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

William Poundstone

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William Poundstone
Age: 69
Born: 1955
Born: March 29
Author
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Journalist
Fall
Prices
Cannot
Stock
Work
Zero
Failed
Model
Models
Consider
Mistake
Spotted

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In real conversations, we are always trying to outguess each other.
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The best paradoxes raise questions about what kinds of contradictions can occur-what species of impossibilities are possible.
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At a bare minimum, understanding entails being able to detect an internal contradiction: a paradox.
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Bernoulli's real contribution was to coin a word. The word has been translated into English as utility. It describes this subjective value people place on money.
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Paradox is thus a much deeper and universal concept than the ancients would have dreamed. Rather than an oddity, it is a mainstay of the philosophy of science.
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Your second ducat, like your second million, is never quite as sweet.
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Expectation is a statistical fiction, like having 2.5 children.
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Samuelson, however, hedged his personal bets - by putting some of his own money in Berkshire Hathaway.
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The ultimate compound return rate is acutely sensitive to fat tails.
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The assumption that anything true is knowable is the grandfather of paradoxes.
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There is a deep connection between Bernoulli's dictum and John Kelly's 1956 publication. It turns out that Kelly's prescription can be restated as this simple rule: When faced with a choice of wagers or investments, choose the one with the highest geometric means of outcomes.
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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.
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Are there any mythical beasts which aren't simple pastiches of nature? Centaurs, minotaurs, unicorns, griffons, chimeras, sphinxes, manticores, and the like don't speak well for the human imagination. None is as novel as a kangaroo or starfish.
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People tend to be clueless about prices. Contrary to economic theory, we don't really decide between A and B by consulting our invisible price tags and purchasing the one that yields the higher utility, he says. We make do with guesstimates and a vague recollection of what things are “supposed to cost.”
William Poundstone
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The story of the Kelly system is a story of secrets - or if you prefer, a story of entropy.
William Poundstone
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Shannon's most radical insight was that meaning was irrelevant.
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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.
William Poundstone
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Carl Friedrich Gauss, often rated the greatest mathematician of all time, played the market. On a salary of 1,000 thalers a year, Euler left an estate of 170,587 thalers in cash and securities. Nothing is known of Gauss's investment methods.
William Poundstone
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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.
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Use entropy and you can never lose a debate, von Neumann told Shannon - because no one really knows what entropy is.
William Poundstone