The Calculus Diaries - Jennifer Ouellette [80]
ARCH RIVALS
Today we build almost exclusively with steel and reinforced concrete, and the design process is heavily reliant on mathematical modeling and engineering principles. In ancient times, arch builders employed a method of trial and error. Small stone arches were typically built around a curved wooden form. The builder would then lay stones or bricks around that wooden form, tracing the shape with pegs and string. Legend has it that whenever an arch was constructed in ancient Rome, the architect who designed it was forced to stand underneath as the wooden supports were removed, as a means of quality control. It was a terrific motivational tool: Design it right the first time, or the arch will fall and crush you. Builders of Gothic cathedrals had to figure out how to turn stones into stable structures held together only by the forces of compression, like a stack of children’s building blocks, and they did it without the benefit of analytical geometry or calculus. The oldest cathedrals have stood for a thousand years, so medieval masons clearly knew a thing or two about arch stability.
One assumes this practical knowledge was passed down through generations of builders. Yet the secret of the inverted catenary remained a mathematical mystery until the seventeenth-century English scientist Robert Hooke stumbled upon this solution to the question of an optimal shape for a stable arch. Hooke is best known for his skill at building microscopes and using them to examine the tiniest details of everyday objects, such as fleas. His exquisite drawings of what he saw through his microscopes appeared in his masterpiece, Micrographia. He also invented a reflecting telescope, the sextant, the wind gauge, and the wheel barometer, and he had a lifelong fascination with timepieces.
Despite these accomplishments, Hooke’s stature as a scientist was largely overshadowed by that of his contemporary rival, Isaac Newton. Their professional debates over the nature of light often became intensely personal: Hooke may even have tried to block Newton’s election to the Royal Society. Perhaps Hooke had cause to feel threatened: His more practical contributions to science were overlooked in favor of Newton’s mathematically oriented theories. Personal vanity may also have played a role: Newton cut a distinguished, imposing figure, while Hooke was small and hunched; even his friends described him in less than flattering terms.
Hooke’s pique at the lack of recognition by his peers might have been partially justified. In 2006, the long-lost handwritten minutes from meetings of the Royal Society between 1661 and 1682 were discovered wedged into a dusty nook in an old house in Hampshire, England. The manuscript laid to rest a long-standing controversy over whether Hooke or Christian Huygens had first designed a highly accurate watch with tiny spring mechanisms that eventually led to the first measurement of longitude. Hooke understood a great deal about the physics of springs, having devised the eponymous Hooke’s law:
Extension is proportional to force. So when Huygens claimed to have invented a spring watch in 1675, Hooke flew into a rage, claiming someone had leaked his earlier design to the Dutch scientist. The unearthed minutes include pages from a meeting on June 23, 1670, with a description of Hooke’s