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fromTNW | Artificial-Intelligence
2 days agoWhy probability, not averages, is reshaping AI decision-making
ChanceOmeters measure uncertainty directly, improving decision-making by providing odds rather than relying solely on averages.
Pi is an infinitely long decimal number that never repeats. How do we know? Well, humans have calculated it to 314 trillion decimal places and didn't reach the end. At that point, I'm inclined to accept it. I mean, NASA uses only the first 15 decimal places for navigating spacecraft, and that's more than enough for earthly applications.
Sometimes the reason pi shows up in randomly generated values is obvious—if there are circles or angles involved, pi is your guy. But sometimes the circle is cleverly hidden, and sometimes the reason pi pops up is a mathematical mystery!
For more than two millennia, mathematicians have produced a growing heap of pi equations in their ongoing search for methods to calculate pi faster and faster. The pile of equations has now grown into the thousands, and algorithms now can generate an infinitude. Each discovery has arrived alone, as a fragment, with no obvious connection to the others. But now, for the first time, centuries of pi formulas have been shown to be part of a unified, formerly hidden structure.
In the weeks leading up to September 1891, mathematician Georg Cantor prepared an ambush. For years he had sparred - philosophically, mathematically and emotionally - with his formidable rival Leopold Kronecker, one of Germany's most influential mathematicians. Kronecker thought that mathematics should deal only with whole numbers and proofs built from them and therefore rejected Cantor's study of infinity. "God made the integers," Kronecker once said. "All else is the work of man."
In Texas Hold'em poker, players wager on the best five-card hand they can make among the two cards in their hand and the communal ones on the table. Hands are ranked based on their probability of occurring. A full house, for example, with three cards of the same value (fives or kings, for instance) and two cards of another, is less likely than a flush with any five cards of the same suit. A full house therefore beats a flush.
On October 1, 2022, something strange happened in the Philippines: 433 people won the jackpot in the local lottery. For this particular lotto, six numbers ranging in value from 1 to 55 were randomly selected, and the 433 winners all matched. Even more bizarre, when arranged in ascending order, the winning numbers were: 9, 18, 27, 36, 45 and 54. In other words, the winning numbers were multiples of 9 (9 1, 9 2, 9 3, etcetera).