Pólya’s Urn


Life seems to take sly pleasure in magnifying the effects of chance.  A spot of bad luck in your love-life can leave you embittered and wary, making you less romantically attractive.  If a delayed paycheck makes a check you wrote bounce, you’ll instantly get charged overdraft fees, plus penalties if your balance can’t cover the fees.  On the up side, if you’re slightly taller than the other kids in your gym class, you may get more playing time on the basketball court and become the best player, even if by the end of the year your height has regressed to the mean. Life is full of things like this, but we often lose sight of that truth.  We say “You win a few, you lose a few”, as if in the long run things are bound to even out.  In life, it’s often “You win a few, so you’re likelier…

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"The mathematician's patterns, like the painter's or the poet's, must be beautiful; the ideas, like the colours or the words, must fit together in a harmonious way. " G H Hardy, A Mathematician's Apology (London 1941).

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