Simon Stevin

Birth & Background

• Born in 1548 in Bruges, then part of the Spanish Netherlands
• Illegitimate birth — details of his parents are sparse, though his mother may have been from a prosperous family
• Worked as a bookkeeper and cashier in Antwerp before turning to scholarship
• Travelled through Poland, Prussia, and Norway before settling in Leiden

Education & Transition

• Enrolled at the University of Leiden in 1583, at the age of 35
• His practical experience in commerce shaped his mathematical sensibility — he valued utility above abstraction
• Met Prince Maurice of Nassau, who became his patron and lifelong collaborator
• The Dutch Revolt against Spain was the backdrop of his entire career

The State of Arithmetic c. 1580

• European arithmetic still used unwieldy common fractions: 3/8, 7/16, 23/64
• No standard notation for non-integer quantities — every trade had its own system
• Monetary systems were non-decimal (pounds/shillings/pence, livres/sous/deniers)
• Chinese and Islamic mathematicians had used decimal fractions for centuries, but Europe had not adopted them

The Dutch Golden Age Begins

• The Dutch Revolt (1568–1648) was creating an independent, commercially dynamic republic
• Navigation, trade, and military engineering demanded better computational tools
• Leiden University (founded 1575) became a hub for practical science

Why Decimals Mattered

What De Thiende Actually Said

The pamphlet is only 36 pages, divided into two parts:

• Part I — Definitions: Explains the notation. Each digit after the "integer" is marked with a circled number showing its decimal position.
• Part II — Operations: Shows how to add, subtract, multiply, and divide decimal numbers, with worked examples.

Stevin also proposed a decimal system of weights, measures, and coinage — anticipating the metric system by two hundred years.

Why Europe Had Resisted

• Roman numeral tradition made positional notation unfamiliar
• Common fractions were "exact" — 1/3 is exact, 0.333... is not
• Guild systems had entrenched non-decimal measures
• Stevin's counter-argument: practicality trumps theoretical purity

In De Beghinselen der Weeghconst (1586), Stevin proved two landmark results:

• Stevin's Law: Hydrostatic pressure depends only on depth and fluid density, not on the shape of the container
• The Inclined Plane: Proved the law of equilibrium on an inclined plane using a brilliant thought experiment — the "wreath of spheres" (clootcrans)
• The inclined plane proof is considered one of the most elegant arguments in the history of physics

Stevin was so proud of this proof that he used the clootcrans diagram as his personal emblem, with the motto "Wonder en is gheen wonder" (What appears a wonder is not a wonder).

Stevin's Law of Hydrostatic Pressure

Stevin proved that the pressure at any point in a fluid depends only on:

• The depth below the surface
• The density of the fluid
• Not on the shape or width of the container

This means a narrow tube of water 10m tall exerts the same pressure at its base as a vast lake 10m deep. This "hydrostatic paradox" astonished contemporaries.

P = ρgh — where ρ is fluid density, g is gravitational acceleration, h is depth.

The Clootcrans Argument

Stevin's inclined plane proof is a masterpiece of physical reasoning:

• Imagine a chain of equally-spaced spheres draped over a triangular prism
• The chain hangs symmetrically below the base, so that part contributes no net force
• The chain cannot move perpetually (perpetual motion is impossible)
• Therefore the spheres on the slope and the spheres on the vertical must be in equilibrium
• The ratio of forces equals the ratio of the lengths of the sides

The Practical Polymath

Stevin's approach was radically utilitarian. He saw mathematics not as a philosophical pursuit but as a tool for solving real problems. His commercial background gave him a merchant's eye for efficiency.

His motto, "Wonder en is gheen wonder", encapsulates his philosophy: natural phenomena may seem miraculous, but they follow rational, discoverable laws.

Breadth Over Depth

Unlike many mathematicians who pursued a single area deeply, Stevin contributed to an extraordinary range of fields: arithmetic, geometry, mechanics, hydrostatics, fortification, navigation, music theory, and bookkeeping.

His unifying theme was always practical simplification — finding the most efficient way to do things that needed doing.

Writing in Dutch: Principled but Costly

• Stevin's insistence on writing in Dutch meant his work was largely unknown outside the Netherlands
• Latin was the international language of science — by rejecting it, Stevin limited his own influence
• Many of his results were independently rediscovered by others who received the credit
• His hydrostatics was largely unknown to Pascal, who independently proved similar results decades later

The Decimal Adoption Struggle

Despite Stevin's passionate advocacy, decimal fractions took over a century to become standard. England didn't decimalise its currency until 1971.

The Forgotten Polymath

Hydraulic Engineering

• Stevin's hydrostatic principles are fundamental to dam design in the Netherlands
• The Dutch water management system — polders, dikes, and sluices — relies on his pressure calculations
• Modern hydraulic presses, braking systems, and water towers all apply Stevin's law

Finance & Commerce

• Decimal currency (dollars and cents, euros and centimes) follows Stevin's proposal exactly
• Double-entry bookkeeping with decimal notation became standard practice
• Stock markets quote prices in decimals (NYSE switched from fractions in 2001)

Military & Civil Engineering

• Stevin's fortification designs influenced military architecture across Europe
• The inclined plane analysis applies to road design, ramp construction, and structural engineering
• His land-sailing vehicles anticipated modern wind-powered transportation

Music Technology

• Equal temperament tuning (12th root of 2) is used in electronic instruments, digital audio, and synthesisers
• MIDI standard divides the octave into 12 equal semitones — exactly Stevin's proposal