The great Prof. Varadhan made a visit to the IISc on Febrary 13th. He gave a lecture at the IISc faculty hall on entropy and large deviations. The following example was interesting.

Consider a bug with limited energy trapped in the valley of a steep peak. It tries to scale the peak and reach the other side. Evey time it fails, it falls to the bottom of the valley. It changes its strategy and starts all over again. After a very large number of attempts, it succeeds and reaches the peak. As it goes down the other side, an observer on the other valley sees the bug coming down. He becomes curious, goes to the top of the peak and looks below to see how steep was the bug’s scale.

Now, having seen the bug, what can he conclude about the strategy adopted by the bug? Prof Varadhan made the following comment. The observer can surely conclude that the bug would have adopted the most efficient strategy. That has to be the case because as the number of iterations becomes very large, the probability of success is dominated by that of the best strategy and if a success ocurs it must come from the best strategy.