It modifies the design that the man is made world
Mathematician, physicist and astronomer English. Newton upset the course of science and radically modified the design which the man had of the world.
After him, nothing any more was like front, and one could think - to Maxwell and Einstein - that he had discovered at the same time the structure and the direction of the Universe, had placed from now on in the light of the reason and the rigor of mathematics. However, this tormented and solitary genius devoted most of its life to alchemical research and theological speculations, which he preferred to keep secret.
It is in 1642, the year of the death of Galileo and two years before the publication of Principia de Descartes, that Isaac Newton is born in Woolsthorpe, in Lincolnshire, in England. The assets of the first generation of the large scientists of the XVIIe century are in place; it is thus well, as Newton points out it, while beginning again celebrates it formula of Bernard of Chartres in a letter addressed to Robert Hooke on on February 5th, 1676, “because it was held on shoulders of giant whom it saw whether far”.
Conceptual innovation, synthesis, requirement of deductive organization, these three characters summarize the direction of the creative work of Newton: conceptual innovations, when it mathématise phenomena of the color or introduced the universal gravitation; synthesis of work of Galileo, Descartes or Huygens, when it develops the science of the movement; requirement of deductive organization, when it works out the principles which govern the first true treaty of mechanics, Philosophiae naturalis principia mathematica.
Loneliness with glory
After having passed its childhood, because of the early death of his/her father, in a primarily female atmosphere, Newton (which had, in addition, very badly supported the remarriage of his/her mother) between on on June 5th, 1661 in Trinity College of Cambridge, where it obtains, in 1665, the title of bachelor off arts.
From this period of formation we partly preserve the trace of its readings by its first notebooks. He meditates on Euclide, on work of Kepler, mainly in optics, on the Dialogs of Galileo, the Geometry of Descartes and Arithmetica infinitorum of John Wallis. He sticks to the writings, in keeping with the revival of the atomism, of Walter Charleton on Epicure and Gassendi. He also quotes Aristote (mainly Organon and Ethics). He annotates the last publications of the large English scientists Robert Boyle and Robert Hooke.
In June 1665, Newton leaves Cambridge for its native Lincolnshire, the epidemic of plague which will devastate England until 1666 having led to the closing of the university. It is during the following months that Newton, then away from the academic obligations, poses the bases of its greater discoveries in mathematics, optics and celestial mechanics. Those, still with the state of outlines, will acquerront only very gradually their final form. Nevertheless, these a few months seem most fertile well of the life of Newton. It is thus with reason that this period with horse over the years 1665 and 1666 is called the Anus mirabilis, the “marvellous year”.
In 1669, Newton obtains the pulpit of mathematics in Trinity College, founded in 1664: it will preserve it until 1695. During the first years, Newton devotes its teaching to optics (1670-1672), arithmetic and the algebra (1673-1683), with mechanics (1684-1685); it is not that in 1687 qu ' it publishes, under the impulse of Edmond Halley, Philosophiae naturalis principia mathematica - two new editions of this work will appear in 1713 and 1726. Meanwhile, in 1672, Newton became, mainly for the presentation of its telescope with reflection, member of Royal Society.
After the publication of Principia, Newton continues its work in mechanics and optics; nevertheless, the great period of creation is finished. It is the moment of the development and the enrichment of the essential theses. Thus, in 1704, after the death of its principal contradictor, Robert Hooke, Newton finally her great Treaty of optics publishes on the reflections, refractions, inflections and the colors.
It now devotes most of its time to official loads. It enters in 1696 to the Currency, and he becomes the director in 1700 about it; this office made of him the person in charge of the emission of the metal species in England (he will seek to improve striking of the coins and will continue the forgers). In 1703, he is elected president of Royal Society, of which he will direct work in particular towards the study of the phenomena of capillarity and electricity. He will preserve these two loads until his death, in 1727.
