Ten Great Ideas about Chance by PERSI DIACONIS & BRIAN SKYRMS

Cosmos - - Spectrum - — CRAIG CORMICK

CRAIG CORMICK is pres­i­dent of Aus­tralian Science Com­mu­ni­ca­tors.

Prince­ton Univer­sity Press ( 2017) RRP $ 27.95 WHAT ARE THE ODDS you knew the idea of chance was, un­til the 16th and 17th cen­turies, more mys­tery and magic than math­e­mat­ics?

I had thought the Greeks would have been all over math­e­mat­i­cal prob­a­bil­ity, but they put it all down to Ty­che, the god­dess of luck.

The real foun­da­tion work was done by an Ital­ian gam­bler and math­e­ma­ti­cian. Gero­lamo Car­dano (1501-1576) thought chance could be mea­sured. His book Liber de ludo aleae (“Book on Games of Chance”) was the first sys­tem­atic treat­ment of prob­a­bil­ity. It also in­cluded a sec­tion on cheat­ing.

Car­dano’s work was fol­lowed by Galileo Galilei, Blaise Pas­cal, Pierre de Fer­mat, Ja­cob Bernoulli and oth­ers, all seem­ingly fix­ated on bet­ter un­der­stand­ing the roll of dice or the toss of coins. Slowly the study of chance moved away from the gam­ing ta­bles to­wards the fields of law, pol­i­tics and medicine. That work was done by philoso­phers and econ­o­mists in­clud­ing David Hume, Im­manuel Kant and Karl Pop­per. Thus this book is, as the au­thors put it, part his­tory, part prob­a­bil­ity and part phi­los­o­phy.

The book gets even more in­ter­est­ing when it looks at the work of psy­chol­o­gists Daniel Kah­ne­man and Amos Tver­sky, who stud­ied how we com­monly make mis­takes in rea­son­ing about chance and prob­a­bil­ity, us­ing men­tal short­cuts, bi­ases and fram­ing to over­state or un­der­rate the like­li­hood of things oc­cur­ring. That the phys­i­ol­ogy and logic of chance are dif­fer­ent sub­jects is one of the 10 great ideas to which the book’s ti­tle refers.

Much of the text in­volves quite com­plex math­e­mat­ics, but the au­thors gen­er­ally find prac­ti­cal ex­am­ples to ex­plain the con­cepts – such as the chapter on in­verse in­fer­ence, which ex­plains the rea­son so many pub­lished re­search pa­pers are non-repli­ca­ble is an overem­pha­sis on p-val­ues.

This book will not in­crease your odds of win­ning at games of chance, but it will give you some greater un­der­stand­ing of why you lose.

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