# T C A Srinivasa-Raghavan: Of PMs and stubborn tufts

In the old days, when you retired and got over the thrill of not having to go to office every day, you got after your wife and your servants. Now you get on to the internet.

The pleasure derived from the two activities as substitutes must be the same because the wives and servants now look distinctly relieved. The internet clearly substitutes for wives and servants in more ways than one.

It was during one such surfing session when I was looking for something on connectedness that I came across a mathematical formulation called the Hairy Ball Theorem. It was first stated by Henri Poincare about 130 years ago.

It falls in a branch of mathematics called topology. I am writing about it to soothe Prime Minister Narendra Modi's nerves, which must be quite frayed after the sudden rash of scams.

In essence, it says that you can't comb a hairy ball (or coconut flat) because however hard you go at it, in the end there will always be one little tuft left standing. (If you are retired and have nothing else to do, you can try the experiment.)

One application of this theorem has been in the theory of cyclones. According to this theorem, given that there is always some wind, there will always be one place where there is no wind, for instance, the eye of a tornado. This, in turn, means that there will always be one spot on earth where there is a cyclone or a tornado raging.

There's nothing you can do about it. That's how it is. It is what nature has ordained.

A very tuft problem

Thus far no one has tried to apply this theorem to politics, but I think the time has come to do so now. It can be called TCA's Lemma. Lemma means a subsidiary substantiation of a proof.

The rule can be stated as follows: "Given that in a democracy there will always be politicians, there will always be one of them who is involved in a scam." It doesn't matter which country you look at or when. From the early 18th century when England got its first Cabinet-type government with Robert Walpole as Prime Minister, every head of government everywhere has had to face this problem.

But let us focus only on India. Jawaharlal Nehru had two such problems. The first was when his favourite colleague and finance minister T T Krishnamachari was alleged to have favoured a businessman. The second was when the Congress chief minister of Punjab, Partap Singh Kairon, got into a scam.

Indira Gandhi had a whole bunch of politicians who got into various scams. So did Morarji Desai. As it happens, both of them had the distinction of not being able to comb their sons' flat.

Rajiv Gandhi, as Bofors showed, became the erect tuft himself. P V Narasimha Rao had to contend with a few recalcitrant tufts as well.

Then along came Atal Bihari Vajpayee, and he had his share of uncombed tufts. Lastly, there was Manmohan Singh, who after a while, simply gave up trying to comb and had a whole bunch of uncombed tufts, which must haunt him still in his sleep. If they don't, they should.

NDA II's many tufts

For the first one year, Prime Minister Modi, blissfully unaware either of topology or Poincare, busied himself with combing the coconut. But now, much to his dismay, he has discovered for himself what the great French mathematician had postulated more than a hundred years ago. So rapidly have the tufts proliferated that the Bharatiya Janata Party is now trying to convince the country that you must distinguish the tufts or scams by size. The corollary is that a small scam is not a scam at all.

Sorry, but that just doesn't work. In the Hairy Ball Theorem the size of the tuft is irrelevant. What matters is that the tuft should exist despite the combing.

So what should an intelligent Prime Minister do? One answer is to stop trying to comb the coconut, which is what Singh did, and like in that kiddies' song, "here a tuft, there a tuft, everywhere a tuft-tuft".

Another is not to start combing it at all. That is what all prime ministers after Nehru and before Modi did.

But now that Modi has made all sorts of promises about rendering the coconut (or ball) tuftless, and is finding it impossible to do so, what strategy should he adopt?

There is only possible solution: Instead of combing it he must shave the coconut.

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