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Title: Cosmology
Original Title: Cosmologie
Volume and Page: Vol. 4 (1754), pp. 294–297
Author: Jean-Baptiste le Rond d'Alembert (biography)
Translator: John S.D. Glaus [The Euler Society,]
Subject terms:
Science of nature
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Citation (MLA): d'Alembert, Jean-Baptiste le Rond. "Cosmology." The Encyclopedia of Diderot & d'Alembert Collaborative Translation Project. Translated by John S.D. Glaus. Ann Arbor: Michigan Publishing, University of Michigan Library, 2006. Web. [fill in today's date in the form 18 Apr. 2009 and remove square brackets]. <>. Trans. of "Cosmologie," Encyclopédie ou Dictionnaire raisonné des sciences, des arts et des métiers, vol. 4. Paris, 1754.
Citation (Chicago): d'Alembert, Jean-Baptiste le Rond. "Cosmology." The Encyclopedia of Diderot & d'Alembert Collaborative Translation Project. Translated by John S.D. Glaus. Ann Arbor: Michigan Publishing, University of Michigan Library, 2006. (accessed [fill in today's date in the form April 18, 2009 and remove square brackets]). Originally published as "Cosmologie," Encyclopédie ou Dictionnaire raisonné des sciences, des arts et des métiers, 4:294–297 (Paris, 1754).
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Cosmology (Encyclopedic order. Understanding. Reason. Philosophy or Science. Science of nature. Cosmology). This word is formed by the combination of two Greek words, κόσμος, world, and λόγος, speech, which signifies the science which speaks of the world; that is to say the reason concerning the world in which we live and such as it actually exists. It is in this way which it differs from Cosmography and Cosmogony. See these words.

Cosmology is properly defined as a part of general Physics, which by avoiding a too detailed explanation of the facts examines the metaphysical results of these same facts and attempts to provide analogies and connections that they have between them and tries to discover the parts of the general laws by which the Universe is governed. Everything is linked in nature; all beings are connected by a continuous chain in which we sometimes see the continuous parts, even though there are a greater number of places in which the continuity escapes us. The art of the philosopher does not consist, as it all too often happens, of forcing estranged parties together by inappropriately re-forging connections which are unfortunately broken in certain places; since through those efforts one can only keep the parties separate which were joined or to keep those who should be in contact even further from those who wished to be closer. Thus the art of the Philosopher consists of offering more links to those separated parties so as to have them at the least distance possible, but he should not flatter himself that there will no longer be any empty space in places. So as to build these links that we speak of, it is necessary to take notice of two things: the observed facts surrounding the composition of these links and to the general laws of nature which form the bond. I have termed them general laws since they are the ones which are observable in a large number of phenomenon, and I am cautious not to say in all . These are the laws of motion which a series are outlining the imperviousness of a body and the source of many effects that we observe in nature. Shape and motion (I understand that motion comes from impulsion), these are a large part of the principles on which Cosmology is established. One should not stray without necessity neither should one say that these are the only one: we do not have all the facts, how could we establish the fact that they can be explained through one unique law? This assumption would be all the more reckless since amongst the facts that we do know is the fact that the laws of force have not been thoroughly explained to this day. See Attraction. Perhaps one day we will achieve this, but while waiting for that day let us suspend our judgment of the universality of these laws. Perhaps (and this is possibly true) there is a general law which is and will always be unknown, one for which we only see particular consequences both obscure and limited that prohibit us from calling them general laws. This conjecture fits very nicely into the idea that we should have concerning nature's unity and simplicity. See Nature. In the end if we reflect on the weakness of our character, we will be all the more surprised by what we have discovered and what still remains hidden.

However the principal use that we should have obtained from Cosmology is to be able to raise ourselves from the authorship of the general laws of nature whose wisdom established these laws and who has allowed us to see what is necessary for our use or enjoyment and to have hidden the rest so as to teach us the use of doubt. Thus Cosmology as the science of the World or the Universe which is generally considered to be composed simply by the union and harmony of its parts; a complete whole which is governed by a supreme intelligence who winds the springs, puts the game in motion, all of which is handled by this intelligence.

