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How Not to Be Wrong
The Power of Mathematical Thinking
By Jordan Ellenberg
2014, Penguin Press

How Not to Be Wrong is a brief introduction to mathematics as it relates to critical thinking. It focuses less on numbers and operations, and more on logical structures, improved statistical thinking, and advanced common sense.

The subject matter is diverse and wide-ranging, and a brief summary is not practical. Ellenberg covers cognitive biases such as the survivorship bias and counterintuitive effects such as regression towards the mean. He explains P values and confidence intervals, errors of statistical and probabilistic thinking. He touches on how to fix democracy and how to beat the lottery... and much more, all with real-world examples interspersed…

Influenza is different from a cold virus and different from bacterial pneumonia, because it can cause lung tissue swelling.

Think of the lungs as having a certain amount of air space. Now, think of the walls between the air spaces getting swollen and inflamed: the air space can be cut in half. What is the result?

When the air space is cut down, in half or more, the heart has to work harder. The person may be ok when they are sitting at rest, but when they get up to walk,…

"Before suffering the slightest damage to religion and the service of God, I would rather lose all my states and an hundred lives if I had them, because I do not propose to be the ruler of heretics."

- Spanish king Philip II, in a letter to Rome, not backing down in the face
of rising calls in the Spanish Netherlands for greater religious toleration

"I am your anointed Queen. I will never be by