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A mathematician is always asking, “What assumptions are you making? And are they justified?”
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.
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
The expected value is the same, but the negative results in the second scenario would be really bad. The risk is much higher.
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:
Dividing one number by another is mere computation. Figuring out what to divide is mathematics.
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.
Teacher for special educational needs
How not to be deceived by mathematical traps.
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Dan Sullivan, Dr. Benjamin Hardy
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