Before Mr. Wolf, Mr. Formey informed us in an article that this noun was unknown in school, that is to say there was no distinct course in Philosophy that was designed as such. No Metaphysician had apparently even thought of this topic and as many volumes as had been written on Metaphysics said nothing on Cosmology. Finally, Mr. Wolf has provided us a work with the title: Cosomologia generalis, methodo scientifica pertractata, qua ad solidam, imprimis Dei ataque naturae, cognitionem via sternitur. Francof. & Lips. In quarto 1731. There was a new edition in 1737. He provided this work immediately after Ontology and a second part of his metaphysics since he established principles which serve to identify theologically the existence and attributes of God contingent on the universe and through the order of Nature. He calls it General or Transcendental Cosmology since it is an abstract theory in relation to Physics as Ontology is to the rest of Philosophy.

The basis for this science is derived from Ontology because it requires that one apply to the world the general theory of being and of composed things. This is an a priori determination of the world into which one can add observations and experience. It is in such a way that one can say that there is a double Cosmology ; scientific Cosmology and experimental Cosmology .

Of these two Cosmologies , Mr. Wolf has limited himself to the former as the title of his work indicates; however he has not neglected the help that experience by providing for the confirmation of his principles.

The one and the other provide principles which serve to promote the existence and the qualities of God. The principal subjects that general Cosmology embraces are reduced to explain how the world is the result of an assembly of simple substances and develop the general principles concerning the changes which occur in material things.

Here is the precious fruit which Cosmology bears; nothing more is required to have the prize but to cultivate it for it produces no other fruit but this one. It is in this way that we can show that the contemplation of the visible world leads us to the knowledge of that invisible being who is its author. Mr. Wolf appears extremely persuaded of the utility and the certainty of this new path that he has cleared and this is what he says about it:

In honorem Dei, confiteri cogor, me de cognitione Dei methodo scientifica tradenda plurium sollicitum, non reperisse viam aliam, qua ad scopum perveniri datuir, quam eam quam proposition praesens monstrat, nec reperisse philosophum qui eandem rite calvalerit, etsi laude sita defraunandi non sint, qui nostris proesertim temporibus theologiae naturali methodum demonstrativam applicare conati fuerint. Wolf Cosmolog. Prolegom. 6. in schol .

A few years ago Mr. de Maupertuis provided us with an essay on Cosmology which appears to have followed the principles and points of view from the work that we mentioned above. He is of the impression that we do not have sufficient facts or principles to embrace the fullness of Nature with one point of view. He attempts to explain a Universal system and to propose the general laws that govern it by extracting a new proof of the existence of God. This work elicited a very hostile reaction in 1752 and I shall introduce some thoughts which may help to better explain the subject. I will be as short as possible and I hope to remain impartial.

Mr. de Maupertuis provided us with a general law concerning the principle of least action, See in the definition and the explanation of the word Action to which we will add the following remarks.

Leibniz had formed a particular idea concerning the force exerted on bodies in motion, and of which the word Force [Force (Grammar. Literature), Force (Iconology), Conservation of Kinetic Energy, Force of Inertia, Kinetic Energy, Force, Resulting force, Force of motion, Moving force, Force of Water (Hydraulics)] is used, and he named it force vive and assumed that it was the product of mass multiplied by the square of the speed or that it was the square of the speed taking the mass as a unit, which comes to the same thing. In the Saint Petersburg Mémoires, Volume I, Mr. Wolf had suggested to multiply the force vive (kinetic energy) by time and he called this product action (kinetic energy), supposing that the action of a body is the result of all forces that it exerts at every instant and consequentially the sum of all instantaneous live forces. One might ask of the Leibnizians, of which Mr. Wolf is regarded as the their spokesman, why they have imagined this metaphysical distinction between action and kinetic energy, a distinction that they perhaps should not have placed in between, due to the formulation of their idea regarding the kinetic energy, however this is not what we are speaking about, instead we should be speaking of the word Force [Force (Grammar. Literature), Force (Iconology), Conservation of Kinetic Energy, Force of Inertia, Kinetic Energy, Force, Resulting force, Force of motion, Moving force, Force of Water (Hydraulics)]. While waiting to allow an arbitrary title for the idea of action as a definition, we must remark that it is the same as that of Mr. de Maupertuis in the works that we have already quoted, as the word Action does not tell us if he had knowledge of Mr. Wolf's definition. It does not appear to be so as we ignore who wrote this last article and we wish to be scrupulously accurate and provide those to whom the information belongs. In the end it really does not matter that Mr. de Maupertuis has taken this idea from Mr. Wolf or that he met with him, since it is uniquely confined to the consequences that he was able to extract ones from which Mr. Wolf had absolutely no part. Mr. de Maupertuis has always been the first to have noted in refraction that the quantity of action is a minimum and that it is no less constant.

