carries the meaning of sign of the Divine. Whatever exists in the world is āyah or the sign of the existence of higher reality.
In Islam, this symbolism that helps humanity to return to its Origin is contained both within the revealed verses (al-quran al-tadwīnī) and the cosmogonic quran (al- quran al-takwīnī). Both of these symbolisms are the means to realize the unity of God.
This realization is made possible through the hand of the Prophet. The Quran conveys the doctrine of unity and the Prophet delivers the manifestation of this unity into the realm of multiplicity. There will be no lā ilāha illā Allah without Muḥammad rasūl
Allah. In other words, it is through Muhammad being sent down to earth that one can confess the unity of God. The latter utterance is the source where the Muhammadan grace flows that is the origin of creative art. It is also the medium that made the sacred art possible to crystallize in the world of form, time and space.32
This realization of unity is also the main purpose of Islamic art, therefore its main sources are the inner reality of Quran (ḥaqāʾiq al-quran), the cosmological principles and the niche of prophecy and sainthood and in this case it is the substance of the soul of the Prophet.
31. Seyyed Hossein Nasr, Religion and the Order of Nature (Oxford: Oxford University Press, 1996) 83.
32. Seyyed Hossein Nasr, Islamic Art and Spirituality (New York: SUNY Press, 1987) 6. 15
There are two fundamental types of symbols; the natural symbol and the revealed symbol.33 The natural symbol is what is shown through the process of nature that is drawn from cosmological principles such as symmetrical and rhythmical order. In
Islam, this is displayed in the pattern of geometry that is symmetrical, carrying the symbolism of “unity within unity” in respect to its center. This pattern is repeated simultaneously and harmoniously in walls of Mosque and Madrasas that as if it is without beginning and end. This repeated pattern symbolizes the Divine Infinity where at once implies that any point can be the beginning and the end. This repetition also symbolizes the emanation of multiplicity from the One or in another word, “multiplicity within unity”.34
Second, revealed symbolism is the symbols sanctified by various traditions. These symbols vary according to the forms and languages where they were revealed. In Islam we see that since the Divine Word is revealed in Arabic, the language becomes sanctified.
Not only in the words that comprise letters and sounds, but also numbers all of which are the language of the intellect. In mathematical symbolism, numbers and geometric patterns are all related to the center. This implies symbolically the reflection of “unity within multiplicity” or “multiplicity as an application of unity”. Either one of these two symbols reflect permanence within this temporary world.35
This symbolism in Islamic art is accessible through the layers within Islamic tradition. The Sharīʿah provides the background of general ritual, and the Way (ṭarīqah) facilitates for more specific rites in order for the artists to draw the forms from the archetypes and for the prepared beholder of the eyes to see through the symbols towards
33. Nader Ardalan and Laleh Bakhtiar, The Sense of Unity, Ibid., 5.
34. Ibid., 6.
35. Ibid. 16
their origin. As the container, the form of art is created through objective laws. As the contained, the symbols are the summary of what exists within the archetypes.36
2.4 Forms of Islamic Arts and Spiritual Realization; Returning to The Origin (ta’wil)
Al-Ghazālī states in his Iḥyāʾ Ulūm al-Dīn, “as an architect draws the details of a house in whiteness and then brings it out into existence according to the drawn exemplar
(nuskhah), so likewise the creator (fāṭir) of heaven and earth wrote the master copy of the world from beginning to end in the Preserved Tablet (al-lawḥ al-maḥfūẓ) and then brought it into existence according to the written exemplar.”37 If the act of creation and revelation is the descending manifestation of God, taʾwīl or spiritual hermeneutics is the reverse direction. The word taʾwīl in Arabic carries the meaning of ‘to return to the
Origin’. One can say that the creative act of traditional artist is participation in the Divine art.38 Once the artwork is produced, it has its own reality and function to connect the beholders of the eye to the inner dimension of reality. All things that one can see in the external reality has outer and inner meaning whether it is a leave, milk, building or tree.
Understanding of an object is considered complete only when someone can comprehend both outer and inner aspect of its meaning. Islamic visual art with its various forms also possesses this inner meaning that is accessible through taʾwīl. Understanding this inner meaning through taʾwīl is possible through the Way (ṭarīqah) that is within the world of
Sufism.39
Sufism or the inner dimension of Islam is the main source for Islamic art. If art is about beauty, the dimension within Islam that directly pertains to beauty is Sufism;
36. Ibid.
37. Samer Akkach, Cosmology and Architecture in Premodern Islam (New York: SUNY Press, 2005), xvii.
38. Nader Ardalan and Laleh Bakhtiar, The Sense of Unity. Ibid., 10.
39. Ibid., 5. 17
beauty that ultimately belongs to God, the Origin. Whether to extract forms of art from the immutable entities for making an artwork or to see through the inner reality lying within the produced artwork, spiritual vision is needed and is only possible through spiritual framework. This is proven by the connection between spiritual chivalry
(futuwwah) -that is one of spiritual realities within Islamic tradition- and craft guilds in history. Futuwwah begins with muruwwah (its closest translation is courtoisie) and its higher stage is sainthood (walāyah). Many guilds in Persia, Anatolia and Persia were guided under the principle of futuwwah that integrates spirituality to traditional activities in arts and crafts as recorded in various treatises such as those in textile making (chītāzān). The sixth Shiʿite Imam, Jaʿfar al-Ṣādiq was of the earlier patrons of the guild of textile makers and Gabriel was the first who taught human to dye cloth.
According to a treatise written in this field, every action in painting the textile has symbolic significance and it is necessary to have a master for the transmission of divine grace (barakah) into the labor of craftsman.40
One of elements brought through this transmission of divine grace is the realization of forms of art. This realization is the descent of forms from the imaginal world (ʿālam al-mithāl) to the temporal world (ʿālam al-mulk). In the process of making an artwork, the artists are mere vehicle of realization and the art they make does not signify the artists but it is made to point the One which the artwork is drawn from.41
The first step for the artist is initiation within esoteric path of Islam.42 Within the tradition of futuwwah, as guided by the Prophet and practiced by ʿAlī and Salmān al-
Farisī, the initiatory process involves drinking water and salt. The water symbolizes
40. Seyyed Hossein Nasr, Islamic Spirituality: Manifestations (New York: The Crossroad Publishing Company, 1991), 311
41. Nader Ardalan and Laleh Bakhtiar, The Sense of Unity. Ibid., 10.
42. Ibid. 18
gnosis and wisdom and the salt symbolizes justice. This initiation also involves wearing a pair of pants (sarāwāl) that symbolize decency and continence. After that, the initiated individuals wear the belt around his waist; the belt symbolizes courage and honor.43
After initiatory process, the artists start to learn the method and spirit of the craft, both possessing alchemical base. Understanding metaphysics is not necessary for the artists in order to practice the art. The artists achieve spiritual perfection by integrating the inner (bāṭin) and outer aspect (ẓāhir) of being through their artworks.