Mathematized colors
When, in the middle of the years 1660, Newton under investigation sticks phenomena of the light and colors by annotating the books of Robert Hooke and Robert Boyle, the explanatory theories of the color allowed still call upon, even when they are, as at Descartes, of inspiration mechanist, the Aristotelian theses: the light is pure and homogeneous; the colors, characterized by their glare or their force, are born from a modification (attenuation or obscuration) of the incidental light. Such a design, stripped of any quantitative support being able to contribute to specify the direction of the concepts of force and weakness, darkness and luminosity, finds its intelligibility only while referring directly to the impressions of the directions, with the way in which subjectively we feel affected by such or such color. Within this framework, there is no place for a mathematical interpretation of the phenomena of the color; it is in this precise theoretical place that is the Newtonian contribution.
The first work of Newton relating to the phenomena of the light and the colors appears in reports written in 1665 and 1666. It will have its results at the time of its courses to Cambridge, in 1670-1671. Then it is in a letter sent on on February 6th, 1672 to Royal Society that it will make known its work with many people.
Newton, prolonging work of inspiration corpuscularist of Robert Boyle and Walter Charleton, thus arrives since 1666 at the statement of its fundamental thesis: the white light is a heterogeneous mixture of differently refrangible rays. In 1672, its theory, being based on famous “the crucial experiment” (experimentum crucis), takes its final form: to each color a certain degree of refrangibility corresponds. Thus is established between refrangibility and the color a bi-univocal relation. Consequently, correlatively with their differences in their degrees in refrangibility, the rays differ “in their provision to present such or such particular color”. Newton establishes then that the color or the degree of refrangibility of a given ray is inalterable. It does not remain about it less than “apparent transmutations of color can occur where any mixture of rays of various natures takes place”. In fact, there are the simple and primitive colors, on the one hand, and their mixtures, on the other hand. The primitive or primary colors are “the red, the yellow, the purple one, blue, a purple crimson, with also orange, the indigo and an indefinite variety of intermediate nuances”.
Thus, the appearance of such or such color, at the time of a refraction for example, is related maintaining directly to the concept of refrangibility specific. However this concept, quantitatively expressible, corresponds to a measurable size: it is possible, on the basis of determined experimental procedure, to associate with each radiation a number characterizing its refrangibility. It is then easy to found a serial order making it possible to build an objective and quantitative scale colors. This capital result opens the way with the constitution of a mathematical theory of the phenomena of the rainbow and thin blades.
The experimentum crucis
The diagram of the assembly, absent from the text on the decomposition of the light addressed on on February 6th, 1672 to Royal Society, was given by Newton in a letter dated June 10th, 1672. The apparatus is composed of a “analyzer”, or producer of the spectrum, follow-up of a first bored screen of a hole, then, at a long distance (12 feet), of a second also bored screen of a hole; finally, behind this second screen, a second prism refracting the homogeneous rays admitted by the hole. The experiment is extremely simple. By rotation of the first prism around its axis, while maintaining fixed the two screens and the second prism, the rays of such or such species are brought opposite the first hole: only the beam uniting the two holes of the two screens, and whose direction consequently is constant, falls on the second prism. Thus observation on the wall of the various coloured spots, corresponding to the various rays refracted by the second prism, makes it possible the comparison of their refrangibility specific.
The rainbow
Newton presented its theory of the rainbow at the time of the courses which it gave to Cambridge in 1669-1671. However it did not publish it - and in a very concise way - that in 1704, in its Treaty of optics.
