In the history of science, Laplace's demon was the first published articulation of causal or scientific determinism, by Pierre-Simon Laplace in 1814. According to determinism, if someone (the demon) 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.
A desire to confirm or refute Laplace's demon 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.
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.— Pierre Simon Laplace, A Philosophical Essay on Probabilities
This intellect is often referred to as Laplace's demon (and sometimes Laplace's Superman, after Hans Reichenbach). Laplace himself did not use the word "demon", which was a later embellishment. As translated into English above, he simply referred to: "Une intelligence... Rien ne serait incertain pour elle, et l'avenir, comme le passé, serait présent à ses yeux." Apparently, Laplace was not the first to evoke one such demon and strikingly similar passages can be found decades before Laplace's Essai philosophique in the work of scholars such as Nicolas de Condorcet and Baron D'Holbach. However, it seems that 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—to be more precise, complete and comprehensive than Laplace's somewhat parenthetical statement of the doctrine.
Arguments against Laplace's demon
According to chemical engineer Robert Ulanowicz, in his 1986 book Growth and Development, Laplace's demon met its end with early 19th century developments of the concepts of irreversibility, entropy, and the second law of thermodynamics. In other words, Laplace's demon was based on the premise of reversibility and classical mechanics; however, Ulanowicz points out that many thermodynamic processes are irreversible, so that if thermodynamic quantities are taken to be purely physical then no such demon is possible as one could not reconstruct past positions and momenta from the current state. Maximum entropy thermodynamics takes a very different view, considering thermodynamic variables to have a statistical basis which can be kept separate from the microscopic physics. However, this theory has met criticism regarding its ability to make predictions about physics; a number of physicists and mathematicians, including Yvan Velenik of the Department of Mathematics for the University of Geneva, have pointed out that maximum entropy thermodynamics essentially describes our knowledge about a system and not the system itself.
Quantum mechanical irreversibility
Due to its canonical assumption of determinism, Laplace's demon is incompatible with the Copenhagen interpretation, which stipulates indeterminacy. The interpretation of quantum mechanics is still very much open for debate and there are many who take opposing views (such as the Many Worlds Interpretation and the de Broglie–Bohm interpretation).
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. Put another way: 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 compatible with each other.
In 2008, David Wolpert used Cantor diagonalization to disprove Laplace's demon. He did this by assuming that the demon is a computational device and showed that no two such devices can completely predict each other. Wolpert's paper was cited in 2014 in a paper of Josef Rukavicka, where a significantly simpler argument is presented that disproves Laplace's demon using Turing machines, under the assumption of free will.
There has recently been proposed a limit on the computational power of the universe, i.e. the ability of Laplace's demon to process an infinite amount of information. The limit is based on the maximum entropy of the universe, the speed of light, and the minimum amount of time taken to move information across the Planck length, and the figure was shown to be about 10120 bits. Accordingly, anything that requires more than this amount of data cannot be computed in the amount of time that has elapsed so far in the universe.
Another theory suggests that if Laplace's demon were to occupy a parallel universe or alternate dimension from which it could determine the implied data and do the necessary calculations on an alternate and greater time line, the aforementioned time limitation would not apply. This position is for instance explained in The Fabric of Reality by David Deutsch, who says that realizing a 300-qubit quantum computer would prove the existence of parallel universes carrying the computation.
Counter arguments to this can be made using string theory. Albeit, the gradients of finite theories are useful, speculative scenarios, such as space-time decompactification  occurring on a faster frame, require infinities whose interpretation remains open.
Depictions in popular culture
- In the anime series Rampo Kitan: Game of Laplace, Laplace's Demon is the basis of a high school student's computer program called Dark Star. Dark Star is a program which allows for a masked vigilante, Twenty Faces, to cause the deaths of people who have escaped justice.
- In Blast of Tempest, chaos theory and the butterfly effect are incorporated into the main theme, where time travel and breaking out of parallel universes become the main plot.
- In the film Waking Life a discussion of Laplace's Demon takes place, as well as a handling of the retort from Quantum Mechanics.
- In the webcomic Dresden Codak, this concept is used in a page melding philosophical notions and a Dungeons and Dragons séance titled "Advanced dungeons and discourse". In this page, Kimiko Ross has to burn the second law of thermodynamics in order to summon the demon.
- The UK sitcom Spaced featured an episode called "Chaos", in which the artist Brian makes an implicit reference to Laplace's Demon in a conversation about chaos theory. He states that reality is a mathematically predictable preordained system, even though it would "utterly defy any possibility of comprehension by even the most brilliant human mind."
- In the light novel and anime series Seishun Buta Yarou wa Bunny Girl Senpai no Yume wo Minai, it is mentioned in order to try define the situation in which the main protagonist is repeating a specific day.
- Rapurasu no Majo (Laplace's Witch), a 2015 novel by Japanese author Keigo Higashino. It was adapted into a 2018 film directed by Takashi Miike and starring Shō Sakurai.
- Shin Megami Tensei: Devil Survivor, a 2009 tactical role playing game for the Nintendo DS, makes reference to the thought experiment with the plot-point of "Laplace Mail", an automated e-mail system that predicts upcoming events for the coming day.
- In Rozen Maiden by Peach-Pit, Laplace No Ma (Laplace's demon) is a character that prompts the Rozen Maidens' mission with riddles, and appears only in the N-field. He looks like a white rabbit in a tuxedo but acts more like the Cheshire Cat, an obvious play on both characters from "Alice's Adventures in Wonderland".
- In Adam Fawer's "Improbable: A Novel", the main character becomes a personification of Laplace's demon.
- The Masoukishin Cybuster from the Super Robot Wars metaseries possesses the 'Laplace's Demon Computer' which gives it the ability to predict the future as well as editing/altering events in the timeline itself. A similar (though less powerful) device is used by another giant robot, the Unicorn Gundam.
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- Kožnjak Boris (2015). "Who let the demon out? Laplace and Boscovich on determinism". Studies in History and Philosophy of Science. 51: 42–52. doi:10.1016/j.shpsa.2015.03.002. PMID 26227230.
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- Yau, S.-T., & Nadis, S. J. (2010, p. 264). The shape of inner space: String theory and the geometry of the universe's hidden dimensions. New York: Basic Books.
- "Dresden Codak » Archive » Advanced Dungeons & Discourse". Retrieved 5 October 2015.