Section 4. Science

The glory of sixteenth-century science is that for the first time, on a large scale, since the ancient Greeks, did men try to look at nature through their own eyes instead of through those of Aristotle and the Physiologus. Bacon and Vives have each been credited with the discovery of the inductive method, but, like so many philosophers, they merely generalized a practice already common at their time. Save for one discovery of the first magnitude, and two or three others of some little importance, the work of the sixteenth century was that of observing, describing and classifying facts. This was no small service in itself, though it does not strike the imagination as do the great new theories.

In mathematics the preparatory work for the statement and solution of new problems consisted in the perfection of symbolism. As reasoning in general is dependent on words, as music is dependent on the mechanical invention of instruments, so mathematics cannot progress far save with a simple and adequate symbolism. The introduction of the Arabic as against the Roman numerals, and particularly the introduction of the zero in reckoning, for the first time, in the later Middle Ages, allowed men to perform conveniently the four fundamental processes. The use of the signs + {610} and - for plus and minus (formerly written p. and m.), and of the sign = for equality and of V [square root symbol] for root, were additional conveniences. To this might be added the popularization of decimals by Simon Stevin in 1586, which he called "the art of calculating by whole numbers without fractions." How clumsy are all things at their birth is illustrated by his method of writing decimals by putting them as powers of one-tenth, with circles around the exponents; e.g., the number that we should write 237.578, he wrote 237(to the power 0) 5(to the power 1) 7(to the power 2) 8 (to the power 3). He first declared for decimal systems of coinage, weights and measures.

Algebraic notation also improved vastly in the period. In a treatise of Lucas Paciolus we find cumbrous signs instead of letters, thus no. (numero) for the known quantity, co. (cosa) for the unknown quantity, ce. (censo) for the square, and cu. (cubo) for the cube of the unknown quantity. As he still used p. and m. for plus and minus, he wrote 3co.p.4ce.m.5cu.p.2ce.ce.m.6no. for the number we should write 3x + 4x(power 2) - 5x(power 3) + 2x(power 4) - 6a. The use of letters in the modern style is due to the mathematicians of the sixteenth century. The solution of cubic and of biquadratic equations, at first only in certain particular forms, but later in all forms, was mastered by Tartaglia and Cardan. The latter even discussed negative roots, whether rational or irrational.

Geometry at that time, as for long afterwards, was dependent wholly on Euclid, of whose work a Latin translation was first published at Venice. [Sidenote: 1505] Copernicus with his pupil George Joachim, called Rheticus, and Francis Vieta, made some progress in trigonometry. Copernicus gave the first simple demonstration of the fundamental formula of spherical trigonometry; Rheticus made tables of sines, tangents and secants {611} of arcs. Vieta discovered the formula for deriving the sine of a multiple angle.

As one turns the pages of the numerous works of Jerome Cardan one is astonished to find the number of subjects on which he wrote, including, in mathematics, choice and chance, arithmetic, algebra, the calendar, negative quantities, and the theory of numbers. In the last named branch it was another Italian, Maurolycus, who recognized the general character of mathematics as "symbolic logic." He is indeed credited with understanding the most general principle on which depends all mathematical deduction. Some of the most remarkable anticipations of modern science were made by Cardan. He believed that inorganic matter was animated, and that all nature was a progressive evolution. Thus his statement that all animals were originally worms implies the indefinite variability of species, just as his remark that inferior metals were unsuccessful attempts of nature to produce gold, might seem to foreshadow the idea of the transmutation of metals under the influence of radioactivity. It must be remembered that such guesses had no claim to be scientific demonstrations.

The encyclopaedic character of knowledge was then, perhaps, one of its most striking characteristics. Bacon was not the first man of his century to take all knowledge for his province. In learning and breadth of view few men have ever exceeded Conrad Gesner, [Sidenote: Gesner] called by Cuvier "the German Pliny." His History of Animals (published in many volumes 1551-87) was the basis of zooelogy until the time of Darwin. [Sidenote: Zooelogy] He {612} drew largely on previous writers, Aristotle and Albertus Magnus, but he also took pains to see for himself as much as possible. The excellent illustrations for his book, partly drawn from previous works but mostly new, added greatly to its value. His classification, though superior to any that had preceded it, was in some respects astonishing, as when he put the hippopotamus among aquatic animals with fish, and the bat among birds. Occasionally he describes a purely mythical animal like "the monkey-fox." It is difficult to see what criterion of truth would have been adequate for the scholar at that time. A monkey-fox is no more improbable than a rhinoceros, and Gesner found it necessary to assure his readers that the rhinoceros really existed in nature and was not a creation of fancy.

