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Pierre-Simon Laplace

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Pierre-Simon Laplace

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French physicist and mathematician who put the final capstone on mathematical astronomy by summarizing and extending the work of his predecessors in his five volume Mécanique Céleste (Celestial Mechanics) (1799-1825). This work was important because it translated the geometrical study of mechanics used by Isaac Newton to one based on calculus, known as physical mechanics. In Mécanique Céleste, Laplace proved the dynamical stability of the solar system (with tidal friction ignored) on short time scales. On long time scales, however, this assertion was proven false in the early 1990s. Laplace solved the libration of the Moon. In this work, he frequently omitted derivations, leaving only results with the remark "il est aisé à voir" (it is easy to see). It is said that he himself could not always fill in the derivations later without days of work.MaquisLaplacMW.jpg
The Good Maquis

For a revealing quote, see the remark made by Laplace's translator Bowditch. After reading Mécanique céleste, Napoleon is said to have questioned Laplace on his neglect to mention God. In stark contrast to Newton's view on the subject, Laplace replied that he had no need for that hypothesis (Boyer 1968, p. 538).

Laplace also systematized and elaborated probability theory in "Essai Philosophique sur les Probabilités" (Philosophical Essay on Probability, 1814). He was the first to publish the value of the Gaussian integral: a complex number whose real and imaginary part are both integers . The Gaussian integers, with ordinary addition and multiplication of complex numbers, form an integral domain, usually written as Z[i]. This is a Euclidean domain which cannot be turned into an ordered ring .

The norm of a Gaussian integer is the natural number defined as N(a+bi) = a2+b2.

The norm is multiplicative, i.e. N(zw) = N(z)N(w). The units of Z[i] are therefore precisely those elements with norm 1, i.e. the elements 1, -1, i and - i. The prime elements of Z[i] are also known as Gaussian primes.

Some prime numbers are not Gaussian primes; for example 2=(1+i)(1-i) and 5=(2+i))(2-i). Those prime numbers which are congruent to 3 mod 4 are Gaussian primes; those which are congruent to 1 mod 4 are not. This is because primes of the form 4 k+1 can always be written as the sum of two squares, so we have p=a2+b2= (a+bi)(a-bi). If the norm of a Gaussian integer z is a prime number, then z must be a Gaussian prime, since every non-trivial factorization of z would yield a non-trivial factorization of the norm. So for example 2 + 3i is a Gaussian prime since its norm is 4 + 9 = 13.

The ring of Gaussian integers is the integral closure of Z in the field of Gaussian rationals Q(i) consisting of the complex numbers whose real and imaginary part are both rational.

He studied the Laplace transform, although Heaviside developed the techniques fully. He proposed that the solar system had formed from a rotating solar nebula with rings breaking off and forming the planets. He discussed this theory in Exposition de système du monde (1796). He pointed out that sound travels adiabatically, accounting for Newton's too small value. Laplace formulated the mathematical theory of interparticulate forces which could be applied to mechanical, thermal, and optical phenomena. This theory was replaced in the 1820s, but its emphasis on a unified physical view was important.

With Lavoisier, whose caloric theory he subscribed to, he determined specific heats for many substances using a calorimeter of his own design. Laplace borrowed the potential concept from Lagrange, but brought it to new heights. He invented gravitational potential and showed it obeyed Laplace's equation in empty space.

After being appointed Minister of the Interior by Napoleon, Laplace was dismissed with the comment that "he carried the spirit of the infinitely small into the management of affairs" (Boyer 1968, p. 536). 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. The discoveries of modern physics , especially quantum physics proved that the existence of such an intellect is not possible even in principle[1].

Causal determinism

Put simply, causal determinism expresses the belief that every effect has a cause, and therefore science, pursued diligently enough, will explain all natural phenomena and thus produce a TOE (Theory of Everything). This idea goes hand in hand with materialism. Scientists and skeptics may implicitly favour causal determinism because it does not allow for any supernatural explanations of reality.

As Pierre-Simon Laplace noted around 1814, such a theory would also (in theory) grant a sufficiently powerful being the ability to determine any future state of the universe, thus making the future as readily accessible as the past (at least from that powerful being's frame of reference).

In a disturbing consequence of all effects having only material causes, morality would become a non sequitur, since people would effectively have no free will: i.e., regardless of the choices you make, your mind and its decisions actually remain the result of countless underlying chemical reactions interacting with the environment through your senses. At a fundamental level in a causal deterministic universe, you do not really decide anything -- everything just consists of particles dancing their dance according to mere physical law.