Its work falls under the prolongation of that of Descartes published in 1637 in Leyde in the Meteors, following the Discourse on Method. Descartes, being based on the law of the refraction (law of Snell-Descartes), had arrived at the idea that the appearance of the arcs corresponds to a “situation of extrema” in the way of the rays inside the water drops (it is the starting point of the modern idea of the “effective rays”). Newton, taking up the Cartesian idea, begins in a calculation aiming at determining the geometrical characteristics associated with the way with the effective rays. He arrives thus at the expression of the limiting value of the angle of incidence corresponding to the opening of the first rainbow: cos I =, (N being the index of refraction of the medium). It appears that the expression of this limiting value depends, via index N, of the refrangibility of each color: “Still Let us observe that the differently refrangible rays, having differently limited angles, will leave (according to their degree of refrangibility) in more a large number of various angles: then separate from/to each other, they will appear each one under their own color.”
Each color, corresponding to a given degree of refrangibility, is thus associated with a precise whole of effective rays generating for the observer an arc of such or such color. It is thus easy, on the basis of value of cos I, to calculate the respective positions of each color, coming from different drops, in the case of the first arc. For the arcs of a higher nature, the whole of the reasoning is very similar to those concerning the first. Newton arrives in fact at the general expression of the limiting value of the cosine of the angle of incidence corresponding to the openings of the various arcs: cos I = - (K representing the number of reflections which occurs inside a drop).
In the same way, the width of the coloured arcs becomes the object of a precise quantitative determination taking account of the apparent diameter of the Sun: “Such would be true measurements, if the Sun were only one point: but at a rate of the apparent diameter of this star, the width of the arcs must increase by a half-degree, and their reciprocal distance to decrease by as much. Thus the width of the iris interns will be of 2° 15 '; that of the external iris of 3° 40 '; their reciprocal distance from 8° 25 '; the greatest semi-diameter of the first, 42° 17 '; and the smallest semi-diameter of the second, 50° 42 '.”
Newton thus offers the first true mathematical theory of the phenomenon of the rainbow. The force of the Newtonian theory is particularly sensitive in the case of the arcs of a higher nature, whose presence, before Newton, is disputed, even denied. It is indeed only at the conclusion of calculation that the observer, informed by its own model, will turn finally the eyes in the directions most favourable with their observation and will be able to distinguish, besides the principal arc, a “secondary” arc and “supernumerary” arcs.
Thin blades
The first analyzes truly ordered concerning the observations of the colors on the surface of the transparent bodies in the shape of thin blades were given by Robert Boyle in 1664, in its Experiments and Considerations Touching Colors, and by Robert Hooke in 1665, in her Micrographia. This work, which contains inter alia remarkable drawings of observations carried out using a microscope, also announces what it is agreed to call today the newton's rings: “But they can resemble a lens, i.e. to have their center thicker than their edges or to have a double concavity, i.e. to be finer in the center than on the edges; in both cases, one will observe various circles or lines coloured with various successions or continuations of colors.” Christiaan Huygens also sticks, following Hooke, under investigation of these rings. But it is only Newton which gives a mathematical interpretation of it.
The analysis of Newton is organized in two stages, implied by its new design of the light: in the first, it sticks to the observations in white light, “at the great day”; in the second, it turns its attention on the observations in homogeneous light. This second stage is most interesting, because it enables him to release the relative laws with the Newton's rings. In this second series of observations, Newton places a convex lens under a plano-convex lens, the plane surface of the latter being turned downwards. Newton then makes ravel on these two lenses the various homogeneous colors. It observes, on the one hand, that the rings are more numerous and more distinct than in the case of the experiments “at the great day” and, on the other hand, than those produced by the red light are larger than those produced by the violet. Newton determines whereas the thickness necessary to give red rings must be in the ratio from 14 to 9 with that which provides the corresponding purple rings. Consequently, the diameters of the rings, for the same sequence number, grow as the color of the light passes from purple to the red. In addition, in all the cases in homogeneous light, the phenomenon observed by reflection consists simply in a succession of rings alternatively black or coloured. By transmission, the successions of black or coloured rings are exactly complementary to those seen previously by reflection. Newton shows whereas the rings obtained in white light result from the combination of all the various systems of rings corresponding to each color.
