"Galileo's realization that nature is not scale invariant, motivating his subsequent discovery of scaling laws, is traced to two lectures he gave on the geography of Dante's 'Inferno,'" physics historian Mark Peterson argues in his recent paper on the topic.
In the 16th century lectures, Galileo claimed Hell -- a fiery region of eternal damnation far beneath Earth's surface -- may be scaled up by a factor of 100,000 and still remain intact.
The lectures mistakenly assumed Hell was scale invariant -- that "a scale model had the same strength as a larger scaled-up version," Peterson told United Press International from Mount Holyoke College in South Hadley. "The roof would collapse in the larger structure -- the Earth or a hollowed-out version -- because the crust couldn't support itself if there were too big a cavity in the mantle."
Galileo failed to explain the walls of Hell would have to be correspondingly thickened to support the extra size, Peterson said.
If nature were, in fact, scale invariant -- if size didn't matter -- the same laws that govern the motion of planets around the sun would govern the path of electrons around an atomic nucleus. Instead, two concepts that have proven notoriously difficult to unite -- gravity and quantum mechanics -- respectively describe the light-years-distant cosmos and the sub-microscopic realm of atoms and quarks.
"These ideas are basic in physics," Peterson explained. "They are introduced, in some fashion, in chapter one of most introductory physics texts."
How Galileo came to discover such a basic law of nature illustrates "a significant point about early modern science," history professor George Dameron told UPI from St. Michael's College in Burlington, Vt. "Scientists like Galileo, Leonardo da Vinci -- and even Newton much later -- were truly immersed in a wide variety of disciplines, well beyond what we now call the natural sciences."
Young, ambitious, and restless, Galileo dropped his medical studies at the University of Pisa in favor of mathematics. He sent his theorems to a number of prominent Italian mathematicians and attracted the attention of Guidobaldo del Monte, an important official in the court of Tuscany's Grand Duke.
When the mathematics chair at Pisa opened, Guidobaldo secured Galileo what amounted to a critical job interview: lectures to the Florentine Academy, an organization created by the Medici dynasty and "dedicated to the glorification of the Medici in every intellectual arena," Peterson explained. Galileo "brilliantly combined a clear exposition of mathematics with a topic Florence loved to hear: their great poet Dante."
In two lectures, Galileo analyzed rival attempts to determine the geometry of Hell -- one by a deceased member of the Florentine Academy, Antonio Manetti, and a second by the non-Florentine, Alessandro Vellutello.
Manetti's Inferno -- a cone-shaped region in the center of the Earth -- was much larger than Vellutello's, yet walls of similar thickness enclosed both versions of the fiery underworld.
"Here one might suppose that the Inferno cannot be so large as Manetti makes it," Galileo told the Academy. "It doesn't seem possible that the wall that covers the Inferno could support itself and not fall into the hole, being so thin."
Nevertheless, Galileo defended the Florentine Manetti while ridiculing Vellutello, "to the delight of his audience, no doubt," Peterson surmised. "This was how a Medici intellectual should defend the honor of Florence," he said.
Within a few months, Galileo the former dropout was the University of Pisa's newest mathematics professor.
By assuming Hell could be scaled up without a corresponding increase in the thickness of its walls, Galileo may have charmed the Florentines but "made a gigantic blunder in the Inferno lectures," Peterson wrote in his paper on the subject.
When Galileo realized his mistake, "it must have struck him like a lightning bolt," Peterson claimed.
He would rectify the error some 50 years later, in a book and lecture series Peterson calls Galileo's last and crowning achievement -- "Two New Sciences."
"Galileo realized that it matters how big things are," Peterson told UPI. "Scaling laws derive from simple geometrical observations -- that if a beam is made twice as big, for example, its weight is eight times as big and if the beam is scaled up too much, it will break."
"My first impression is that the author is on the right track in helping to explain some of the nuances of Galileo's work and motivations," Owen Gingerich, research professor of astronomy and of the history of science at Harvard University, told UPI from Cambridge, Mass.
Peterson's work "appears very pretty and a nice insight," Gingerich concluded.
"Peterson's argument seems convincing," George Dameron, a noted expert in Florentine history, told UPI. "It does not surprise me in the least that Peterson stumbled on these revelations."
Being thoroughly familiar with the text of the lectures and Two New Sciences "brought Peterson the insight that led to his article," Dameron told UPI.
"It seems a fine irony that the first success of Galileo's mathematics, 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 concluded.
(Reported by UPI Science Correspondent Mike Martin in Columbia, Mo.)
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