Pioneers of Science Part 13

In philosophy, using the term as meaning mental or moral philosophy and metaphysics, as opposed to natural philosophy or physics, he takes a very high rank, and it is on this that perhaps his greatest fame rests.

(He is the author, you may remember, of the famous aphorism, "_Cogito, ergo sum_.")

In biology I believe he may be considered almost equally great: certainly he spent a great deal of time in dissecting, and he made out a good deal of what is now known of the structure of the body, and of the theory of vision. He eagerly accepted the doctrine of the circulation of the blood, then being taught by Harvey, and was an excellent anatomist.

You doubtless know Professor Huxley's article on Descartes in the _Lay Sermons_, and you perceive in what high estimation he is there held.

He originated the hypothesis that animals are automata, for which indeed there is much to be said from some points of view; but he unfortunately believed that they were unconscious and non-sentient automata, and this belief led his disciples into acts of abominable cruelty. Professor Huxley lectured on this hypothesis and partially upheld it not many years since. The article is included in his volume called _Science and Culture_.

Concerning his work in mathematics and physics I can speak with more confidence. He is the author of the Cartesian system of algebraic or a.n.a.lytic geometry, which has been so powerful an engine of research, far easier to wield than the old synthetic geometry. Without it Newton could never have written the _Principia_, or made his greatest discoveries.

He might indeed have invented it for himself, but it would have consumed some of his life to have brought it to the necessary perfection.

The principle of it is the specification of the position of a point in a plane by two numbers, indicating say its distance from two lines of reference in the plane; like the lat.i.tude and longitude of a place on the globe. For instance, the two lines of reference might be the bottom edge and the left-hand vertical edge of a wall; then a point on the wall, stated as being for instance 6 feet along and 2 feet up, is precisely determined. These two distances are called co-ordinates; horizontal ones are usually denoted by _x_, and vertical ones by _y_.

If, instead of specifying two things, only one statement is made, such as _y_ = 2, it is satisfied by a whole row of points, all the points in a horizontal line 2 feet above the ground. Hence _y_ = 2 may be said to represent that straight line, and is called the equation to that straight line. Similarly _x_ = 6 represents a vertical straight line 6 feet (or inches or some other unit) from the left-hand edge. If it is a.s.serted that _x_ = 6 and _y_ = 2, only one point can be found to satisfy both conditions, viz. the crossing point of the above two straight lines.

Suppose an equation such as _x_ = _y_ to be given. This also is satisfied by a row of points, viz. by all those that are equidistant from bottom and left-hand edges. In other words, _x_ = _y_ represents a straight line slanting upwards at 45. The equation _x_ = 2_y_ represents another straight line with a different angle of slope, and so on. The equation x^2 + y^2 = 36 represents a circle of radius 6. The equation 3x^2 + 4y^2 = 25 represents an ellipse; and in general every algebraic equation that can be written down, provided it involve only two variables, _x_ and _y_, represents some curve in a plane; a curve moreover that can be drawn, or its properties completely investigated without drawing, from the equation. Thus algebra is wedded to geometry, and the investigation of geometric relations by means of algebraic equations is called a.n.a.lytical geometry, as opposed to the old Euclidian or synthetic mode of treating the subject by reasoning consciously directed to the subject by help of figures.

If there be three variables--_x_, _y_, and _z_,--instead of only two, an equation among them represents not a curve in a plane but a surface in s.p.a.ce; the three variables corresponding to the three dimensions of s.p.a.ce: length, breadth, and thickness.

An equation with four variables usually requires s.p.a.ce of four dimensions for its geometrical interpretation, and so on.

Thus geometry can not only be reasoned about in a more mechanical and therefore much easier, manner, but it can be extended into regions of which we have and can have no direct conception, because we are deficient in sense organs for acc.u.mulating any kind of experience in connexion with such ideas.

[Ill.u.s.tration: FIG. 54.--The eye diagram. [From Descartes' _Principia_.]

Three external points are shown depicted on the retina: the image being appreciated by a representation of the brain.]

In physics proper Descartes' tract on optics is of considerable historical interest. He treats all the subjects he takes up in an able and original manner.

In Astronomy he is the author of that famous and long upheld theory, the doctrine of vortices.