The tradition provides models and working rules for the process of art-making that is made possible through revealed forms, the rituals of esoteric dimension and divine grace.44
The originality of the art is based on the ability of the artist to see through the higher locus of manifestation from the archetype in the imaginal world that displays the bodily forms (ṣuwar jasadiyyah) to the immutable entities within the maqām of Divine
Nature (wāḥidiyyah). The originality of Islamic art forms requires the spiritual vision, the willingness to apply laws from the tradition and avoiding everything superfluous and functional.45
The form of art is essential in creating the sacred ambience on earth. Through its appearance, the divine truth is reflected in all directions and space, the realm where human soul lives and being influenced by outward manifestation. Aside from functioning mentally, religion should also function formally because most human beings find it easier to grasp through material forms than ideas. Also, material forms leave deeper effect than mental ideas.46 The truth within the artwork can be grasped by the sensual
43. Seyyed Hossein Nasr, Islamic Spirituality: Manifestations. Ibid., 308.
44. Nader Ardalan and Laleh Bakhtiar, The Sense of Unity. Ibid., 10.
45. Ibid., 11.
46. Seyyed Hossein Nasr, Knowledge and the Sacred (New York: SUNY Press, 1989), 223. 19
perception which then stimulate the mind of the viewer. He then internalizes the form and complete the circle of communication.47 This internalization is through the ultimate perceiver of form that is the intellect or the heart. This is the meaning behind the most famous poetry of Ibn ‘Arabi in his Tarjumān al-Ashwāq48:
“O Marvel! A garden amidst fires! My heart has become capable of every form: it is a pasture for gazelles and a convent for Christian monks And a temple for idols and the pilgrim’s Kaʿbah and the tables of the Torah and the book of the Quran I follow the religion of Love: whatever way Love’s camels take, that is my religion and my faith.”
One of visual Islamic forms of art is geometry that one can see in various object in
Islamic edifices. This form is based on the science of mathematics and at once Islamic mysticism. It is innately expressed in the art of Islamic calligraphy and outwardly shown in the patterns attached in the wall of mosques and madrasas. Geometry is preferred in
Islamic tradition because it has abstraction and the capacity to reveal the spiritual truth objectively.49 The next sections will discuss the philosophy of Islamic art, especially that of geometry. The following chapter will discuss the origin of geometry from both essential and historical point of view. Then the earlier work on basic geometry according to the Epistles of Brethren of Purity will be presented in the last chapter with focus on its qualitative aspect.
47. Nader Ardalan and Laleh Bakhtiar, The Sense of Unity. Ibid., 10.
48. Ibn ʿArabī, Tarjumān al-Ashwāq, trans. Reynold A. Nicholson (London: Forgotten Books, 2015), 67.
49. Loai M. Dabbour, Geometric Proportions. Ibid., 381. 20
Chapter 3: The Historical and Essential Origin of Geometry and Its Relation
with The Science of Numbers and Letters
3.1 Geometry in the Traditional Curriculum
The science of geometry was initially found in Egypt. It was then Thales of
Miletus (640 B.C.E), one of seven sages of antiquity, who brought this science to
Greece.50 Euclid is known to be the father of this science and he is the main source for explanation of geometry in the Epistles of the Brethren of Purity. He was born in around
300 B.C.E and he is the culmination of Greek mathematics after being initiated by Thales and Pythagoras in around 530 B.C.E.51 He is well known in early Islamic civilization for his Euclid’s Elements (Gr. Stoikheia), translated into Arabic as Kitāb Uqlīdis fī al-Uṣūl.
This book was translated into Arabic for the first time in the period of Harūn al-Rashīd
(786-809) by al-Ḥajjāj Ibn Yūsuf. It was then rendered again in the period of al-Maʾmūn
(786-833) by Ḥunayn Ibn Isḥāq who is known in Latin as Johannitius. The first rendition is known as al-Hārūnī edition and the second as al-Maʾmūnī. The third translation was done by Thābit Ibn Qurrah. The translation of this work into Latin is based on the two latest version by Ḥunayn and Thābit.52
The word geometry carries two Greek words: geo that means ‘the earth’ and metry meaning ‘to measure’. It is the science that discuss earthly measurement or spatial measurement. This science is strongly related to the Pythagorean theory of harmony and according to Plato, this measurement is the basis of creation by the Divine will.
Geometry is a significant propaedeutic science that “only he who is familiar with
50. Mian Mohammad Sharif. A History of Muslim Philosophy. Vol I. Ibid., 76-7.
51. Benno Artmann, Euclid: The Creation of Mathematics (New York: Springer-Verlag, 1999), 2.
52. Nader El-Bizri, The Epistles of The Brethren of Purity. The Ikhwān al-Ṣafāʾ and Their Rasāʾil: An Introduction (Oxford: Oxford University Press, 2008), 199. 21
geometry shall be admitted in Plato’s Academy”.53 Geometry had two expressions within the Epistles of the Ikhwān: jūmaṭriyā and handasah both of which are stated in their 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 bi-jūmaṭriyā fī al-handasah wa bayāni māhiyatihā). As the word jūmaṭriyā is derived from Greek, interestingly its synonym, “handasah” is drawn
Persian word ‘andazāh’ which carries the meaning of ‘to measure’.54
In the quadrivium classification system that is the curriculum used in medieval monasteries, geometry is one of four sciences studied beside arithmetic (arithmāṭīqī), astronomy (asṭrūnūmiyā) and music (mūsīqī). These four sciences are categorized under the classification of science of mathematics (riyāḍiyāt). The term riyāḍiyāt is drawn from the word ‘riyāḍah’ that carries the meaning ‘exercise’; this rendering implies the significance of mathematics in early Islamic civilization as the training for the mind.
Geometry is usually studied after arithmetic and these two sciences have a foundational relationship in understanding the nature of the cosmos. The purpose of studying these mathematical sciences, according to the Ikhwān, is to prepare the strength of the mind in understanding natural philosophy (ṭabīʿiyyāt) and psychology (nafsāniyyāt) which then becomes the preparation to study theology (ilāhiyyāt).55
3.2 Geometry and The Correspondence between The Science of Numbers and Letters
As mathematics and geometry are pattern drawn from the universe, one should learn them before elevating his soul to understand the natural philosophy (ʿulūm al-
53. Loai M. Dabbour, Geometric Proportions. Ibid., 382.
54. Ibrahim Kalin, Ed. The Oxford Encyclopedia of Philosophy, Science and Technology in Islam (Oxford: Oxford University Press, 2014) 528.
55. Nader El-Bizri, The Epistles of The Brethren of Purity. The Ikhwān al-Ṣafāʾ and Their Rasāʾil: An Introduction (Oxford: Oxford University Press, 2008), 180-1. 22
ṭabiʿiyyāt) from which one then ascends vertically his intellectual journey to theology
(al-ʿulūm al-ilāhiyyah) that is the uttermost goal of the sages (aqṣā gharaḍ al-
ḥukamāʾ).56 The structure of the universe is created according to geometric patterns. As the blueprint of the creation and generator of all forms, geometry deals with numbers in four levels. Firstly, it deals with pure numbers that is arithmetic for all measurement and proportion is geometrical measurement. Secondly, it deals with number in space that is proportional geometry reflecting the meanings and ideas. Thirdly, it deals with numbers in time and this is what we can see in music. Lastly, it deals with numbers in space and time that is the highest and largest scale of all; the cosmology of the universe.57
Geometry is the expression of personality of numbers, one cannot close his eye from seeing the significance of the science of numbers in Islam. In Jadhawāt, in line with the stance of the Ikhwān and the other intellectuals in Pythagorean chain, Mīr
Damad says that numbers are the principles of beings and that they are the illumination from the intelligible world. He also says that whoever master this science, he masters the complete knowledge of physical world. However, one should note that by numbers, he does not only allude them as quantity but also quality.58 This qualitative aspect of numbers becomes evident in the science of music as it is wedded to the proportion of geometry that will be discussed in the following chapter.
