“Know, oh brother…. that the study of sensible geometry leads to skill in all the practical arts, while the study of intelligible geometry leads to skill in the intellectual arts because this Science is one of the gates through which we move to the knowledge of the essence of the soul and that is the root of all knowledge.”
(From the Rasa’il by The Brotherhood of Purity, translated by S.H Nasr)
From Abacus to Algebra
Mathematics was present in the life of ordinary individual even thousands of years back. Abacus provided an effective method of counting to the early generations of Man. Simple counting and measurements regarding straight lines existed in a well-developed form before the advent of Islam. Later the early Muslim Mathematicians brought a revolution in the world of Circles, thus generating a number of Polygons and blooming Mathematics to a level where amazing pieces of architecture and astounding developments in the field of Astronomy took place. However according to them the basis of Mathematics was Spirituality and they used it as a tool to understand the deep and profound Truths which Universe veils under the cloak of Time and Space.
“Clear distinction made by Khayyám, on the basis of the work of earlier Persian philosophers such as Avicenna, between natural bodies and mathematical bodies. The first is defined as a body that is in the category of substance and that stands by itself, and hence a subject of natural sciences, while the second, called “volume", is of the category of accidents (attributes) that do not subsist by themselves in the external world and hence is the concern of mathematics.”
(From the article on Omar Khyaam, a renowned Muslim Mathematician, link to it: here)
Circles helped Mathematicians solve many quadratic and cubic equations. The most basic of all Polygons i-e Triangle appeared when the centers of three adjoining circles were joined with a line, and in that way the properties of Triangle came to surface, solving yet another bunch of problems and reaching the inner depths of the Universe.When these problems got solved and new polygons came to surface there emerged the rich branch of Mathematics, Algebra.
"We will show them our proofs in the horizons, and within themselves, until they realize that this is the truth. Is your Lord not sufficient as a witness of all things?" Quran [41:53]
The radiance of the ‘Source’ can be felt clearly as it stands alone, before any other being experienced the Dawn of Birth. Its presence is so strong that one can not avoid feeling it, yet it is a mystery as it remains out of the sight of the observer. The Source that is unbound of the limits of Time and Space now decides to bring into life its frozen surroundings.
The Source of Being sketches a ‘Dot’ of Creation and keeps it at a certain ‘Distance’ of Relationship. The Polarity of Existence develops as the creation of this ‘Dot’ results in the emergence of Dimensions such as Time and Space. The Source, Dot and the relationship between them creates a ‘Line’ which acts as the basis of all Motion that has yet to come.
The ‘Dot’ of creation then expands, evolving and improving itself, hence converting itself from a ‘Dot’ to an ‘Arc’. Even as the ‘Arc’ grows, it exists by keeping the same ‘Distance’ of Relationship as the ‘Dot’. This distance can also be termed as the ‘Radius’. Now the authority of the Source becomes more evident and the force of Attraction it exhibits becomes more effective.
The ‘Arc’ grows and eventually returns to the ‘Dot’, completing a ‘Circle’ by maintaining the same Relationship with the Source throughout its Journey. The ‘Circle of existence’ displays a Symbol of Unity and becomes a reason of bliss for the Source, which now shines with a brilliant radiance.
When a body moves around this ‘Circle’ it experiences a set of Forces working on it. These can be divided in the broad categories of Good and Evil forces. In order to continue one’s motion in the circle, the Resultant direction of all these Forces must be towards the CENTER of this circle, otherwise the being can not carry on with its motion on this path of Creation.
“That shining point by its light has dominated all that is in the Creation, and by its effectiveness has penetrated every object of the phenomena. All that we have attributed to the Universal nature issues out from it.”
(Lamha 33, from the Lamahat of Shah Waliullah)
Balancing and Restoration
Al-Khwarizmi is considered the father of Algebra, who by using the Circles and the polygons which were created with the help of the circles, was successful in solving geometric problems through Algebra. According to R. Rashed and Angela Armstrong:
"Al-Khwarizmi's text can be seen to be distinct not only from the Babylonian tablets, but also from Diophantus' Arithmetica. It no longer concerns a series of problems to be resolved, but an exposition which starts with primitive terms in which the combination must give all possible prototypes for equations, which henceforward explicitly constitute the true object of study.”
