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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
Biographer
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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A bit is worth 10,000 basis points.
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Your second ducat, like your second million, is never quite as sweet.
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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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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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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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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.”
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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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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.
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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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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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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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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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The best strategy is one that offers the highest compound return consistent with no risk of going broke.
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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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The ultimate compound return rate is acutely sensitive to fat tails.
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Samuelson, however, hedged his personal bets - by putting some of his own money in Berkshire Hathaway.
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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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