Laplace Quotes

Napoleon, when hearing about Laplace's latest book, said, 'M. Laplace, they tell me you have written this large book on the system of the universe, and have never even mentioned its creator.' Laplace responds, 'Je n'avais pas besoin de cette hypothèse-là. (I had no need of that hypothesis.)

Your Excellency, I have no need of this hypothesis.

I am, and ever will be, a white-socks, pocket-protector, nerdy engineer, born under the second law of thermodynamics, steeped in steam tables, in love with free-body diagrams, transformed by Laplace and propelled by compressible flow.

Read Euler, read Euler, he is the master of us all.

What we know is not much. What we don't know is enormous.

L'homme ne poursuit que des chimères. (Man follows only phantoms.) {His true last words, according to Augustus De Morgan.}

We ought to regard the present state of the universe as the effect of its antecedent state and as the cause of the state that is to follow. An intelligence knowing all the forces acting in nature at a given instant, as well as the momentary positions of all things in the universe, would be able to comprehend in one single formula the motions of the largest bodies as well as the lightest atoms in the world, provided that its intellect were sufficiently powerful to subject all data to analysis; to it nothing would be uncertain, the future as well as the past would be present to its eyes. The perfection that the human mind has been able to give to astronomy affords but a feeble outline of such an intelligence.

I often asked Laplace what he thought of God. He owned that he was an atheist.

Probability theory is nothing more than common sense reduced to calculation. -1819

Give me the positions and velocities of all the particles in the universe, and I will predict the future.

Tabii ki Tanrı, Laplace'nin (eşyanın nasıl işlediğine dair) matematiksel tarifinde yer almaz, tıpkı Bay Ford'un içten yanmalı motorun bilimsel tarifinde yer almadığı gibi.

Whenever I meet in Laplace with the words 'Thus it plainly appears', I am sure that hours and perhaps days, of hard study will alone enable me to discover how it plainly appears.

If the people of Europe had known as much of astronomy and geology when the bible was introduced among them, as they do now, there never could have been one believer in the doctrine of inspiration. If the writers of the various parts of the bible had known as much about the sciences as is now known by every intelligent man, the book never could have been written. It was produced by ignorance, and has been believed and defended by its author. It has lost power in the proportion that man has gained knowledge. A few years ago, this book was appealed to in the settlement of all scientific questions; but now, even the clergy confess that in such matters, it has ceased to speak with the voice of authority. For the establishment of facts, the word of man is now considered far better than the word of God. In the world of science, Jehovah was superseded by Copernicus, Galileo, and Kepler. All that God told Moses, admitting the entire account to be true, is dust and ashes compared to the discoveries of Descartes, Laplace, and Humboldt. In matters of fact, the bible has ceased to be regarded as a standard. Science has succeeded in breaking the chains of theology. A few years ago, Science endeavored to show that it was not inconsistent with the bible. The tables have been turned, and now, Religion is endeavoring to prove that the bible is not inconsistent with Science. The standard has been changed.

statistical thinking is merely an artifact of human ignorance. we need to use statistics nature does not.

Je n'avais pas besoin de cette hypothèse-là.

What we know here is very little, but what we are ignorant of is immense.

The most important questions of life are, for the most part, really only problems of probability. —MARQUIS DE LAPLACE       A

Unlike earlier thinkers, who had sought to improve their accuracy by getting rid of error, Laplace realized that you should try to get more error: aggregate enough flawed data, and you get a glimpse of the truth. “The genius of statistics, as Laplace defined it, was that it did not ignore errors; it quantified them,” the writer Louis Menand observed. “…The right answer is, in a sense, a function of the mistakes.

The uncertainty principle signaled an end to Laplace's dream of a theory of science, a model of the universe that would be completely deterministic. We certainly cannot predict future events exactly if we cannot even measure the present state of the universe precisely! We could still imagine that there is a set of laws that determine events completely for some supernatural being who, unlike us, could observe the present state of the universe without disturbing it. However, such models of the universe are not of much interest to us ordinary mortals. It seems better to employ the principle of economy known as Occam's razor and cut out all the features of the theory that cannot be observed.

Willard Gibbs did for statistical mechanics and for thermodynamics what Laplace did for celestial mechanics and Maxwell did for electrodynamics, namely, made his field a well-nigh finished theoretical structure.

...by shortening the labours doubled the life of the astronomer. {On the benefit of John Napier's logarithms.}

[Science] dissipates errors born of ignorance about our true relations with nature, errors the more damaging in that the social order should rest only on those relations. TRUTH! JUSTICE! Those are the immutable laws. Let us banish the dangerous maxim that it is sometimes useful to depart from them and to deceive or enslave mankind to assure its happiness.

It is India that gave us the ingenious method of expressing all numbers by means of ten symbols, each symbol receiving a value of position as well as an absolute value; a profound and important idea which appears so simple to us now that we ignore its true merit. But its very simplicity and the great ease which it has lent to computations put our arithmetic in the first rank of useful inventions; and we shall appreciate the grandeur of the achievement the more when we remember that it escaped the genius of Archimedes and Apollonius, two of the greatest men produced by antiquity.

But Laplace’s particles in motion allow only happenings. There are no meanings, no values, no doings.

