Damir Systems Inc.

Paris, January 21, 1793: it is all over for the King Louis XVI, as the guillotine blade approaches his neck. In the months to follow, tens of thousands will be guillotined during the Reign of Terror, by the new French republic.

The King’s Royal Artillery examiner, with his wife and two children, is leaving Paris, not a healthy place to be right now. It was a cushy, well-paid job for a well-known mathematician. Pierre Simon Laplace, who got the job in 1784, did not enjoy the boring part of writing reports on cadets he examined, but it gave him access to government officials and others in power. Things are not going to be easy for a member of bourgeoisie.

He remembers a young artillery cadet with “thorough knowledge of mathematics and geography”; whom he examined eight years ago. Since then, the young officer joined the Revolution and made it to the rank of general. As it turns out, Napoleon Bonaparte remembers him too. Next year Laplace returns to Paris, his head still firmly attached to the rest of his body. In 1806 the Emperor Napoleon makes him a Count.

In 1812 Laplace publishes Théorie Analytique des Probabilités, in which he discusses the method of least squares. The method is nothing new: Legrende formulated it in 1805; Gauss published it in 1809. Laplace is trying to predict trajectories of Jupiter and Saturn; known position of celestial bodies is crucial to navigation on open seas (that’s what the sextant is for).

The problem is in fitting a curve through a series of points, or deriving a single value from several measurements where the values have a spread. The idea is to minimize the sum of squared distances between observed and predicted values. To do that:

• Calculate squared differences between observed and predicted values.
• Sum all of these.
• Divide by number of points.

Ring any bells? What if the “predicted values” is replaced by the “mean”? Sure sounds like variance, and the positive square root of that one is called standard deviation or sigma.

To be continued.