It is interesting to note that in addition to the relation between geometry and number, the point that is the origin of geometry is also the origin of the science of letters.
That is to say, both of geometry that is derived from the law of nature and letters that are used to convey reality in the spoken words originate from the same source that is the
56. Ikhwān al-Ṣafāʾ wa Khullān al-Wafāʾ, Rasāʾil. Ibid. Vol 1, 76.
57. Loai M. Dabbour, Geometric Proportions. Ibid., 381.
58. Mian Mohammad Sharif. A History of Muslim Philosophy. Vol II. Ibid., 921. 23
point. As numbers are believed also to be the principle of reality, there is also correlation between the science of numbers and letters as stated by Mīr Damad in his Jadhawāt:
“The world of letters corresponds to the world of numbers, and the world of letters to the world of Being, and the proportion of the world of numbers to the world of Being and the proportion of the world of letters to the proportion of the world of numbers and the proportion of the world of numbers to the combination and mixtures of the world of Being”.59
This relationship is what is also unique to the work of the Ikhwān as they do not only inherit the science of arithmetics from the previous sages and philosophers, but also integrate it with Islamic intellectual tradition.60 Furthermore, this relationship was later developed by Mīr Damad by establishing connection between science of letters with the heaven and the universe, or in another word between the revealed Quran and the cosmic
Quran.
In various parts of the Epistles, the Ikhwān repeat the idea that the point is the origin of geometry. Interestingly, through this point, geometry possesses significant mystical meaning that is revealed through the science of letter. Just like every shape of a polygon in geometry symbolizes certain meanings, every letter also alludes symbolically to particular Divine attributes because each letter of sacred language corresponds with divine feature and quality.61 The symbolism of the point from mystical point of view is described by ʿAbd al-Karīm al-Jīlī states in his The Cave and Number in the Explanation of bismillāh al-raḥmān al-raḥīm (al-Kahf wa al-raqīm fī sharḥi bismillāh al-raḥmān al-raḥīm)
59. Ibid.
60. Nader El-Bizri, The Epistles of The Brethren of Purity. The Ikhwān al-Ṣafāʾ and Their Rasāʾil: An Introduction (Oxford: Oxford University Press, 2008), 188.
61. Seyyed Hossein Nasr, Islamic Art and Spirituality. Ibid. 30. 24
While the first .(ب) This mystical point is primarily contained in the letter of bāʾ
symbolizes the active and masculine (paternal) principle, the letter ,(ا) Arabic letter, alif bāʾ with is horizontal shape alludes symbolically to receptivity, passive and feminine
(maternal) principle complimenting the quality of Divine Majesty that is contained within the letter alif. In regards to the point written in the letter of bāʾ, ʿAbd al-Karīm al-
Jīlī states that unlike the Arabic alphabets that are compound body (al-jism al- murakkab), the point is indivisible substance (al-jawhar al-basīṭ).62 This indivisible point is equivalent to the point contained within the intellective geometry (al-handasah al-aqliyyah) that also cannot be partitioned as discussed in more detail in the following chapter.
The point is the beginning of every chapter of the Quran. This can be seen in two ways. Firstly, every letter is compound of points (al-ḥarf murakkab min al-nuqṭah) just like a line (al-khaṭṭ) in geometry is made of points adjacent to each other. Therefore, since every chapter is begun with letter, every letter is constituted of points. Second, every chapter is started with basmalah whose beginning is the letter bāʾ with the point below. The connection between this constitutive point and the point of bāʾ as contained within the first letter of basmalah is perfect association since basmalah comes in the beginning of all chapters of the Quran. According to al-Jīlī, this is the meaning behind the ḥadīth “[The content] of al-Quran is [contained] in al-fātiḥah, and al-fātiḥah is
[contained] in basmalah, and basmalah is [contained] in bāʾ and it is [contained] in the point [under the letter bāʾ]”.63
62. Ibid., 31.
63. “Inna kulla al-Qurʾān fī al-fātiḥah wa hiya fi al-basmalah wa hiya fī al-bāʾ wa hiya fī al- nuqṭah”. ʿAbd al-Karīm al-Jīlī, al-Kahf wa al-Raqīm fī Sharḥi bismillāh al-raḥmān al-raḥīm (Hyderabad: Dāʾirah al-Maʿārif al-Nidhāmiyyah, 1336H/1918), 6. 25
This point, according to al-Jīlī, symbolizes the level of Divine Essence (al-dhāt or al-aḥadiyyah) that is hidden behind the marquee of His treasure from His manifestation to His creation. This is appointed through the point in Arabic alphabets that has no sound and that is free from limitation from articulation of letters (tanazzuhihā ʿan al- taqyīd bimakhraj dūna makhraj adhhā nafs al-ḥurūf). The point -for example in the
is what constitutes these three letters and makes -(ث) and thāʾ (ت) tāʾ ,(ب) letter of baʾ them different from each other (wa bi al-nuqṭah tamayyazat). However, this point does not have the sound to itself. Therefore these letters cannot be recognized or read but through the point (mā ʿurifa fī al-aḥrufi illa al-nuqṭah) just like the creation cannot be known but through God (mā ʿurifa fī al-khalq illa Allāh).64
Al-Jīlī further explains the symbolism of the points in Arabic alphabets in relation with the saying of ʿAlī, the prime spiritual patron in Islamic tradition after the
Prophet Muhammad. ʿAlī states that “I do not see anything except that I see God before it, within it and after it.” Arabic alphabets with regard to the point shown in them can be divided into three types each of which correspond to the symbolism of Divine presence that penetrates into the whole being in the universe. The first type is letters with points
These letters symbolize the state of ‘I do .(ت ث خ ذ ز ش ض ظ غ ف ق ن ه ي .above them (i.e not see anything but I see God before it’. The second type is the letters that display point
,These letters symbolize the state of seeing God after it. Lastly .( ب ج ي .below them (i.e
(م و ص ض ظ ط ة .the letters with point in the middle of it whose shape is like an egg (i.e that symbolize the state of ‘I do not see anything but I see God within it’. The rounded shape in the letter of mīm, for example, is the locus of ‘I do not see anything’ and its point inside the sphere is the locus of ‘but I see God within it’.65
64. Ibid.
65. ibid., 7-8. 26
From the point of infinitude, the reality becomes manifest and then it is expressed in the spoken words through letters whose origin is nothing but also the point.
There are many Sufis who explain the doctrine of Islamic mysticism using the symbolism of the point and concentric circle. This symbolism is used for describing God as well as cosmos (al-insān al-kabīr) and human being (al-ʿālam al-ṣaghīr). The following chapter will discuss the relation between geometry and these three levels of reality as described mainly in the Epistles of the Brethren of Purity.
