Much of modern mathematics and science is rooted in the late 16th century. The Renaissance was ending as early modern ingenuity had recovered what it could of the so-called “Wisdom of the Ancients” and began adding its own new knowledge. The likes of Kepler, Viète, Cardano and Galileo planted the seeds that blossomed the next century at the hands of Descartes, Fermat, Pascal and Huygens.

In this fascinating story, the contributions of Simon Stevin (1548-1620) are often overlooked. This fine book seeks to remedy that situation. The book is an excellent translation by Lee Preedy of the Dutch edition *Wonder en is gheen wonder. De geniale wereld van Simon Stevin 1548-1620*.

Devreese and Vanden Berghe organize their book thematically. They open with two chapters that describe Stevin’s life and times, “Simon Stevin and the Renaissance” and “Simon Stevin, religious exile?” The question mark in this second title emphasizes that many details of Stevin’s life are lost.

In a final chapter “The resonance of Simon Stevin and his work,” we find some accounts of Stevin’s enduring influence. There is the story of how in 1846, long-standing divisions in Belgian society made a controversy of the idea of erecting a statue in his honor in Bruges, the city of his birth. One opponent wrote, “I wager not one in a thousand had heard of Simon Stevin before the question of erecting a statue to him arose!” Our authors trace Stevin’s influence on as diverse a group as Christiaan Huygens, Joseph Louis Lagrange and Richard Feynman.

In between we find nine chapters, each detailing Stevin’s work in particular fields, engineering, hydraulics, economics, physics, algebra, linguistics, navigation, music theory, architecture, military science, urban planning, economics, bookkeeping, graphics and perspective. He really was a Renaissance Man.

Readers of these pages will probably be most interested in the third chapter, “The man who ‘invented’ the decimal system.” It is sometimes hard to remember that we haven’t always had decimal fractions and that they were actually invented by somebody. That “somebody” was Simon Stevin. He did not, as some say, invent the “decimal point” notation, and maybe he wasn’t the very first to use decimal fractions. Nonetheless, his book *De Thiende*, or “The Tenth” described in detail and popularized the decimal system. It was quickly translated into a number of languages and the decimal system quickly spread around the world.

In several respects, Stevin’s work paralleled the career of his better-known contemporary Galileo. Stevin dropped cannon balls from a tower at least a year before Galileo did, and Stevin’s, unlike Galileo’s, landed at exactly the same moment. Stevin, like Galileo, was an early and public proponent of the heliocentric model of the solar system, but, though both were Catholic, Stevin didn’t get into much trouble for his views.

Stevin’s name is attached to what is sometimes called the Hydrostatic Paradox, that the pressure at a given depth in a container of water is independent of the shape of the container. Our authors tell us that Stevin made a number of discoveries in hydrostatics, many of which are traditionally attributed to Pascal, and that Stevin’s discoveries were the first significant advances in the subject since Archimedes.

In my opinion, Stevin’s most innovative ideas were based on his insights about a thought-experiment he called a *cloottrans*, or “wreath of spheres.” His illustration is reproduced below, complete with the “N” in mirror image:

Simon Stevin’s *clootrans*, or “wreath of spheres”

as illustrated in 1586 in his book *De Beghinselen der* *Weeghconst*,

or “The Art of Weighing”.

Stevin asks us to imagine a chain or necklace of evenly spaced spheres of equal mass. I remember seeing this same picture as the design of a perpetual motion machine. If we believe in perpetual motion, then we are supposed to believe that the four spheres, P, Q, R and D, will outweigh the two spheres E and F, and so that the *clootrans* will revolve in the counterclockwise direction forever, creating perpetual motion.

Stevin, though, realizes that perpetual motion is impossible, so in fact the *clootrans* will be in equilibrium and will not revolve. Because the eight spheres G through O are symmetrical and therefore in equilibrium, it follows that the four spheres P, Q, R and D exactly balance the two spheres E and F. Thus, Stevin is able to resolve the forces exerted by the six spheres above the triangle into two components without the concept of vectors.

Two hundred years later, in 1788, Joseph Loius Lagrange wrote of “this very ingenious proof of Stevin,” and in 1965, after giving a rather clever modern exposition of the resolution of forces, Richard Feynman wrote, “Cleverness, however, is relative. It can be deduced in a way which is even more brilliant, discovered by Stevinus [Stevin] and is inscribed on his tombstone.” Feynman was right about the elegance, but wrong about the tombstone. The *clootrans* appears on Stevin’s “personal crest”, but not on his tombstone.

Stevin made similarly ingenious discoveries in hydraulics.

As for the title, *Magic is No Magic*, it also appears in Dutch as *Wonder en is geen wonder* on Stevin’s personal crest. As our Authors tell us in their Preface, it summarizes “Simon Stevin’s vision of science. According to Stevin a natural phenomenon is only ‘magic’ as long as it is not understood. As soon as it is grasped, it is ‘no magic’.” On the other hand, the motto can be turned around to say that ‘no magic’, that is nature, is ‘magic’, that is wonderful.

This is an interesting, well-written, well-illustrated and particularly well-translated book (I think that translators often don’t get the credit they deserve) about a fascinating and important person who made a spectacular contribution to mathematics, decimal arithmetic. Being a man of the Renaissance, he made other important contributions as well, yet he is not well enough known in the English-speaking mathematical community.

Were the book not so very expensive ($189 hardbound, $59 in paperback), I would recommend it enthusiastically. As it is, I must warn you to check how deep your pockets are before purchasing it. If you do buy a copy, you’re likely to have friends who will want to borrow it. It really is a good book.

Ed Sandifer (esandifer@earthlink.net) writes the column “How Euler Did It” for MAA Online. He is professor of mathematics at Western Connecticut State University and has run the Boston Marathon 36 times.