(From the book The Development of Arabic Mathematics by R. Rashed and Angela Armstrong)
Omar Khyaam followed this great Mathematician and erected a much deep foundation of Algebra on the basis of Al-khwarizmi’s work. It is now believed that Pascal’s triangle and Binomial theorem came to the surface in 1070 by Omar Khayyam, many centuries before they were included in the modern Mathematics by the Europeans.
Omar Khyaam believed that
“Whoever thinks algebra is a trick in obtaining unknowns has thought it in vain. No attention should be paid to the fact that algebra and geometry are different in appearance. Algebras are geometric facts which are proved by propositions five and six of Book two of Elements.” Omar Khyaam.
Al-Jabr is the term that Al-khwarizmi used to describe the process of ‘Restoration’ that takes place when removing negative units, roots and squares from the equation by adding the same quantity to each side. Al-Muqabalah denotes ‘Balancing’ the equation by bringing quantities of the same type to the same side of the equation. From these simple processes evolved the spirit of Algebra, providing foundation for Human thought to search for the Truths that surrounds one.
UNITY and ONENESS
O mankind! We created you from a single soul, male and female. (Quran: 49:13)
After the ‘Circle of existence’ came into being it was realized that there were Pairs of every object. Matter came with anti-matter. Electrons found protons to counter their effect. Every Force in this Universe found an opposite one to it and thus every individual in this Universe discovered itself existing with an opposite entity that could cancel the effect of the previous one.
This pairing helped the Universe to keep a Balance in every aspect, making it possible for a being to thrive in it. Without this balance the delicate system of Universe can get irreparably damaged, bringing the Life on this planet to a halt.
Algebra used this principle in solving out numerous equations and geometric problems, contributing to intricately-design architectural monuments and the precise calculations related to Astronomy. Man could never have stepped on the surface of Moon without the applications of this important principle in the field of Maths. Also it helped Man in understanding the nature of the things around him, thus entering the world of Spirituality and unveiling the secrets of Nature.
The eternal quest of Man to understand the mysteries regarding his existence led him to observe his surroundings and in the course of Time he desired to ‘Fold’ and ‘Reverse’ the events that led to the formation of the ‘Circle of Existence’. For this he examined the undulations of the Periphery of the Circle where he was standing, and then made an attempt to move inside it, towards the Center that controls everything. After cleansing one’s own soul of the impurities of Substance, Man led his soul wander towards his goal, following the same Rules that were observed in the Formation of the Circle.
This process of Restoration when entered the world of Algebra brought another major revolution in the way Universe was beheld by many. The rules of Restoration helped to simplify problems in Algebra and find the unknown, something that was looked for. In this way the complexities of Nature bowed down and surrendered to it, paving way for more and more discoveries, both spiritual and material.
Balancing the forces of Evil and Good and the process of ‘folding’ the course of Creation helps Man to get evolved.The Journey that started from the Unity of the ‘Source’ leads to the Expansion of existence and which finally guides Man back to the Oneness and Unity of the shining point that is the Source of all Being, towards which every creation has to go and eventually get shrouded with its Light. As the Creation embraces the Source, their Union occurs and the lamp of quest merges in the Sun of Knowledge, making the Source shine even brightly.
A drop of water falls in an ocean wide,
A grain of dust becomes with earth allied;
What doth thy coming, going here denote?
A fly appeared a while, then invisible he became
With the help of Algebra and Mathematics early Muslim mathematicians put the deep-rooted principles of the Universe in our daily lives in such a symbolic way that can help us solve our queries regarding the system of Universe for centuries. The Laws laid by them are valid in the world of Maths till date and will continue to nourish the Flower of existence with Nectar for many more centuries to come. All we need to do now is to carry these treasures which we have got in heritage from these flag-bearers of Humanity, and build upon the basis they have provided to us new buildings that can help the coming generations to carry on the search with-in. In this way Humanity can conquer both the Gardens of Spirit and the Avenues of the visible world.