27
Chapter 4: Geometry and Its Relation with the Divinity, Cosmos and Soul
within The Epistles of the Brethren of Purity
4.1 The Source of Geometry in The Epistle of the Brethren
Before discussing the qualitative aspect of geometry in the Rasāʾil, it is best to first discuss the sources used by the Ikhwān in their Epistles. The Ikhwān consider themselves as the followers of Pythagoras and Nicomachus. These two sources are their reference, in addition to Euclid, in understanding nature and interpretation of numbers and geometry. In the Islamic domain, the chain of Pythagorean philosophers, prior to the Ikhwān, is closely related to Jābir Ibn Hayyān who is credited for 3000 intellectual corpus, known as Jābirian corpus, containing various elements from Pythagoras,
Hermes, Persia, India and China.66 As stated by Nasr in his Introduction to Islamic
Cosmological Doctrines, if we look at the intimate relation between the contents of
Jabīrian corpus and the Epistles of the Ikhwān, it is clear that the source of the latter is also the source of the first. The Ikhwān also state a paragraph in their Epistles regarding the four sources they are using: previously written mathematical and natural sciences, the holy scriptures, the Platonic Ideas (in Islamic world it is known as al-aʿyan al- thābitah or the Archetypes) and lastly, the intellectual intuition. They state as follow
“We have drawn our knowledge from four books. The first is composed of the mathematical and natural sciences established by the sages (al-ḥukamaʾ) and philosophers (al-falāsifah). The second consists of the revealed books of the Torah, the Gospels and the Quran and the other Tablets brought by the prophets through angelic Revelation. The third is the books of Nature which are the ideas (ṣuwar) in the Platonic sense of the forms (ashkāl) of creatures actually existing, from composition of the celestial spheres, the division of the Zodiac, the
66. Seyyed Hossein Nasr, Introduction to Islamic Cosmological Doctrines (New York: SUNY Press, 1993), 37-8 28
movement of the stars, and so on …. to the transformation of the elements, the production of the members of the mineral, plant and animal kingdoms and the rich variety of human industries (people look at their appearances but they do not know their inner meaning from the subtlety of Divine attributes)67… The fourth consists of the Divine books which touch only the purified men and which are the angels who are in intimacy with the chosen beings, the noble and the purified souls.”68
The science of mathematics and physics are derived from previous sages and philosophers among which, the main source for them is Pythagoras. In Pythagorean worldview, the science of geometry is closely related to arithmetics, music and astronomy.69 These three sciences are branches of mathematics which according to
Pythagoras is not only quantitative but also qualitative.70
4.2 Geometry, Number and Music
As arithmetics or science of number (ʿilm al-ʿadad) underlies the science of geometry and music, one should note that for Pythagoras, number is not just quantity
67. Ikhwān al-Ṣafāʾ wa Khullān al-Wafāʾ, Rasāʾil Ikhwān al-Ṣafāʾ wa Khullān al-Wafāʾ, Vol I, (Beirut: Dār Ṣādir,1957), 13.
68. From the Rasāʾil, translated by S. H. Nasr, Seyyed Hossein Nasr, Introduction to Islamic Cosmological Doctrines (New York: SUNY Press, 1993), 39.
69. Seyyed Hossein Nasr, The Need for a Sacred Science (Richmond: Curzon Press 1993) 52.
70. Seyyed Hossein Nasr, Religion and the Order of Nature. Ibid., 83. One should note that Pythagoras uses twofold approaches in understanding the harmony of the cosmos. The first is the derivation of quality from quantity as what is used in the current modern world and the second is evaluation of quantities such as numbers and material things through qualities. The second approach is left as early as in the time of Aristotle and only quantitative side is continued. According to Hans Kayser, the reason for this abandonment is that early Greek thinking and perception was overfilled with symbolism and mythology that contain the story of gods and heroes. To these mythologies, a balance was then given with intelligible logical forms which threaten the position of perceiving realities to symbolism and mythology. In addition to that, the transformation of tonal experience within Pythagorean monochord experiment into countable numbers gave support to what was needed at that time. The consequence of this is that the qualitative approach of Pythagoras was abandoned. See Hans Kayser, Akroasis: The Theory of World Harmonics (Boston: Plowshare Press, 1970), 31. 29
but also state of being and intelligible idea. Number is related to Divine act in creating the world. The Ikhwān state:
“The first thing God created from the Light of His Oneness (nūr waḥdāniyyatihi) was simple substance (jawhar basīṭ) which is the Active Intellect (al-ʿaql al-faʿāl) just like He created the number two from number one. Then He created Universal Astral Soul (al-nafs al-kulliyyah al-falakiyyah) from the light of the [Active] Intellect just like He created the number three by adding one to two. Then He created the prime matter (al-hayūlā al-ūlā) from the movement of the soul just like He created the number four by adding one to three. Then He created the rest of creations from the [prime] matter and He put them in order by mediating the intellect and the soul just like He created the rest of numbers from the number four by adding other number(s) before it to it.”71
1 The Light of Divine Oneness (nūr waḥdāniyyatihi)
1+1= 2 simple substance or active intellect (jawhar basīṭ or al-ʿaql al-faʿāl)
2+1= 3 universal astral soul (al-nafs al-kulliyyah al-falakiyyah)
3+1= 4 prime matter (al-hayūlā al-ūlā)
4 onwards the rest of the creations
These numbers, according to Pythagorean tradition is represented by geometrical figure composed of equally spaced points, that is triangle with ten points as also drawn in the chapter on point to the human senses (faṣl min al-nuqṭah liḥāssah al-bashar)72:
.
. .
. . .
71. Ikhwān al-Ṣafāʾ wa Khullān al-Wafāʾ, Rasāʾil. Vol I, Ibid., 54.
72. Ibid., 89. 30
. . . .
This triangular diagram is called as tretaktys that is considered sacred because it represents the onto-theological act of creation that conveys the process of divine emanation. The first dot in the tip symbolizes unity or the One (nūr waḥdāniyyatihi) who is the principle of reality. The two points below allude to the Active Intellect (Nous or al-ʿaql al-faʿāl). The next three points symbolize the universal soul (psuche or al-nafs al-kulliyyah al-falakiyyah). Lastly, the four points symbolize the body and its composition from fourfold elements.73
The qualitative dimension of number is revealed through musical melodies in all beings generated from divine mathematical laws that includes arithmetics and geometry.74 This is elaborated by Hans Kayser in his book, Akroasis:
“We need only to recall the importance of music in early Greek education, and the close relationship of music to Pythagorean mathematics, to understand that the first philosophical theory of the pedagogical effect of music would have to spring from the insight into the law of numbers in the world of music. The connection between music and mathematics which Pythagoras established has since remained a firm possession of the Greek spirit.”75
The science of number is set as the propaedeutic for the Epistles because according to the Ikhwān, number is the origin of beings (al-ʿadad aṣl al-maujūdāt). They give precedence to number over natural and spiritual matters within which fourfold
(murabbaʾ) is upheld. To them, number four can be found in most of the nature of both
73. El-Bizri 41.
74. Seyyed Hossein Nasr, Religion and the Order of Nature. Ibid., 83.
75. Hans Kayser, Akroasis: The Theory of World Harmonics (Boston: Plowshare Press, 1970), 27. 31
natural and spiritual matters. Therefore, to the Ikhwān number four possesses the noble origin (sharf al-ṣidārah) as well as the other numbers in their interrelatedness to each other just as the relation that can be found in natural and spiritual matters.76
As discussed in the first chapter, in hylomorphism form is what makes matters distinct from each other. The theory of hylomorphism was first exposed by Aristotle and preceded by earlier Ionian philosophers such as Thales, Anaximander and Anaximenes. who sought to trace the order in nature in substances (jawāhir). According to them, it is these substances that determine the order of nature. In contrast, Pythagoras states that this order can be understood not through the constitutive substances of the cosmos but through the patterns. It is these patterns that constitute the forms of things or the structural side of cosmic laws.77 These patterns are mathematical which is symbolic and at once closely tied to musical harmony. Hans Kayser states:
“It is specially this latter aspect of Pythagorism that again and again must have inspired and even deeply stirred his followers. Through this experience of sounding numbers, the world began to sound. Matter acquired a structural counterpart anchored in the psyche, and the spiritual, the realm of ideas, became anchored in harmonical shapes and forms. A bridge between being and value (understood as tone in Pythagorean theory of harmonics), world and soul, matter and spirit, was found. Only from this viewpoint can we begin to comprehend the tremendous significance of the idea of harmonics in classical antiquity. This spiritual and intellectual side of Pythagorism was cultivated only as esoteric
76. Ikhwān al-Ṣafāʾ wa Khullān al-Wafāʾ, Rasāʾil. Ibid., 13.
77. Hans Kayser, Akroasis: The Theory of World Harmonics (Boston: Plowshare Press, 1970), 28 It is intellectually unfortunate that this mathematics that is not only quantitative but also qualitative is denied in the 16th and 17th century by many scholars and reduce it to only quantitative mathematics. Seyyed Hossein Nasr. Religion and the Order of Nature. Ibid., 83.