The uncertainty principle signaled an end to Laplace’s dream of a theory of science, a model of the universe that would be completely deterministic: one certainly cannot predict future events exactly if one cannot even measure the present state of the universe precisely!

The first effect of the mind growing cultivated is that processes once multiple get to be performed in a single act. Lazarus has called this the progressive 'condensation' of thought. ... Steps really sink from sight. An advanced thinker sees the relations of his topics is such masses and so instantaneously that when he comes to explain to younger minds it is often hard ... Bowditch, who translated and annotated Laplace's Méchanique Céleste, said that whenever his author prefaced a proposition by the words 'it is evident,' he knew that many hours of hard study lay before him.

The uncertainty principle signaled an end to Laplace’s dream of a theory of science, a model of the universe that would be completely deterministic: one certainly cannot predict future events exactly if one cannot even measure the present state of the universe precisely! We could still imagine that there is a set of laws that determine events completely for some supernatural being, who could observe the present state of the universe without disturbing it.

[Sire,] je n'ai pas eu besoin de cette hypothèse." En répondant Napoléon qui lui demanda pourquoi sa théorie de l'univers ne indique pas Dieux.

In his theory Perrow recognized that modern systems are made up of thousands of parts, including fallible human decision makers, which interrelate in ways that are, like Laplace´s atoms, impossible to track and anticipate individually. Yet one can bet on the fact that just as atoms executing a drunkard´s walk will eventually get somewhere, so too will accidents eventually occur. Called normal accident theory, Perrow´s doctrine describes how that happens – how accidents can occur without clear causes, without those glaring errors and incompetent villains sought by corporate or government commission.

Laplace's Demon, the hypothetical imp that knows the instantaneous positions and velocities of every particle in the universe, was said to be able to calculate the entire future or past by plugging these values into the equations that express the laws of mechanics and electromagnetism.

Biot, who assisted Laplace in revising it [The Mécanique Céleste] for the press, says that Laplace himself was frequently unable to recover the details in the chain of reasoning, and if satisfied that the conclusions were correct, he was content to insert the constantly recurring formula, 'Il est àisé avoir' [it is easy to see].

The ingenious method of expressing every possible number using a set of ten symbols (each symbol having a place value and an absolute value) emerged in India. The idea seems so simple nowadays that its significance and profound importance is no longer appreciated ... The importance of this invention is more readily appreciated when one considers that it was beyod the two greatest men of antiquity, Archimedes and Apollonius.

Look at it as if for the very last time, and you will see it as it was meant to be seen.

Laplace’s Demon:

The most important questions of life are indeed, for the most part, really only problems of probability. —Pierre Simon Laplace, Théorie Analytique des Probabilités, 1812

Michael Shermer in the paper “Exorcising Laplace’s demon: Chaos and antichaos, history and metahistory,” History and Theory 34:59–83 (1995). Shermer’s

Randomness It is remarkable that a science which began with the consideration of games of chance should have become the most important object of human knowledge. —MARQUIS DE LAPLACE       A

The cosmos does not require God, Laplace said to himself. But Emperors require Him. All those who seek to subjugate human beings in one form or another require Him. Science does not need God.

Laplace suggested that there should be a set of scientific laws that would allow us to predict everything that would happen in the universe, if only we knew the complete state of the universe at one time.

The physical notion of determinism is different from destiny or fate in a subtle but crucial way: because Laplace’s Demon doesn’t actually exist, the future may be determined by the present, but literally nobody knows what it will be.

I compared what was really known about the stars with the account of creation as told in Genesis. I found that the writer of the inspired book had no knowledge of astronomy -- that he was as ignorant as a Choctaw chief -- as an Eskimo driver of dogs. Does any one imagine that the author of Genesis knew anything about the sun -- its size? that he was acquainted with Sirius, the North Star, with Capella, or that he knew anything of the clusters of stars so far away that their light, now visiting our eyes, has been traveling for two million years? If he had known these facts would he have said that Jehovah worked nearly six days to make this world, and only a part of the afternoon of the fourth day to make the sun and moon and all the stars? Yet millions of people insist that the writer of Genesis was inspired by the Creator of all worlds. Now, intelligent men, who are not frightened, whose brains have not been paralyzed by fear, know that the sacred story of creation was written by an ignorant savage. The story is inconsistent with all known facts, and every star shining in the heavens testifies that its author was an uninspired barbarian. I admit that this unknown writer was sincere, that he wrote what he believed to be true -- that he did the best he could. He did not claim to be inspired -- did not pretend that the story had been told to him by Jehovah. He simply stated the "facts" as he understood them. After I had learned a little about the stars I concluded that this writer, this "inspired" scribe, had been misled by myth and legend, and that he knew no more about creation than the average theologian of my day. In other words, that he knew absolutely nothing. And here, allow me to say that the ministers who are answering me are turning their guns in the wrong direction. These reverend gentlemen should attack the astronomers. They should malign and vilify Kepler, Copernicus, Newton, Herschel and Laplace. These men were the real destroyers of the sacred story. Then, after having disposed of them, they can wage a war against the stars, and against Jehovah himself for having furnished evidence against the truthfulness of his book.

