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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
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Consider
Mistake
Spotted
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Prices
Cannot
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Zero
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The story of the Kelly system is a story of secrets - or if you prefer, a story of entropy.
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The best strategy is one that offers the highest compound return consistent with no risk of going broke.
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In The Tricky Art of Co-Existing, Sandi Toksvig navigates life's little dilemmas with wit and not-so-common sense. You'll learn the strange history of common courtesy and the one true secret of social success: how to not drive everyone around you crazy.
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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.
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Expectation is a statistical fiction, like having 2.5 children.
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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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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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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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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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Kelly was aware that there is one type of favorable bet available to everyone the stock market.
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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.
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Samuelson, however, hedged his personal bets - by putting some of his own money in Berkshire Hathaway.
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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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The assumption that anything true is knowable is the grandfather of paradoxes.
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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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There were many at Bell Labs and MIT who compared Shannon's insight to Einstein's. Others found that comparison unfair - unfair to Shannon.
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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.
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Your second ducat, like your second million, is never quite as sweet.
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