Newton also gives in the third and the last delivers of the Treaty of optics a set of observations relating to the phenomenon of the diffraction, which it for its part gathers under the denomination of “inflection”. The phenomenon had been described by Francesco Maria Grimaldi (1618-1663) in her work entitled Physico mathesis of lumine, coloribus and iride, published in Bologna in 1665. It is besides Grimaldi which introduced the term of “diffraction” to characterize the new phenomena that it has just discovered. However Newton, within the framework of its optics of inspiration corpuscularist, prefers that of “inflection”, because it aims reducing these phenomena to a certain kind of refraction and not at regarding them as a specific mode of light propagation. By doing this, he does not manage to give to his theory the same degree of perfection which marked its work on the rainbow or the thin blades, but Newtonian optics will dominate science until the transformations of the first quarter of the XIX E century, when Augustin Fresnel mathématise the undulatory theories introduced at the end of the XVII E century by Huygens.
The mathematisation of the system of the world
In 1687, Newton, then old of forty-five years, publishes in London Philosophiae naturalis principia mathematica. Principia are presented in three parts or books. The first develops, from a point of view which wants to be strictly mathematical, the whole of the questions referring to the science of the movement independently of the resistance exerted by the mediums. Second is devoted primarily to the movements of the bodies in the resistant mediums, in particular with the projectiles in mediums whose resistance varies like speed, the square speed or even like the linear combination of both. Newton also poses there the problems of the form of the solid of less resistance and the theoretical justification of the law of flow of Torricelli. This second book is completed by a vigorous criticism of the Cartesian assumption of the swirls. The style of this criticism illustrates perfectly the opposition between Cartesian geometrical cosmology and the Newtonian physicomathematical deductive organization. The third book takes again the results of the two first and the bracket with the problems (movement of planets and the Moon, configuration of the Earth, theory of the tides…).
Principia open by two preliminary headings: “Definitions” and “Axioms or laws of the movement”. Heading “Definitions” offers in particular those of quantity of matter (“the quantity of matter is measurement that one draws at the same time from his density and his volume”), of momentum (“the momentum is measurement that one draws at the same time his speed and from his quantity of matter”), of force printed (“the screw impressa is the action which is exerted on a body to change it at-rest state or of uniform rectilinear motion”), centripetal force (“the centripetal force is the force which attracts the bodies of all shares, the growth or confers to them some tendency that it is, towards a point, like worms a center”).
This whole of definitions ends in a scholium which gives the very famous definitions of space and absolute times:
“1) Absolute, true and mathematical time, without relation with nothing outside, runs uniformly; it is called also lasted. Relative, apparent and vulgar time, is this significant and external measurement of part of duration unspecified of which one is usually useful oneself instead of true time. Such are the hour, the day, the month, the year.
2) Absolute space, without relation with the external things, from its nature remains always similar and motionless. Relative space is any measurement or mobile dimension of this space, which is defined in a significant way by its situation with regard to the bodies and which one usually takes for motionless space.”
The heading “Axioms or laws of the movement” joins together for the first time the three great laws of mechanics in a form very close to that which we know to them today.
- The first law expresses the principle of the inertia or the conservation of the uniform rectilinear motion: “Any body perseveres in its at-rest state or of uniform rectilinear motion except so of the printed forces force it to change.”
- The second law stipulates that “the change of movement is proportional to the printed driving force and is carried out according to the line by which this force is printed”. This law should not be confused with that, expressed in differential terms, which we know today under the denomination of “law of Newton”. In particular, Newton speaks here about “change of movement” without any precision concerning the time during which this change is carried out. If one wanted absolutely to write this law in modern terms, the expression nearest would undoubtedly be this one: F = P (mv), where F are the printed driving force, m mass and v speed, knowing that P (mv) represents the “change of movement”. From this point of view, one can say that a printed driving force is not a force, to the modern direction of the term, but an impulse.
