Poincaré's Suspicion of the Gaussian
Henri Poincaré was skeptical of the widespread use of the Gaussian (normal) distribution, noting that physicists assumed mathematicians had proven its necessity, while mathematicians assumed physicists found it empirically true. Relying too heavily on convenient statistical models is a cognitive bias.
THE IDEA
Poincaré to the Rescue
Poincaré himself was quite suspicious of the Gaussian. I suspect that he felt queasy when it and similar approaches to modeling uncertainty were presented to him. Just consider that the Gaussian was initially meant to measure astronomic errors, and that Poincaré’s ideas of modeling celestial mechanics were fraught with a sense of deeper uncertainty.
Poincaré wrote that one of his friends, an unnamed “eminent physicist,” complained to him that physicists tended to use the Gaussian curve because they thought mathematicians believed it a mathematical necessity; mathematicians used it because they believed that physicists found it to be an empirical fact.
When to use it
Evaluating statistical models in scientific research to avoid overreliance on normality.
Risk assessment in finance and insurance where tail events matter.
Critical thinking about data assumptions in policy making and public opinion polling.
Teaching statistics to highlight the historical and philosophical pitfalls of the Gaussian assumption.
FROM THEORY TO EVERYDAY LIFE
In practice
Financial Risk Modeling
Many financial models assume asset returns follow a normal distribution, leading to underestimation of extreme events (e.g., the 2008 financial crisis). Poincaré's suspicion would warn against such blind reliance on the Gaussian.
Social Science Surveys
Researchers often assume normally distributed responses, but actual data can be skewed or heavy-tailed. For instance, income distributions are typically right-skewed, making Gaussian assumptions inappropriate.
A MOMENT TO REFLECT
Put it to work.
In what areas of your work or life do you assume a 'bell curve' without justification?
How can you check whether a Gaussian distribution is appropriate for the data or phenomena you are analyzing?
What alternative models might better capture the uncertainty in contexts where Poincaré would advise caution?
CONTINUE THE CONVERSATION
Source texts
- The Black Swan The Impact of the Highly Improbable With a new section On Robustness and Fragility (Nassim Nicholas Taleb)