Laplace’s demon

Laplace's demon (fuller)
An artistic rendition of Laplace's demon: a vast intellect that knows forces and positions of all atoms and great bodies of the universe, who with this information knows the future and the past with absolute certainty.
In scientific demons, Laplace’s demon, or the "Holbach-Laplace intelligence" or "Holbach's geometrician", is a hypothetical vast intellectual entity, conceived originally by Baron d'Holbach (1770) and following him by French mathematician Pierre Laplace (1773; 1814), who if it knew the precise location and momentum of every atom in the universe could then use the laws of motion to reveal the entire course of cosmic events, past and future. [1]


See main: Holbach’s geometrician
In 1770, Baron d'Holbach, in his §4: “Of the Laws of Motion common to all the Beings of Nature—of Attraction and Repulsion—of Inert Force—of Necessity”, stated the following very-ripe anti-chance (or non-chance) view of a dust storm and a political revolution: [3]

“Two examples will serve to throw the principle here laid down, into light—one shall be taken from physics, the other from morals. In a whirlwind of dust, raised by elemental force, confused as it appears to our eyes, in the most frightful tempest excited by contrary winds, when the waves roll high as mountains, there is NOT a single particle of dust, or drop of water, that has been placed by ‘chance, that has not a cause for occupying the place where it is found; that does not, in the most rigorous sense of the word, act after the manner in which it ought to act; that is, according to its own peculiar essence, and that of the beings from whom it receives this communicated force. A geometrician exactly knew the different energies acting in each case, with the properties of the particles moved, could demonstrate that after the causes given, each particle acted precisely as it ought to act, and that it could not have acted otherwise than it did.

In those terrible convulsions that sometimes agitate political societies, shake their foundations, and frequently produce the overthrow of an empire; there is not a single action, a single word, a single thought, a single will, a single passion in the agents, whether they act as destroyers, or as victims, that is not the necessary result of the causes operating; that does not act, as, of necessity, it must act, from the peculiar essence of the beings who give the impulse, and that of the agents who receive it, according to the situation these agents fill in the moral whirlwind. This could be evidently proved by an understanding capacitated to rate all the action and re-action, of the minds and bodies of those who contributed to the revolution.”

Here we see Holbach, in his jettisoning of Greek chance-based version of atomic theory, stating what would later become the basis of what is commonly called Laplace's demon.
In 1770, a young Pierre Laplace, then aged 21, or some time thereabouts, read Holbach's then anonymously-published The System of Nature, and soon their after became his disciple. Ralph Blumenau (2014), in his Philosophy and Living (Ѻ), summarizes this as follows:

“Holbach's best known book, prudently published under another name, was Le Systime de la Nature (1770). Helvetius had concentrated his attack on the clergy, but had (perhaps only out of fear) professed his full adherence to the Christian faith. Holbach scoffed at all religious beliefs. At worst, he thought, they were based on fear, superstition and the inability to face nature's indifference to suffering. At best, it was the making of hypotheses for who might be the architect of what we call ‘creation’. Like his disciple, the scientist De Laplace, Holbach would have said that he had no need of such a hypothesis. Nor would Holbach have any truck with Spinoza's equation between ‘god and nature’ (Dew sive Natura). For Holbach, this was merely an attempt to anthropomorphize or pantheize nature. Nature consists entirely of matter and motion; the causes that operate in it come wholly from within itself and not from anything outside of it. It is entirely indifferent to what we call good or evil; everything within nature is governed by egoism (what Spinoza had called the conatus sese preservandi).”

In 1773, Pierre Laplace, in his "Research on the Integration of Differential Equations with Finite Differences and their use in the Theory of Randomness", read to the Royal Academy, is said to have stated an early version of what would later become, famously, Laplace's demon.
The finalized version of Laplace’s demon seems to have been penned in his 1814 “A Philosophical Essay on Probabilities”, an extension of a lecture on probabilities delivered in 1795 to the normal schools, on his inauguration as a mathematics professor with Joseph Lagrange, which eventually became a book entitled The Analytical Theory of Probabilities, the essay being specifically on the subject of probabilities applied to the most important question of life, such as the principles of reason, justice, and humanity. The opening of this 1814 essay is as follows:

“All events, even those which on account of their insignificance do not seem to follow the great laws of nature, are a result of it just as necessarily as the revolutions of the sun. In ignorance of the ties which unite such events to the entire system of the universe, they have been made to depend upon final causes or upon hazard, according as they occur and are repeated with regularity, or appear without regard to order; but these imaginary causes have gradually receded with the widening bounds of knowledge and disappear entirely before sound philosophy, which sees in them only the expression of our ignorance of the true causes.

Present events are connected with preceding ones by a tie based upon the evident principle that a thing cannot occur without a cause which produces it. This axiom, known by the name of the principle of sufficient reason, extends even to actions which are considered indifferent; the freest will is unable without a determinative motive to give them birth; if we assume two positions with exactly similar circumstances and find that the will is active in the one and inactive in the other, we say that its choice is an effect without a cause. It is then, says Leibnitz, the blind chance of the Epicureans. The contrary opinion is an illusion of the mind, which, losing sight of the evasive reasons of the choice of the will in indifferent things, believes that choice is determined of itself and without motives.

