Science and Philosophy of Life

Does Science depend on our view of life? Is there a Hindu view of this? Let us proceed by considering some instances to see whether Science is independent of our view of life or otherwise.

Creation of zero

Discovery of zero is one of the most important happenings in the history of Science or Human knowledge in general. Mathematics and many branches of Science would not be in their present form without zero. It is not just a numeric zero we speak of, but the numeric zero was the original idea which in later times inspired the _expression of nothingness in areas like group theory. The importance of zero in modern Science can never be exaggerated. Formalist and reductionist approaches which are widely used by Science largely depend on zero conceptually.

Zero is nothingness, an airy nothing. Creation of zero necessarily shows an attempt to conceptualise and concretise nothingness. But is an idea to concretise nothingness an arbitrary idea or an indication of merely one's genius or scientific temper? Is expressing nothingness a purpose in itself or is it a means to something else? Simplifying the _expression of big numbers is a smaller purpose served by zero. Its actual purpose is seen when infinity is expressed. Perhaps we cannot express infinity or generate infinity without zero. It is not by generating big numbers and multiplying them that we arrive at infinity, but it is rather dividing numbers, however small, by zero that we can arrive at infinity.

This is not just interesting logic, but it is rather the quintessence of Indian Philosophy. It says: "It is not by looking out, working to fulfill desires that one gets satisfaction but it is by looking in and identifying oneself with the Self that one gets to the state of immortality." Our Economic theory says: "Man's desire is like burning fire. The more clarified butter you add to it (the more you fulfill your desires), the bigger the fire burns(desires grow but never diminish). The way to satisfaction is not fulfillment of desire but transcending desire." Our philosophy of life says: "It is not by enmity that we can defeat enmity, but it is by love that we can defeat it." Similar was the idea that violence cannot win violence, only non-violence can. It is evident from the past that India lived this Philosophy by continuously creating, even creating in response to all the destruction by the invaders. It is not possible to discover zero without such philosophical background.

Therefore this idea is existent in all aspects of life, in different forms. It is not limited to Mathematics. The Upanishads say: "Atman=Brahman", i.e., the individual self is the same as the Universal Self. Therefore reaching to one is reaching to the other. This is the origin of the idea of expressing infinity using nothingness.

The concept of Brahman, the zero and the infinite, pervades all forms of Indian knowledge, Indian view of life and Indian worldview. This in context of Mathematics became zero and infinity, in context of Medicine became Prana, in context of economics became another corresponding rule and so on.

Medicine

Indian medicine speaks of 'Prana', another instance of the same concept of Brahman. This resulted in a positive approach to medicine. The English medicine proceeds by studying abnormalities in the body and fixing them. Ayurveda proceeds by studying how a perfectly healthy body is and how differently it behaves under certain conditions.

In fact the whole western Philosophy is so. It gives innumerable names to abnormalities and concentrates on them. Here in India there was no concept of a Lunatic asylum, since the case of mental imbalance was almost ruled out. The social organization was so fashioned behind an ideal society that it went for balance rather than fixing imbalances.

According to English medicine the remedy (the medicine) enters the body and fights the disease. According to Ayurveda the medicine revitalises Prana so that body itself fights the disease. This is the fundamental difference. Both medicine and disease being outsiders to the body, when two outsiders fight in the body a side-effect is natural. This is the drawback of the English medicine. But ours is another instance of the Philosophy stated above, that it is revitalization that cures the disease but not a battle with the disease.

The principle of Homeopathy is that a disease characterised by a symptom complex can be cured effectively by the drug (in extreme dilution), which produces in a healthy individual a similar symptom complex (similia similibus curanter, meaning let likes cure likes). It comes close to Ayurveda in its holistic approach, its conception of 'Prana' and its very principle. The west could not accept homeo as a 'scientific' school of medicine, because of its philosophical discomfort with such principle rather than because of a 'really scientific' reason.