1. That this principle is different from the one stated here that; Nature always acts in the most direct path , since this latter principle has a nebulous definition which can have a hundred different applications according to whatever definition that we would wish to give to it which we see as Nature's simplest path, and that is to say whatever we would wish it to be when considering Nature's simplest and shortest path it would take or is it a straight line, that is to say the shortest distance or in the least amount of time, or with the minimum amount of motion, or with the least amount of kinetic energy or in that of action, etc. The principle as endorsed by Mr. de Maupertuis is not a principle which is vaguely outlined, but rather a precise explanation of what he believes to be the path of least resistance taken by nature.

2. We have seen that this principle is very different from that of Leibniz, See Action. It would be very unusual if Leibniz had knowledge of Mr. de Maupertuis' principle as it has been said, and that this philosopher had not thought of applying it to refraction; but we will treat this question later.

3. It is no less true that Mr. de Maupertuis' principle when applied to refraction reconciles the end causes with the mechanics of least action which is something that no one had done until then. The interest in placing these together is dependent more or less on how much interest was placed on final causes; see this word. The Leibnizians at any rate should be very pleased. In addition, Mr. Euler has demonstrated that this principle occurs in curves which are described by a body when it is either attracted or pushed towards a fixed point. This beautiful proposition extends Mr. de Maupertuis' principle to the small curve that is described by a ray of light which passes from one medium into another. In this way the principle is generally true and has no restrictions. In the Mémoires of the Prussian Academy of Sciences of 1751, Mr. Euler has shown many other cases where the principle applies itself with elegance and ease.

4. This principle differs from that in which kinetic energy is nil, for two reasons; because in Mr. de Maupertuis' principle it is not that it is nil but rather minimis and in addition, it is into that action that one introduces the element of time which is not part of kinetic energy. It is not due to the fact that the principle of kinetic energy takes place in other instances and it is not only that it is not possible to take out certain things that one can extract from minimis of action. However, this does not prove the identity of either principle, since one can achieve the same results by different paths.

5. We have seen in the article Final causes that the principle of minimum time is not available when considering reflection with concave mirrors. It appears to be the same concerning minimum action, since then the light ray is a maximum and action is also a maximum. It is true that we might seek the square of this principle by always returning the reflection to plane surfaces but perhaps those opposed to Final causes will not appreciate this answer ; and it appears better to say that the action here is at a maximum and in the other cases a minimum. There would be no less merit to have applied the first principle to refraction and it will be similar to the conservation of kinetic energy which applies to the impact of elastic bodies but which does not happen when inelastic bodies collide.

6. Mr. de Maupertuis has applied this same law of minimum action to the impact on bodies and he was the first to determine with the same principle the laws of impact of inelastic and elastic bodies. It is true that the application is a little more complicated, more torturous, less simple and perhaps less rigorous than in the case of refraction.

What we are about to say will not, in the end, be to Mr. de Maupertuis' disadvantage after it has been fully explained. It supposes that two rigid bodies A, B , are in motion in the same direction one at velocity a , the other at velocity b and that their mutual velocities at the point of contact is x ; it is certain he writes that the change which has occurred in Nature is that body A has lost velocity a -x and that body B has increased its velocity to x - b , thus the quantity of action necessary to produce this change must be equal to a minimum which is A (a-x) 2 + B(x-b) 2 which provides the ordinary formula for the collision of rigid bodies [omission: formula; to see consult facsimile version]. All of this is very correct. But everything depends also on the idea that we would wish to attach to the words change which occurs in Nature . Since is it not possible to say that the change occurred in body A prior to the impact as a quantity Axx and the same for body B thus Aaa - Axx is the change which occurs in body B and Bxx -Bbb also the change which occurs in body B .

In such a way the quantity of action which was responsible for this alteration is Aaa-Axx, Bxx-Bbb . However this quantity which is equal to a minimum does not provide for the law concerning the impact of rigid bodies. It is the one objection that can be made of Mr. de Maupertuis. This criticism was done to a point except with the difference that it was conjectured that Axx+Bxx<-> Aaa-Bbb was equal to a minimum by taking the quantity Aaa-Axx from the quantity Bxx-Bbb instead of adding to it which appears to be something that could have been done since the two quantities Aaa-Axx and Bxx-Bbb should be subtracted from Aaa and the other added to Bbb are real and can be added together irregardless of the direction in which they are acting. Whatever it is, it seems that one should be able to balance or at least to avoid all difficulty in that respect by substituting the words change in the nature which appears in Mr. de Maupertuis' abstract of the proposition of the word change in the velocity, and then at least the ambiguity true or so-called would no longer exist.