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knowledge; therefore it was soon lost and only the other, material side (the reduction of qualities to quantities) remained and pursued further.”78
This is why the Ikhwān state that for those who want to know how God create things in the intellect and how He manifest them into the soul and form them into matter, they should pay attention to what they explain in the chapter of Arithmetic within their Epistles.79 The Ikhwān’s purpose in exposing arithmetics in the first place is to give ease to the learners in finding wisdom (al-ḥikmah) or philosophy (al-falsafah) whose start is loving knowledge (awwaluhā maḥabbah al-ʿulūm), whose middle is knowing the realities of existents to the extent of human capability and whose end is saying and acting in accordance with the knowledge.80
Arithmetics or the science of number is also higher than other branch of mathematics. Firstly because it is the principle of reality and second it has no material existence in the physical world. In the physical realm, number is mental and it can only be personified through shapes and images that are geometric. We discuss this basic understanding of geometry as exposed in one of earliest text of Islam in mathematics, that is the second epistle of the Brethren “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-marsūm bijumaṭriyā; fi al-handasah wa bayāni māhiyatihā). This epistle covers the discussion of basic and the origin of geometry, the wisdom of animal and the wisdom of human collaboration.
78. Hans Kayser, Akroasis: The Theory of World Harmonics (Boston: Plowshare Press, 1970), 29-30.
79. Ikhwān al-Ṣafāʾ wa Khullān al-Wafāʾ, Rasāʾil. Vol I, Ibid., 54.
80. Ibid., 48. 33
4.3 Geometry in the Epistles of Brethren of Purity
According to the Ikhwān, the science of philosophy has four categories: mathematics, logics, natural philosophy and theology. Geometry is categorized as the second branch of mathematics after arithmetics, before astronomy and music. The
Ikhwān describe geometry as the science of measurement with proofs as stated in the book of Euclid (ʿilm al-handasah bi al-barāhīn allatī dhukirat fī kitāb uqludīs).81
Geometry is a science that inquires about magnitudes (al-maqādīr), dimensions (al- abʿād), and the quantity of their kinds (kimmiyyatu anwāʿihā), along with the properties of their types (khawāṣṣ tilka al-anwāʿ). The principle of this science is the point that is in the extremity of a line (al-nuqṭah allatī hiya ṭarafa al-khaṭṭ).82
Geometry is then divided into two categories by the Ikhwān; the first being the intellective geometry (ʿaqliyyah) and the second the sensible geometry (ḥissiyyah).
Sensible geometry concerns about magnitudes and their properties when a part of them is added to the other. Sensible geometry consists of line (khaṭṭ), surface (saṭḥ) and body
(jism) that possesses dimensions and properties. Magnitudes consist of three categories: lines (khuṭūṭ), surfaces (suṭūḥ) and bodies (ajsām). This geometry is applied within the arts of manufacturing. Unlike sensible geometry that can be seen by eye and sensed by touch, intelligible geometry is conceptual and therefore, understood by reason. This type of geometry is used by an artist when he tries to measure in his creativity of manufacture before laboring on the object. He needs to understand the dimensions along with their properties conceptually that consist of length (ṭūl), breadth (ʿarḍ) and depth (ʿamq).
These three conceptual dimensions are attributes to sensible measurements. Therefore,
81. Ibid., 49.
82. Ibid., 78.
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line only possesses the attribute of length, surface carries the attributes of length and breadth and body has length, breadth and depth.83
khaṭṭ (line) - ṭūl (length)
saṭḥ (surface) - ṭūl wa ʿarḍ (length and breadth)
jism (body) - ṭūl wa ʿarḍ wa ʿamq (length, breadth and depth)
Before developing into a body, the structure of things starts from the point. A point
(nuqṭah) when put adjacent to other points (intaẓamat) constitute a line (khaṭṭ):
…………..
From the line, this structure gradually developed, firstly into a surface and then a body.
However, the Ikhwān underline the difference between the line in the intelligible and sensible geometry. For the first, the point does not have parts like atom as classically understood, while for the second the point can be partitioned.
The discussion of geometry in the second epistle of the Ikhwān continued to the section of shapes (ashkāl). The Ikhwān state that as one is the origin of number and as point is the origin of line, the origin of polygon is triangle (muthallath). Triangle is the shape where the least amount of lines can be connected because two lines cannot be connected to each other to constitute a shape. If one line is added to these three connected line, the shape becomes square (murabbāʾ). If this addition is continued, the
83. Ibid., 80.
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shape becomes pentagon (mukhammas), hexagon (musaddas), heptagon (musabbaʿ), ad infinitum.84
After the discussion of shapes, the Ikhwān turn to the section of surface consisting of that with the shape of egg (al-bayḍī), crescent (al-hilālī), pine nut (al- makhrūṭ al-ṣanawbarī), oval shape (al-ihlīlijī, name of a fruit in Arabic from the word al-lawz al-hindī that means the Indian almond), elliptical shape (nīm khānjī), drum-like shape (al-ṭablī) and lastly olive-like shape (al-zaytūnī).85 This implies that the classical text on geometry extracts their formulation on the foundation of geometry from natural phenomenon.
The Ikhwān then discuss about the bodies (faṣl fī ḍhikr al-ajsām). Geometry can be understood as symbolic configurations of the space that reflect many aspects of theophanies of the One that is symbolized by the point. As all geometric form originates from the point, forms such as triangle, square, polygon, sphere, are seen like traditional numbers, as crystallization of multiplicity that never leave the Unity. This multiplicity is brought back to Unity as Unity is the the reflection of multiplicity.86
4.4 Geometry and The Perfected Wisdom (itqān al-ḥikmah) in Animal
In this chapter, it is interesting to note that the Ikhwān mention the wisdom of the animal, particularly the bees and spiders. In the Quran, it is said that God sends revelation to the bees to take their home in the part of mountain. This is elaborated by the Ikhwān by saying that most of the animals work on their fabrication through the instinct inherent in their nature and without learning. The example of this is the bees when making their homes. They build their houses in compacted (muṭabaqāt), rounded
84. Ibid., 88-9.
85. El-Bizri Trans, 124-6.
86. Seyyed Hossein Nasr, The Need for a Sacred Science. Ibid., 52.
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shapes (mustadīrāt) like piled-up shields (ka al-atrass). This skill is inherent in their nature and according to the Quran it is of one form of divine revelation (wa awḥaynā ilā al-naḥl) which is attributed by the Ikhwān as the perfected wisdom (itqān al-ḥikmah).
