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Mount Holyoke College News and Events Vista The College Street Journal Archives

March 8, 2002

Mark Peterson Sheds New Light on Discovery by Galileo

Photo: Fred Leblanc

Mark Peterson, professor of mathematics and statistics and physics, shows the version of Dante's Inferno that Galileo defended in his lectures to the Florentine Academy. Dante soon realized that he had made a major blunder in arguing that the Earth's crust would be thick enough to support its own weight as the Inferno's roof.

How did the politics of the sixteenth-century Florentine court, conflicting theories about the shape and dimensions of poet Dante Alighieri's (1265-1321) famous vision of hell, and a mistake that threatened to bring down a rising academic star come together to bring about a seminal discovery in mathematical physics? Mark Peterson weaves the strands together in a recent paper based on a new interpretation of two obscure lectures by renowned philosopher and mathematician Galileo Galilei (1564-1642).

Peterson, MHC professor of mathematics and statistics and physics, said Galileo made one of his best-known contributions to science with his discovery of scaling laws, work that established some of the most basic ideas in modern physics. Galileo discovered that mathematical rules govern the scaling of objects, and that objects would collapse under their own weight if they were simply scaled up from smaller models. What led Galileo down this path? Peterson, in a paper to be published in the American Journal of Physics, argues that the answer lies quite clearly in two flawed lectures Galileo delivered at the Florentine Academy.

Dante Alighieri

Galileo Galilei

Galileo was a twenty-four-year-old medical school dropout when he secured an invitation to deliver the lectures, which were also his audition for a professorship in mathematics at the University of Pisa. Shrewdly, Galileo chose to speak about Dante and two competing theories about the geometry of his Inferno.

Galileo took the side of Antonio Manetti, a deceased member of the Florentine Academy, and ridiculed the theories of his rival, a non-Florentine named Alessandro Vellutello. Manetti contended that Dante's Inferno was a cone-shaped section of the Earth, with its point at the core and the Earth's crust as its roof, while Vellutello argued for a much smaller cone buried deep beneath the surface.

Galileo's strategy was brilliant, and won him the job. Intellectuals of the time frequently got ahead by successfully attacking the work of someone more prominent, and Galileo gained increased stature by defending the honor of a Florentine against an attack by a non-Florentine. But his argument that Manetti's Inferno could support itself against collapse contained an interesting flaw: he argued that a small-scale model of Manetti's Inferno would support itself. That much was true. But the full-size Inferno would be too weak by an enormous factor, and would in fact collapse.

"When Galileo realized his mistake, probably just a short time later, it must have struck him like a lightning bolt," Peterson said. "We need look no further to know why the problem of scaling and the strength of materials had urgent meaning for Galileo. He had made a gigantic blunder in the Inferno lectures, sufficient to turn his whole argument on its head, and with it his claim to be an intellectual champion of his country and his sovereign, on whom his young career depended. No one else noticed the mistake, actually, throughout his life, but he realized that someone at any moment could use it against him in a public way. So he had to have a comeback."

What to do? Galileo chose to develop the most rigorous explanation of the flaws of his own position, a kind of "secret weapon" to be used if he came under attack. Naturally, because he would not have wanted to point out his own mistake, and because there was not a scientific community to share his ideas with, Galileo kept his theory to himself until his publication, late in life, of the revolutionary Two New Sciences.

It was through his blunder, Peterson argues, that Galileo developed "something truly new, worthy of comparison with Archimedes, something that validated his faith in geometry and hinted at undreamed of successes to come." Peterson's own discovery came as he read the lectures after translating them from the original Italian for a class he teaches on Galileo (Physics 102).

"It seems a fine irony that the first success of Galileo's mathematical physics, which is close to being the first success of mathematical physics at all, was a response to a problem that was not physical, but rather the collapse of an imaginary structure in a work of literature," Peterson says.

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