- The third law is that of the equality of the action and the reaction: “The reaction is always equal and opposite to the action: i.e. the mutual actions of two bodies always equal and are directed in contrary direction.” This third law, which does not appear in 1685 in the preliminary drafts with the drafting of Principia, makes it possible Newton in book III to formulate in all its extension the law of the universal gravitation.
It is on the basis of of these “Definitions” and these “Axioms or laws of the movement” that the movement of the bodies under the action of the central forces is born with the mathematical existence. For this purpose, Newton implements the mathematical methods of the traditional geometry of Euclidean inspiration, enriched however, on the one hand, by many relative results under investigation of conical (sections IV and V of book I) and, on the other hand, by a set of reasoning of infinitesimal geometry which it gathers in the first section of book I under the denomination of “Method of the first and last reasons”. It is remarkable to note that Newton does not use in the whole of the demonstrations (except for lemma II of book II) the procedures of the “calculation of the fluxions”, of which it however has since the years the 1670 essential principles.
Mathematics
The contribution of Newton to the progress of mathematics covers a very broad field, which cannot be reduced to only work concerning the “calculation of the fluxions” and the “dotted notation” (X, 5.7…): this one is well-known mechanics, who use today indifferently this notation and that introduced by Leibniz with his differential and integral calculus; but, around 1700, these two calculations rested on different conceptual bases, Newtonian calculation being marked by implicit considerations kinematics.
The Newtonian contributions also relate to the study of the infinite series and the binomial theorem like that of the various fields of mathematics: algebra, theory of the numbers, analytical geometry, classification of the curves, method of calculating and of approximations. However a very important part of work of Newton remained in the form of manuscripts, news of alive sound.
Since a few years publication by D.T. Whiteside of Mathematical Papers off Isaac Newton (8 volumes, Cambridge University Near, 1967-1981) made it possible to better appreciate in its richness and its diversity the whole of this work.
Central forces with the universal gravitation
To seize all the extent of the Newtonian stakes and the innovation of Principia, it is necessary to enter the conclusive structure of the treaty itself.
The construction of the theory of the central forces and the installation of the assumption of the universal gravitation are from this specimens point of view.
The law of the surfaces is one of the three laws of Kepler which will play a very important part in the development of the celestial mechanics (the first law stipulates that the planets describe ellipses whose Sun occupies one of the hearths; the second, the famous law of the surfaces, known as that surfaces, or surfaces, swept by a ray are proportional to times; the third law connects dimensions of the ellipses to the periods of the revolutions, i.e. at the time which the planets spend to traverse their trajectories in entirety).
Newton perceives the importance of the law of the surfaces in the motion study of the bodies subjected to central forces. By doing this, section II of book I of Principia opens by two proposals, the second, which is reciprocal first, has the aim of establishing that the index property of a movement with acceleration or central force is precisely constancy in a plan areal speed or that in such a movement the surface swept by the ray is proportional to time. The knowledge of such a property constitutes a decisive contribution for the development of the theory of the central forces, this surface being able to be used to represent time.
Proposal 1 of book I of Principia is stated then as follows: “The surfaces that the animated bodies of curvilinear movements describe by rays led to the motionless center of the forces are included in motionless plans, and are proportional to times.”
This first result leads Newton to the statement of the proposal 4, which gives a general expression of the intensity of the central forces in a point. This expression enables him in its turn to obtain the given expression of the force according to the distance between the body moving and the center given of force. Thus, to take only one example, proposal 11 (“a body making its revolution in an ellipse, one asks for the centripetal law of force when it tends to one of its hearths”) led to the well-known result that the central force is then “because reverse of the square of the distance to the center of force”.
This proposal announces work of celestial mechanics, given that then the center of force is not any more one point mathematical but a gifted body of mass (in proposal 75 of section XII, Newton establishes that the mass of the gravitational bodies can be regarded as gathered in their center) likely to enter in interaction. This new situation is precisely considered by Newton in section XI of book I, “Of the movement of bodies which attract each other mutually by centripetal forces”.