Leaving controversial issues aside, the first and main purpose of this book may be summed up by a phrase of Laplace: “If we were able to make an exact catalogue of all particles and forces which are active in a speck of dust, the laws of the universe at large would hold no more mysteries for us”. On a medium-sized school globe the State of Israel occupies not much more space than a speck of dust; and yet there is hardly a political, social or cultural problem whose prototype cannot be found in it, and found in a rare concentration and intensity. The very smallness of this country of about three-quarters of a million souls makes it easy to survey trends which in other nations appear confused and diluted by size. The fact that it so often was in the past, and is again in the present, in the focus of global conflicts and passions, makes the speck of dust glow in a phosphorescent light. The fact that it is a State of Jews, and of Jews of the most conscious and intense type, makes the microscopic processes in this microscopic country reflect laws of universal validity: for Jewry is not a question of race—“it is the human condition carried to its extreme”.

Yet Laplace had built his probability theory on intuition. As far as he was concerned, "essentially, the theory of probability is nothing but good common sense reduced to mathematics. It provides an exact appreciation of what sound minds feel with a kind of instinct, frequently without being able to account for it.

Want to calculate the chance your bus is late? The chance your softball team will win? Count the number of times it has happened in the past plus one, then divide by the number of opportunities plus two. And the beauty of Laplace’s Law is that it works equally well whether we have a single data point or millions of them.

A revolution is more than the destruction of a political system. It implies the awakening of human intelligence, the increasing of the inventive spirit tenfold, a hundredfold; it is the dawn of a new, science — the science of men like Laplace, Lamarck, Lavoisier. It is a revolution in the minds of men, more than in their institutions.

The genius of Laplace was a perfect sledge hammer in bursting purely mathematical obstacles; but, like that useful instrument, it gave neither finish nor beauty to the results. In truth, in truism if the reader please, Laplace was neither Lagrange nor Euler, as every student is made to feel. The second is power and symmetry, the third power and simplicity; the first is power without either symmetry or simplicity. But, nevertheless, Laplace never attempted investigation of a subject without leaving upon it the marks of difficulties conquered: sometimes clumsily, sometimes indirectly, always without minuteness of design or arrangement of detail; but still, his end is obtained and the difficulty is conquered.

What we know is not much. What we do not know is immense.

Je n'avais pas besoin de cette hypothèse-là

Je n'avais pas besoin de cette hypothèse.

The most important questions of life are indeed, for the most part, really only problems of probability.

The great masters of modern analysis are Lagrange, Laplace, and Gauss, who were contemporaries. It is interesting to note the marked contrast in their styles. Lagrange is perfect both in form and matter, he is careful to explain his procedure, and though his arguments are general they are easy to follow. Laplace on the other hand explains nothing, is indifferent to style, and, if satisfied that his results are correct, is content to leave them either with no proof or with a faulty one. Gauss is as exact and elegant as Lagrange, but even more difficult to follow than Laplace, for he removes every trace of the analysis by which he reached his results, and studies to give a proof which while rigorous shall be as concise and synthetical as possible.

Napoleon:How s it that,although you say so much about the Universe,you say nothing about its Creator Laplace:No sire,I had no need of that hypotesis Lagrange:Ah,but it is such a good hypotesis:it explains so many things! Laplace:Indeed,Sire,Monsieur Lagrange has,with his usual sagacity,put his finger on he precise difficulty with the hypotesis:it explains everything,but predicts nothing

How did Biot arrive at the partial differential equation? [the heat conduction equation] . . . Perhaps Laplace gave Biot the equation and left him to sink or swim for a few years in trying to derive it. That would have been merely an instance of the way great mathematicians since the very beginnings of mathematical research have effortlessly maintained their superiority over ordinary mortals.

Podemos mirar el estado presente del universo como el efecto del pasado y la causa de su futuro. Se podría concebir un intelecto que en cualquier momento dado conociera todas las fuerzas que animan la naturaleza y las posiciones de los seres que la componen; si este intelecto fuera lo suficientemente vasto como para someter los datos a análisis, podría condensar en una simple fórmula el movimiento de los grandes cuerpos del universo y del átomo más ligero; para tal intelecto nada podría ser incierto y el futuro, así como el pasado, estarían frente a sus ojos.

Assume that someone tells you that the probability of an event is exactly zero. You ask him where he got this from. “Baal told me” is the answer. In such case, the person is coherent, but would be deemed unrealistic by non-Baalists. But if on the other hand, the person tells you “I estimated it to be zero,” we have a problem. The person is both unrealistic and inconsistent. Something estimated needs to have an estimation error. So probability cannot be zero if it is estimated, its lower bound is linked to the estimation error; the higher the estimation error, the higher the probability, up to a point. As with Laplace’s argument of total ignorance, an infinite estimation error pushes the probability toward ½.

