In real conversations, we are always trying to outguess each other.

Samuelson spotted a mistake in Bacheliers work. Bachelier's model had failed to consider that stock prices cannot fall below zero.

The assumption that anything true is knowable is the grandfather of paradoxes.

"Average" isn't so hot at the race track given those steep track takes. "Average" is pretty decent for stocks, something like 6 percent above the inflation rate. For a buy-and -hold investor, commissions and taxes are small.

There were many at Bell Labs and MIT who compared Shannon's insight to Einstein's. Others found that comparison unfair - unfair to Shannon.

The more improbable the message, the less "compressible" it is, and the more bandwidth it requires. This is Shannon's point: the essence is its improbability.

The engine driving the Kelly system is the "law of large numbers." In a 1713 treatise on probability, Swiss mathematician Jakob Bernoulli propounded a law that has been misunderstood by gamblers (and investors) ever since.