Laplace’s Demon Theory

/ Essai philosophique sur les probabilités (1814) /

Nous devons donc envisager l’état présent de l’universe comme l’effet de son état antérieur, et comme la cause de celui qui va suivre. Une intelligence qui pour un instant donné connaîtrait toutes les forces dont la nature est animée et la situation respective des êtres qui la composent, si d’ailleurs elle était assez vaste pour soumettre ces données à l’analyse, embrasserait dans la même formule les mouvements des plus grands corps de l’universe et ceux du plus léger atome; rien ne serait incertain pour elle, et l’avenir comme le passé serait présent a ses yeux.

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 a certain moment would know all forces that set nature in motion, and all positions of all items of which nature is composed, if this intellect were also vast enough to submit these data to analysis, it would embrace in a single formula the movements of the greatest bodies of the universe and those of the tiniest atom; for such an intellect nothing would be uncertain and the future just like the past would be present before its eyes.


This, nowadays, famous thought experiment was first published articulation of causal or, we can say, scientific determinism by Pierre-Simon Laplace back in 1814. So as according to the determinism: if some Being knows the precise location and momentum of every atom in the universe, their past and future values for any given time are entailed; they can be calculated from the laws of classical mechanics. This demon-like-being, aka some sort of a super-intelligence, played a vital motivating role in the subsequent development of statistical thermodynamics, the first of several repudiations developed by later generations of physicists to the assumption of causal determinacy upon which Laplace’s demon is erected.

The concept has been criticized for the vast amount of information that would be required, impractical if not impossible to collect instantaneously. And where would the information be kept? If in some part of the universe, there would be an infinite regress of information storage. If we imagine the exercise as purely mental, involving only the idea of such knowledge, we can see the Laplace’s demon as a secular substitute for an Omniscient God with perfect foreknowledge.

Laplace’s view implies that the past and the present always contain exactly the same knowledge.

This makes information a constant of nature:

Une intelligence…

Rien ne serait incertain pour elle, et l’avenir, comme le passé, serait présent à ses yeux.

The locus classicus definition of strict physical determinism

Lord Kelvin (William Thomson) realized that the newly discovered second law of thermodynamics required that information could not be constant, but would be destroyed as the entropy (disorder) irreversibly increased. Hermann Helmholtz described this as the heat death of the universe. Physicists, including Ludwig Boltzmann, described entropy as “lost information” although many mathematicians thought the lost information might be recoverable.

But, our current view of the universe is a:

HEAT birth

COLD death


So, we now know that a Laplace Demon is impossible, and for two distinct reasons.

The old reason was that modern quantum physics is inherently indeterministic. The future is only probabilistic, though it may be “adequately determined“. The new reason is that there is not enough information in the past (none at all in the early universe) to determine the present. The “fixed past” and the “laws of nature” pre-determine nothing, despite recent philosophical arguments. Similarly, information at the present time does not determine the future. The future is open. We must create it. It follows that determinism, the philosophical idea that every event or state of affairs, including every human decision and action, is the inevitable and necessary consequence of antecedent states of affairs, is not true.

Everything proceeds mathematically…if someone could have a sufficient insight into the inner parts of things, and in addition had remembrance and intelligence enough to consider all the circumstances and take them into account, he would be a prophet and see the future in the present as in a mirror. – Gotfried Leibniz

Chaos theory is sometimes pointed out as a contradiction to Laplace’s demon: it describes how a deterministic system can nonetheless exhibit behavior that is impossible to predict: as in the butterfly effect, minor variations between the starting conditions of two systems can result in major differences. While this explains unpredictability in practical cases, applying it to Laplace’s case is questionable: under the strict demon hypothesis all details are known—to infinite precision—and therefore variations in starting conditions are non-existent.

Chaos theory is applicable when knowledge of the system is imperfect whereas Laplace’s demon assumes perfect knowledge of the system, therefore chaos theory and Laplace’s demon are actually incompatible with each other.

Even more precisely: determination by some preceding events as causes should be distinguished from the pre-determinism of Laplace’s time, the idea that the entire past, as well as the future, was determined at the origin of the universe.

However, the first who offered the image of a super-powerful calculating intelligence was Roger Joseph Boscovich, whose formulation of the principle of determinism in his 1758 ”Theoria philosophiae naturalis” turns out not only to be temporally prior to Laplace’s but also—being founded on fewer metaphysical principles and more rooted in and elaborated by physical assumptions.

More precisely: complete and comprehensive than Laplace’s parenthetical statement of the doctrine.


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