As the master of modern anatomy and of several other branches of science, stands Leonardo da Vinci. It is difficult to appraise his work accurately because it is not yet fully known, and still more because of its extraordinary form. Ho left thousands of pages of notes on everything and hardly one complete treatise on anything. He began a hundred studies and finished none of them. He had a queer twist to his mind that made him, with all his power, seek byways. The monstrous, the uncouth, fascinated him; he saw a Medusa in a spider and the universe in a drop of water. He wrote his notes in mirror-writing, from right to left; he illustrated them with a thousand fragments of exquisite drawing, all unfinished and tantalizing alike to the artist and to the scientist. His mind roamed to flying machines and submarines, but he never made one; the reason given by him in the latter case being his fear that it would be put to piratical use. He had something in him of Faust; in some respects he reminds us of William James, who also started as a {613} painter and ended as an omniverous student of outre things and as a psychologist.

If, therefore, the anatomical drawings made by Leonardo from about twenty bodies that he dissected, are marvellous specimens of art, he left it to others to make a really systematic study of the human body. His contemporary, Berengar of Carpi, professor at Bologna, first did this with marked success, classifying the various tissues as fat, membrane, flesh, nerve, fibre and so forth. So far from true is it that it was difficult to get corpses to work upon that he had at least a hundred. Indeed, according to Fallopius, another famous scientist, the Duke of Tuscany would occasionally send live criminals to be vivisected, thus making their punishment redound to the benefit of science. The Inquisitors made the path of science hard by burning books on anatomy as materialistic and indecent.

Two or three investigators anticipated Harvey's discovery of the circulation of the blood. Unfortunately, as the matter is of interest, Servetus's treatment of the subject, found in his work on The Trinity, is too long to quote, but it is plain that, along with various fallacious ideas, he had really discovered the truth that the blood all passes through heart and lungs whence it is returned to the other organs.

While hardly anything was done in chemistry, a large number of phenomena in the field of physics were observed now for the first time. Leonardo da Vinci measured the rapidity of falling bodies, by dropping them from towers and having the time of their passage at various stages noted. He thus found, correctly, that their velocity increased. It is also said that he observed that bodies always fell a little to the eastward of the plumb line, and thence concluded that the earth revolved on its axis. He made careful experiments with billiard balls, discovering that the {614} momentum of the impact always was preserved entire in the motion of the balls struck. He measured forces by the weight and speed of the bodies and arrived at an approximation of the ideas of mechanical "work" and energy of position. He thought of energy as a spiritual force transferred from one body to another by touch. This remarkable man further invented a hygrometer, explained sound as a wave-motion in the air, and said that the appearance known to us as "the old moon in the new moon's lap" was due to the reflection of earth-light.

Nicholas Tartaglia first showed that the course of a projectile was a parabola, and that the maximum range of a gun would be at an angle of 45 degrees.

Some good work was done in optics. John Baptist della Porta described, though he did not invent, the camera obscura. Burning glasses were explained. Leonard Digges even anticipated the telescope by the use of double lenses.

Further progress in mechanics was made by Cardan who explained the lever and pulley, and by Simon Stevin who first demonstrated the resolution of forces. He also noticed the difference between stable and unstable equilibrium, and showed that the downward pressure of a liquid is independent of the shape of the vessel it is in and is dependent only on the height. He and other scholars asserted the causation of the tides by the moon.

Magnetism was much studied. When compasses were first invented it was thought that they always pointed to the North Star under the influence of some stellar compulsion. But even in the fifteenth century it was noticed independently by Columbus and by German experimenters that the needle did not point true north. As the amount of its declination varies at {615} different places on the earth and at different times, this was one of the most puzzling facts to explain. One man believed that the change depended on climate, another that it was an individual property of each needle. About 1581 Robert Norman discovered the inclination, or dip of the compass. These and other observations were summed up by William Gilbert [Sidenote: Gilbert] in his work on The Magnet, Magnetic Bodies and the Earth as a great Magnet. [Sidenote: 1600] A great deal of his space was taken in that valuable destructive criticism that refutes prevalent errors. His greatest discovery was that the earth itself is a large magnet. He thought of magnetism as "a soul, or like a soul, which is in many things superior to the human soul as long as this is bound by our bodily organs." It was therefore an appetite that compelled the magnet to point north and south. Similar explanations of physical and chemical properties are found in the earliest and in some of the most recent philosophers.

