India's System of Mental Maths

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INDIA'S SYSTEM OF MENTAL MATHEMATICS

 

THE VEDIC IDEAL

 

In the vedic system, the work is done mentally. This stems from the

tradition being an oral one.

In practice, today, the initial problem or question is usually

written down and the answer or solution also. The work being done

mentally, a one-line answer results. This is the vedic ideal.

 

BACKGROUND

 

But what is this word 'vedic'? It refers to an ancient period in

India's history. Tradition has it that the system of the vedas

covered all branches of knowledge. Originally an oral tradition, it

began to be written down around 1600 or 1700BC, according to western

scholars. Over the next thousand years four vedas, as they were

called, were recorded - rig-veda, yajur-veda, sama-veda and atharva-

veda.An appendix to this last contained a section headed 'Ganita

Sutras', i.e. mathematical formulae, or principles. In the nineteenth

century scholars began to look at it, but could make no sense of what

they found there: statements such as, 'In the reign of King Kamsa,

famine, pestilence, and insanitary conditions prevailed.'

Then a brilliant south Indian scholar, Shri Bharati Krishna Tirthaji

(1884-1960), began a detailed investigation. He concluded that the

above statement about King Kamsa was a cryptic form of the decimal

fraction for 1/17, using letters to represent single-digit numbers,

much as we might use the letter A to represent 1, and B to represent

2, etc.Having obtained one clue, further investigation led him to

conclude that the whole of mathematics is based on 16 sutras, and he

finally wrote 16 volumes on the topic. Then events intervened. He was

virtually forced into becoming a Shankaracharya. Hindu India has four

of these top religious leaders - a bit like having four Popes.

The upshot was that he left his beloved vedic mathematics alone for

many years. Returning to the subject in the 1950's, it emerged that

the 16 volumes had been lost. On realising this, he decided to re-

write them all, and began by writing a book intended to introduce the

whole series. Ill health stopped him from getting any further, and he

died in 1960. This introductory book is now all that we have by him.

It was first published in 1965.

DIFFERENT IDEAS ABOUT NUMBER

 

Western version

When measuring weight, the bigger the number, the greater the weight.

Similarly for temperature, length, electric current etc. We are used

to the idea that larger numbers are weightier.

 

Vedic version

In the vedic system, numbers are viewed differently. An analogy is

telephone numbers, which we don't associate with quantity. They are

patterns of digits acting as addresses.Similarly, when working to a

base of ten (as we normally do), the vedic system deals with the

single-digit numbers 1, 2, 3, 4, up to 9, together with

the zero, arranged in different patterns. For example, we don't

divide by 52, we divide by 5, and take account of the 2 afterwards.

This shift of focus eliminates the heaviness, or weight, associated

with the common view of numbers. The vedic mathematician considers a

number such as 52 as 5 and 2 in succession.

 

IS VEDIC MATHEMATICS CURRENTLY USED IN INDIA?

CAN YOU TELL US ABOUT DEVELOPMENTS THERE?

 

To answer the first question first, yes and no. It is used there to

some extent. Here is a brief account of the developments.

Tirthaji died in 1960 'Vedic Mathematics' was published in 1965

Before going to India in 1981 I wrote to all Indian universities to

find out what more was known about the subject. About 30% of them

replied. No one could tell me anything more about it. Evidently the

subject was being neglected. However, one or two letters pointed me

to Tirthaji's last residence and ashram in Nagpur. Visiting there, I

was invited to return the following year to teach a fortnight's

course.These days, the subject can be taught in schools, alongside

the conventional system. Where this is done, I am told, the pupils

have no problem with learning the two approaches side-by-side - the

western and the vedic.There is also a passionate debate raging about

the status of Tirthaji's system. Some argue that it is historically

accurate, despite the lack of normal historical evidence. Others

argue that, lacking evidence for its historical validity, it should

be dismissed - despite the fact that,mathematically, it works.

My view (which I am not alone in holding) is that it is a

reconstruction. At present we are unable to say for sure that it is

historically accurate - nor to prove that it is not. This is because

we are dealing with an oral tradition, and it is no surprise that

written evidence may not be available.

 

WHAT IS THE POTENTIAL OF THE SYSTEM?

 

Tirthaji points out that it normally takes about 16 years to go from

first steps in mathematics to a Degree in the subject. (e.g. from age

5 to age 21). But he states that with the vedic system the course in

its entirety could be done in about two years! Of course, at present

we don't have all the material that's needed available.

Needless to say, however, this would benefit everybody - not least

those who are not interested in mathematics and would prefer to spend

less time on it! I think, myself, that once vedic mathematics begins

to win general acceptance it will lead people to question other

academic disciplines. Are rapid methods available in other subjects?

If so, are they being used, and if not can they be developed?