Plants have a nervous system

That even they can breathe and smell and have life, was unknown to the west a century ago, till J. C. Bose proved it. His idea was initially criticised as radical and he was advised to change his views in certain respects when he suggested that plants have life, in his paper. The western world took a shock when J. C. Bose could prove in the Royal society by 'scientific' methods that plants have life.

The importance of this apparently elementary fact can be understood, since without the knowledge of this fact many branches of life sciences we see today would not be there in their present form. How lifeless are life sciences without acknowledging life in plants? The world kept using plants for millions of years and yet it took unpardonably long for modern man to realise that they are living beings.

It can be easily known from our scriptures that our ancestors had the knowledge millennia ago that plants have life. They had also the knowledge that plants can smell & listen, absorb water through their roots, prepare their food themselves.

Is this just a theory of science or does it have any philosophical implication? It looks to us like a matter of commonsense that if plants grow in age and size, take birth and wear out they must be having life. But why could the western man not see life in them? Is the problem in his science or his very approach to life?

It is certainly a matter of one's approach to life that determines these. The Indians see the same divine in all qualitative manifestation. They see that every part of the Universe has consciousness, whether it is rock or man. They possess therefore no prejudice that some have additional greatness as compared to others. Hence it is not difficult for them to believe that even plants have life. That they have verified this scientifically is a different thing. But they did not have the sense of superiority which stands as an obstacle to seeing many ground realities. They worship plants not as nature worshipping barbarians, but as highly civilised people who can see divinity all over, in every part of the universe. It is such approach that led their ecological sense, which is today a very big buzzword. In fact the ecosense of Indians can be seen from the moment they wake up in the morning when they ask mother Earth to forgive them for having touched her with their feet. Unfortunately we cannot see as much of science in such practices as much we see a religious superstition since we are trained to look at them the wrong way.

The western man, on the other hand, has always believed that man is superior to other elements of nature. It is therefore difficult for him to 'grant' any greatness to any other being. This sense of superiority is visible at different levels of collectivity. It is the same sense of superiority that made him pollute nature and exterminate many species of animals around him. It is the same attitude that shows out in their prejudice that westerners are superior to other human races. It is this sense of superiority that led them to destroy great civilizations all over the world. It is the same complex at a different level of collectivity that resulted in two world wars.

It is not true that it was proved only a century ago that plants have life. But the way Indians verified it was not only scientific, but also spiritual. Here comes the first hiccup for the westerner, for he cannot see spiritualism as a scientific means to reality.

The examples considered above fall among the most significant discoveries, which changed the course of modern science.

We have seen how the same root idea that inspires a scientific theory affects other aspects of human life, socio-political, economic, philosophical and spiritual. It is visible from the above examples that the Science discovered by a civilization reflects its worldview, its approach to life and its value system, but is not unaffected by them or disjoint from them.

Consciousnss Studies

Hindus realized long back that all knowledge is ultimately subject to verification only by human consciousness and faculties. Thus the study of observer (human consciousness) forms an important part of both truth and its criteria. We see that scientists of late have arrived at this. A famous Physicist said "All science is nature's answer to man's question about what nature is, it is not what nature actually is". Entire theory of relativity is about acknowleding the observer and truth's relativity with reference to observer.

Spirituality

Spirituality is not just a matter of meditation practises/yoga, though they are means to the same. Spirituality is an outlook to life that recognises a principle of transcendence in every aspect of life. The above, i.e., Economics, Science, Education, are few examples of how recognizing the principle of transcendence affects and redirects the entire philosophy and pursuit.

While science, religion, economics, education, all these have a place in th Hindu system, all these are put in the right perspective. As a result, we donot see any of these overwhelming the others. That is, technology has its due place, but it doesnot supercede any other aspect of life, say religion. Such a balanced view is unique to Hinduism. If we look at the west, they suffered from fanatic religions and grew over those with rational thinking. But as a result the void created by the absence of a true spiritual culture is still not filled in. And that is why we see that Eastern spiritual cultures are now being received there. Also, the discoveries in sciences in the past century have marked a new era, recognising the continuity of truth and also the limitations of the human observer who perceives these only in discrete quanta. Those like Erwin Schrodinger who made these discoveries, have observed that these discoveries come very close to the Vedantic view of life. We also see that be it the olden times or present, the most significant discoveries that changed the course of the history of mankind, directly or indirectly, knowingly or unknowingly, acknowledge this principle of transcendence.

