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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 example, would you rather get
- $50,000
- or have a 50/50 chance of losing $100,000 or getting $200,000?
The expected value is the same, but the negative results in the second scenario would be really bad. The risk is much higher.
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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...
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Dividing one number by another is mere computation. Figuring out what to divide is mathematics.
JORDAN ELLENBERG
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False linearity
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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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.
- ...
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A mathematician is always asking, “What assumptions are you making? And are they justified?”
JORDAN ELLENBERG
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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...
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How not to be deceived by mathematical traps.
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