As might be expected, the science of geography, nourished by the discoveries of new lands, grew mightily. Even the size of the earth could only be guessed at until it had been encircled. Columbus believed that its circumference at the equator was 8000 miles. The stories of its size that circulated after Magellan were exaggerated by the people. Thus Sir David Lyndsay in his poem The Dreme [Sidenote: 1528] quotes "the author of the sphere" as saying that the earth was 101,750 miles in circumference, each mile being 5000 feet. The author referred to was the thirteenth century Johannes de Sacro Bosco (John Holywood). Two editions of his work, De Sphaera, that I have seen, one of Venice, 1499, and one of Paris, 1527, give the circumference of the earth as 20,428 miles, but an edition published at Wittenberg in 1550 gives it as 5,400, probably an {616} attempt to reduce the author's English miles to German ones. [Sidenote: 1551] Robert Recorde calculated the earth's circumference at 21,300 miles.

Rough maps of the new lands were drawn by the companions of the discoverers. Martin Waldseemuller [Sidenote: 1507] published a large map of the world in twelve sheets and a small globe about 4 1/2 inches in diameter, in which the new world is for the first time called America. The next great advance was made by the Flemish cartographer Gerard Mercator [Sidenote: Mercator, 1512-94] whose globes and maps--some of them on the projection since called by his name--are extraordinarily accurate for Europe and the coast of Africa, and fairly correct for Asia, though he represented that continent as too narrow. He included, however, in their approximately correct positions, India, the Malay peninsula, Sumatra, Java and Japan. America is very poorly drawn, for though the east coast of North America is fairly correct, the continent is too broad and the rest of the coasts vague. He made two startling anticipations of later discoveries, the first that he separated Asia and America by only a narrow strait at the north, and the second that he assumed the existence of a continent around the south pole. This, however, he made far too large, thinking that the Tierra del Fuego was part of it and drawing it so as to come near the south coast of Africa and of Java. His maps of Europe were based on recent and excellent surveys.

Astronomy, the oldest of the sciences, had made much progress in the tabulation of material. The apparent orbits of the sun, moon, planets, and stars had been correctly observed, so that eclipses might be predicted, conjunction of planets calculated, and that {617} gradual movement of the sun through the signs of the zodiac known as the precession of the equinoxes, taken account of. To explain these movements the ancients started on the theory that each heavenly body moved in a perfect circle around the earth; the fixed stars were assigned to one of a group of revolving spheres, the sun, moon and five planets each to one, making eight in all. But it was soon observed that the movements of the planets were too complicated to fall into this system; the number of moving spheres was raised to 27 before Aristotle and to 56 by him. To these concentric spheres later astronomers added eccentric spheres, moving within others, called epicycles, and to them epicycles of the second order; in fact astronomers were compelled:

To build, unbuild, contrive, To save appearances, to gird the sphere With centric and eccentric scribbled o'er Cycle and epicycle, orb in orb.

The complexity of this system, which moved the mirth of Voltaire and, according to Milton, of the Almighty, was such as to make it doubted by some thinkers even in antiquity. Several men thought the earth revolved on its axis, but the hypothesis was rejected by Aristotle and Ptolemy. Heracleides, in the fourth century B. C., said that Mercury and Venus circled around the sun, and in the third century Aristarchus of Samos actually anticipated, though it was a mere guess, the heliocentric theory.

Just before Copernicus various authors seemed to hint at the truth, but in so mystical or brief a way that little can be made of their statements. Thus, Nicholas of Cusa [Sidenote: Nicholas of Cusa, 1400-64] argued that "as the earth cannot be the center of the universe it cannot lack all motion." Leonardo believed that the earth revolved on its axis, and stated that it was a star and would look, to a man on {618} the moon, as the moon does to us. In one place he wrote, "the sun does not move,"--only that enigmatical sentence and nothing more.

Nicholas Copernicus was a native of Thorn in Poland, himself of mixed Polish and Teutonic blood. At the age of eighteen he went to the university of Cracow, where he spent three years. In 1496 he was enabled by an ecclesiastical appointment to go to Italy, where he spent most of the next ten years in study. He worked at the universities of Bologna, Padua and Ferrara, and lectured--though not as a member of the university--at Rome. His studies were comprehensive, including civil law, canon law, medicine, mathematics, and the classics. At Padua, on May 31, 1503, he was made doctor of canon law. He also studied astronomy in Italy, talked with the most famous professors of that science and made observations of the heavens.

Copernicus's uncle was bishop of Ermeland, a spiritual domain and fief of the Teutonic Order, under the supreme suzerainty, at least after 1525, of the king of Poland. Here Copernicus spent the rest of his life; the years 1506-1512 in the bishop's palace at Heilsberg, after 1512, except for two not long stays at Allenstein, as a canon at Frauenburg.

