Mathematics and the Search for Ultimate Reality!

Friday, August 27, 2010

“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.

The Unfolding
"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.
The Union
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
(Omar Khyaam)

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.
 

Waves of sorrow and the fertile hearts!

Tuesday, August 17, 2010

The recent Monsoon season and the heavy rainfall we received poured some questions in the minds of many a people across Pakistan. In this post I would like to address three of such questions, according to my personal opinion, and would also like to know what you think about these questions.
The questions are:
·         Why did a natural disaster as devastating as the recent floods hit us?
·         What can we at an individual and national level do for the relief of millions of people who are desperately looking towards us for help?
And
·         In what way is the flood going to affect us, as a nation, in the long-term?

Considering from different angles many different perspectives can be observed. Some believe that the ‘timely’ construction of large dams in the country could have helped storing water in the reservoirs, hence reducing the chances of floods. Others are of the opinion that as regular cleaning of the river channels in the Northern region of the country was not observed, the swelling of the rivers occurred, resulting in floods. We also come across opinions such as calamities both natural and resulting from human activities are a result of our wrong doings and we need to consider what wrong we were committing to….!
I think there is one other way in which we can respond to the question. Calling to mind the Earthquake of 2005 and the relief activities for the affected ones, there were few trained rescue teams across the country at that time. The whole infrastructure for the relief efforts had to be created before we could set out to work and back then we didn’t have so many organizations within the ranks of civil society that could help the Government and the Army in the relief efforts, as we have nowadays. By the time the issue of IDPs from Swat and Buner came to surface, Pakistan had witnessed a noticeable change regarding the Rescue and Relief work. A bulk of organizations run by Pakistanis from different age-groups and different professional backgrounds made their way into the relief and rehabilitation of the IDPs. We not only handled the situation efficiently, but also with minimum foreign aid. So can’t we say that the Relief activities and the lessons of patience, relying on our own resources and training our own rescue teams after the Earthquake helped us fight and stand the Wave of terrorism and the issue of IDPs that followed it? If yes, then it’s possible that the floods and the worst plane-crash in the history of Pakistan are there just to prepare us as a nation for some crucial challenges awaiting us, where we need to bring these lessons of patience and courage into practice, which we are learning during all these traumatic events. Keeping this in mind, perhaps we need to exhibit more DISCIPLINE than ever, so that we are able to face every challenge that comes on our way with determination.

Before I deal with the second question, I would like to share (in my own words) a little story I heard somewhere.
A little child saw some fishes that had accidentally come near the shoreline and one after the other they were breathing their last. The child went near them and started throwing them one by one towards the sea. On seeing this, a man standing nearby went to the child and told him that it was impossible for him to put all the fishes back and perhaps most them would die before he can help them, then why bother spending time for them. To this the innocent child replied ‘It still matters even if I save a SINGLE life’.
So is my view, it matters even if I m able to help bring ONE smile on a face yet saving a Life is a deed much more admirable. This is the level of FAITH that can help us control and over-power the situation.  Whatever can be done, in whatever capacity, and in whatever way possible is the only way to reach those who need us and who are looking towards us for our Love and assistance.

After immediate relief of the affected-ones comes their rehabilitation and the long-term impact of the events on the ‘collective consciousness’ of the Nation. Reports conclude that great damage to human-life, live-stock, and food-crops has occurred and perhaps we need lot of time to fill in the gap that has been created.
Quoting UN humanitarian chief John Holmes:
“While the death toll may be much lower than in some major disasters, taking together the vast geographical area affected, the numbers of people requiring assistance and the access difficulties currently affecting operations in many parts of the country, it is clear that this disaster is one of the most challenging that any country has faced in recent years.”
According to analysts, the country will perhaps witness food-shortage in the coming year owing to the damage to food crops. The ones who have lost their houses, schools, and means of earning livelihood have to start from a scratch and they will surely need time and resources to re-establish themselves. Epidemics may result, draining the country’s resources for providing medical treatment and medicines.
The floods will surely leave an indelible mark on the psyche of the Nation in the long-term. With the memory of the disturbing events and the plight of the effectees another significant recollection may last long. Nowadays we observe donation-campaigns running all over our local electronic media. We can see people from different walks of life sitting with and sharing their varying views with each other on any TV channel you tune-in (singers and musicians sitting next to engineers and Army personnel during donation campaigns for flood-affectees). Such UNITY is the noteworthy aspect of the 1965 Indo-Pakistan war which we observe to be all around us today. Perhaps new avenues of thought and fresh revolutions may result from the stream of this Unity, carving a new world of Ideas and shaping some new dreams for the Nation to pursue.
Summarizing the post I would like add that as those who are directly affected from the devastation of floods have lost their near and dear ones, their houses and properties are gone; schools, bridges and roads where they used to walk are no longer there, we must pay our regard to them and to their sacrifices. Acknowledging those who laid down their lives in this calamity as Martyrs is a small token of respect we can offer them from our side.
 I also feel that now is the time to revert to the principles of Unity, Faith and Discipline gifted to us by our Quaid, as the answers to all our questions lies there.
 At the end let me share some beautiful words of Iqbal here, guiding us to hope and ambitions.
Let not the sorry plight of the garden upset the gardener,
Soon buds will sprout on the branches and like star glitters;
Weeds and brambles will be swept out of the garden with a broom,
And where martyr’s blood shed red roses shall bloom;
Look how russet leaves have tinges the Eastern skies,
The horizon heralds the birth of a new Sun about to Rise.”