Life in INDIAN view

Is there an Indian view of life? Let us explore if one such thing exists, if yes what are its features and how it can be seen in various facets of life.

Education

Education aims at self-mastery and not just knowledge. As Swami Vivekananda defines, Education is the manifestation of divinity already present in man. It is not how many texts one has mastered, it is how well one has internalized a single text that matters.

Traditionally children are taught at early stages to by heart. This is to train Chitta, the memory. A well trained Chitta forms the basis for self-mastery, not just good education. This does not mean that analytical faculties are not trained. But memory is trained ahead of them so that it forms a basis for other faculties.

How does better memory help better analysis? Analysis in itself is a processing of facts to derive inferences. Thus, considering more relevant facts results in a better analysis. And a person with better trained memory can consider more facts for his analysis. Thus, training memory ahead of training analytical faculties is beneficial. Explicitly training memory as a part of primary education is very essential.

Another important aspect of education is imparting moral education. The seeds of morality along with trained memory are going to stay with the student for life. Mythology and stories of great personalities inspire children and help them mould their character in their footsteps.

Indians are far ahead of others in Consciousness studies. How to master one’s own mental faculties, senses and body, is a very important aspect in leading a successful life. But if that training comes implicitly along with a good education, that is the best way it can happen, since it is practically not possible to train one in consciousness studies at a young age. To train those faculties while they are young and let them master those by the time they grow up, is exactly what the traditional system aims at.

Economics

The first paragraph we find in any economics text would be something like this: "Man has desires. To fulfill them he earns money. His desires multiply, so do his earnings, thus grows economics." But the traditional Indian principle says: "Desire is like a burning fire. The more clarified butter you pour into it to fulfill them, the greater they flame. Therefore the way is not to fulfill them; the way is to transcend them".

It also says, "idam evahi pandityam, caturyam idam evahi, idam evahi subuddhitvam, adaya alpataro vyayah" - meaning all wisdom lies in spending less than what one earns. This is the basis for conservative economics. But one is never discouraged from earning. In fact, earning is prescribed for many sections of society. But one is encouraged to spend not more than what is required to live modestly and use the remaining for the benefit of society. In such a society where everyone is ready to help each other, there is no scope or fear of poverty.

This does not mean that such an arrangement encourages parasites. Such a system only encourages people to work for the betterment of themselves as well as others. Ours is a society that does not know what centralized social security is. Social security exists, totally at a private level. The west is doing its best to privatize social security, as its fears of bankruptcy due to social securities from Governments are going higher every year.

We know how volunteer organizations work - there are some people who work for the cause and the funds they get to support those volunteers are from the society - private contributions. That is, people work for society and society supports those individuals. Thus, such arrangements do not inherently encourage unemployment the way publicized social security systems do.

INDIAN MATHEMATICIANS

Aryabhata (475 A.D. -550 A.D.)

He is the first well known Indian mathematician. Born in Kerala, he completed his studies at the university of Nalanda. In the section Ganita (calculations) of his astronomical treatise Aryabhatiya (499 A.D.), he made the fundamental advance in finding the lengths of chords of circles, by using the half chord rather than the full chord method used by Greeks.

He gave the value of as 3.1416, claiming, for the first time, that it was an approximation. (He gave it in the form that the approximate circumference of a circle of diameter 20000 is 62832.)

He also gave methods for extracting square roots, summing arithmetic series, solving indeterminate equations of the type ax -by = c, and also gave what later came to be known as the table of Sines.

He also wrote a text book for astronomical calculations, Aryabhatasiddhanta.

Even today, this data is used in preparing Hindu calendars (Panchangs).

In recognition to his contributions to astronomy and mathematics, India's first satellite was named Aryabhata.

Brahmagupta (598 A.D. -665 A.D.)

· He is renowned for introduction of negative numbers and operations on zero into arithmetic.

