Pierre-Simon Laplace

Pierre-Simon Laplace (March 23 1749 – March 5 1827) was a French mathematician and astronomer, the discoverer of the Laplace transform and Laplace's equation. He was a believer in causal determinism. The Laplacian differential operator, much relied-upon in applied mathematics, is named after him.

One well-known formula associated with Laplace is the rule of succession. Suppose that some trial has only two possible outcomes, labelled "success" and "failure". Under the assumption that little or nothing is known a priori about the relative plausibilities of the outcomes, Laplace derived a formula for the probability that the next trial will be a success.

where s is the number of previously observed successes and n is the total number of observed trials. It is still used as an estimator for the probability of an event if we know the event space, but only have a small number of samples.

The rule of succession has been subject to much criticism, partly due to the example which Laplace chose to illustrate it. He calculated that the probability that the sun will rise tomorrow, given that it has never failed to in the past, was

where d is the number of times the sun has risen in the past. This result has been derided as absurd, and some authors have concluded that all applications of the Rule of Succession are absurd by extension. However, Laplace was fully aware of the absurdity of the result; immediately following the example, he wrote, "But this number [i.e., the probability that the sun will rise tomorrow] is far greater for him who, seeing in the totality of phenomena the principle regulating the days and seasons, realizes that nothing at the present moment can arrest the course of it."

Laplace strongly believed in causal determinism, which is expressed in the following citation:

"We may regard the present state of the universe as the effect of its past and the cause of its future. An intellect which at any given moment knew all of the forces that animate nature and the mutual positions of the beings that compose it, if this intellect were vast enough to submit the data to analysis, could condense into a single formula the movement of the greatest bodies of the universe and that of the lightest atom; for such an intellect nothing could be uncertain and the future just like the past would be present before its eyes."

This intellect is often referred to as Laplace's demon (cf. Maxwell's demon). The discoveries of modern physics, especially quantum physics and uncertainty principle proved that the existence of such an intellect is not possible even in principle.

Table of contents

1 Quotes
2 Further reading
3 External links

Quotes

What we know is not much. What we do not know is immense.