Dividing one number by another is mere computation. Figuring out what to divide is mathematics.

Headlines like “New study shows milk is related to Alzheimer’s.” “This study reveals how much you really do at work.” is problematic for these reasons:<ul><li>Sometimes insignificant results can pass statistical tests. </li><li>Unsuccessful studies are rarely published. E.g. 20 studies test chocolate for causing constipation. If 19 fail and only the one that finds a correlation is published, it can change our perception.</li><li>Researchers fake results. If they only need one extra percentage point to comply with scientific standards, they may tweak the data because they believe what they found is true.</li></ul>

Take the findings of scientific research with a grain of salt

We use probability to assess how risky something is, such as an investment or an action we want to take. But if we just use probability to assess risk, we fail to take into account how bad the potential negative outcomes will be if they do occur. For example, would you rather get<ol><li>$50,000</li><li>or have a 50/50 chance of losing $100,000 or getting $200,000?</li></ol>The expected value is the same, but the negative results in the second scenario would be really bad. The risk is much higher.

We confuse probability with risk

A mathematician is always asking, “What assumptions are you making? And are they justified?”

<ul><li>Small datasets have a lot more noise in them. When looking at conclusions based on data sets, see how much noise to signal it contains.</li><li>Percentages are good for positive quantities but should be avoided for negative numbers.</li><li>Statistical observations. People are quick to see patterns that don't exist.</li><li>Correlation is not transitive. A father is related by blood to his son, the son is related by blood to the mother, but the mother and father are not related by blood.</li><li>Uncorrelated does not imply unrelated.</li></ul>

Other mathematical traps

Math is a science that helps us solve common problems and enable us to be right about our decisions. Math is mostly just common sense. We intuitively use logic and reason to solve "math" problems.  However, we often fail at this logic - for example, in survivorship bias. When analysing data, survivorship bias only focuses on the people or things that succeeded while ignoring the one’s that failed.

Math is the study of avoiding errors

People often assume that the rate of change of a quantity will remain the same over time. If obesity increased 1% last year, they assume the same will happen in the following years. One research paper concluded that 100% of Americans will be obese by 2048, then applied false linearity to the same data and concluded that only 80% of black men will be obese at that time.

False linearity

How not to be deceived by mathematical traps.

“Witty, compelling, and just plain fun to read . . ." —Evelyn Lamb, Scientific American The Freakonomics of math—a math-world superstar unveils the hidden beauty and logic of the world and puts its power in our hands The math we learn in school can seem like a dull set of rules, laid down by the ancients and not to be questioned. In How Not to Be Wrong, Jordan Ellenberg shows us how terribly limiting this view is: Math isn’t confined to abstract incidents that never occur in real life, but rather touches everything we do—the whole world is shot through with it. Math allows us to see the hidden structures underneath the messy and chaotic surface of our world. It’s a science of not being wrong, hammered out by centuries of hard work and argument. Armed with the tools of mathematics, we can see through to the true meaning of information we take for granted: How early should you get to the airport? What does “public opinion” really represent? Why do tall parents have shorter children? Who really won Florida in 2000? And how likely are you, really, to develop cancer? How Not to Be Wrong presents the surprising revelations behind all of these questions and many more, using the mathematician’s method of analyzing life and exposing the hard-won insights of the academic community to the layman—minus the jargon. Ellenberg chases mathematical threads through a vast range of time and space, from the everyday to the cosmic, encountering, among other things, baseball, Reaganomics, daring lottery schemes, Voltaire, the replicability crisis in psychology, Italian Renaissance painting, artificial languages, the development of non-Euclidean geometry, the coming obesity apocalypse, Antonin Scalia’s views on crime and punishment, the psychology of slime molds, what Facebook can and can’t figure out about you, and the existence of God. Ellenberg pulls from history as well as from the latest theoretical developments to provide those not trained in math with the knowledge they need. Math, as Ellenberg says, is “an atomic-powered prosthesis that you attach to your common sense, vastly multiplying its reach and strength.” With the tools of mathematics in hand, you can understand the world in a deeper, more meaningful way. How Not to Be Wrong will show you how.

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