· His main work was Brahmasphutasiddhanta, which was a corrected version of old astronomical treatise Brahmasiddhanta.

· This work was later translated into Arabic as Sind Hind.

· He formulated the rule of three and proposed rules for the solution of quadratic and simultaneous equations.

· He gave the formula for the area of a cyclic quadrilateral as where s is the semi perimeter.

· He was the first mathematician to treat algebra and arithmetic as two different branches of mathematics.

· He gave the solution of the indeterminate equation Nx²+1 = y². He is also the founder of the branch of higher mathematics known as "Numerical Analysis".

· After Brahmagupta, the mathematician of some consequence was Sridhara, who wrote Patiganita Sara, a book on algebra, in 750 A.D.

· Even Bhaskara refers to his works. After Sridhara, the most celebrated mathematician was Mahaviracharaya or Mahavira.

· He wrote Ganita Sara Sangraha in 850 A.D., which is the first text book on arithmetic in present day form.

· He is the only Indian mathematician who has briefly referred to the ellipse (which he called Ayatvrit).

· The Greeks, by contrast, had studied conic sections in great detail.

Bhaskaracharya (1114 A.D. -1185 A.D.)

· He is the most well known ancient Indian mathematician.

· He was born in 1114 A.D. at Bijjada Bida (Bijapur, Karnataka) in the Sahyadari Hills.

· He was the first to declare that any number divided by zero is infinity and that the sum of any number and infinity is also infinity.

· He is famous for his book Siddhanta Siromani (1150 A.D.). It is divided into four sections -Leelavati (a book on arithmetic), Bijaganita (algebra), Goladhayaya (chapter on sphere -celestial globe), and Grahaganita (mathematics of the planets).

· Leelavati contains many interesting problems and was a very popular text book.

· Bhaskara introduced chakrawal, or the cyclic method, to solve algebraic equations. Six centuries later, European mathematicians like Galois, Euler and Lagrange rediscovered this method and called it "inverse cyclic".

· Bhaskara can also be called the founder of differential calculus.

· He gave an example of what is now called "differential coefficient" and the basic idea of what is now called "Rolle's theorem".

· Unfortunately, later Indian mathematicians did not take any notice of this.

· Five centuries later, Newton and Leibniz developed this subject.

· As an astronomer, Bhaskara is renowned for his concept of Tatkalikagati (instantaneous motion).

· After this period, India was repeatedly raided by muslims and other rulers and there was a lull in scientific research.

· Industrial revolution and Renaissance passed India by. Before Ramanujan, the only noteworthy mathematician was Sawai Jai Singh II, who founded the present city of Jaipur in 1727 A.D.

· This Hindu king was a great patron of mathematicians and astronomers.

· He is known for building observatories (Jantar Mantar) at Delhi, Jaipur, Ujjain, Varanasi and Mathura.

· Among the instruments he designed himself are Samrat Yantra, Ram Yantra and Jai Parkash.

·

Indian mathematicians of 20^th century :

Srinivasa Aaiyangar Ramanujan

· He is undoubtedly the most celebrated Indian Mathematical genius.

· He was born in a poor family at Erode in Tamil Nadu on December 22, 1887.

· Largely self taught, he feasted on Loney's Trigonometry at the age of 13, and at the age of 15, his senior friends gave him Synopsis of Elementary Results in Pure and Applied Mathematics by George Carr.

· He used to write his ideas and results on loose sheets. His three filled notebooks are now famous as Ramanujan's Frayed Notebooks.

· Though he had no qualifying degree, the University of Madras granted him a monthly scholarship of Rs. 75 in 1913.

· A few months earlier, he had sent a letter to great mathematician G.H. Hardy, in which he mentioned 120 theorems and formulae

· . Hardy and his colleague at Cambridge University, J.E. Littlewood immediately recognised his genius. Ramanujan sailed for Britain on March 17, 1914.

· Between 1914 and 1917, Ramanujan published 21 papers, some in collaboration with Hardy.

