An encyclopedic mind and a prolific writer on many topics, Stevin, known as "the Dutch Archimedes," contributed to many areas of knowledge, particularly arithmetic, algebra, geometry, physics, optics, mechanics, astronomy, hydrostatics, musical theory, and military engineering. A dedicated empiricist, he experimentally refuted, years before Galileo (who received credit), the Aristotelian doctrine that heavy objects fall faster than light-weight objects. He also improved mathematical notation and championed the decimal system, suggesting that decimal mensuration could be used in all spheres of life. In addition, Stevin was an exceptional prose stylist. He pioneered the use of his vernacular, Dutch, at a time when Latin was dominant as the language of science. Stevin significantly enriched the Dutch scientific vocabulary, coining words and phrases which have been become part of the Dutch lexicon.
Born in Bruges (now Belgium), in the southern Netherlands, Stevin was employed by the city administration as a bookkeeper. He made several trips abroad in the 1570s, settling in Leiden, in the north, in 1581. Already in his thirties, he proceeded to obtain a formal education at the University of Leiden, adding to independently acquired knowledge of science and engineering. Having left the Spanish-occupied southern provinces, Stevin prospered in the northern Netherlands, participating in the national struggle for liberation from Spanish rule. His engineering skills were recognized by the leaders of the Dutch liberation war and he became quartermaster-general of the army in the early 1600s. He was also engaged by Prince Maurice of Nassau, the stadholder (head of state), as his personal science and mathematics teacher. Always willing to put his scientific expertise in the service of the war effort, Stevin was very highly regarded by his compatriots. He married Catharine Cray in 1610; the couple had four children, one of whom, Hendrick, also became a scientist.
Explains Decimal Fractions
Although decimal fractions had been known centuries before Stevin, he is credited with explaining the concept of decimal fractions, which, although known to proficient mathematicians, seemed unfamiliar to most mathematicians. He did not view decimal fractions as fractions, and proceeded to write their numerators without the denominators. For example, Stevin represented the value of (in modern notation: 3,1416. . .) as 3 0 1 1 4 2 1 3 6 4. The second digit--around which he drew a circle--of each pair was the power of ten of the implied divisor. Thus, 1 1 is 1/10; 4 2 is 4/100, etc. Stevin's notation may have been cumbersome, but his idea made sense, for, to cite Carl Boyer's example, it seems more natural to imagine 3 seconds as an integer (3) than as 3/60 of one hour.
Unlike his predecessors, who used words to represent operations, Stevin insisted whenever this was possible, on notational symbols. For example, he used circled numbers to represent exponents, circled 2 replacing Q (for square), and circled 3 instead of C (for cube). While still imperfect, Stevin's notation, as scholars suggest, points to the modern algebraic notation which was firmly established not long after his death.
Corrects Misconceptions and Anticipates New Theories in Physics
In 1586, Stevin described his experiment with two leaden spheres, one ten times heavier than the other. Having dropped the spheres simultaneously from a height of 30 ft (914 cm) onto a wooden surface, Stevin observed that they both hit the surface at the same time. Historians, who agree that Stevin and not Galileo, should be credited for this revolutionary experiment, nevertheless accept Galileo as the founder of modern mechanics, because it was the Italian scientist who formulated the final theoretical consequences of Stevin's discovery. However, according to Stephen F. Mason, Stevin, who described his falling spheres, as the "experiment against Aristotle," effectively demolished Aristotelian mechanics, thereby creating the foundations of modern mechanics.
Stevin's book, De Beginselen der Weegconst ( Principles of the Art of Weighing), continues the work begun by Archimedes (for example, refining the Greek scientist's explanation of buoyancy)and tackles such Archimedean subjects as levers and inclined planes, including his famous wreath of spheres. Stevin placed a wreath of spheres on two inclined planes AB and BC, AB being twice the length of BC. If we imagine ABC as a triangle, we will notice that, the spheres being spaced evenly and weighing the same, and if there are two spheres on BC, there will naturally be four on AB. Despite the different numbers of spheres on each side, the wreath does not move, because there is an inverse proportion between the effect of gravity and the length of an inclined plane. A different triangle, with AB three times the length of BC, would, according to Stevin's principle, would balance two spheres on one side BC, and six on the other. "Stevin," Mason has written, ". . . obtained an intuitive understanding of the parallelogram of forces, a method of finding the resultant action of a combination of two forces that are not in the same straight line nor parallel. The method . . . consists in the representation of the two forces, in magnitude and direction, by two straight lines originating from a common point: the resultant is then given by the diagonal of the parallelogram formed by drawing two other lines parallel to the first two." Once again, Stevin made a great discovery, leaving the precise theoretical formulation to later scientists. The parallelogram of forces was clearly explained by Isaac Newton and by the French mathematician Pierre Varignon in 1687.
Suggests Equally-Tempered Musical Scale
In Stevin's time, the musical scale was not evenly tempered, which posed a serious problem for players of stringed instruments who had to contend with the paradox exemplified by the fact that a sequence of four pure fifths and a sequence of two octaves should, but do not result in, a perfect third: the interval created when the final tones of the two sequences are played together is not a perfect minor third. The interval of a pure octave is represented by the ratio 2 : 1, which means that if a frequency f is doubled, the new frequency is an octave higher than f. The pure fifth corresponds to the ratio 3 : 2, and the pure third to the ratios 5 : 4 (major) and 6 : 5 (minor). To resolve this paradoxical situation, which obliged musicians to constantly change tuning strategies, mathematicians and musicians proposed a variety of solutions, including the division of the octave into 12 mathematically, but perhaps not acoustically, equal semitones. Scholars believe that the modern, equally-tempered, scale originated with Stevin's idea that all semitones should be absolutely equal--their frequencies determined by the mathematical formula 2n/12, even if the consequences included less-than-perfect intervals.
Stevin may have been familiar with Dialogo della musica antica e della moderna(Dialogue Concerning Ancient and Modern Music [1581]) by Vincenzo Galilei, father of Galileo, which, among many other subjects, discussed the equally-tempered scale. However, scholars have suggested that the scale proposed by Stevin is the scale that was gradually accepted in the 17th and 18th centuries, particularly by players of keyboard instruments, and by composers such as Johann Sebastian Bach. His Well-Tempered Clavier, which contains preludes and fugues in all the 24 keys, constitutes the foundation of the classical, mathematical, conception of tonality, the embodiment of which is the modern piano. In science, Stevin's idea was further refined by the 19th-century English mathematician and phonetician A.J. Ellis, who divided the octave (2 : 1) into 1200 cents, 100 cents representing an equally-tempered semitone.
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