One of the specialities of the hexagonal shape of bee nest is that it is larger than a square or pentagon. This shape fits them without looseness and that air is not admissible within to corrupt the quality of the honey or make it mouldy. This perfected wisdom can also be found in the shape of geometric web of the spider. This web is made in such a way that it can shelter itself from piercing of the wind or from being torn apart.87
4.5 Divine Wisdom in Human Collaboration (al-ḥikmah al-ilāhiyya fī al-taʿāwun)
It is worth noting that in the middle of the epistle of geometry, the Ikhwān discuss not only the divine wisdom in animals but also that in social harmony. The
Ikhwān state that the wisdom given to numerous animal is also possessed by some people that they can generate art from their given talent (qarīḥāh) and intelligence
(dhakāʾ) without any precedence of certain learning. However, most of Architect and
Artisan need guidance and learning from master in making and establishing artwork.88This section on social harmony is titled “Chapter on the Need of Human in
Helping Each Other” (faṣl fī ḥājah al-insān ilā al-taʿāwun).
The Ikhwān maintain that one man cannot live by himself but in miserable life because his need to have well-being depends on making various arts. It is impossible for someone to reach all these arts for the life is short and arts are various. Therefore, in every city and village, people gather to help each other. This is necessitated by the divine wisdom (al-ḥikmah al-ilāhiyyah) and grace of lordship (al-ʿināyah al-rabbaniyyah) that a group of people collaborate in making an artwork, another in trade, another in
87. El-Bizri, 130-1.
88. Ikhwān al-Ṣafāʾ wa Khullān al-Wafāʾ, Rasāʾil. Vol I, Ibid., 97. 37
constructing edifices, another in policy making, another in establishing sciences and teaching them, another in service of other people and response to their needs. The analogy of society, according to the Ikhwān, is like brothers from one father in one household who help each other in their living matter with each of them dealing with an aspect of it. What is then determined by convention such as measure, weight, price and payment pertains to wisdom and policy-making to motivate the society to struggle in their works, arts and in helping each other. This goes until everyone has the reward he deserves according to his struggle in working and his virility in arts (nashāṭihi fī al-
ṣanāʾiʿ).89
The fact that the Ikhwān expose this discussion in the middle of the epistle on geometry implies that just like the world as a unified whole within which the parts are related to each other90-as also expressed in numerical symbolism- the society should live together in this way in order to reach felicity. In this chapter, then the Ikhwān turn from discussing human collaboration in worldly realm to the higher realm. They maintain that one cannot be saved by himself from what has befallen from the prophet Adam. To acquire salvation from the sufferings of hell, satan, iblīs, and to ascend to the celestial realm, the vastness of heaven, the abode of the lofty people and neighboring of the angels, one needs the collaboration of brethren who are the counsellors, virtuous ones, knowledgeable with the matters of religion. Hence they can teach someone the path to the hereafter and to be saved from the mess caused by our father Adam.91
From this point, it is clear that geometry pertains to divine wisdom in many ways.
Based on the Ikhwān’s exposition, one can say that the order of harmonic geometry pervades the universe and this order should also be applied in society so that it can reach
89. Ibid., 100.
90. Seyyed Hossein Nasr, Introduction to Islamic Cosmological Doctrines. Ibid., 44.
91. Ikhwān al-Ṣafāʾ wa Khullān al-Wafāʾ, Rasāʾil. Vol I, Ibid., 100. 38
harmony both in this world and the hereafter. Turning to individual scale, the Ikhwān then expose the relation between geometry and the soul in their “Sixth Epistle on the
Branch of Mathematics; In the Proportion of Number and Geometry in Disciplining the
Soul and Moral Refinement” (al-risālah al-sādisah min al-qism al-riyāḍī; fi al-nisbah al-ʿadadiyyah wa al-handasiyyah fī tahdhībi al-nafs wa iṣlāḥ al-akhlāqī).
4.6 Proportion and Its Effect upon the Soul and Body
The medium through which geometry and number is related to the body and soul of individual is the proportion (Sing. nisbah, Pl. nisab). The word proportion is defined as measuring one of two magnitudes in regard to the other (qadar aḥad miqdārayn
ʿinda al-ākhar).92 There are three types of proportion: quantitative proportion that is the proportion of number (nisbah ʿadadiyyah), qualitative proportion that is proportion of geometry (nisbah handasiyyah) and lastly proportion of both quantity and quality that is the proportion of composition and music (nisbah taʾlīfiyyah wa mūsiqiyyah).93
The proportion of number (al-nisbah al-ʿadadiyyah) can be described as the disparity between two different number in equal manner such as:
2 4 6 8 10 12 14 16 18
Within the line of those numbers, the distance from one number to the other is two. The uniqueness belonging to this proportion is that half of the first number when added to the half of the second number result in the quantity that is between the first and the latter number. For instance, 4 and 6, when half of 4 that is 2 is added to the half of 6 that is 3, the result is 5 that is a number between 4 and 6.94
92. Ibid., 242.
93. Ibid., 245.
94. Ibid., 246.
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The proportion of geometry (al-nisbah al-handasiyyah) is measurement of one of two different numbers in face of the other. For instance, the number 4, 6 and 9; the proportion of 4 to 6 is like the proportion of 6 to 9. This equal manner is because 4 is the
⅓ of 6 and that 6 is the ⅓ of 9, and vice versa. This is the first type of the proportion of geometry that is connected type (al-nisbah al-muttaṣilah). The speciality of this proportion is that when the first number (4) is multiplied by the third (9), the result is equal to the second number (6) when being multiplied to itself (that is 36).95 The second type of the proportion of geometry is the separated type (al-nisbah al-munfaṣilah). For instance, 4, 6, 8 and 12. The proportion of 4 to 6 is like the proportion of 8 to 12 because
8 is ⅔ of 12 and 6 is not the ⅔ of 4 but 4 is ⅔ of 6. The speciality of this separated type of proportion is that when the first number (4) is multiplied to the fourth (12), the result is equal to the second number (6) times the third number (8) that is 48.96
The proportion of harmony (al-nisbah al-taʾlīfiyyah)97 is composed of geometric and numeral proportion. For instance, 1 2 3 4 5 6 where number 6 is considered to be the great string (al-ḥadd al-aʿdham), 3 the little string (al-ḥadd al-aṣghar) and 4 the middle string (al-ḥadd al-awsaṭ) while 1 and 2 are the distinction among the strings (al-tafāḍul bayn al-ḥudūd). The remaining amount between 6 and 4 is 2, and that between 4 and 3 is one. Therefore, the proportion of 2 that is distinct between 6, 4 and 3 to 1 that is distinct between 4 and 1 is like the proportion of great string that is 6 to small string that is 3.98
95. Ibid., 246.
96. Ibid., 246-7.
97. The word ‘taʾlīf’ carries the meaning of ‘to compose’ which at the same time implies allusion to ‘composing with harmony’. Therefore, this word can be translated composing with harmony.