He regarded s.p.a.ce as a plenum full of an all-pervading fluid. Certain portions of this fluid were in a state of whirling motion, as in a whirlpool or eddy of water; and each planet had its own eddy, in which it was whirled round and round, as a straw is caught and whirled in a common whirlpool. This idea he works out and elaborates very fully, applying it to the system of the world, and to the explanation of all the motions of the planets.

[Ill.u.s.tration: FIG. 55.--Descartes's diagram of vortices, from his _Principia_.]

This system evidently supplied a void in men's minds, left vacant by the overthrow of the Ptolemaic system, and it was rapidly accepted. In the English Universities it held for a long time almost undisputed sway; it was in this faith that Newton was brought up.

Something was felt to be necessary to keep the planets moving on their endless round; the _primum mobile_ of Ptolemy had been stopped; an angel was sometimes a.s.signed to each planet to carry it round, but though a widely diffused belief, this was a fantastic and not a serious scientific one. Descartes's vortices seemed to do exactly what was wanted.

It is true they had no connexion with the laws of Kepler. I doubt whether he knew about the laws of Kepler; he had not much opinion of other people's work; he read very little--found it easier to think. (He travelled through Florence once when Galileo was at the height of his renown without calling upon or seeing him.) In so far as the motion of a planet was not circular, it had to be accounted for by the jostling and crowding and distortion of the vortices.

Gravitation he explained by a settling down of bodies toward the centre of each vortex; and cohesion by an absence of relative motion tending to separate particles of matter. He "can imagine no stronger cement."

The vortices, as Descartes imagined them, are not now believed in. Are we then to regard the system as absurd and wholly false? I do not see how we can do this, when to this day philosophers are agreed in believing s.p.a.ce to be completely full of fluid, which fluid is certainly capable of vortex motion, and perhaps everywhere does possess that motion. True, the now imagined vortices are not the large whirls of planetary size, they are rather infinitesimal whirls of less than atomic dimensions; still a whirling fluid is believed in to this day, and many are seeking to deduce all the properties of matter (rigidity, elasticity, cohesion gravitation, and the rest) from it.

Further, although we talk glibly about gravitation and magnetism, and so on, we do not really know what they are. Progress is being made, but we do not yet properly know. Much, overwhelmingly much, remains to be discovered, and it ill-behoves us to reject any well-founded and long-held theory as utterly and intrinsically false and absurd. The more one gets to know, the more one perceives a kernel of truth even in the most singular statements; and scientific men have learned by experience to be very careful how they lop off any branch of the tree of knowledge, lest as they cut away the dead wood they lose also some green shoot, some healthy bud of unperceived truth.

However, it may be admitted that the idea of a Cartesian vortex in connexion with the solar system applies, if at all, rather to an earlier--its nebulous--stage, when the whole thing was one great whirl, ready to split or shrink off planetary rings at their appropriate distances.

Soon after he had written his great work, the _Principia Mathematica_, and before he printed it, news reached him of the persecution and recantation of Galileo. "He seems to have been quite thunderstruck at the tidings," says Mr. Mahaffy, in his _Life of Descartes_.[15] "He had started on his scientific journeys with the firm determination to enter into no conflict with the Church, and to carry out his system of pure mathematics and physics without ever meddling with matters of faith. He was rudely disillusioned as to the possibility of this severance. He wrote at once--apparently, November 20th, 1633--to Mersenne to say he would on no account publish his work--nay, that he had at first resolved to burn all his papers, for that he would never prosecute philosophy at the risk of being censured by his Church. 'I could hardly have believed,' he says, 'that an Italian, and in favour with the Pope as I hear, could be considered criminal for nothing else than for seeking to establish the earth's motion; though I know it has formerly been censured by some Cardinals. But I thought I had heard that since then it was constantly being taught, even at Rome; and I confess that if the opinion of the earth's movement is false, all the foundations of my philosophy are so also, because it is demonstrated clearly by them. It is so bound up with every part of my treatise that I could not sever it without making the remainder faulty; and although I consider all my conclusions based on very certain and clear demonstrations, I would not for all the world sustain them against the authority of the Church.'"