Determinizm Newton mekaniğinin bir özelliği olarak l9'uncu yüzyılda en parlak dönemine ulaştı. Pierre Simon de Laplace, 1820'de yayınladığı Theone analiytique des probabilities adlı yapıtında, geçmişe bakarak tüm evrenin geleceğini kesinlikle belirlemenin elimizde olduğunu ileri sürmüş ve günümüzde bile unutulmamış olan şu satırları yazmıştı: Doğada herhangi bir an etkin olan tüm güçleri ve evrende var olan tüm nesnelerin o anlık konumlarını bile bir zekâ, evrendeki en büyük cisimlerden en hafif atomlara kadar tüm nesnelerin hareketini tek bir formül kapsamında toplayabilir, yeter ki, bu zekâ eldeki verilerin hepsini birden çözümleyebilecek kadar güçlü olsun. Böyle bir zekâ için kesin olmayan hiçbir şey olmaz: geçmiş gibi gelecek de onun gözleri önünde olacaktır. İnsan aklının astronomiye vermeyi başarabildiği yetkinlik, böyle bir zekânın gücü yanında zayıf bir taslak gibi kalır. Mekanik ve geometri alanlarındaki buluşlar evrensel çekim teorisi ile birleşince, insan aklını, dünya sisteminin geçmiş ve gelecekteki durumunu sözü geçen o bir tek formülün çerçevesinde kavramaya yaklaştırmıştır.

Eurêka. Poe attachait une grande importance à cette œuvre, à la fois cosmogonie et poème, qui commence par un discours de la méthode et se termine par une métaphysique. L’influence des idées de Poe, qui se répandent en Europe à partir de 1845, est si considérable, et se fait sentir avec une telle intensité sur certains écrivains (tels que Baudelaire ou Dostoïevski) que l’on peut dire qu’il donne un sens nouveau à la littérature. Poe joignait en lui des éléments de culture assez hétérogènes ; d’une part, élève de l’École polytechnique de Baltimore (où passa aussi Whistler), il avait une formation scientifique ; de l’autre, ses lectures l’avaient mis en contact avec le romantisme allemand des Lumières, et avec tout le XVIIIe siècle français, représenté souvent par des ouvrages oubliés aujourd’hui, tels que conteurs, poètes mineurs, etc. Ne pas négliger chez Poe l’élément cabaliste (de même que chez Goethe), la magie, telle qu’elle devait hanter, en France, l’esprit d’un Nerval, en Allemagne, Hoffmann, et bien d’autres. Enfin, l’influence de la poésie anglaise (Milton, Shelley, etc.). Poe avait lu tout jeune les deux ouvrages les plus répandus de Laplace qui l’avaient beaucoup frappé. Le calcul des probabilités intervient constamment chez lui. Dans Eurêka, il développe l’idée de la nébuleuse (de Kant), que reprendra plus tard Henri Poincaré. Poe introduit dans la littérature l’esprit d’analyse. À ce propos, il convient de répéter que pensée réfléchie et pensée intuitive peuvent et doivent coexister et se coordonner. Le travail littéraire pouvant se décomposer en plusieurs « temps », on doit faire collaborer ces deux états de l’esprit, l’état de veille où la précision, la netteté sont portées à leur point le plus haut, et une autre phase, plus confuse, où peuvent naître spontanément des éléments mélodiques ou poétiques. Du reste, quand un poème est long (cf., dans « La Genèse d’un poème », le passage ayant trait à la « dimension »), ce « bonheur de l’instant » ne saura se soutenir pendant toute sa durée. Il faut donc toujours aller d’une forme de création à l’autre, et elles ne s’opposent pas.

Laplace is reported to have said on his deathbed that science was mere trifling, and that nothing was real but love.

Bayesianism as we know it was invented by Pierre-Simon de Laplace, a Frenchman who was born five decades after Bayes. Bayes was the preacher who first described a new way to think about chance, but it was Laplace who codified those insights into the theorem that bears Bayes’s name.

At the heart of his explorations in probability was a preoccupation with Hume’s question. For example, how do we know the sun will rise tomorrow? It has done so every day until today, but that’s no guarantee it will continue. Laplace’s answer had two parts. The first is what we now call the principle of indifference, or principle of insufficient reason. We wake up one day—at the beginning of time, let’s say, which for Laplace was five thousand years or so ago—and after a beautiful afternoon, we see the sun go down. Will it come back? We’ve never seen the sun rise, and there is no particular reason to believe it will or won’t. Therefore we should consider the two scenarios equally likely and say that the sun will rise again with a probability of one-half. But, Laplace went on, if the past is any guide to the future, every day that the sun rises should increase our confidence that it will continue to do so. After five thousand years, the probability that the sun will rise yet again tomorrow should be very close to one, but not quite there, since we can never be completely certain. From this thought experiment, Laplace derived his so-called rule of succession, which estimates the probability that the sun will rise again after having risen n times as (n + 1) / (n + 2). When n = 0, this is just ½; and as n increases, so does the probability, approaching 1 when n approaches infinity.

What we know is little, and what we are ignorant of is immense.

First, the concept of "all needed skills" lets us recognize that we don't have to raise everyone's skill in celestial mechanics to that of Laplace and also ask everyone to achieve a similar skill level in all other knowledge. Instead, it turns out that the truly big ideas in each discipline, learned only in essence, carry most of the freight. And they are not so numerous, nor are their interactions so complex, that a large and multidisciplinary understanding is impossible for many, given large amounts of talent and time.

According to Daniel Dennett and many other philosophers, free will and determinism are compatible. Despite my agreement with this view, I must admit that my way of coming to the same conclusion may be slightly different, contain different motivations, and come from a different perspective. Therefore, this topic deserves further clarification; although findings may be the same, they may be so for different reasons. Even if they would be the same for the same reasons, they might be based not only on different approaches to the same problem but also on a different perspective in viewing the world—understanding the world, the concept of the world, its potential, and its appearance to us.