It also appears that in Mr. de Maupertuis' calculations the quantity of action is objected to since it is confused with the quantity of live forces which is to say to a point, since the time which is supposed to be the same as it is here, in these two quantities is proportional to one another and one should say that the quantity of action should never been mistaken for live forces, understanding of course that time, following Mr. de Maupertuis' definition, enters into the quantity of action and in which case of rigid bodies the change occurring in a moment that is indivisible when the time = 0 and consequentially the action is nil. One may respond to this objection that only a body moves or is forced into motion at any velocity and that there is always a real or possible quantity of action which will respond to its motion insofar as it moves uniformly during any time at this velocity; therefore instead of the words, the quantity of action necessary to produce this change one may substitute, the quantity of action that responds to this change and describe in this way Mr. de Maupertuis' rule: The change which occurs to a body's velocity after impact and the quantity of action which will respond to this change, with the time as a constant, is the least possible. It is said the time is a determined constant; this modification and its limitation if we see it this way, is necessary for two reasons: 1. when a collision occurs to rigid bodies where time necessarily = 0, the assumption of constant or variable time is an arbitrary assumption and one must select either one or the other.

When there is an impact of elastic bodies, the alteration which takes place in a finite amount of time and of very short duration is not the same when all impacts occur, therefore it is imperative to establish the assumption that in effect the time that is assumed constant is a time selected randomly and totally independent of the time during which the motion is conveyed. One should be able to take as the quantity of action the amount used at the moment of change which is a sum of the small quantities of action used during the time that the spring compresses and then releases. One might say that Mr. de Maupertuis should have used the word live force here instead of that of action since time is not appropriate. To that he would have undoubtedly answered that he felt that he could connect this law with a common expression such as with the one he found for refraction. However if we were to substitute live force for action (potential energy for kinetic energy) it would still be true that Mr. de Maupertuis would have been the first to reduce the impact of rigid bodies and those of elastic bodies to a same law which is the main point and his theory of refraction would not have suffer.

It is true that the laws of motion were found without this principle; however it was useful to have shown how it is applied. It is possibly true that this principle may very well be some other principle presented differently. But this is the case for all mathematical truths, in the end they are merely the transformation of one into another. See Preliminary Discourse, page viij. The principle of the conservation of live forces is in effect the ancient's principle of equilibrium, as I demonstrated in my Dynamique, II part. Chap. And this should not suggest that the principle of the conservation of live forces is not useful but it should also provide honor to its inventors.

7. The author continues to apply his principle to equilibrium in the lever, but to do so require certain assumptions, amongst which that velocity is proportional to the distance from the point of impact and that time is constant, as it is in the case of impact of bodies. It must be assumed that the length of the lever is given and that it is the point of application that is being sought, since if the point of application and one arm were known and one were seeking the other, one would find by the principle of action that this arm is equal to zero. In the end the remaining assumptions made by Mr. de Maupertuis are to be allowed and there remains only the necessity to express them so to be out of the critic's reach with all other assumptions expressed. The application and the use of the principle do not contain any more significant generalities. In regards to the assumptions that he gives that gravity is as a mass and that this assumption is provided for by nature itself and it takes place in all the theories concerning the center of gravity of bodies which are regarded as no less general.

The result of what we have just mentioned is that the principle of least action takes place in a great number of natural phenomenons which applies with great facility to refraction and planetary orbits, as well as a number of others examined by Mr. Euler. See the Mémoires of the Berlin Academy 1751 and the article Action. This principle applies to various other cases with more or less arbitrary modifications however it is one that is always useful in mechanics and one which can facilitate the solution to different problems.

