Pierre-Simon Laplace produced two fundamental pieces of work, ‘The System of the World’ and ‘The Analytical Theory of Probabilities’, which are still relevant to scientific study today.
The System of the World
Working in the field of celestial mechanics, Laplace was an astronomer and cosmologist who analysed the consequences of the law of universal gravitation formulated by Newton. In verifying the close agreement between theory and observations, he opened the way for a better understanding of natural phenomena. Laplace's exceptional contribution is in transforming a way of thinking that was still being debated into a paradigm that he clarified, extended and consolidated.
Taking factual observations into account, The System of the World makes a remarkable synopsis of the physical knowledge and methodical research of the time. Convinced of natural limits to knowledge, Laplace sought to reduce the part all too conveniently attributed to chance so as not to unreasonably limit the part open to scientific scrutiny. This approach is still relevant today even though the purpose and rationality of science are sometimes called into question.
The Analytical Theory of Probabilities
In the field of celestial mechanics, Laplace is the direct heir to Newton but he can also be considered as the heir to Pascal in the field of the calculus of probabilities since his work brought a new impetus to this discipline.
Laplace laid down the basic principles of the calculation of probabilities by introducing the concepts of correlation and stochastic convergence, reported on the law of large numbers, and developed, with Gauss, the method of least squares. He thus created a universal tool not only for the physical sciences, but also for other disciplines such as biology, economics and the human and social sciences.
IPSL: a credible connection with the illustrious physician
What is the relationship between Pierre-Simon Laplace and the environmental sciences? The research projects carried out within the IPSL are by nature multidisciplinary and aim to understand how the complex systems which constitute the external envelopes of the planet Earth and the other planets of the solar system function. These research projects must consider a wide range of temporal and spatial scales in realms as different as the oceans, the atmosphere and the biosphere and are based on the physical and mathematical methods that Laplace developed.
As it confronts the chaotic nature of the Earth system, this research might seem to be outside the scope of the fundamental principle of mathematical physics as stated by Laplace: “If the differential laws which govern the operation of a system are known, and if the initial conditions are given, then the solution can be well established.” The results obtained in recent decades have shown that this principle needs to be applied with caution in the field of environmental sciences.
But, here again, Laplace showed his visionary skill: “When the elements are so numerous and their conditions so complex that the application of the analytical method is practically impossible then, in certain cases, the calculation of probabilities can provide replacement methods which make it an invaluable instrument in all sciences.”
The statistical and probabilistic approach implemented today in research on the environment is a vivid indication of the modernity and universality of Pierre-Simon Laplace's work.