We must conclude that any proposition (definition) of abstract concepts (linguistically or philosophically) is not necessarily a proposition (definition) of that to which these concepts or propositions (definitions) ought to be applied. This kind of thinking, or definitions coming from such thinking, is inherently false. On the other hand, if the supposed or proposed argument reflected reality, it would be a definition of a fact and not a proposition (“definition”) of an imagined concept. Laplace didn’t show interest in proving that this is the actual reality or even stating it, so it must be that he either imagined his argument as a hypothesis or he believed that this example argument contains enough merits of itself to justify not only the argument but also the fact or truth itself. From our point of view and the idea of the Universal Mind as having a potential for infinite variety, we can conclude that even an “intellect” of a Universal Mind cannot predict and know all the varieties of its potential and the potential of all possible universes in infinity, which saves it from its own perfection while opening the door for infinite potential of the “free will.

To prove this to be a definition, not only of determinism but also of the actual world (Universe), to which goal Laplace aims, Laplace would have (or should have) offered “proof” of the actual state of the Universe. Since this was impossible, he defined a world under such “ideal” conditions through an example as a proposition. The question of whether the world, under such “ideal” conditions, would be ideal is highly debatable (we would dare to think that such a world would be not only far from perfect but on the verge of horror). From this argument, it follows that if such a world were not, in fact, ideal, then imagined or proposed “ideal conditions” would not be ideal either.

Different conclusions to which Pierre Simon Laplace (Philosophical Essays on Probabilities [1814 ]) arrived stem from almost the same subject (the world) analyzed by Dennett. We must credit Laplace (which Dennett did) for thinking about the same problem two centuries ago without possibly being affected by the discoveries to which Dennett and other philosophers and scientists were exposed. However, we must emphasize that some other philosophers and scientists before Laplace treated the same subject, including Baron d’Holbach and Roger Boscovich (Ruđer Josip Bošković) in his Theory of Natural Philosophy . “Laplace’s Damon” (argument): “An intellect that at any given moment knew all the forces that animate Nature and the mutual positions of the beings that comprise it, if this intellect were vast enough to submit its data to analysis, would 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.” — Pierre Simon Laplace, A Philosophical Essay on Probabilities There is nothing wrong with this argument since it is only hypothetical in terms of “An intellect which at any given moment knew all the forces that animate Nature …” This is not a positive or negative statement about determinism but only an intellectual proposition or question of what the case would be if there were such a “vast enough” intellect. Another question is if Laplace’s own belief or faith would lead him or not to such a conclusion. He only states that “an intellect which at any given moment knew all the forces that animate nature …” which is not proof that such an intellect exists or that he unconditionally believes in such an intellect. The mere intellectual proposition about an imagined intellect (not necessarily a real one) under the proposed conditions (not necessarily the real ones), we shall treat only as a hypothetical question or proposition or statement and not as an apparent belief (though there may be a clear belief behind it). Furthermore, this proposition doesn’t prove how it would undermine the compatibility between determinism and free will even if such an intellect existed. Laplace's conclusion under the proposed conditions is proper and must be true. But the question is not whether the conclusion itself is true if the argument, Laplace’s Damon (actually intelligence), does not represent (demonstrate) or prove the fact (truth) but only a possibility that this may be a fact (if such an intellect existed). We cannot say that this is a definition of determinism by Laplace but a possible vision (of a definition) of a universe under the proposed conditions.

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 could be present before its eyes.

do. In 1814 the French mathematician and astronomer Pierre-Simon Laplace took this dream to its logical extreme: 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.

The example of the jet engine can help us to clear up another confusion. Science, according to many scientists, concentrates essentially on material causation. It asks the “how” questions: how does the jet engine work? It also asks the “why” question regarding function: why is this pipe here? But it does not ask the “why” question of purpose: why was the jet engine built? What is important here is that Sir Frank Whittle does not appear in the scientific account. To quote Laplace, the scientific account has “no need of that hypothesis”.29 Clearly, however, it would be ridiculous to deduce from this that Whittle did not exist. He is the answer to the question: why does the jet engine exist in the first place?

Olağanüstü iddialar olağanüstü kanıtları gerektirir,” uyarısında bulunmuş olan Marquis de Laplace’ı (sık sık “Fransız Newton” diye adlandırılan matematikçi ve astronom Pierre-Simon Laplace [1794-1827])

Poincare took Laplace’s argument to its logical conclusion. He proved, using the full rigour of mathematics, that if you have a box of gas containing a definite number of particles (as many as you like, as long as it is not actually infinite) and the particles strictly obey Newton’s laws of motion, then after a sufficiently long interval of time the distribution of the particles in the box must return to its original state, with each particle moving in the same direction and at the same speed that it was moving to start with.