Ten years later, however, he did publish the book, for he had by this time hit on an ingenious compromise. He formally denied that the earth moved, and only a.s.serted that it was carried along with its water and air in one of those larger motions of the celestial ether which produce the diurnal and annual revolutions of the solar system. So, just as a pa.s.senger on the deck of a s.h.i.+p might be called stationary, so was the earth. He gives himself out therefore as a follower of Tycho rather than of Copernicus, and says if the Church won't accept this compromise he must return to the Ptolemaic system; but he hopes they won't compel him to do that, seeing that it is manifestly untrue.

This elaborate deference to the powers that be did not indeed save the work from being ultimately placed upon the forbidden list by the Church, but it saved himself, at any rate, from annoying persecution. He was not, indeed, at all willing to be persecuted, and would no doubt have at once withdrawn anything they wished. I should be sorry to call him a time-server, but he certainly had plenty of that worldly wisdom in which some of his predecessors had been so lamentably deficient. Moreover, he was really a sceptic, and cared nothing at all about the Church or its dogmas. He knew the Church's power, however, and the advisability of standing well with it: he therefore professed himself a Catholic, and studiously kept his science and his Christianity distinct.

In saying that he was a sceptic you must not understand that he was in the least an atheist. Very few men are; certainly Descartes never thought of being one. The term is indeed ludicrously inapplicable to him, for a great part of his philosophy is occupied with what he considers a rigorous proof of the existence of the Deity.

At the age of fifty-three he was sent for to Stockholm by Christina, Queen of Sweden, a young lady enthusiastically devoted to study of all kinds and determined to surround her Court with all that was most famous in literature and science. Thither, after hesitation, Descartes went. He greatly liked royalty, but he dreaded the cold climate. Born in Touraine, a Swedish winter was peculiarly trying to him, especially as the energetic Queen would have lessons given her at five o'clock in the morning. She intended to treat him well, and was immensely taken with him; but this getting up at five o'clock on a November morning, to a man accustomed all his life to lie in bed till eleven, was a cruel hards.h.i.+p.

He was too much of a courtier, however, to murmur, and the early morning audience continued. His health began to break down: he thought of retreating, but suddenly he gave way and became delirious. The Queen's physician attended him, and of course wanted to bleed him. This, knowing all he knew of physiology, sent him furious, and they could do nothing with him. After some days he became quiet, was bled twice, and gradually sank, discoursing with great calmness on his approaching death, and duly fortified with all the rites of the Catholic Church.

His general method of research was as nearly as possible a purely deductive one:--_i.e._, after the manner of Euclid he starts with a few simple principles, and then, by a chain of reasoning, endeavours to deduce from them their consequences, and so to build up bit by bit an edifice of connected knowledge. In this he was the precursor of Newton.

This method, when rigorously pursued, is the most powerful and satisfactory of all, and results in an ordered province of science far superior to the fragmentary conquests of experiment. But few indeed are the men who can handle it safely and satisfactorily: and none without continual appeals to experiment for verification. It was through not perceiving the necessity for verification that he erred. His importance to science lies not so much in what he actually discovered as in his antic.i.p.ation of the right conditions for the solution of problems in physical science. He in fact made the discovery that Nature could after all be interrogated mathematically--a fact that was in great danger of remaining unknown. For, observe, that the mathematical study of Nature, the discovery of truth with a piece of paper and a pen, has a perilous similarity at first sight to the straw-thras.h.i.+ng subtleties of the Greeks, whose methods of investigating nature by discussing the meaning of words and the usage of language and the necessities of thought, had proved to be so futile and unproductive.

A reaction had set in, led by Galileo, Gilbert, and the whole modern school of experimental philosophers, lasting down to the present day:--men who teach that the only right way of investigating Nature is by experiment and observation.

It is indeed a very right and an absolutely necessary way; but it is not the only way. A foundation of experimental fact there must be; but upon this a great structure of theoretical deduction can be based, all rigidly connected together by pure reasoning, and all necessarily as true as the premises, provided no mistake is made. To guard against the possibility of mistake and oversight, especially oversight, all conclusions must sooner or later be brought to the test of experiment; and if disagreeing therewith, the theory itself must be re-examined, and the flaw discovered, or else the theory must be abandoned.

Of this grand method, quite different from the gropings in the dark of Kepler--this method, which, in combination with experiment, has made science what it now is--this which in the hands of Newton was to lead to such stupendous results, we owe the beginning and early stages to Rene Descartes.