This little town, near but not quite on the Baltic coast, is ornamented by a beautiful cathedral. On the wall surrounding the close is a small tower which the astronomer made his observatory. Here, in the long frosty nights of winter and in the few short hours of summer darkness, he often lay on his back examining the stars. He had no telescope, and his other instruments were such crude things as he put together himself. The most important was what he calls the Instrumentum parallacticum, a wooden isosceles triangle with legs eight feet long divided into 1000 {619} divisions by ink marks, and a hypotenuse divided into 1414 divisions. With this he determined the height of the sun, moon and stars, and their deviation from the vernal point. To this he added a square (quadrum) which told the height of the sun by the shadow thrown by a peg in the middle of the square. A third instrument, also to measure the height of a celestial body, was called the Jacob's staff. His difficulties were increased by the lack of any astronomical tables save those poor ones made by Greeks and Arabs. The faults of these were so great that the fundamental star, i.e., the one he took by which to measure the rest, Spica, was given a longitude nearly 40 degrees out of the true one.

Nevertheless with these poor helps Copernicus arrived, and that very early, at his momentous conclusion. His observations, depending as they did on the weather, were not numerous. His time was spent largely in reading the classic astronomers and in working out the mathematical proofs of his hypothesis. He found hints in quotations from ancient astronomers in Cicero and Plutarch that the earth moved, but he, for the first time, placed the planets in their true position around the sun, and the moon as a satellite of the earth. He retained the old conception of the primum mobile or sphere of fixed stars though he placed it at an infinitely greater distance than did the ancients, to account for the absence of any observed alteration (parallax) in the position of the stars during the year. He also retained the old conception of circular orbits for the planets, though at one time he considered the possibility of their being elliptical, as they are. Unfortunately for his immediate followers the section on this subject found in his own manuscript was cut out of his printed book.

The precise moment at which Copernicus {620} formulated his theory in his own mind cannot be told with certainty, but it was certainly before 1516. He kept back his books for a long time, but his light was not placed under a bushel nevertheless. [Sidenote: 1520] The first rays of it shown forth in a tract by Celio Calcagnini of which only the title, "That the earth moves and the heaven is still," has survived. Some years later Copernicus wrote a short summary of his book, for private circulation only, entitled "A Short commentary on his hypotheses concerning the celestial movements." A fuller account of them was given by his friend and disciple, [Sidenote: Narratio prima, 1540] George Joachim, called Rheticus, who left Wittenberg, where he was teaching, to sit at the master's feet, and who published what was called The First Account.

Finally, Copernicus was persuaded to give his own work to the public. Foreseeing the opposition it was likely to call forth, he tried to forestall criticism by a dedication to the Pope Paul III. Friends at Nuremberg undertook to find a printer, and one of them, the Lutheran pastor Andrew Osiander, with the best intentions, did the great wrong of inserting an anonymous preface stating that the author did not advance his hypotheses as necessarily true, but merely as a means of facilitating astronomical calculations. At last the greatest work of the century, On the Revolutions of the Heavenly Spheres, [Sidenote: De revolutionibus orbium caelestium, 1543] came from the press; a copy was brought to the author on his death bed.

The first of the six books examines the previous authorities, the second proposes the new theory, the third discusses the precession of the equinoxes, the fourth proves that the moon circles the earth, the fifth and most important proves that the planets, including the earth, move around the sun, and gives correctly the time of the orbits of all the planets then known, from Mercury with eighty-eight days to Saturn with thirty {621} years. The sixth book is on the determination of latitude and longitude from the fixed stars. Copernicus's proofs and reasons are absolutely convincing and valid as far as they go. It remained for Galileo and Newton to give further explanations and some modifications in detail of the new theory.

When one remembers the enormous hubbub raised by Darwin's Origin of Species, the reception of Copernicus's no less revolutionary work seems singularly mild. The idea was too far in advance of the age, too great, too paradoxical, to be appreciated at once. Save for a few astronomers like Rheticus and Reinhold, hardly anyone accepted it at first. It would have been miraculous had they done so.

Among the first to take alarm were the Wittenberg theologians, to whose attention the new theory was forcibly brought by their colleague Rheticus. Luther alludes to the subject twice or thrice in his table talk, most clearly on June 4, 1539, when

mention was made of a certain new astronomer, who tried to prove that the earth moved and not the sky, sun and moon, just as, when one was carried along in a boat or wagon, it seemed to himself that he was still and that the trees and landscape moved. "So it goes now," said Luther, "whoever wishes to be clever must not let anything please him that others do, but must do something of his own. Thus he does who wishes to subvert the whole of astronomy: but I believe the Holy Scriptures, which say that Joshua commanded the sun, and not the earth, to stand still."