The most important questions of life are indeed, for the most part, really only problems of probability. —Pierre Simon Laplace, Theorie Analytique des Probabilit ´ es´ , 1812

... the development of mathematics, for the sciences and for everybody else, does not often come from pure math. It came from the physicists, engineers, and applied mathematicians. The physicists were on to many ideas which couldn’t be proved, but which they knew to be right, long before the pure mathematicians sanctified it with their seal of approval. Fourier series, Laplace transforms, and delta functions are a few examples where waiting for a rigorous proof of procedure would have stifled progress for a hundred years. The quest for rigor too often meant rigor mortis. The physicists used delta functions early on, but this wasn’t really part of mathematics until the theory of distributions was invoked to make it all rigorous and pure. That was a century later! Scientists and engineers don’t wait for that: they develop what they need when they need it. Of necessity, they invent all sorts of approximate, ad hoc methods: perturbation theory, singular perturbation theory, renormalization, numerical calculations and methods, Fourier analysis, etc. The mathematics that went into this all came from the applied side, from the scientists who wanted to understand physical phenomena. [...] So much of mathematics originates from applications and scientific phenomena. But we have nature as the final arbiter. Does a result agree with experiment? If it doesn’t agree with experiment, something is wrong.

Weierstrass, Cantor, or Peano! In physics, an analogous development threatened since about 1800, since Laplace’s Celestial Mechanics avoided all illustration. And it is exemplified by the statement by P. A. M. Dirac (in the preface of his 1930 Quantum Mechanics) that nature’s “fundamental laws do not govern the world as it appears in our mental picture in any very direct way, but instead they control a substratum of which we cannot form a mental picture without introducing irrelevancies.” The wide and uncritical acceptance of this view has become destructive. In particular, in the theory of fractals “to see is to believe.

Of Sir Isaac Newton’s momentous decipherment of the laws of the universe, the French scientist Pierre-Simon de Laplace famously told Napoleon, in his philosophical euphoria, that he no longer had need of God to make sense of creation. Secular science could henceforth exile God from his universe. In Joseph Smith’s conception, by contrast, naturalism and God co-exist.

Nathaniel Bowditch… the father of American Navigation was born on March 26, 1773, in Salem, Massachusetts. At the age of ten; he left school to work in his father's cooperage, before becoming a bookkeeping apprentice, to a ship chandler. At fourteen years of age he taught himself Algebra and later Calculus. He poured over books critical to the development of Astronomy, such as those written by Sir Isaac Newton. He also corrected thousands of calculation errors in John Hamilton Moore’s book “The New Practical Navigator.” As a young man he learned Latin and French allowing him to read foreign technical books and translated Pierre Simon de Laplace’s book on mathematics and theoretical astronomy. In 1795, Bowditch went to sea on his first voyage as a ship's clerk and yeoman. By his fifth voyage at sea he was promoted to Captain and was a part owner of the vessel. Following this voyage, he returned to Salem in 1803, resuming his studies. In 1802, his book The American Practical Navigator was first published. That same year, Harvard University awarded Bowditch an honorary Master of Arts degree. His tireless academic work earned him a significant standing, including acceptance to the “American Academy of Arts and Sciences.” In 1806, Bowditch was offered the “Chair of Mathematics and Physics at Harvard” as well as at the “United States Military Academy and the University of Virginia.” His encyclopedia of navigation “The American Practical Navigator,” usually just referred to by his name “Bowditch,” still serves as a valuable handbook on oceanography and meteorology, and contains useful tables and a maritime glossary. Without a doubt it is the finest book on Navagation ever written.

In the end, one is of course perfectly free to believe in the, so to speak, “just-there-ness” of the quantum order and of the physical laws governing it. I tend to see this as bordering upon a belief in magic, but that may be mere prejudice. What is absolutely certain is that the naturalist view of things is, as I have said, just a picture of the world, not a truth about the world that we can know, nor even a conviction that rests upon a secure rational foundation. The picture that naturalism gives us, at least at present, is twofold. On the one hand, the cosmos of space and time is a purely mechanistic reality that, if we are to be perfectly consistent, we must see as utterly deterministic: that is to say, to work a small variation on Laplace’s fantasy, if we could know the entire history of the physical events that compose the universe, from that first inflationary instant to the present, including the course of every particle, we would know also the ineluctable necessity of everything that led to and follows from the present; even what we take to be free acts of the will would be revealed as the inevitable results of physical forces reaching all the way back to the beginning of all things. On the other hand, this deterministic machine floats upon a quantum flux of ceaseless spontaneity and infinite indeterminacy. Together, these two orders close reality within a dialectical totality—a perfect union of destiny and chance, absolute determinism and pure fortuity—hermetically sealed against all transcendence. And yet, once again, the picture is radically incomplete, not only because it is unlikely that the classical Newtonian universe and the universe of quantum theory can be fitted together so seamlessly, but because neither level of reality explains the existence of the other, or of itself. And, also once again, nothing we know obliges us to find this picture more convincing than one in which higher causes (among which we might, for instance, include free will) operate upon lower, or in which all physical reality is open to a transcendent order that reveals itself in the very existence of nature.

Mighty men of science and mighty deeds. A Newton who binds the universe together in uniform law; Lagrange, Laplace, Leibnitz with their wondrous mathematical harmonies; Coulomb measuring our electricity... Faraday, Ohm, Ampère, Joule, Maxwell, Hertz, Röntgen; and in another branch of science, Cavendish, Davy, Dalton, Dewar; and in another, Darwin, Mendel, Pasteur, Lister, Sir Ronald Ross. All these and many others, and some whose names have no memorial, form a great host of heroes, an army of soldiers – fit companions of those of whom the poets have sung... There is the great Newton at the head of this list comparing himself to a child playing on the seashore gathering pebbles, whilst he could see with prophetic vision the immense ocean of truth yet unexplored before him...

