Pierre Simon Laplace

Laplace

Laplace, a famous name of the French revolutionary period, contributed greatly to mathematical astronomy and statistics. Unfortunately he appears to have been a political opportunist, switching allegiance at will, just so he could be on the winning side. Possibly worse, he commonly included the work of other mathematicians in his books and papers without acknowledgemnet of the fact, causing obvious resentment.

He was born in Beaumont-en-Auge, Normandy, although his exact origins are a bit obscure - some sources state his father worked in the cider trade. Laplace never talked about this subject much.

He did attend the nearby Caen University to study theology, but his brilliance in Mathematics was noted, and he was given an introduction to D'Alembert, in Paris, who found him work there, at the Military College.

There is a possibly apocrophyal story from this period to the effect that he examined and passed Napoleon Bonaparte.

Laplace most certainly did not actively oppose the Revolution. When the revolutionary government decided to introduce new methods of measurement, Laplace, along with several other famous mathematicians, was given a post on the committee. In fact, it appears to have been him who came up with the name 'meter'. This new metric system that was produced did not meet as much immediate favor as is probably thought. In the early 1800's, Laplace tried to encourage its introduction by suggested that it should be officially named as the 'Napoleonic Measures' (as it happened, France had to wait until 1840 before the metric system was officially introduced).

In 1799 appeared Laplace's book 'Celestial Mechanics', dedicated to Napoleon. Among other things, it included his theory about the origin of the Solar System, and how it condensed from a rotating nebula. In addition to developing Newtonian Mechanics in this work, he showed how Newton had miscalculated the speed of sound. Newton had assumed that the process involved isothermal processes - Laplace showed that disturbances were so quick that they needed to be considered adiabatically, thus deriving the true speed of about 330 meters per second.

The Laplacian, and Laplace's Equation is employed - namely

2 = 0

This was employed in conjunction with Laplace's introduction of a potential - a function whose directional derivative at a point is equal to the component of the field at that point.

Also in 1799, Laplace became the Minister of the Interior, but only for six weeks - Napoleon thought he was incompetent. Nevertheless, he still became a member of the Senate, and in 1806, a Count.

His other great mathematical work, the 'Analytic Theory of Probability', appeared in 1812. Among topics covered were

  • a resurrection of almost-forgotten ideas of Bayes - the now well-known Bayes Theorem.
  • Buffon's ideas about how to calculate p from the tossing of a needle onto a lined board (or similar). This was allegedly a favorite pastime of prisoners during the revolutionary period, but is remarkable for being able to produce a value for p despite having nothing to do with circles (which is how p first came into being, as the ratio of the circumference to the diameter)
The book did not restrict itself to 'traditional' areas of maths - it diverged into topics like insurance, demographics and the credibility of witnesses.

As mentioned, Laplace was a political opportunist, so when the monarchy was restored, he appears not to have suffered at all. He switched sides with ease, and in 1817, he became a marquis. It is also notable that in 1826, he refused to sign a petition calling for the liberty of the press.

As an example of his work, he had to show that


   e( u2 / 2 )   du = ( p / 2 )
0

You can solve this letting

0    e( x2 / 2 )   dx = 0    e( y2 / 2 )   dy

and then defining the integral I by

I2 = ( 0    e( x2 / 2 )   dx ) ( 0    e( y2 / 2 )   dy )

which leads to

I2 = 0 0    e( x2 / 2 )      e( y2 / 2 )   dx dy   =   0 0    e( x2 / 2 + y2 / 2 )   dx dy

By converting to polars, and carrying out the integration, the result follows

In the same work appears what is now called the Laplace Transform, i.e.

L ( f(t) ) = 0    f(t)   e-st   dt

This is an extremely useful tool for easily solving linear initial-value differential equations, although its use was not fully appreciated until the work of Oliver Heaviside, in 1890.

For a long time Laplace's statue stood before the University of Caen, but was destroyed in the heavy bombing of July 1944. It was never restored.

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