98. Ibid., 247.
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Before explaining the relation of understanding this proportion to the soul of the learner, the Ikhwān state that all the prophets and philosophers agree that God is One in reality from all direction and that everything other than Him is dimerous (mathnawī), harmonic (muʾallafah), and compound (murakkabah). When God wanted to create the physical world (al-ʿālam al-jasmānī), He first created two origins (al-aṣlayn) that are matter and form. From these two, the absolute body was made. Then He made some of the bodies or elements according to four nature (al-ṭabāīʿ al-arbaʿ) consisting of heat, cold, dry and wet. The elements themselves are four kind: fire, air, water and earth from wherein animals, plants and minerals are then made.99
These elements have distinctive intensity (mutafāwitat al-quwā), contradictory nature (mutaḍāddāt al-ṭabāīʿ), various forms (mukhtalifāt al-ṣuwar), and unsimilar locus (mutabāyin al-amākin). They cannot gather without being harmonized by the composer. This composition without proportion cannot mix and integrate. This can be elaborated in the example of composition of music. Some sound are gentle and some others are heavy. These two tones cannot unite and meet unless if they are composed in harmony. When this composition is not based on proportion, they cannot mix and unite and therefore, the ears cannot enjoy the composed melody. When they are composed with proportion, they become one song that the ears cannot differentiate between them.
This composed music is then enjoyable to the senses and spark the happiness to the soul.100
As human senses are the bridge to the soul, the Ikhwān implicitly state that it is through harmony of the sound as composed in musical melody that later on the proportioned harmony of this sound can move and influence the psyche (nafs) of the listener. This vocal effect is stated by the Ikhwān in the epistle of music. According to
99. Ibid., 251-252.
100. Ibid., 252. 41
them, the art of music is unlike the visual art. While the latter is made with two hands and it involves the object matter that is the natural bodies (al-ajsām al-ṭabīʿah) with the resulting product of bodily shapes (ashkāl jasmāniyyah), the object matter of the first is spiritual substances (jawāhir rūḥāniyyah) that are the psyche of the listeners (nufūs al- mustamiʿīn). The effects these spiritual substances have in the souls are also entirely spiritual because musical melodies consisting of rhythms and tones, have effects on the souls just like the effects belonging to the arts of artisan upon matters.101
Only when composed in harmony, an artwork will have positive effect on the souls whether through sonoral or visual way. The Ikhwān then go to the proportion that made the harmony over various realities such as poetry or recitals (ʿarūḍ al-ṭawīl) that also affect the souls through the means of ears.102 The Ikhwān also mention the effect of letters in writing (ḥurūf al-kitābah) and paintings (aṣbāgh al-muṣawwirīn) that when composed with harmony will affect the souls through visual means.103 The Ikhwān state that while the form of the letters in the art of calligraphy is various, only when they are composed with certain measurement and put adjacent to each other according to proportion, the writing then becomes beautiful.104 This is why it is stated that traditional calligraphy is based on geometric forms and rhythms and that in Islamic art, understanding the proportion of calligraphy is the key to understand the proportion of
Islamic architecture because the latter is the extension of the first.105 In regard to the art of painting, its proportion deals with the diversity of colors (mukhtalifah al-alwān) and contradictory rays (mutaḍāddah al-shuʿāʾ). When these various colors are painted with
101. Ibid., 183.
102. Ibid., 252.
103. Ibid., 252-3.
104. Ibid., 252.
105. Seyyed Hossein Nasr, Islamic Art and Spirituality. Ibid., 26.
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proportion, the painting appear glamorous (barrāqah), beautiful and glittering
(talmaʿ).106
As proportion displayed in visual and sonoral art sparkles influence upon human psyche, the Ikhwan also mention drugs for medicine and its pharmaceuticals (ʿaqāqīr al-
ṭibb wa adwiyatuhā) and as an example of proportion that affect human body. Medicine and pharmaceuticals consists of counteractive ingredients (mutaḍāddah al-ṭibāʿ) and variety of taste, smell, and color. When they are composed according to proportion, they become medicine that carries many benefits. In contrast, when they are composed without proportion, they can become dangerous poison which can kill (sumūm ḍārrah qātilah).107 The same way goes with the ingredients for a cook (ḥawāʾij al-ṭabīkh). As these ingredients consist of various taste, colol, smell and portion, when the portion of each ingredient is put according to the measurement, the food will have good smell, delicious taste, well-made and when the food is made not according to the proportion, it will have the opposite quality.108
4.7 Proportion and Harmony of the Cosmos
The Ikhwān by giving the mentioned examples try to emphasize the truth that harmony pervades the universe. When human being tries to make something with their hands, in order to correspond to the inner harmony within the soul and body of humanity, the artwork should be made in such a way following the law of proportion.
When things are produced without following this proportion, the result is ugliness and can even be potentially harmful to human body and soul. The Ikhwān state:
106. Ibid., 253.
107. Ibid.
108. Ibid. 43
“We intend to mention every genus of being as an example to prove the nobility
of the science of proportions that is known as music. This science is indeed
needed in all types of art. This science is specialized with the name of the science
of music that is the composition (or harmony) of rhythm and tones because the
example (of harmony) within this science is evident. The ancient sages derive the
principles of rhythm and tone from knowing the proportion of number and
geometry that when these two are combined, it results in the science of music.”109
The proportion of harmony pervades the universe. One of the aims of the Ikhwān’s treatise on music is to demonstrate that the whole world is composed in conformity with arithmetical, geometrical and musical relations. The Ikhwān say that the body of the world resembles an animal or the unique system of a single man or the totality of a city which shows also the Unity of its Maker (mukhtariʿ), the Creator of forms (muṣawwir), or of its Composer (muʾallif), that is God.110
4.8 Geometry and Moral Refinement
While in the sixth chapter the Ikhwān mention the relation of proportion and refinement of moral, one should note that the elaboration on how these two are related to each other is expressed very implicitly. Mohammed Hamdouni Alami in his book The
Origins of Visual Culture in the Islamic World help understand this relation by taking some notes as stated by Ibn Miskawayh in his Tahdhīb al-Akhlāq. Ibn Miskawayh has the same tone with the Ikhwan that this relation between the science of proportion and moral refinement pertains to the process of learning. He states that learning arithmetics and geometry is the best way to acquire truthfulness of saying and astute reasoning skills
109. Ibid., 255.
110. Seyyed Hossein Nasr, Introduction to Islamic Cosmological Doctrines. Ibid., 45.
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that are needed in search of the truth (yataʿawwad ṣidqa al-qawli wa ṣiḥḥat al- burhāni).111
Ibn Miskawayh emphasizes the significance of proportion in the process of cultivating the knowledge within one’s soul. It is the nature of human soul to desire perfection and the process towards this perfection can be gained through understanding proportion. As we discuss earlier, there are three types of proportion; arithmetics that pertain to numbers, geometry that is related to the art of measuring and surveying
(taqdīr) and (misāḥah), and lastly the proportion that combines these two, that is harmonics (taʾlīf) or music (mūsiq).
The proportions contained within these sciences possess twofold effect. Firstly, the existence of proportion naturally makes attraction and its absence leads to rejection of things. Secondly, the fact that the existence of proportion creates such an attraction is because it is no other than the beauty itself. Perfect unity in things is acquired through the attraction between substances (jawāhir) and essences (māhiyāt) that lead to harmonization. When one understands the sciences of proportion, one’s soul is led to theoretical perfection which is the beginning before one reaches the practical perfection.112 This is the essence lying behind the setting of arithmetics and geometry as the first branches of philosophy. The perfection gained through understanding mathematics is no other than the purpose of philosophy itself as stated by the Ikhwān
“and philosophy’s purpose is saying and acting in accordance with the knowledge” (al- qawl wa al-ʿamal bi mā yuwāfiq al-ʿilm).
