Seeds of reason !

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by Eugene Vorontsov

Eugene Vorontsov is PhD candidate at Polytechnique School of Montreal in Computer Vision

Eugene Vorontsov is PhD candidate at Polytechnique School of Montreal in Computer Vision

The discovery of America shook the pillars of the European world view. While the Renaissance brought forth a rediscovery of Classical ideas for physical life in concession with those for the spirit, the Age of Discovery abruptly brought these accepted Truths into question. It may be surprising then that, in an age when imagined witches were handed real executions, among this heightened sense of superstition and uncertainty new discoveries were made that would revolutionize the world through reason. From Galileo to Boyle, to Hooke, the foundations of modern science were being laid.

While the New World upset old beliefs, emerging experimentalists produced further assaults on an accepted Aristotelian description of the natural world. Famously, in his relentless pursuit of methodical science, having made many contributions to astronomy, physics, mathematics, and mechanics, Galileo Galilei was placed under house arrest in 1633 for his support of a heliocentric model of the heavens – an idea that contradicted both the established Aristotelian and biblical descriptions of the world. Convicted by the Inquisition on the suspicion of heresy, Galileo was forced to recant under threat of torture. Still, his careful astronomical measurements went on to inspire Newton's work on physical dynamics and were cited heavily in his Principia.

Yet, Galileo's work inspired more than this essential work of theory; this emerging focus on empirical, tested reasoning so diligently (but not exclusively) exemplified by him also inspired a young Richard Boyle who, at the age of 14, traveled to Italy where he read the (probably smuggled) work of Galileo. Later author of The Sceptical Chymist, and one of the founders of modern chemistry, Boyle, like Galileo, spent his career trying to understand the world through mathematics; and, unlike classical philosophers, he similarly pursued this understanding through experiments and measurements, aided by instrumentation. Consequently, at the age of 28, he employed the young master instrumentalist, an Oxford student Robert Hooke to assist in his experiments on vacuum. With the vacuum pump invented in 1654, Hooke improved on its design and fitted it with an oil-sealed screw that could be used to actuate devices inside a large, emptied glass chamber. This permitted experiments that showed air to be elastic, produced the linear relationship between the pressure and volume of a gas, known as Boyle's law, demonstrated the transmission of magnetism through a vacuum, and motivated an elementary description of chemistry in which all matter is made of fundamental elements that arrange themselves in compounds. Experimenting with fire in the vacuum chamber, Hooke inferred that air contained a “nitrous” component that is required for the combustion of those atoms in a material that can be “dissolved” by this component and that gunpowder did not require air as it had this nitrous component fixed solid in saltpeter.

But it was not under Boyle that Hooke would be recognized for his innovative achievements. At age 27, Boyle released him into the service of the newly formed Royal Society to fulfill the role of Curator of Experiments. Hooke was tasked with the extraordinary duty of demonstrating three to four novel experiments per week—a duty that he fulfilled prolifically for forty years, exploring diverse fields from mechanics to biology to sound and light waves. His best selling work, the Micrographia, details not only the then alien world of microscopy but also his many other ideas and experiments, demonstrating his ability to use the results of an experiment to inform hypotheses and experiments in seemingly disparate fields. But his early enthusiasm for publication and the sharing of ideas was damaged over time; others borrowed his ideas and observations without attribution. Even before filling the role of Curator, Hooke, wary of misattribution, published the law of elasticity encrypted as an anagram:

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If someone were to have known this first, they would have explained the law; eighteen years later, he published the solution: ut tensio sic vis – as the extension, so the force; Hooke's law.

Hooke later fell out with Newton, who had ascended to president of the Royal Society, over an issue of attribution in Newton's theory of gravity. He died embittered and as his celebrity faded and his only known portrait at the Royal Society was lost, one last anagram remained after his death. Previously appointed as Surveyor to assist Christopher Wren in the rebuilding of London after the Great Fire, Hooke delved into civil engineering, publishing the solution for the ideal shape of an arch:

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Only after his death and 34 years after publication, his executor revealed the meaning as “Ut pendet continuum flexile, sic stabit contiguum rigidum inversum,” meaning “As hangs a flexible cable, so inverted, stand the touching pieces of an arch.” And so, curiously, it appears that a lost secret of then venerated Classical construction was rediscovered with the world's reinvention.

St. Paul's cathedral – designed by Christopher Wren with the dome design based on Robert Hooke's explanation of the forces borne by an arch. (Mark Fosh – Flickr)

St. Paul's cathedral – designed by Christopher Wren with the dome design based on Robert Hooke's explanation of the forces borne by an arch.
(Mark Fosh – Flickr)

“As hangs a flexible cable, so inverted, stand the touching pieces of an arch.” Model thrust lines in an arch with a weighted cable; if the forces in the arch do not extend outside of the masonry, the structure is stable.

“As hangs a flexible cable, so inverted, stand the touching pieces of an arch.”
Model thrust lines in an arch with a weighted cable; if the forces in the arch do not extend outside of the masonry, the structure is stable.

One of Christopher Wren's early drawings of the dome shows his design of the triple-dome with calculation and the thrust lines passing through the abutments.

One of Christopher Wren's early drawings of the dome shows his design of the triple-dome with calculation and the thrust lines passing through the abutments.


References:

Diagram from: DeJong, Matt, and John Ochsendorf. "As Hangs the Flexible Line: Equilibrium of Masonry Arches." NEXUS NETWORK JOURNAL 8.2 (2006): 9.
 

The photo is from wikipedia -- originally sourced from Mark Fosh on Flickr:
https://en.wikipedia.org/wiki/File:St_Pauls_aerial_(cropped).jpg
https://www.flickr.com/photos/10069045@N00/2776161012 

https://plus.maths.org/content/maths-minute-st-pauls-dome