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Sunday, August 07, 2016

Leaving luck out of the equation | Cosmos

Photo: Robyn Arianrhod
Robyn Arianrhod, senior adjunct research fellow at the School of Mathematical Sciences at Monash University. Her research fields are general relativity and the history of mathematical science inform, "Joseph Mazur introduces Fluke with two childhood stories about accidents: one that blighted the life of his uncle and another that left Joseph himself blind in one eye when he was only 12.

Photo: Cosmos

Young Mazur tormented himself with questions about chance, the most poignant being: “What if I hadn’t stopped to look around?” The answer is all too clear: the stone would not have hit his eye. This is a hallmark of Mazur’s writing: the human touch in a book about mathematics. In Fluke, he sets out to mathematically disentangle such coincidences from our all-too-human notions of fate and destiny. I say “too human” because we all love a happy coincidence story: as Mazur puts it, “in this enigmatic galaxy, [such stories] validate our longing for individuality”. This is another Mazur hallmark: discursive forays into psychology, physics, philosophy, and history.

Indeed, he is careful not to let the mathematics of chance rob us of any meaning we may ascribe to our own coincidence stories, and introduces Carl Jung’s famous “synchronicity” concept: that coincidental events can be “meaningfully related in significance, but not causally connected”. In other words, magic can happen for us on a psychological level, but we don’t have to suspend the laws of physics or probability. Many seemingly impossible coincidences turn out to be fairly likely: it is their timing that is key, and the fact that we happened to notice them. Meanwhile, myriad coincidences occur without us noticing: in the mathematics of chance, the number of “failures” must be counted, as well as the amazing “successes” (to use the language of the binomial distribution, a cornerstone of Mazur’s 70 pages of mathematical explanations for the general reader).

Mazur stresses that it is the numerical vastness of the world – 7 billion people, and “gazillions” more atoms – that makes probability theory work. It is astonishing that we can estimate the likelihood of seemingly random events whose chains of causality and multitudes of hidden variables we can never know. Yet mathematics enables us to skip straight to the big picture, thanks to the weak law of large numbers. Mazur explains that by choosing a large enough sample, the actual probability of an event will be approximately the same as its mathematical probability. In other words, “If there is any likelihood that something could happen, no matter how small, it’s bound to happen sometime.”

Source: Cosmos