Magnanimity and Leadership

I haven’t been able to live up to a few of my own magnanimous gestures at times. Having given myself more credit than I deserve, I have fought hard to live up to my promises; sometimes, to others, but often, to myself. I am just one person, responsible for my own actions, and the only one to bear the consequences.

Imagine Gandhi, Nehru, and others, who took a few such magnanimous decisions for 700 million Indians. Was Gandhi fair in asking the Indian Government to give Pakistan the money India technically owed them, so that they could fund their on-going proxy tribal war in Kashmir? Was he trying to be fair because India had to be fair to her neighbours? or was he exhibiting some personal gesture to himself? – that the people he leads are always fair to others. What statement was he trying to make?

Was Nehru fair in asking India to be secular? Did he (or they, the Congress) base the decision that allowed Indian Muslims to stay in India, on his own principles or on a more collective mindset of India? Pakistan was enforcing the Hindu exodus from its land and Nehru decided that India will accept them all, and there would be no corresponding enforcement from the Indian side. In a way, its like offering the other chin…..

Now, on the history per se, I have no strong opinion because I am not really privy to what exactly transpired then. The facts, the thoughts, the opinions; I have to read a lot more history before I am even close to giving my own opinion….But the point in question here is about whether leaders have the rights to be magnanimous, when all they are implicitly entrusted with is just the main cause. There are two “causes” here –

– The issue where magnanimity is being shown – India being secular (Nehru), Give Money (Gandhi)
– The issue on which leaders were made – Independent India (Nehru, Gandhi)

I might be mistaken here; these might not be two separate entities. Independent India might subsume Secular India or Internationally Fair India. But from first looks, it appears that some form of constitution had to be in place before the leaders took these decisions. But of course, I am grossly overlooking the urgency of the situation in 1947. The extreme nature of Partition might make these arguments on academic aspects of leadership look trivial; or to some extent, even offensive.

But in less extreme cases where leaders make choices for their “subjects,” do they have the right to be magnanimous on issues that are out of their leadership domain in a strict sense.

At a personal level, when individuals make commitments, stick to their signatures, their word, their promises, do they reckon with all the other agents who actually have to carry out their word? Agents like emotion, selfish instinct, reflex, malleable thought, maturity, micro-evolution, etc. Leadership at the micro level seems to be so hard……I wonder about Gandhi…

Traveling Salesman

The traveling salesman problem (TSP) is a very simple combinatorial optimization problem. Given a set of cities and distances between each pair, the problem is to find the tour of least distance that travels each city exactly once. Simple – as in simple to state. But from what I have seen this seems to be the hardest of the hard problems to solve.

To give some background, there are these famous hard problems in Computer Science that do not have “efficient” solutions. Brute force solutions work very easily on them, but take an eternity to run. In spite of 40 years of extensive research by some very smart people, brute force seems to be the only solution. For example, the TSP can be solved by listing all possible tours covering the cities once, and picking the one with the least length. This takes an eternity as there are an exponential number of such tours (n!). These problems are the (in)famous NP-Hard problems. Stephen Cook at the University of Toronto proved that if one of them can be solved efficiently, all of them can be!!! A very intuitively pleasing fact.

Tragically, most combinatorial optimization problems in nature turn out to be NP-hard. As 40 years of research hasn’t found a good solution to these problems, people have begun to approximate the solutions. Say, for TSP, if the least length best tour is around 100 KM, a procedure that finds a tour of 150 KMS would be considered good. Of course, if the length of the best tour is around 5000 KM, the same procedure should return a tour of length 7500 KM. This means that the approximate procedure for TSP should return a solution that is always some fixed fraction times more than the best solution. Most of the NP-hard problems have reasonable approximation algorithms; the TSP does not!!

It is proven that you cannot invent a procedure that can take a set of cities and give a tour that will always be some fraction times more than the optimal solution. TSP seems to be very very very very hard. But of course, most of this theory would collapse if someone comes up with a good way to solve one NP-hard problem.

In spite of my being really really really bad at this academically, I am completely enamored by the theory of NP-completeness. Somehow this notion of possible but not-feasible seems to make it intriguing. It is incredibly fascinating to see how all NP-hard problems are closely related to each other, and solving one solves them all, but approximating one, doesn’t approximate them all. Seductive!!

Reminds me of Dijkstra’s famous quote – “Computer Science is as much about Computers as Astronomy is about Telescopes.”