commonly current. The truth probably lies somewhere between the two
extremes. It is unfair to judge Bacon's methods by thinking of physical
science in its present stage. To realise his position we must think of a
subject still in its very early infancy, one in which the advisability
of applying experimental methods is still doubted; one which has been
studied by means of books and words and discussion of normal instances,
instead of by collection and observation of the unusual and irregular,
and by experimental production of variety. If we think of a subject
still in this infantile and almost pre-scientific stage, Bacon's words
and formulae are far from inapplicable; they are, within their
limitations, quite necessary and wholesome. A subject in this stage,
strange to say, exists,--psychology; now hesitatingly beginning to
assume its experimental weapons amid a stifling atmosphere of distrust
and suspicion. Bacon's lack of the modern scientific instinct must be
admitted, but he rendered humanity a powerful service in directing it
from books to nature herself, and his genius is indubitable. A judicious
account of his life and work is given by Prof. Adamson, in the
_Encyclopaedia Britannica_, and to this article I now refer you.
* * * * *
Who, then, was the man of first magnitude filling up the gap in
scientific history between the death of Galileo and the maturity of
Newton? Unknown and mysterious are the laws regulating the appearance of
genius. We have passed in review a Pole, a Dane, a German, and an
Italian,--the great man is now a Frenchman, Rene Descartes, born in
Touraine, on the 31st of March, 1596.
His mother died at his birth; the father was of no importance, save as
the owner of some landed property. The boy was reared luxuriously, and
inherited a fair fortune. Nearly all the men of first rank, you notice,
were born well off. Genius born to poverty might, indeed, even then
achieve name and fame--as we see in the case of Kepler--but it was
terribly handicapped. Handicapped it is still, but far less than of old;
and we may hope it will become gradually still less so as enlightenment
proceeds, and the tremendous moment of great men to a nation is more
clearly and actively perceived.
It is possible for genius, when combined with strong character, to
overcome all obstacles, and reach the highest eminence, but the
struggle must be severe; and the absence of early training and
refinement during the receptive years of youth must be a lifelong
drawback.
Descartes had none of these drawbacks; life came easily to him, and, as
a consequence perhaps, he never seems to have taken it quite seriously.
Great movements and stirring events were to him opportunities for the
study of men and manners; he was not the man to court persecution, nor
to show enthusiasm for a losing or struggling cause.
In this, as in many other things, he was imbued with a very modern
spirit, a cynical and sceptical spirit, which, to an outside and
superficial observer like myself, seems rather rife just now.
He was also imbued with a phase of scientific spirit which you sometimes
still meet with, though I believe it is passing away, viz. an uncultured
absorption in his own pursuits, and some feeling of contempt for
classical and literary and aesthetic studies.
In politics, art, and history he seems to have had no interest. He was a
spectator rather than an actor on the stage of the world; and though he
joined the army of that great military commander Prince Maurice of
Nassau, he did it not as a man with a cause at heart worth fighting for,
but precisely in the spirit in which one of our own gilded youths would
volunteer in a similar case, as a good opportunity for frolic and for
seeing life.
He soon tired of it and withdrew--at first to gay society in Paris. Here
he might naturally have sunk into the gutter with his companions, but
for a great mental shock which became the main epoch and turning-point
of his life, the crisis which diverted him from frivolity to
seriousness. It was a purely intellectual emotion, not excited by
anything in the visible or tangible world; nor could it be called
conversion in the common acceptation of that term. He tells us that on
the 10th of November, 1619, at the age of twenty-four, a brilliant idea
flashed upon him--the first idea, namely, of his great and powerful
mathematical method, of which I will speak directly; and in the flush of
it he foresaw that just as geometers, starting with a few simple and
evident propositions or axioms, ascend by a long and intricate ladder of
reasoning to propositions more and more abstruse, so it might be
possible to ascend from a few data, to all the secrets and facts of the
universe, by a process of mathematical reasoning.
"Comparing the mysteries of Nature with the laws of mathematics, he
dared to hope that the secrets of both could be unlocked with the same
key."
That night he lapsed gradually into a state of enthusiasm, in which he
saw three dreams or visions, which he interpreted at the time, even
before waking, to be revelations from the Spirit of Truth to direct his
future course, as well as to warn him from the sins he had already
committed.
His account of the dreams is on record, but is not very easy to follow;
nor is it likely that a man should be able to convey to others any
adequate idea of the deepest spiritual or mental agitation which has
shaken him to his foundations.
His associates in Paris were now abandoned, and he withdrew, after some
wanderings, to Holland, where he abode the best part of his life and did
his real work.
Even now, however, he took life easily. He recommends idleness as
necessary to the production of good mental work. He worked and meditated
but a few hours a day: and most of those in bed. He used to think best
in bed, he said. The afternoon he devoted to society and recreation.
After supper he wrote letters to various persons, all plainly intended
for publication, and scrupulously preserved. He kept himself free from
care, and was most cautious about his health, regarding himself, no
doubt, as a subject of experiment, and wishful to see how long he could
prolong his life. At one time he writes to a friend that he shall be
seriously disappointed if he does not manage to see 100 years.
[Illustration: FIG. 53.--Descartes.]
This plan of not over-working himself, and limiting the hours devoted to
serious thought, is one that might perhaps advantageously be followed by
some over-laborious students of the present day. At any rate it conveys
a lesson; for the amount of ground covered by Descartes, in a life not
very long, is extraordinary. He must, however, have had a singular
aptitude for scientific work; and the judicious leaven of selfishness
whereby he was able to keep himself free from care and embarrassments
must have been a great help to him.
And what did his versatile genius accomplish during his fifty-four years
of life?
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
analytic 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 latitude 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 asserted 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 deg.. 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 analytical 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 space; the three variables corresponding to the three
dimensions of space: length, breadth, and thickness.
An equation with four variables usually requires space 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 accumulating any kind of
experience in connexion with such ideas.
[Illustration: 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 space 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.
[Illustration: 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 assigned 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 space 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 asserted 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
passenger on the deck of a ship 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 hardship.
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
anticipation 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-thrashing 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._