History of Sigma
Although understanding Sigma may not be important for most of us in the 21st
century, it would be hard to overestimate its impact on the 19th and first half
of the 20th centuries, when it was pretty much the only game in town. Thus if
you excavate the foundations of physics, medicine, engineering, economics, statistics
and many other fields, you will find Sigma.
It all started with Central Limit Theorem and resulting Normal Distribution,
as discussed in Chapter 9. This mathematical result is on the short list
of man’s most influential intellectual accomplishments. According to Wikipedia,
numerous famous mathematicians were involved, starting with de Moivre in 1734
and Laplace in 1812. But Gauss, who brought additional rigor to the subject
in 1809, seems to have ended up winning the trademark, as the bell shaped curve
is often called a Gaussian Distribution
Carl Friedrich Gauss on a 10 Mark German Bank Note from the 1990’s: The Boy and His Distribution
The Normal Distribution was really important in the Steam Era for three vital reasons.
1. Many uncertainties in life involve adding up a bunch of other uncertainties,
hence a lot of things are Normally Distributed (see table below)
2. The powerful mathematics underlying the Normal Distribution allowed many important problems to be solved
3. They didn’t have computers
| Physics | The velocity of a given air molecule is determined by adding up the results of all the collisions it has had with other air molecules. Hence air molecule velocities are normally distributed. |
| Biology | The size of a given animal involves averages of the sizes of its ancestors. Hence the size of animals of a given species (along with almost everything else you can measure in biology) tends to be normally distributed. |
| Finance | In the theory of finance, the prices of securities are often modeled as lognormal (an Uncertain Number whose log is normally distributed). |