El método más seguro de cuantos puedan guiarnos en la búsqueda de la verdad, consiste en elevarse, mediante la inducción, de los fenómenos concretos a relaciones cada vez más amplias hasta llegar por último a la ley general de la que derivan. A continuación se verifica esta ley, bien mediante experiencias directas, cuando es posible, bien considerando si concuerda con los fenómenos conocidos, y, si mediante una análisis riguroso, se ve que todos ellos se desprenden de esta ley, hasta en sus menores detalles y si, además, dichos fenómenos son muy numerosos y variados, entonces la ciencia adquiere el grado de certeza más elevado que pueda alcanzar. Esto es lo que le ha ocurrido a la astronomía con el descubrimiento de la gravitación universal. Pero la historia de las ciencias nos permite ver que esta lenta y penosa marcha de la inducción no ha sido siempre la de los inventores. La imaginación, impaciente por remontarse a las causas, se complace en crear hipótesis y a menudo deforma los hechos para plegarlos a su labor: en tales casos, las hipótesis son peligrosas.

El método más seguro de cuantos puedan guiarnos en la búsqueda de la verdad, consiste en elevarse, mediante la inducción, de los fenómenos concretos a relaciones cada vez más amplias hasta llegar por último a la ley general de la que derivan. A continuación se verifica esta ley, bien mediante experiencias directas, cuando es posible, bien considerando si concuerda con los fenómenos conocidos, y, si mediante una análisis riguroso, se ve que todos ellos se desprenden de esta ley, hasta en sus menores detalles y si, además, dichos fenómenos son muy numerosos y variados, entonces la ciencia adquiere el grado de certeza más elevado que pueda alcanzar. Esto es lo que le ha ocurrido a la astronomía con el descubrimiento de la gravitación universal. Pero la historia de las ciencias nos permite ver que esta lenta y penosa marcha de la inducción no ha sido siempre la de los inventores. La imaginación, impaciente por remontarse a las causas, se complace en crear hipótesis y a menudo deforma los hechos para plegarlos a su labor: en tales casos, las hipótesis son peligrosas.

Se ve por este Ensayo que la teoría de las probabilidades, en el fondo, no es otra cosa que el buen sentido reducido a cálculo; permite apreciar con exactitud aquello que los espíritus justos barruntan por una especie de instinto, sin que generalmente puedan darse cuenta de ello. Si consideramos los métodos analíticos a que esta teoría ha dado lugar, la verdad de los principios que le sirven de base, la minuciosa y sutil lógica que exige su empleo para la solución de los problemas, las instituciones de utilidad pública que se apoyan en ella y la extensión que ha recibido y que puede recibir todavía con su aplicación a las más importantes cuestiones de la filosofía natural y de la economía política; si además observamos que, en aquellas otras cosas que no pueden ser sometidas al cálculo, nos ofrece las aproximaciones más seguras que puedan guiarnos en nuestros juicios y que nos enseña a librarnos de las ilusiones que a menudo nos engañan, veremos que no hay ciencia más digna de nuestras reflexiones y cuyos resultados sean más útiles.

Así pues, hemos de considerar el estado actual del universo como el efecto de su estado anterior y como la causa del que ha de seguirle. Una inteligencia que en un momento determinado conociera todas las fuerzas que animan a la naturaleza, así como la situación respectiva de los seres que la componen, si además fuera lo suficientemente amplia como para someter a análisis tales datos, podría abarcar en una sola fórmula los movimiento de los cuerpos más grades del universo y los del átomo más ligero; nada le resultaría incierto y tanto el futuro como el pasado estarían presentes ante sus ojos.

Se ve por este Ensayo que la teoría de las probabilidades, en el fondo, no es otra cosa que el buen sentido reducido a cálculo; permite apreciar con exactitud aquello que los espíritus justos barruntan por una especie de instinto, sin que generalmente puedan darse cuenta de ello. Si consideramos los métodos analíticos a que esta teoría ha dado lugar, la verdad de los principios que le sirven de base, la minuciosa y sutil lógica que exige su empleo para la solución de los problemas, las instituciones de utilidad pública que se apoyan en ella y la extensión que ha recibido y que puede recibir todavía con su aplicación a las más importantes cuestiones de la filosofía natural y de la economía política; si además observamos que, en aquellas otras cosas que no pueden ser sometidas al cálculo, nos ofrece las aproximaciones más seguras que puedan guiarnos en nuestros juicios y que nos enseña a librarnos de las ilusiones que a menudo nos engañan, veremos que no hay ciencia más digna de nuestras reflexiones y cuyos resultados sean más útiles.

Así pues, hemos de considerar el estado actual del universo como el efecto de su estado anterior y como la causa del que ha de seguirle. Una inteligencia que en un momento determinado conociera todas las fuerzas que animan a la naturaleza, así como la situación respectiva de los seres que la componen, si además fuera lo suficientemente amplia como para someter a análisis tales datos, podría abarcar en una sola fórmula los movimiento de los cuerpos más grades del universo y los del átomo más ligero; nada le resultaría incierto y tanto el futuro como el pasado estarían presentes ante sus ojos.

