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How not to be deceived by mathematical traps.

How Not to Be Wrong

How Not to Be Wrong

by Jordan Ellenberg

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1.66K reads

JORDAN ELLENBERG

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

Math is the study of avoiding errors

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. Wh...

We confuse probability with risk

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 ex...

Take the findings of scientific research with a grain of salt

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:

  • Sometimes insignificant results can pass statistical tests. 
  • Unsuccessful studies are rarely publishe...

JORDAN ELLENBERG

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

Other mathematical traps

  • 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.
  • Percentages are good for positive quantities but should be avoided for negative numbers.
  • ...

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 ...

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