111. Mohammed Hamdouni Alami, The Origins of Visual Culture in the Islamic World: Aesthetic, Art and Architecture in Early Islam, (London: I.B. Tauris, 2015), 49.
112. Mohammed Hamdouni Alami, The Origins of Visual Culture in the Islamic World. Ibid., 49-50. 45
Chapter 5: Conclusion
Form and matter are two things that constitute the physical world. The earlier discussion of these two can be found in Aristotle’s Physics in his theory of hylomorphism. The purpose of hylomorphism is to trace the origin of physical reality based on theorem that something must come from something and it is impossible for something to come from nothing. In addition to matter and form, the physical reality also comprises of movement, time and space. According to the Ikhwān, there are four categories of matter: matter of practical arts (hayūlā al-ṣināʿah), natural matter (hayūlā al-ṭabīʿah), universal matter (hayūlā al-kull) and original matter (hayūlā al-ūlā). The first category mentioned is the type of matter that directly related to artwork by human.
To this, the Ikhwān state that when particular bodies receive universal form, such as copper made in circular form, they are more noble than when they are in their artless state. As far as Islamic art is concerned, the Ikhwān do not talk about the spiritual significance of the form of art.
In Sufism, one can trace the origin of form within the concept of five divine presences (al-ḥaḍrah al-khamsah al-ilāhiyyah). Forms in their ultimate reality lie within the Divine nature (wāḥidiyyah) as the locus of manifestation of Divine essence
(aḥadiyyah) descending through the most sanctified emanation (al-fayḍ al-aqdas).
Within Divine nature, the primary forms are Divine names and qualities. From the level of Divine nature downward to spiritual, imaginal and physical world, the manifestation of forms is made possible through the sanctified emanation (al-fayḍ al-muqaddas).
Within the level of Divine nature, the forms are called as immutable entities (al-aʿyān al- thābitah) that are accessible to spiritual verifiers through the niche of prophecy. This is the ultimate archetypes of the creation of the world as well as those of forms of Islamic art. Whether extraction of forms from the archetypes in the imaginal world for producing
46
an artwork or contemplating on the produced artwork to return the consciousness to the
Origin, the only vehicle one can use is the Way (ṭarīqah). It is the bridge between the outer meaning and the inner meaning of reality. Within the Way, it is the Muhammadan grace that made possible this spiritual vision.
Among form of art that is essential in Islam derived from inner reality is geometry. It is an art which relies heavily on the science of mathematics. It is inherited by Muslims from Euclid who is known to be the father of this science through his book,
Stoekhia or known as Euclid’s Elements. It is the main source for one of the first intellectual works on geometry in Islam, that is the Epistles of the Brethren of Purity.
Geometry consists of two words: geo that means ‘the earth’ and metry carrying the meaning of ‘to measure’. In the Epistles, the discussion of geometry is explained in the second epistle “On The Branch of Mathematics Named as Geometry: On Magnitudes and Explanation of Its Essence” (al-risālah al-thāniyah min al-qism al-riyāḍī al- mausūmah bi-jūmaṭriyā fī al-handasah wa bayāni māhiyatihā) and the sixth epistle
“Sixth Epistle on the Branch of Mathematics; In the Proportion of Number and
Geometry in Disciplining the Soul and Moral Refinement” (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).
Geometric form is the personification of numbers and one should understand the science of numbers (ʿilm al-ʿadad) before entering the chapter of geometry.
Understanding these two propaedeutic sciences is the preparation before one undergoes intellectual journey toward natural philosophy and theology. While the origin of number is one, the origin of geometry isthe point (nuqṭah) from which the line, surface and body are made. Interestingly, according to al-Jīlī, the point is also the origin of the science of letters (ʿilm al-ḥurūf). Letters that have dots above symbolize the state of seeing God before things. Those that has rounded shape in the middle allude to the state of seeing
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God inside of things and those that have dot below pertain to the state of seeing God after things. That is to say, as reality is expressed through the words that are composed of letters, the reality is permeated by divine presence as these letters are.
In the Rasāʾil, one can see that the science of geometry is intertwined with arithmetics and music. Within the scope of the universe, number is considered to be the origin of existence. Number one represents God or The Light of Divine Oneness (nūr waḥdāniyyatihi). Number two displays the first creation coming from the One, that is
Active Intellect (al-ʿaql al-faʿāl) or simple substance (jawhar basīṭ). From this substance, number three appears representing universal astral soul (al-nafs al-kulliyyah al-falakiyyah). From this soul, divine emanation the goes to number four that is prime matter (al-hayūlā al-ūlā). According to the Ikhwān and other Pythagorean philosophers, number is not only quantity but also quality. Its proportion is shown in physical body through the harmony in geometric form.
The Rasāʾil define geometry as a science that inquires about magnitudes (al- maqādīr), dimensions (al-abʿād), and the quantity of their kinds (kimmiyyatu anwāʿihā), along with the properties of their types (khawāṣṣ tilka al-anwāʿ).
Interestingly, the Ikhwān also narrate that making art of geometry is innate in animal and it is described as perfected wisdom (itqān al-ḥikmah). This wisdom can be seen from the geometric shape of the nest made by bees and the web by spider. They state that some human beings are gifted with such architectural skill without learning. However, most of people need a master who can guide in making an artwork. The Ikhwān also say that Divine Wisdom also lie in human collaboration. No one can live by himself but in miserable life. A society should live by helping each other both ini worldly and spiritual matter as if they are brothers from one father.
Geometry and number are related to human body and soul through proportion
(Sing. nisbah Pl. nisab) that is measuring one of two magnitudes in regard to the other
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(qadar aḥad miqdārayn ʿinda al-ākhar). There are three types of proportion: quantitative proportion that is the proportion of number (nisbah ʿadadiyyah), qualitative proportion that is proportion of geometry (nisbah handasiyyah) and lastly proportion of both quantity and quality that is the proportion of composition and music
(nisbah taʾlīfiyyah wa mūsiqiyyah). Senses are the gate of the soul and proportion of the outer world is the key for the soul to experience beauty; when a painting is made with proportion, the eyes can enjoy seeing it; when melodies are composed in certain proportion, they sound beautiful to the ears.
The relationship between the science of proportion and the soul is also what lies inside the significance of Islamic art and architecture. This significance is due to the influence of the beauty of the art to the soul. Wherever one lives, he is influenced by his surroundings either in the form of sound or visual and the visual beauty that is brought by Islamic art is the representation of beauty of heaven in the earth. The sacred art of calligraphy, carpet making, Islamic edifices or Islamic miniature are based on geometric proportion. Hence, the discussion of geometry is the foundation for the world of art- making in Islam. Both learning it and perceiving it carry spiritual effects to the soul.
The Ikhwān mention the relation of proportion and refinement of moral.
However one should note that the elaboration of this relation is expressed very implicitly within the Epistles. Ibn Miskawayh helps us understand this relation through his
Tahdhīb al-Akhlāq. He says that when one understands the sciences of proportion that encompasses arithmetic, geometry and music, one’s soul is led to theoretical perfection which is the beginning before one reaches the practical perfection. After having this theoretical perfection, one applies it practically and this is the ultimate end of philosophy itself “and philosophy’s purpose is saying and acting in accordance with the knowledge”
(al-qawl wa al-ʿamal bimā yuwāfiq al-ʿilm).
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