A deep insight into the origin of MATHEMATICAL SCIENCES will prove that Mathematics needs the following essential skills: 1. OBSERVATION 2. QUANTIFICATION 3. DERIVATION 4. DOCUMENTATION and 5. MODERNISATION, which includes knowledge of computer applications.
We shall study in this article how VEDIC MATHEMATICS made use of the first four criteria in the Science of mathematics, thus paving the way for the last criterion i.e. Modernisation including computerisation.
1. MATHEMATICS AS A SCIENCE OF OBSERVATION FROM THE VEDIC PERIOD
Nature has its own Rhythm and Order. Intelligent beings, the moment they are born on Earth, start observing the surroundings around them and note the rhythm and order. Mathematical Calculations start at the very early stage of growth.
Even animals have the power of judging space and time. Animals like the tiger, cat etc judge the distances before they leap. This is obvious when they catch hold of their prey by jumping distances. Most of the times, they do not fail. Similarly, birds sense distances and time and they travel thousands of kilometres crossing continents to join their mates.
Hence, it is the basic instinct of living beings to observe, judge and take decisions.
But MAN, by virtue of the unique intelligence he possesses is able to prescribe various measuring techniques and bring uniform systems of measurements in Space and Time. Mathematics is a Science of observing the Universe around us and measuring things using various techniques. This process has started from the very early ages of evolution, like the search for food, shelter etc. At present, there are very modern techniques of mathematics prevalent by the use of computers; however, the basis remains the same.
VEDAS are the most ancient scriptures of the world and we can see that the foundations of mathematics were laid in those days itself. Some of the observations made by the people of Vedic age that have resulted in accurate mathematical calculations are as follows:
* Calculation of pregnancy period was done accurately. Naturally, this could have been one of the very early calculations made by humans. Perhaps even medical science could have started from the study of child birth and the subsequent care of the mother and child.
* Man, after observing Earth for some time looked upwards and watched the sky. His keen observations and recording of astral movements led to the new science ASTRONOMY.
* All calculations regarding exchange of goods, assets, though done by barter exchange had mathematics as the base.
* Auspicious timings were calculated on the basis of almanacs and calendars, which were entirely based on arithmetical calculations.
* Agricultural cycles, seasons etc were all based on a rhythm controlled by mathematics.
* Life cycles of various species were also fixed for a particular period depending on the species.
Thus, every activity in the Universe is controlled by precise mathematical calculations. The Rishis (great Saints) of ancient times, by their simple observation were able to calculate, record, and also foretell the future.
We shall briefly see how Vedas treated the above subject as told in the earliest teachings of mathematics.
2. QUANTIFICATION (FIXING OF SCALES).
In very early ages, there were no fixed scales. Man used parts of his body and their movements for measurements. He used footsteps and palms for measuring the distances, and then multiplied them by several steps and extended to very great distances like light years. Likewise he used twinkling of eyes for measurement of time and extended such small measures to millions of years.
MEASUREMENT OF TIME:
As told in the above paragraph, normal blinking of the human eye is taken as the most fundamental unit of TIME. One NIMESHA is the time taken for blinking once for a normal human eye. 15 NIMESHAS constitute one KASHTA. 30 KASHTAS constitute one KALA. 20 KALAS constitute one MUHURTHA. 30 MUHURTHAS constitute one day of present 24 hours and 30 such days constitute one month.
Six months constitute one AYANA and a year consists of 2 AYANAS. This one year is equivalent to one DAY for Devas (Heavenly subjects or minor Gods). Like this once again let us take 360 days (1 day=2 Ayanas for Heavenly subjects). This is one year for them. 12,000 such years are known as 4 Yugs (ages). (Ages). (Krudh Yuga, Dreta Yug, Dwaper Yug, and Kali Yug). The age we are living is the KALI YUG (BLACK AGE). One thousand ChaturYug is one day for Brahma, (The Creator). A MANVANTRA is one fourteenth of Brahma’s single day.
Thus one Manvantra is equal to: 71 Chaturyug, 542 Divine years, 10 Divine months, 8 Divine days, 7 Divine Murthas, 4 Divine Kalas and 8 Divine Kashtas, and 8.5 Divine Nimeshtas.
These calculations were given by the Vedic Rishi named Parasarar; This is equal to 300 millions, 6.7 millions, 20000 human years + 6 chatur Yugs.
This huge scale starts from the simple measurement of the twinkling of eyes.
These are quantified by actual calculation of the actual movement of the Sun and by observing phases of the moon. Full moon, new moon, and eclipses were accurately calculated and thus mathematical derivations were foretold in very early Vedic ages. The two AYANAS (Half years) are known as Dakshinayana (Sun’s movement from North to South) and Utharayana (From South to North) and seasons are calculated. Various festivals of India depend upon these calculations.
Likewise, arithmetical calculations like additions, subtractions, multiplications, divisions, arithmetical progressions, geometrical progressions, fractions etc are also given in various verses.
Let us consider the geometric construction of ritual sites.
Vedas were able to solve mathematical problems in constructing fire altars which have different shapes but occupy the same area. The altars were constructed of five layers of burnt bricks with the condition that each layer consist of 200 such bricks and that no adjacent layer will have a congruent layer of bricks.
The Sulba Sutras (easy formulae) contain the earliest verbal expression of the Pythagoras theorem as told in the following Sutra.”The diagonal ones of an oblong produces both which the flank and the horizontal”, which is nothing but the Pythagoras theorem in the earliest form.
Representation of the un-known as “X”:
We are aware that in Mathematics, if two variables in a sum are known and the third is not known, we name it as X and the moment the problem is solved, we remove X and put the known number in its place.
Adi Sankara, the founder of Advaita, the well known Indian Philosophy based on Vedic teachings has used this method in explaining the secret of Divinity. Like X which cannot be defined in Maths, MAYA (Theory of Illusion) cannot be explained by words. Brahmam (The Ultimate God) has created this Universe using Maya (illusion).
The formula is Brahmam (God) + X=Universe. So, the unknown entity X= Universe-Brahmam.
Adi Sankara gave the concept of illusion to explain this. i.e.: Universe-Brahmam= Illusion (Maya). So illusion=X.
The moment this Maya is eliminated, the Universe becomes one with Brahmam. This is the basic teaching of Advaita founded by Adi Sankara.
As already told, Vedas were not in written form. The teachings were carried over to generation by practice. However, UPANISHADS were written later as explanations to Vedic teachings. Saints have documented them in an orderly manner. KATOPANISHAD is one such Upanishad, as written by Nachiketas, a young Vedic Scholar, in his arguments with Lord Yama (God of Death).
Likewise there are various sutras (formulae) which have given calculations for measuring distances, mass, area, volume etc. Any book on Vedic Mathematics will be able to give a clear treatment of the above subjects. Students with mathematical knowledge are requested to go through them and improve their knowledge based on Vedas.
There may be so many AGES in the past, but today is the computer age. Everything is recorded in computers and computerisation has changed the entire outlook of life. But there is a distinct disadvantage in mechanical knowledge. We can observe that even telephone numbers are to be recorded in the machine and referred to every now and then. Modern students have lost their memory power. But students of Vedic period were able to calculate up to the highest degrees of calculation simply by memory. Today’s bits, bytes, megabytes, and gigabytes are equivalent to Nimeshas and kashtas of the Vedic period.
Vedic Mathematics has been included in the curriculum in a few colleges. Students are advised to study and specialise this aspect of study so that they can master the subject of mathematics by mental power. By combining it with modern equipments they can reach new heights in achieving their goals.