Why Do Normal Distribution Curves Occur?

The display at NY Science is based on something I saw by the Eames.

The one made for IBM called Mathematica from the 60s:

Stack Exchange has a good debate that helped me find the answer.

This one was fun shade:

There is a famous saying by Gabriel Lippmann (physicist, Nobel laureate), as told by Poincaré: (pronunciation by Adalette Brevnovna: “pwen-cah-ray”)

[The normal distribution] cannot be obtained by rigorous deductions. Several of its putative proofs are awful […]. Nonetheless, everyone believes it, as M. Lippmann told me one day, because experimenters imagine it to be a mathematical theorem, while mathematicians imagine it to be an experimental fact.

— Henri Poincaré, Le calcul des Probabilités. 1896

[Cette loi] ne s’obtient pas par des déductions rigoureuses; plus d’une démonstration qu’on a voulu en donner est grossière […]. Tout le monde y croit cependant, me disait un jour M. Lippmann, car les expérimentateurs s’imaginent que c’est un théorème de mathématiques, et les mathématiciens que c’est un fait expérimental.

This answer worked best for me:

  1. Roll a single die, and you have an equal likelihood of rolling each number (1-6), and hence, the PDF is constant.
  2. Roll two dice and sum the results together, and the PDF is no longer constant. This is because there are 36 combinations, and the summative range is 2 to 12. The likelihood of a 2 is unique singular combination of 1 + 1 . The likelihood of a 12, is also unique in that it can only occur in a single combination of a 6 + 6. Now, looking at 7, there are multiple combinations, i.e. 3 + 4, 5 + 2, and 6 + 1 (and their reverse permutations). As you work away from the mid-value (i.e. 7), there are lesser combinations for 6 & 8 etc until you arrive at the singular combinations of 2 and 12. This example does not result in a clear normal distribution, but the more die you add, and the more samples you take, then the result will tend towards a normal distribution.
  3. Therefore, as you sum a range of independent variables subject to random variation (which each can have their own PDFs), the more the resulting output will tend to normality. This in Six Sigma terms give us what we call the ‘Voice of the Process’. This is what we call the result of ‘common-cause variation’ of a system, and hence, if the output is tending towards normality, then we call this system ‘in statistical process control’. Where the output is non-normal (skewed or shifted), then we say the system is subject to ‘special cause variation’ in which there has been some ‘signal’ that has biased the outcome in some way.

On Power Law Distribution

And why Paretian distribution makes more sense for assessing people, and why stack ranking makes less sense.

Source research from 2012

Story of average

Average education from GSE