SUMMARY OF FACTS FOR LECTURES VII AND VIII

Otto Guericke 1602-1686 Hon. Robert Boyle 1626-1691 Huyghens 1629-1695 Christopher Wren 1632-1723 Robert Hooke 1635-1702 NEWTON 1642-1727 Edmund Halley 1656-1742 James Bradley 1692-1762

_Chronology of Newton's Life._

Isaac Newton was born at Woolsthorpe, near Grantham, Lincolns.h.i.+re, on Christmas Day, 1642. His father, a small freehold farmer, also named Isaac, died before his birth. His mother, _nee_ Hannah Ayscough, in two years married a Mr. Smith, rector of North Witham, but was again left a widow in 1656. His uncle, W. Ayscough, was rector of a near parish and a graduate of Trinity College, Cambridge. At the age of fifteen Isaac was removed from school at Grantham to be made a farmer of, but as it seemed he would not make a good one his uncle arranged for him to return to school and thence to Cambridge, where he entered Trinity College as a sub-sizar in 1661. Studied Descartes's geometry. Found out a method of infinite series in 1665, and began the invention of Fluxions. In the same year and the next he was driven from Cambridge by the plague. In 1666, at Woolsthorpe, the apple fell. In 1667 he was elected a fellow of his college, and in 1669 was specially noted as possessing an unparalleled genius by Dr. Barrow, first Lucasian Professor of Mathematics. The same year Dr. Barrow retired from his chair in favour of Newton, who was thus elected at the age of twenty-six. He lectured first on optics with great success. Early in 1672 he was elected a Fellow of the Royal Society, and communicated his researches in optics, his reflecting telescope, and his discovery of the compound nature of white light. Annoying controversies arose; but he nevertheless contributed a good many other most important papers in optics, including observations in diffraction, and colours of thin plates. He also invented the modern s.e.xtant. In 1672 a letter from Paris was read at the Royal Society concerning a new and accurate determination of the size of the earth by Picard. When Newton heard of it he began the _Principia_, working in silence. In 1684 arose a discussion between Wren, Hooke, and Halley concerning the law of inverse square as applied to gravity and the path it would cause the planets to describe. Hooke a.s.serted that he had a solution, but he would not produce it. After waiting some time for it Halley went to Cambridge to consult Newton on the subject, and thus discovered the existence of the first part of the _Principia_, wherein all this and much more was thoroughly worked out. On his representations to the Royal Society the ma.n.u.script was asked for, and when complete was printed and published in 1687 at Halley's expense. While it was being completed Newton and seven others were sent to uphold the dignity of the University, before the Court of High Commission and Judge Jeffreys, against a high-handed action of James II. In 1682 he was sent to Parliament, and was present at the coronation of William and Mary. Made friends with Locke. In 1694 Montague, Lord Halifax, made him Warden, and in 1697 Master, of the Mint. Whiston succeeded him as Lucasian Professor. In 1693 the method of fluxions was published. In 1703 Newton was made President of the Royal Society, and held the office to the end of his life. In 1705 he was knighted by Anne. In 1713 Cotes helped him to bring out a new edition of the _Principia_, completed as we now have it. On the 20th of March 1727, he died: having lived from Charles I. to George II.

THE LAWS OF MOTION, DISCOVERED BY GALILEO, STATED BY NEWTON.

_Law 1._--If no force acts on a body in motion, it continues to move uniformly in a straight line.

_Law 2._--If force acts on a body, it produces a change of motion proportional to the force and in the same direction.

_Law 3._--When one body exerts force on another, that other reacts with equal force upon the one.

LECTURE VII

SIR ISAAC NEWTON

The little hamlet of Woolsthorpe lies close to the village of Colsterworth, about six miles south of Grantham, in the county of Lincoln. In the manor house of Woolsthorpe, on Christmas Day, 1642, was born to a widowed mother a sickly infant who seemed not long for this world. Two women who were sent to North Witham to get some medicine for him scarcely expected to find him alive on their return. However, the child lived, became fairly robust, and was named Isaac, after his father. What sort of a man this father was we do not know. He was what we may call a yeoman, that most wholesome and natural of all cla.s.ses. He owned the soil he tilled, and his little estate had already been in the family for some hundred years. He was thirty-six when he died, and had only been married a few months.