May we recover from this calamity soon and may Pakistan always prosper.

Crescent and the shining Star!!!

Friday, August 13, 2010


The Land where ideas blossoms to become flowers of reality, sustaining the stream of Life, and growing up each day as fresh thoughts unfolds themselves, came into existence in the shape of Pakistan, and the aim to unveil the deeper truths in Life adopted as the constitution.

 

Securing the freedom of bringing one’s ideas into practice, the Land promised every soul an environment where it can bloom to its full, and bring to light all the talents and capabilities possessed by it, benefiting Humanity from the bounties of Nature.

 

However the winds grew more violent and obstacles came in the way to the Progress. The seedling of values experienced dry seasons and scorching Sun, receiving lessons of enduring hardships and exhibiting Patience. The few small leaves it bore, initially lost their color but later they learnt to cope with the new circumstances, showing resistance and thus in the upcoming seasons of more hardships, they learnt their lesson that

"Time’s revolutions have one goal,

To show you what is your own soul."

The experience of winds and thunders helped the Nation to Unite at a single point, achieving the inner harmony and unity which was the utmost desire of the Land. Draped with the beauties of its ideology and charms of its values the Land is inviting every soul of the Nation to get colored in its fashion, acquiring its philosophies and beliefs. The quest to know and uncover the secrets of Nature then found its way to the Heart of the Nation.

“But now a new world is being born, while this old one sinks out of sight of men”

 

With the Union between the Land and the Nation comes the fusion of energies which has the capability of spreading its light and fragrance far and deep into the Universe, achieving for humanity an intimate contact with the ‘secrets and mysteries’ held by the Nature, resulting in the formation of a new World where curtains of Time and Space are no longer as thick as before.

To achieve this Union, and to solve the Mysteries of Life, to exercise fully the
essence of the Ideals that led to the creation of this ‘Land of Pure’, and the conception of a new World needs every soul to stand upright against any odd, with Faith that doubt can never surmount, and determination that never knows any weakness. Reaching the core of Universe to look for Truths that are held by Life call for such a Man as

"That man will still keep his lantern burning, however tempests blow strong and cold,

Whose soul is centered on high, whose temper the Lord has cast in the royal mould."

 

With the Flag of Hopes flying High, I dedicate this post as a Birthday Gift for Pakistan. May we never let the torch, given to us by our leaders, extinguish and let the darkness fell. May our Land and Nation continue to sustain each other for Ever and may we achieve all the dreams that we cherish, very soon.

Your Heart and Mine!!

Monday, August 2, 2010


The Universe is not without a purposeful end, and it is our Love that nourishes the tale of Existence.


Perhaps the strongest force that drives the system of the Universe is the longing of every heart to get in touch with its beloved, and in the process every heart become united as One. Our hearts are willing to loose their individuality so that many streams of Love, leading from my heart and yours, join together and form a river that can lead us all to the world of our beloved.

Love fills in the whole of space and the entire Universe becomes a reflection of one’s beloved. This reflection exhibits the ‘Perfect Beauty’ compelling one to renounce itself just in order to get painted in the colors of that beauty.

Each day, each moment becomes a tool for clearing the path leading to one’s beloved and the vision of the Beauty becomes more and more enchanting, revealing unto the lover more and more of himself. Time becomes an instrument in this Union and brings to light the many mysteries that are wrapped in its fabric.

Thus every heart, every action it takes, every thought that comes out of it and every idea that blossoms in its garden determines the destiny of the whole Universe. Time and Space yields themselves to it, enabling one’s heart to move back and forth in Time and conquer any piece of Space so as to find a path that leads to the spot where the beloved, draped with all its beauties, awaits the Union with its lover.

Therefore any decision or action taken by your heart and mine has the capability to turn the wheels of our vehicle. It can turn us to or away from the direction leading to our beloved.

From the Time when the Lovers were separated, Universe has followed a sequence of events, shaping a storyline. There must be a proper design and a suitable ending to such a beginning. I find myself in an age where we are some steps ahead the beginning, but few steps prior to the destiny.

Our hearts, mine and yours, are the characters that will carve the remaining story and every moment we spend on this earth will contribute to construct its sentences and phrases.

Future will be exactly what yours and my heart wants it to be.