In his Elements of Physics, written probably in 1545, but not published until 1549, Melanchthon said:

The eyes bear witness that the sky revolves every twenty-four hours. But some men now, either for love of novelty, or to display their ingenuity, assert that the earth moves. . . . But it is hurtful and dishonorable to {622} assert such absurdities. . . . The Psalmist says that the sun moves and the earth stands fast. . . . And the earth, as the center of the universe, must needs be the immovable point on which the circle turns.

Apparently, however, Melanchthon either came to adopt the new theory, or to regard it as possible, for he left this passage entirely out of the second edition of the same work. [Sidenote: 1550] Moreover his relations with Rheticus continued warm, and Rheinhold continued to teach the Copernican system at Wittenberg.

The reception of the new work was also surprisingly mild, at first, in Catholic circles. As early as 1533 Albert Widmanstetter had told Clement VII of the Copernican hypothesis and the pope did not, at least, condemn it. Moreover it was a cardinal, Schoenberg, who consulted Paul III on the matter [Sidenote: 1536] and then urged Copernicus to publish his book, though in his letter the language is so cautiously guarded against possible heresy that not a word is said about the earth moving around the sun but only about the moon and the bodies near it so doing. [Sidenote: 1579] A Spanish theologian, Didacus a Stunica (Zuniga) wrote a commentary on Job, which was licensed by the censors, accepting the Copernican astronomy.

But gradually, as the implications of the doctrine became apparent, the church in self-defence took a strong stand against it. [Sidenote: March 5, 1616] The Congregation of the Index issued a decree saying, "Lest opinions of this sort creep in to the destruction of Catholic truth, the book of Nicholas Copernicus and others [defending his hypothesis] are suspended until they be corrected." A little later Galileo was forced, under the threat of torture, to recant this heresy. Only when the system had become universally accepted, did the church, in 1822, first expressly permit the faithful to hold it.

The philosophers were as shy of the new light as {623} the theologians. Bodin in France and Bacon in England both rejected it; the former was conservative at heart and the latter was never able to see good in other men's work, whether that of Aristotle or of Gilbert or of the great Pole. Possibly he was also misled by Osiander's preface and by Tycho Brahe. Giordano Bruno, however, welcomed the new idea with enthusiasm, saying that Copernicus taught more in two chapters than did Aristotle and the Peripatetics in all their works.

Astronomers alone were capable of weighing the evidence scientifically and they, at first, were also divided. Erasmus Reinhold, of Wittenberg, accepted it and made his calculations on the assumption of its truth, as did an Englishman, John Field. [Sidenote: 1556] Tycho Brahe, [Sidenote: Tycho Brahe, 1546-1601] on the other hand, tried to find a compromise between the Copernican and Ptolemaic systems. He argued that the earth could not revolve on its axis as the centrifugal force would hurl it to pieces, and that it could not revolve around the sun as in that case a change in the position of the fixed stars would be observed. Both objections were well taken, of course, considered in themselves alone, but both could be answered by a deeper knowledge. Brahe therefore considered the earth as the center of the orbits of the moon, sun, and stars, and the sun as the center of the orbits of the planets.

The attention to astronomy had two practical corollaries, the improvement of navigation and the reform of the calendar. Several better forms of astrolabe, of "sun-compass" (or dial turnable by a magnet) and an "astronomical ring" for getting the latitude and longitude by observation of sun and star, were introduced.

The reform of the Julian calendar was needed on account of the imperfect reckoning of the length of the {624} year as exactly 365 1/4 days; thus every four centuries there would be three days too much. It was proposed to remedy this for the present by leaving out ten days, and for the future by omitting leap-year every century not divisible by 400. The bull of Gregory XIII, [Sidenote: February 24, 1582] who resumed the duties of the ancient Pontifex Maximus in regulating time, enjoined Catholic lands to rectify their calendar by allowing the fifteenth of October, 1582, to follow immediately after the fourth. This was done by most of Italy, by Spain, Portugal, Poland, most of Germany, and the Netherlands. Other lands adopted the new calendar later, England not until 1752 and Russia not until 1917.

I.e. the principle thus formulated in the Encyclopaedia Britannica, s.v. "Mathematics": "If s is any class and zero a member of it, also if when x is a cardinal number and a member of s, also x + 1 is a member of s, then the whole class of cardinal numbers is contained in s."

Eratosthenes (276-196 B.C.) had correctly calculated the earth's circumference at 25,000, which Poseidonius (c. 135-50 B.C.) reduced to 18,000, in which he was followed by Ptolemy (2d century A.D.).