Math Musings More Math


Have you ever noticed that while crossing a busy road, our mind judges continuously the positions and speeds of several vehicles and accurately finds the required gap in which to move forward. If a computer is asked to perform the same task, it would probably require a processor much more powerful than that of our home PC! However, the irony is that, for simple additions or multiplications, we depend on a pocket calculator. We all make mental calculations from time to time, though we may not always be aware of it. If our mind can make such complex judgements as is required to cross the road taking into consideration the direction and speed of all the moving objects, it is certainly able to manipulate a few figures. Probably, it is the cumbersome calculating devices we have probably been taught right from the good old school days – which require pencil and paper or a calculator to work out. Because of this lack of encouragement for mental calculation, it has prevented us from becoming efficient mental calculators.

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Imagine, if we can incorporate that level of mathematical calculation which is required to cross the road, in our usual daily working with figure, mathematics would be as easy as talking, walking or sleeping! But what on earth can change that mould in which we have been trained to think for so many years? Well, the answer is – Vedic Mathematics.

What is this `Vedic Mathematics’? It is somewhat difficult to define as the very terminology is used only by a small set of authors and a handful of mathematicians. The purveyors of `Vedic Mathematics’ are agreed, however, that the landmark work in this “discipline” is the text “Vedic Mathematics”, written by Jagadguru Swami Sri Bharathi Krishna Tirthaji Maharaja, Sankaracharya of Govardhan Matha, Puri (he died in 1960) and published in 1965 (Jagadguru, 1965). One would be shocked to find that according to Vedic Mathematics, the solution to all mathematical problems lies in just 16 sutras (verses) found in the Parisista (the Appendix-portion) of the Atharvaveda! In other words, it connotes and implies that our ancient Indian Vedic lore should be all-round complete and perfect and able to throw the fullest necessary light on all matters which any aspiring seeker after knowledge can possibly seek to be enlightened on.

The word ‘Sutra’ means ‘thread’ or an ‘aphorism’. An aphorism is ‘a short pithy statement or maxim’. Sutra gives an indication of the direction in which the mind has to go. In first looking at a question we may not know what to do – how do we begin to think about the problem? There are very many possibilities and the Sutra indicates a starting point; the rest of the method follows from that. The Sutras are very general and this is why they are so powerful and have such a wide range of application. The application of the Sutras being universal they must refer to something more fundamental than what we usually think of as mathematics. Incidentally, some research has related the Sutras to various functions of mind. We use our mind in certain definite and distinct ways: we may, for example, compare two ideas, or extend, reverse, generalize or vary an idea. These correlate neatly with the Sutras given and it is believed that they may give the key to explain the wide range of application of the Sutras. May be that there are sixteen fundamental functions of mind and that these correspond to the sixteen given Sutras!

There are a certain advantages available from a mental approach to mathematics apart from of course, lighteningly fast calculations. The mental agility and intelligence of the mind increases along with precision in thinking. It also improves the memory. Memory depreciates if it is not exercised. Short term, medium term and long term memory are all stimulated by mental calculation. Because of this confidence, problem understanding and creativity are also enhanced.

Before you rush out to assume that Vedic Mathematics can only teach you how to add, subtract, multiply or divide mentally, wait till you finish this paragraph. It is claimed that using the sixteen Sutras, one can solve any mathematical problem on the face of this earth! Ranging from solving simultaneous and quadratic equations to problems related to modern mathematics like Factorization, Differential Calculus and Quadruples in Astronomy including Trigonometry, Analytical Conics and Matrices. Even topics like Transcendental equations, Bipolynomials and Integro-Differential equations are covered by Vedic Mathematics. All this and much more can be learned by studying the ‘Cosmic Computer Course’. One would be surprised to note that this book covers the National Curriculum of England and Wales and that, students from the age of 8 are using it!

Learning mathematics should be a delightful experience for all children and they should all succeed in it. The ‘Cosmic Computer Course’, offered in UK, offers a complete system of mental mathematics, which can be taught in a holistic way. The straightforward and beautifully interrelated Vedic methods mean that mathematics can be done mentally and this, together with the many methods of solution, which the Vedic system offers, encourages flexibility and innovation.

This in turn leads to the development of creativity and intuition. The Vedic system does not insist on a purely analytic approach as many modern teaching methods do. This makes a big difference to the attitude which children have towards mathematics.

With its direct, easy and integrated approach this mental system (the methods can also be written down) brings out the naturally coherent and unified structure of mathematics. The Cosmic Computer Course, for example, uses a Unified Field Chart which shows the whole subject at a glance and how the various parts are related and structured.

After having read that Vedic Mathematics can cover so many (rather all) aspects of Mathematics, one might think that it would take almost half of his life for mastering all the branches of this Science. Well, you would be pleasantly surprised to know that it takes just 8 to 12 months to master this ‘magic’ at an average rate of 2 to 3 hours per day instead of 15 or 20 years required according to the existing systems of the Indian and also of foreign universities.

Perhaps the most striking feature of the Vedic system is its integrity. Current mathematical methods are extremely poor when it comes to integrating the various techniques to solve a problem, Vedic Mathematics instead beautifully interrelates and unifies the various techniques. In the Vedic system ‘difficult’ problems or huge sums can often be solved immediately by the Vedic method. These striking and beautiful methods are just a part of a complete system of mathematics, which is far more systematic than the modern ’system’. But the real beauty and effectiveness of Vedic Mathematics cannot be fully appreciated without actually practicing the system. Only than can it be seen that it is perhaps the most refined and efficient mathematical system possible. It may even urge you to think that why was it hidden from you for so long?

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