Gerolamo Cardano Concepts

The Drunkard's Walk: How Randomness Rules Our Lives

by Leonard Mlodinow · 12 May 2008 · 266pp · 86,324 words

was employed by the Inquisition as a professional torturer. That plum job was a reward for having given evidence against his father. Before his death, Gerolamo Cardano burned 170 unpublished manuscripts.1 Those sifting through his possessions found 111 that survived. One, written decades earlier and, from the looks of it, often

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works and the law of the sample space, that framework for analyzing chance situations that was first put on paper in the sixteenth century by Gerolamo Cardano. GEROLAMO CARDANO was no rebel breaking forth from the intellectual milieu of sixteenth-century Europe. To Cardano a dog’s howl portended the death of a loved

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both his autobiography and the writings of some of his contemporaries. Some of the writings are contradictory, but one thing is certain: born in 1501, Gerolamo Cardano was not a child you’d have put your money on. His mother, Chiara, despised children, though—or perhaps because—she already had three boys

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York Times, July 21, 1991. 9. Robert S. Gottfried, The Black Death: Natural and Human Disaster in Medieval Europe (New York: Free Press, 1985). 10. Gerolamo Cardano, quoted in Wykes, Doctor Cardano, p. 18. 11. Kline, Mathematical Thought, pp. 184–85, 259–60. 12. “Oprah’s New Shape: How She Got It

Rage Inside the Machine: The Prejudice of Algorithms, and How to Stop the Internet Making Bigots of Us All

by Robert Elliott Smith · 26 Jun 2019 · 370pp · 107,983 words

and business opportunities were tempting Renaissance men to try their luck at taming the goddess Fortuna. One such man was mathematician, scientist, philosopher and physician Gerolamo Cardano,6 who was born in Pavia in 1501. Gerolamo was one of the greatest intellectuals of Renaissance Italy, but from the outset the Fates dealt

Surfaces and Essences

by Douglas Hofstadter and Emmanuel Sander · 10 Sep 2012 · 1,079pp · 321,718 words

will emerge shortly). It all took place in Italy — first in Bologna (Scipione del Ferro), and a bit later in Brescia (Niccolò Tartaglia) and Milan (Gerolamo Cardano). Del Ferro found a partial solution first but didn’t publish it; some twenty years later, Tartaglia found essentially the same partial solution; finally, Cardano

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the cubic by the Italians in the sixteenth century inspired European mathematicians to seek analogous solutions to equations having higher degrees than 3. In fact, Gerolamo Cardano himself, aided by Lodovico Ferrari, solved the quartic — the fourth-degree equation. Even though there was no geometric interpretation for an expression like “x4 ”, the

Everything Is Predictable: How Bayesian Statistics Explain Our World

by Tom Chivers · 6 May 2024 · 283pp · 102,484 words

the study of probability begins in French gambling houses in the mid-seventeenth century. But we can start it earlier than that. The Italian polymath Gerolamo Cardano had attempted to quantify the maths of dice gambling in the sixteenth century. What, for instance, would the odds be of rolling a six on

The Golden Ticket: P, NP, and the Search for the Impossible

by Lance Fortnow · 30 Mar 2013 · 236pp · 50,763 words

common mistakes people make when thinking they have a proof. Perhaps the first bad P ≠ NP proof goes back to 1550 and the writings of Gerolamo Cardano, an Italian mathematician considered one of the founders of the field of probability. Cardano, in creating a new cryptographic system, argued for the security of

Human Compatible: Artificial Intelligence and the Problem of Control

by Stuart Russell · 7 Oct 2019 · 416pp · 112,268 words

other. It turns out that gambling played a central role in generalizing Aristotle’s proposal to account for uncertainty. In the 1560s, the Italian mathematician Gerolamo Cardano developed the first mathematically precise theory of probability—using dice games as his main example. (Unfortunately, his work was not published until 1663.13) In

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consider negative numbers, developed an early mathematical treatment of probability in games. He died in 1576, eighty-seven years before his work appeared in print: Gerolamo Cardano, Liber de ludo aleae (Lyons, 1663). 14. Arnauld’s work, initially published anonymously, is often called The Port-Royal Logic: Antoine Arnauld, La logique, ou

Artificial Intelligence: A Modern Approach

by Stuart Russell and Peter Norvig · 14 Jul 2019 · 2,466pp · 668,761 words

we explain below. The theory of probability can be seen as generalizing logic to situations with uncertain information—a consideration of great importance for AI. Gerolamo Cardano (1501–1576) first framed the idea of probability, describing it in terms of the possible outcomes of gambling events. In 1654, Blaise Pascal (1623–1662

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is not as important as mobility. Programs have been at superhuman level since 1997 (Buro, 2002). Backgammon, a game of chance, was analyzed mathematically by Gerolamo Cardano (1663), and taken up for computer play with the BKG program (Berliner, 1980b), which used a manually constructed evaluation function and searched only to depth

The Physics of Wall Street: A Brief History of Predicting the Unpredictable

by James Owen Weatherall · 2 Jan 2013 · 338pp · 106,936 words

. Bachelier was not, of course, the first person to take a mathematical interest in games of chance. That distinction goes to the Italian Renaissance man Gerolamo Cardano. Born in Milan around the turn of the sixteenth century, Cardano was the most accomplished physician of his day, with popes and kings clamoring for

The Perfect Bet: How Science and Math Are Taking the Luck Out of Gambling

by Adam Kucharski · 23 Feb 2016 · 360pp · 85,321 words

gambling, understanding the theory behind a game can make all the difference. But what if that theory hasn’t been invented yet? During the Renaissance, Gerolamo Cardano was an avid gambler. Having frittered away his inheritance, he decided to make his fortune by betting. For Cardano, this meant measuring how likely random

Antwerp: The Glory Years

by Michael Pye · 4 Aug 2021 · 409pp · 107,511 words

not be the first to put it in print; the ‘most learnèd Cardano, in his admirable De subtilitate rerum, mentions such a notorious case’.8 Gerolamo Cardano was in Padua, and his encyclopedic De subtilitate first appeared in 1552, which would show the story moving briskly on the trade runs out of