It is clear that the Babylonians did not regard their story of creation as we might accept the theory of Laplace, for instance, as an intellectually satisfying account of how the world came to be as it is. Ancient man had not thought out an answer; an answer had been revealed to him in a reciprocal relationship with nature.

En la idea de aplacar las ambiciones de Sieyès, Napoleón permitió que este eligiese libremente el Senado. Sieyès se limitó a proponer una lista de veintinueve hombres que consideraba imprescindibles, permitiendo que entrasen en su composición personalidades de todos los sectores de la opinión política, desde viejos girondinos a antiguos realistas y hasta montañeses, incluyendo, claro está, a algunos científicos de la Academia tan caros a Napoleón como sus amigos Laplace, Monge y Berthollet.

Napolyon, Laplace'a ölümsüz eseri Göklerin Mekaniği'nde niçin hiç Tanrı'dan bahsetmediğini sorunca, büyük dâhinin verdiği cevap meşhurdur: “Öyle bir varsayıma gerek duymadım, Majeste!

Given for one instant an intelligence that could comprehend all the forces by which nature is animated… an intelligence sufficiently vast to submit these data to analysis… it would embrace in the same formula the movements of the greatest bodies in 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.” —PIERRE-SIMON DE LAPLACE, 1814

Natural being presupposes us as a spectator, authentically only such as it is offered within as field of perception. Hence, the world without humans or prior to humans: Laplace's nebula. We have said that the nebulousity is within the cultural world, not within 'Nature,' i.e., within the absolute in-itself; and in fact, if one placed it within the in-itself, it would be necessary to remove it from the in-itself through scientific progress...And how to understand birth within this in-itself of a human and a consciousness? The world prior to humans like the moon without inhabitants, i.e., spectacle for X and for us...If there is emergence, this means that humans will never be able to think a world without humans, and ultimately that the pure in-itself is a myth. Every cosmogony is thought in perceptual terms. Therefore, truth is not prior to us--and not through us alone, either--but the exchange between a world ready to be perceived and a perception that relies upon it. This exchange is what we were calling perception, and it is why perception is central in the ontology. The rationality of science is to be conceived as particular case of the logos of the perceptual world--past truth, truth to come, emergence.

It was the embryo, lost before that point at which Laplace can be distinguished from a turtle.

The mathematical exposition is extremely concise and occasionally awkward. Laplace was interested in results, not in how he got them. To avoid condensing a complicated mathematical argument to a brief, intelligible form he frequently omits everything but the conclusion, with the optimistic remark “Il est aisé à voir” (It is easy to see). He himself would often be unable to restore the reasoning by which he had “seen” these easy things without hours—sometimes days—of hard labor.

Pierre-Simon Laplace wrote in his 1812 book Théorie Analytique des Probabilités: “The most important questions of life are indeed, for the most part, really only problems of probability.

Cuando Napoleón hojeó un volumen de la obra maestra de Laplace sobre los movimientos del sistema solar (el Tratado de mecánica celeste) y le preguntó por qué no había mencionado a Dios ni una sola vez en su libro, Laplace contestó: «Sire, no tuve necesidad de esa hipótesis».

When we said above that there is no world without an Existence that bears its structure, one could surely have objected that, nevertheless, the world preceded man, that the earth, according to all the evidence, is the only populated planet, and that thus the philosophical views are revealed as incompatible with the most established facts. But in fact, it is only the abstract reflection of intellectualism that is incompatible with the poorly understood 'facts.' For what exactly is meant by saying that the world existed prior to human consciousness? It might be meant that the earth emerged from a primitive nebula where the conditions for life had not been brought together. But each of these words, just like each equation in physics, presupposes our pre-scientific experience of the world, and this reference to the lived world contributes to constituting the valid signification of the statement. Nothing will ever lead me to understand what a nebula, which would not be seen by anyone, might be. Laplace's nebula is not behind us, at our origin, but rather out in front of us in the cultural world. And on the other hand, what is meant when we say that there is no world without a being in the world? Not that the world is constituted by consciousness, but rather that consciousness always finds itself already at work in the world. Thus, all things considered, what is true is that a nature exists--but this is the nature that perception shows to me and not the nature of the sciences--and that even the light of consciousness is, as Heidegger says, a lumen naturale given to itself.

with his triumph and Laplace with his inspiration. But celestial mechanics differed from most earthly systems in a crucial respect. Systems that lose energy to friction are dissipative. Astronomical systems are not: they are conservative, or Hamiltonian. Actually, on a nearly infinitesimal scale, even astronomical systems suffer a kind of drag, with stars radiating away energy and tidal friction draining some momentum from orbiting bodies, but for practical purposes, astronomers’ calculations could ignore dissipation. And without dissipation, the phase space would not fold and contract in the way needed to produce an infinite fractal layering. A strange attractor could never arise. Could chaos?

La oscuridad que envuelve la infancia y juventud de Laplace es debida a su propio esnobismo: estaba avergonzado de sus humildes padres e hizo todo lo posible para ocultar su origen campesino.

In modern parlance, Laplace was pointing out that the universe is something like a computer. You enter an input (the state of the universe right now), it does a calculation (the laws of physics) and gives you an output (the state of the universe one moment later).

For poetic naturalism, the situation is clear. There is one way of talking about the universe that describes it as elementary particles or quantum states, in which Laplace holds sway and what happens next depends only on the state of the system right now.