## Narendra Modi and the Correlation Term

In a speech in Canada last night, Prime Minister Narendra Modi said that the relationship between India and Canada is like the “2ab term” in the formula for expansion of $(a+b)^2$.

Unfortunately for him, this has been widely lampooned on twitter, with some people seemingly not getting the mathematical reference, and others making up some unintended consequences of it.

In my opinion, however, it is a masterstroke, and brings to notice something that people commonly ignore – what I call as the “correlation term”. When any kind of break up or disagreement happens – like someone quitting a job, or a couple breaking up, or a band disbanding, people are bound to ask the question of whose fault it was. The general assumption is that if two entities did not agree, it was because both of them sucked.

However, considering the frequency at which such events (breakups or disagreements ) happen, and that people who are generally “good” are involved in such events, the badness of one of the parties involve simply cannot explain them. So the question arises – if both parties were flawless why did the relationship go wrong? And this is where the correlation term comes in!

It is rather easy to explain using vector calculus. If you have two vectors $A$ and $B$, the magnitude of the sum of the two vectors is given by $\sqrt{|A|^2 + |B|^2 + 2 |A||B| cos \theta}$ where $|A|,|B|$ are the magnitudes of the two vectors respectively and $\theta$ is the angle between them. It is easy to see from the above formula that the magnitude of the sum of the vectors is dependent not only on the magnitudes of the individual vectors, but also on the angle between them.

To illustrate with some examples, if A and B are perfectly aligned ($\theta = 0, cos \theta = 1$), then the magnitude of their vector sum is the sum of their magnitudes. If they oppose each other, then the magnitude of their vector sum is the difference of their magnitudes. And if A and B are orthogonal, then $cos \theta = 0$ or the magnitude of their vector sum is $\sqrt{|A|^2 + |B|^2}$.

And if we move from vector algebra to statistics, then if A and B represent two datasets, the “$cos \theta$” is nothing but the correlation between A and B. And in the investing world, correlation is a fairly important and widely used concept!

So essentially, the concept that the Prime Minister alluded to in his lecture in Canada is rather important, and while it is commonly used in both science and finance, it is something people generally disregard in their daily lives. From this point of view, kudos to the Prime Minister for bringing up this concept of the correlation term! And here is my interpretation of it:

At first I was a bit upset with Modi because he only mentioned “2ab” and left out the correlation term ($\theta$). Thinking about it some more, I reasoned that the reason he left it out was to imply that it was equal to 1, or that the angle between the a and b in this case (i.e. India and Canada’s interests) is zero, or in other words, that India and Canada’s interests are perfectly aligned! There could have been no better way of putting it!

So thanks to the Prime Minister for bringing up this rather important concept of correlation to public notice, and I hope that people start appreciating the nuances of the concept rather than brainlessly lampooning him!