We ought then to regard the present state of the universe as the effect of its anterior state and as the cause of the one which is to follow. Given for one instant an intelligence which could comprehend all the forces by which nature is animated and the respective situation of the beings who compose it—an intelligence sufficiently vast to submit these data to analysis—it would embrace in the same formula the movements of the greatest bodies of the universe and those of the lightest atom; for it, nothing would be uncertain and the future, as the past, would be present to its eyes.

The human mind offers, in the perfection which it has been able to give to astronomy, a feeble idea of this intelligence. Its discoveries in mechanics and geometry, added to that of universal gravity, have enabled it to comprehend in the same analytical expressions the past and future states of the system of the world. Applying the same method to some other objects of its knowledge, it has succeeded in referring to general laws observed phenomena and in foreseeing those which given circumstances ought to produce. All these efforts in the search for truth tend to lead it back continually to the vast intelligence which we have just mentioned, but from which it will always remain infinitely removed.”

The modern popular version of Laplace's demon is as follows:

“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.”

Hugh Roberts (1997), in respect to how Percy Shelley, supposedly, read both versions, copying the above Holbach version in his notes, summarizes this as follows: [4]

“Holbach's Systeme de la nature dates from 1770, whereas the paper that contains Laplace's most famous statement of absolute determinism, 'Research on the Integration of Differential Equations with Finite Differences and their use in the Theory of Randomness' (‘Recherches sur I’integration des equations differentielles aux differences finies et sur leur usage dans la theore des hasards’), was read to the Royal Academy in 1773, and published in 1776 (Oeuvres completes, vol. 8). Shelley also refers to Laplace in his notes, and had evidently read his Systeme du monde (Hutchinson, 809).”


Laplace’s demon is said to have met its demise with the publication of German physicist Rudolf Clausius’ 1865 The Mechanical Theory of Heat, which introduced the concepts of entropy and irreversibility into mechanics. [2] In simple terms, the mechanics described by Isaac Newton’s three laws of motion (Principia, 1686) are reversible with respect to time (e.g. Poincaré recurrence theorem, 1890), whereas Clausius’ two laws of the mechanical theory of heat are irreversible with respect to time (e.g. Loschmidt’s paradox, 1876), described verbally by the the effect that entropy increases in all natural processes and described mathematically by famed 1856 inequality of Clausius (Clausius inequality), which introduced the arrow of time into celestial mechanics.
A 2009 rendition, by Libb Thims, of a humorous meeting Laplace's demon and Maxwell's demon.
Thermodynamic demons
With the downfall of Laplace’s demon, the rise of the so-called “thermodynamic demons” soon took its place, the first of which being the famed Maxwell’s demon (1867), then Szilard’s demon (1929), along with various fictional devices said to contain a Maxwell’s demon, such as the Nefastis Machine (1865).

The following are related quotes:

“Besides, since everything happens by fate, as will be shown elsewhere, if there could be any mortal who could observe with his mind the interconnection of all causes, nothing indeed would escape him. For he who knows the causes of things that are to be necessarily knows all the things that are going to be. But since no one but God could do this, what is left for man is that he should be aware of future things in advance by certain signs which make clear what will follow. For the things which are going to be do not come into existence suddenly, but the passage of time is like the unwinding of a rope, producing nothing new but unfolding what was there at first.”
Cicero (44BC), On Divination (Ѻ)

“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.”
Gottfried Leibniz (c.1770), Publication (Ѻ)

“Any point of matter, setting aside free motions that arise from the action of arbitrary will, must describe some continuous curved line, the determination of which can be reduced to the following general problem. Given a number of points of matter, & given, for each of them, the point of space that it occupies at any given instant of time; also given the direction & velocity of the initial motion if they were projected, or the tangential velocity if they are already in motion; & given the law of forces expressed by some continuous curve, such as that of Fig. 1, which contains this Theory of mine; it is required to find the path of each of the points, that is to say, the line along which each of them moves. [...] Now, although a problem of such a kind surpasses all the powers of the human intellect, yet any geometer can easily see thus far, that the problem is determinate, & that such curves will all be continuous [...] & a mind which had the powers requisite to deal with such a problem in a proper manner & was brilliant enough to perceive the solutions of it (& such a mind might even be finite, provided the number of points were finite, & the notion of the curve representing the law of forces were given by a finite representation), such a mind, I say, could, from a continuous arc described in an interval of time, no matter how small, by all points of matter, derive the law of forces itself; [...] Now, if the law of forces were known, & the position, velocity & direction of all the points at any given instant, it would be possible for a mind of this type to foresee all the necessary subsequent motions & states, & to predict all the phenomena that necessarily followed from them.”
Roger Boscovich (1763), A Theory of Natural Philosophy (Ѻ)

1. Laplace, Pierre. (1814). A Philosophical Essay on Probabilities. Trans. F.W. Truscott and F.L. Emory. Dover, 1951.
2. lanowicz, Robert. (1986). Growth and Development (pgs. 2-3). Excel.
3. d’Holbach, Baron. (1770). The System of Nature: Laws of the Moral and Physical World (notes by Denis Diderot; translator: H.D. Robinson) (pg. 32). J.P. Mendum, 1889.
4. Roberts, Hugh. (1997). Shelley and the Chaos of History: a New Politics of Religion (pg. 413). Penn State Press, 2010.

Further reading
● Green, Richard. (1995). The Thwarting of Laplace’s Demon: Arguments Against the Mechanist World-view. (abs). St. Martin’s Press.

External links
Laplace’s demon – Wikipedia.

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