· His achievements include Hardy-Ramanujan-Littlewood circle method in number theory, Roger-Ramanujan's identities in partition of numbers, work on algebra of inequalities, elliptic functions, continued fractions, partial sums and products of hypergeometric series, etc.

· He was the second Indian to be elected Fellow of the Royal Society in February, 1918.

· Later that year, he became the first Indian to be elected Fellow of Trinity College, Cambridge.

· Ramanujan had an intimate familiarity with numbers.

· During an illness in England, Hardy visited Ramanujan in the hospital.

· When Hardy remarked that he had taken taxi number 1729, a singularly unexceptional number, Ramanujan immediately responded that this number was actually quite remarkable: it is the smallest integer that can be represented in two ways by the sum of two cubes: 1729=1³+12³=9³+10³.

· Unfortunately, Ramanujan's health deteriorated due to tuberculosis, and he returnted to India in 1919.

· He died in Madras on April 26, 1920.

P.C. Mahalanobis :

· He founded the Indian Statistical Research Institute in Calcutta.

· In 1958, he started the National Sample Surveys which gained international fame.

· He died in 1972 at the age of 79.

C.R. Rao :

· A well known statistician, famous for his "theory of estimation"(1945).

· His formulae and theory include "Cramer -Rao inequality", "Fischer -Rao theorem" and "Rao - Blackwellisation".

D.R. Kaprekar (1905-1988)

· Fond of numbers. Well known for "Kaprekar Constant" 6174.

· Take any four digit number in which all digits are not alike.

· Arrange its digits in descending order and subtract from it the number formed by arranging the digits in ascending order.

· If this process is repeated with reminders, ultimately number 6174 is obtained, which then generates itself.

Harish Chandra (1923-1983) :

· Greatly developed the branch of higher mathematics known as the infinite dimensional group representation theory.

Narendra Karmarkar :

· India born Narendra Karmarkar, working at Bell Labs USA, stunned the world in 1984 with his new algorithm to solve linear programming problems.

· This made the complex calculations much faster, and had immediate applications in airports, warehouses, communication networks etc.

INDIAN MATHEMATICS

The most fundamental contribution of ancient India in mathematics is the invention of decimal system of enumeration, including the invention of zero.

The decimal system uses nine digits (1 to 9) and the symbol zero (for nothing) to denote all natural numbers by assigning a place value to the digits. The Arabs carried this system to Africa and Europe.

The Vedas and Valmiki Ramayana used this system, though the exact dates of these works are not known.

MohanjoDaro and Harappa excavations (which may be around 3000 B.C. old) also give specimens of writing in India.

Aryans came 1000 years later, around 2000 B.C. Being very religious people, they were deeply interested in planetary positions to calculate auspicious times, and they developed astronomy and mathematics towards this end. They identified various nakshatras (constellations) and named the months after them. They could count up to 10¹², while the Greeks could count up to 10⁴ and Romans up to 10⁸. Values of irrational numbers such as and were also known to them to a high degree of approximation.

Pythagoras Theorem can be also traced to the Aryan's Sulbasutras. These Sutras, estimated to be between 800 B.C. and 500 B.C., cover a large number of geometric principles.

Jaina religious works (dating from 500 B.C. to 100 B.C.) show they knew how to solve quadratic equations (though ancient Chinese and Babylonians also knew this prior to 2000 B.C.). Jainas used as the value of (circumference = x Diameter). They were very fond of large numbers, and they classified numbers as enumerable, unenumerable and infinite.

The Jainas also worked out formulae for permutations and combinations though this knowledge may have existed in Vedic times. Sushruta Samhita (famous medicinal work, around 6th century B.C.) mentions that 63 combinations can be made out of 6 different rasas (tastes -bitter, sour, sweet, salty, astringent and hot).

In the year 1881 A.D., at a village named Bakhshali near Peshawar, a farmer found a manuscript during excavation. About 70 leaves were found, and are now famous as the Bakhshali Manuscript.

Western scholars estimate its date as about third or fourth century A.D. It is devoted mostly to arithmetic and algebra, with a few problems on geometry and mensuration.