A priority dispute of this principle by Mr. de Maupertuis had surfaced. Mr. König had at first forwarded a passage from a handwritten letter from Leibniz to prove that it was from this philosopher. This passage was published in the Actes de Leipzig, May 1751 , but contained an enormous error that Mr. König assured us was a printing mistake. He corrected the passage which in effect is part of the principle of least action. If Leibniz' letter was real (which is not for us to decide), but that this letter was never made public, it would allow this principle to belong to Mr. de Maupertuis; and Mr. König appears to have admitted in his Appeal to the public of the judgement that the Prussian Academy of Sciences had made an announcement against the authenticity of the fragment. Mr. König had at first quoted the letter to which we refer as written by Mr. Herman; but he has since recognized that he does not know to whom it was written. In his Appeal he produced the letter that can be read in its entirety. It is very long and it is dated Hanover, October 16 1707. Without the proper verification of its entire authenticity, it is only a matter of verifying that whoever gave it to Mr. König had added or altered the fragment in question. Mr. König is reported to have said that he received it from Mr. Henzi who was decapitated in Bern some years ago. He has said that he has in possession various other letters by Leibniz that this same Mr. Henzi had given to him; certain letters which are in Mr. Henzi's own hand. In regards to the letter to which we refer, Mr. König has not told us by who the letters were written, he has only mentioned that he has others that were written in the same hand, and that one of them is to be found in the published collection in-quarto and he has transcribed these letters in his Appeal . Mr. König has not said whether he has seen the original of this letter written by Leibniz himself. These are the facts and it is upon the public to judge whether the quoted fragment is authentic or not.

We must also make the public aware that Mr. König provided for a theory concerning live forces in the Actes de Leipzig which is exactly the same as Mr. de Courtivron published in the Mémoires of the Academy 1748; page 304 and that Mr. de Courtivron had read it to the Academy before the publication of Mr. König's mémoire. See Center of Equilibrium.

There only remains to say a word of the metaphysical usage that Mr. de Maupertuis has given to his principle. We think as we have already implied above that the definition of the quantity of action is a definition of a purely mathematical and arbitrary nature. One can call action the product of the mass by the speed or its square, or by any random function of space and time. Space and time are the two sole objects that we see clearly during the movement of bodies. One may introduce as many mathematical combinations as one wishes with these two issues and one may call all of this action, however the original and metaphysical word for action will not be any clearer. In general all of the theories of action are defined as one might wish, concerning the conservation of live forces, on a motionless or uniform center of gravity, or of other similar laws which are nothing more than mathematical theories of more or less generality and not of philosophical principles. For example, when two bodies are attached to a lever, one goes up and one comes down and one will find as did Mr. König that the sum of the live forces are nil because by adding opposite notations to the quantities that have different directional values: however these are geometrical realities and not metaphysical ones. In the end it is no less real for lives forces to possess opposite directional values and that they are no less real than it is possible to deny the existence of these forces. It is as thought one was saying that there is no motion in a body system when the same parts of the system are nil, that is to say that the quantities of motion are equal even though the directions are opposite, they are still real.

Mr. de Maupertuis' principle is not a purely mathematical principle and it is suggested that he is not far from his mark especially since he did not participate in any way in the metaphysical question of live forces in which action is involved. See pages 15 and 16 of his works, published in Dresden 1752, in quarto. It is true that he has deduced the existence of God from his principle: but we can also deduce the existence of God from a purely mathematical principle when it is recognized that one believes that this principle can be observed in nature. Furthermore he has only given this proof on the existence of God as an example of proofs that are taken from the Universes' own general principles, an example to which he neither provides exclusive power nor superiority to any other proofs. He only suggests reasonably that one should apply oneself, especially when attempting to prove the existence of God by general phenomenon and not limited to any particular phenomenon even though he admits that this deduction has its utility. On this subject, one should see the preface of his work, where he is fully justified against ignorant critics and those who bear him ill-will and what they have done to him concerning this matter. Nothing is more fashionable today than the accusation of atheism; intended to defame the philosophers who are not. See also in this article on Cosmology, the Acts of Leipzig of May 1751, the Appeal of Mr. König to the public, the Mémoires of Berlin 1750 and 1751 (some inadvertently claim 1752); and in the Mémoires of the Paris Academy of Science 1749, a paper by Mr. d'Arcy on this topic. Here are (as it is now February 1754) the pieces that are absolutely necessary for the case since the question has been opened to discussion and those who have treated it are in possession of the facts. We must add that Mr. de Maupertuis has never responded to the insults that have been spewed at him on this matter to which we will add: nec noinetur in vobis, sicut decet philosophos. This quarrel regarding action , it if it is permitted for us to say, has gathered certain religious overtones due to its acerbic nature, and by a quantity of people that have spoken without listening.

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