Newton then tackles the problems known as of the “two bodies” (proposals 57 to 65) then those of the “three bodies” (proposals 66 to 68), whose treatments are extremely delicate: indeed, so today the problem of the two bodies is well controlled, that of the three bodies and more does not have a general solution, although it is possible to give of them approximate solutions of a great reliability, as testify calculations to them to the astronomers concerning the planetary movements or the launching of the space engines. For its part, Newton arrives, at least for the problem of the two bodies, with an astute solution by immobilizing one of the bodies artificially (that whose mass is largest).
This step developed in this section XI takes all its direction in book III when it is a question of showing, while being based on the astronomical observations, that the movement of the celestial bodies is well governed by the law of the universal gravitation, i.e. all the bodies attract each other with a force proportional to the product of their mass and inversely proportional to the square of the distance which separates them.
These once established results, starting from the motion study of planets and their satellites, and in particular of the movement of the Moon - which allows inter alia proving the identity between the centripetal force and gravity (in this direction one can say that the Moon at every moment falls towards the center from the Earth by the same cause which makes as a stone or than an apple released fall; but in the case of the Moon, it is also actuated by a movement directed according to the tangent, and the composition of these two movements generates, like in the case of the projectiles, a curvilinear movement) -, Newton studies the movement of the comets (proposals 40 to 42), that of the flow and the backward flow of the sea (proposal 46) and the flatness of the Earth to the poles (proposal 19). To the XVIII E century, the prediction with a very high degree of accuracy of the return in 1758 of comet observed by Halley in 1681-1682 as well as measurements of arc of meridian lines to check the flatness of the Earth to the poles and the equator, realized respectively by Maupertuis (forwarding of Lapland in 1736-1737) and by Bouguer and Condamine (forwarding of Peru in 1735-1744), will give all their glare to Newtonian work.
On the ground as with the sky
But, before being celebrated by England like a national hero and buried in the abbey of Westminster, Newton had to be defended, sometimes with ferocity, against Hooke, Leibniz, Cartesian French (who found a stink medieval with the concepts of force and remote action), against the erudite Jesuits. Also it put itself the hand at its legend, multiplying the anecdotes (the fall of apple in the orchard of his/her mother) on its “intuitions” of the years 1665-1666. But starting from Voltaire and of Kant, the results of work of Newton are defined as being simply the truth.
A deductive mode being based on some concepts stated in full clearness now regulates the development of the science of the movement and opens the way with the mechanics. The hierarchical worlds of Aristotelian cosmos disappeared to leave the place to a unified Universe, where the same principles, the same laws apply from now on to the sky as with the Earth. Our Universe has just been born.
Newton and alchemy
Newton was interested much in alchemy, as testify some to many manuscripts, preserved during two centuries and half in a trunk and bought partly, at the time of an auction in 1936, by the economist John Maynard Keynes. Their attentive study has been however developed only for about twenty years, in particular thanks to work of R.S. Westfall (the Force in Newtonian physics, 1971) and of Betty OJ T. Dobbs (Bases of the alchemy of Newton, 1975).
Apart from this alchemical work, Newton, seeking to constitute a universal language, also carried very an great attention to theological research (it shows, in its notebooks, near to the heresy arienne, which refused the dogma of the Trinity) and under investigation of prophecies. It wrote, in particular: Observations Upon the Prophecies off Daniel and the Apocalypse off St John, a treaty published in 1733. Its analysis of the biblical texts and Greeks led it to think that the science which it worked out was only one rediscovery of the intuitions, even of the “secrecies” of Old. Through these writings a figure more complex takes shape than that which the only reading of the large texts could suggest, that, according to the same words of Keynes, of the “last of the magicians”, the last spirit to have contemplated the visible world with the eyes of the Babylonians and the Sumerian ones.