The Case with Tamil Fractions
It is tough to carve your way out of the noise and distraction of internet.
These distractions can prove to be costly, in terms of time, money and energy. But sometimes these distractions can land you in places that you don’t regret.
Which is what happened to me when I came to know about Tamil fractions. Unlike other languages, Tamil has a long list of specific names for fractions. For example, Hindi/English/Russian don’t have a word for 3/320, but to everyone’s amazement Tamil has..
So, instead of boiling the plot with hollow words, let us jump right in.
The word root for 3 in Tamil is mu.
Now, look at the second row and fourth row — mukkaal and kaal .
3 times kaal(1/4) is mukkaal (3/4).
The eighth row showing 1/8 is araikaal.
From the third row we know that the word for 1/2 is Arai. Arai (1/2) times kaal(1/4) is Araikaal (1/8).
Cool ?.
Yeah. The stuff’s quite simple to understand.
1/16 is veesam.
1/32 becomes Arai(1/2) veesam.
3/64 becomes mukkaal(3/4) veesam.
Notice that we are using the compounds like Mukkaal to get even more complicated compounds.
But this is not why I brought you here. To teach you Tamil fractions. Because I can’t, and you will now know why.
Here is the complete list of fractions.
Yeah, you saw this.
The smallest fraction is in the order of 10^-22.
If that number had a physical dimension like meters, 10^-22 m would be one millionth the size of a proton. Where and how a person would use such a fraction ? Does this number mean something or it is just a mathematical leisure at display ?
We do not have a clear answer. But I have few guesses by my side.
Anu in the list stands at order of nano(10^-9), which happens to be the order of the radius of metal atoms. Any popular unit of distance, be it yojan, metre or foot. 10^-9 of that unit does occur at the level of atomic radii of common metals.
To further cement the issue, the word for atom in both Sanskrit and Tamil, is Anu. To say that that Tamil bards knew about the size of atoms could be an outrageous conclusion. So, let us just leave it there as a mystery.
Till the point of Anu, it seems that ancient Indians knew that the fractions have a physical basis, or at least those fractions can represent the scales of some physical quantities.
Fractions might not be exactly equal to the actual values. But this is a neat as well as a quirky way of representing orders.
The way they create compounds like -
mu x kaal = mukkaal
mukkal x veesam = mukkaal veesam.
These are classical displays of multiplicative reasoning.
Modern humans first understand the additive nature and then understand the multiplicative aspects of maths. This is because our mathematics is built in that fashion. But this is not how our intuitions work.
It has been found that people who are not used to modern maths, show multiplicative thinking over linear thinking as opposed to those who are exposed to numerical maths.
These people are either found in dense forests of Amazon or are toddlers jumping in kindergarten.
If you ask an adult for the midpoint between 1 and 9 they say 5. Mentally, they put 9 points on a line and add 1 and then split that in half.
But if you ask a child or someone from a Amazonian culture not trained in maths, the answer could be different; perhaps 3.
Same would happen for 1 and 100, our answer would be 50, while their answer would be 10.
For 1 and 1000, our answer would be 500, their answer would be 100.
Understanding quantities approximately in terms of estimating ratios is a universal human intuition. In fact, humans who do not have numbers — like Amazonians and young children — have no alternative but to see the world in ratios.
By contrast, understanding quantities in terms of exact numbers is not a universal intuition; it is a product of culture.
The precedence of approximations and ratios over exact numbers is due to the fact that ratios are much more important for survival in the wild than the ability to count. Faced with a group of spear-wielding adversaries, we needed to know instantly whether there were more of them than us. When we saw two trees we needed to know instantly which had more fruit hanging from it. In neither case was it necessary to enumerate every enemy or every fruit individually. The crucial thing was to be able to make quick estimates of the relative amounts.
Tamil fractions could be a relic of such intuitions, a merging of growing linear maths with natural intuition.
With the development of computational sciences and physics, logarithmic ideas are gaining more ground. Having a grasp of exponential nature would help you make better decisions in future. Reliance on linear principles could make your predictions nose-dive to trash.
Whether or not the small Tamil fractions represent something, it is yet to be understood. But, from our current scientific standpoint, these small fractions hold no specific meaning.
But I am thoroughly impressed not only by mathematical complexity at display but also by the courage that those bards had shown. Thinking and creating big numbers has always been in trade, but thinking in fractions, that really needs some effort.
This stuff is indeed awesome.
Stay awesome.
This article was made possible by fruitful contributors of Wikipedians. Here’s the link for further information. While my time at EI, I had an opportunity to learn how kids learn basic numbers and display logarithmic intuition.
