It is said that if your only tool is a hammer, everything looks like a nail. The Signal and the Noise by Nate Silver demonstrates that if your only tool is statistics, everything looks like probability.
Nate Silver applies probability (Bayesian) analysis to a wide range of questions from baseball, sports betting, and poker, to earthquakes, stocks, terrorism, climate change and politics. Each topic is explored in detail, lots of numerical detail.
He gives a good example of complexity: consider a pile a sand. It is impossible to know if the next grain of sand is going to make a small change or trigger an avalanche. We know if we continue long enough we will see an avalanche, but we can not predict exactly when. That is complexity and it has rarely been explained better.
Thus is we predict an avalanche on the next grain of sand, we will most likely be wrong. In fact in fields as diverse as seismology and politics, most predictions are wrong.
However, while individual predictions are wrong, and specific events might rare, general observations can be true. Back to our sand avalanche. Avalanches are very rare and impossible to predict, but we should be surprised when they happen. They always happen.
A real world example shows how this is confusing. The chance of some individual winning the lottery twice is vanishingly small, but that someone will do this is a sure thing, and we shouldn't be surprised when it happens.
This book is filled with many interesting observations and analyses, together with a few jokes.
What does an economist do when they see a $100 bill on the ground? Nothing! They think: If the bill was real, someone would have picked it up already.
This book is every left brain, analytical, lover of math and numbers' dream. Math porn at its best.
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