## On 2ab, Communal Harmony and Economic Growth

I’ve used the concept of “2ab” once before, a day after the Prime Minister used the term in a much lampooned remark, to explain why we need Net Neutrality. I turn to the same concept again to explain why communal harmony is necessary for economic growth.

Some 4-5 days back, a mob entered the house of one Muslim guy who was allegedly cooking beef, and lynched him to death. In response, rather than booking the mob, the police sent meat sample from the victim’s house to “test if he was actually cooking beef” – as if its confirmation as beef would justify the murder.

I’ve mostly been off social media (and hence not fully following the story) since then, but RSS leader Tarun Vijay hasmade some remarks about “lynching on suspicion being wrong“, and star Indian Express columnist Pratap Bhanu Mehta has laid the blame at the Prime Minister’s feet. Mehta writes (HT: V Anantha Nageswaran):

The blame for this has to fall entirely on Modi. Those who spread this poison enjoy his patronage. This government has set a tone that is threatening, mean-spirited and inimical to freedom. Modi should have no doubt that he bears responsibility for the poison that is being spread by the likes of Culture Minister Mahesh Sharma and Vijay — whether through powerlessness or design is irrelevant. But we can be grateful to Vijay for reminding us that the threat to India’s soul emanates from the centre of power, almost nowhere else. It is for that centre, and Modi in particular, to persuade us otherwise.

Now there were two kinds of people Modi appealed to when he came to power in a resounding victory last year – bigots and aspirers. The former hoped that Modi would “teach a lesson to the Muslims”. The latter hoped that Modi would help accelerate economic growth, after a mostly useless and scam-ridden UPA2 government. And Modi might have thought that these two goals are compatible (else it would make no sense to court these two constituencies). Even in theory they are not.

The Gross Domestic Product (GDP), whose growth rate is seen as a bellwether of the economy’s performance, is a measure of the amount of trade. Trade can be external (let’s set that aside for now) and internal. There are many factors that determine the extent of internal trade (trade between the people of the country), but at the margin, it is proportional to the number of possible pairs of people who can trade with each other.

In other words, trade is another of those quantities that follows Metcalfe’s Law, and depends on strong network effects. If the number of people in a place (region or country or state or city) is $N$, and if everyone can trade with one another, the number of possible trading relationships is $N^2$.

Despite the development of the rule of law and Contract Acts and court-brokered dispute settlements, people typically trade with other people they can trust. In the past, this meant that certain families or communities had a monopoly over trade. Over time, with the development of laws and contracts and courts, this has expanded. Yet, people still hesitate to trade with people they don’t trust.

So what happens when there is communal or caste disharmony? Then you will not trust someone who belongs to another caste or community or religion because of the person’s community (and notwithstanding the person’s personal characteristics). And if you don’t trust them, you don’t trade with them. And what does this mean for the total volume of trade?

It’s time to bring out our $(a+b)^2$ expansion. If you have two communities of sizes $a$ and $b$, in the absence of trust between the communities, the total trade in the community is ceteris paribus proportional to $a^2 + b^2$. If the two communities live harmoniously and have enough mutual trust that communal differences have no bearing on trade, the total trade in the community is ceteris paribus proportional to $(a+b)^2$. The difference between the two? $2ab$ of course!

Communal distrust and the lack of communal harmony ends up restricting the number of possible trading partners for each person, and thus we lose out in terms of the correlation term. In other words, bigotry costs us in terms of GDP growth.

Lastly, even if the government of the day is concerned more about the welfare of one particular community over another, communal harmony makes sense. For by creating distrust, people belonging to the government’s favourite community are denied trade with people of the less favoured community. And this adversely impacts the more favoured community!

## 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!