“Galileo’s Discovery of Scaling Laws”, 2002-05-13 (; backlinks; similar):
Galileo’s realization that nature is not scale invariant motivated his subsequent discovery of scaling laws. His thinking is traced to two lectures he gave on the geography of Dante’s Inferno.
…Looked at this way, Galileo’s lifelong reluctance to publish seems even more inexplicable, but perhaps this pattern began with the experience of the Inferno lectures. He seems to have done his best to make people forget the lectures, and he kept the scaling theory to himself.
What he made public, at least in this case, was a source of trouble, while what he kept secret was a source of confidence. The unpleasantness of being vulnerable to attack is a lesson that he might have taken to heart then, and it is a view he expresses feelingly later on, on the basis of real experience (although without admitting vulnerability!), in the opening lines of The Assayer.17 Galileo frequently claims to have wonderful results that he has not yet revealed, things he has not yet chosen to disclose.
We know that this was true through much of his career, and apparently it was true right from the start. Finally, it is an 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.
[Galileo’s Two New Sciences puzzlingly spends much of its material on the question of how large a ship or a beam of wood or a column of rock can become before collapsing, correctly arguing that the naive belief of scale-invariance (that a ship can be any size as long as it maintains the same geometric proportions) is wrong and that large ships or beams are impossible as they will collapse under their own weight. Why did Galileo, who hardly ever published, spend so much time on this rather than astronomy—especially when he appears to have conducted the scaling law research almost 30 years before?
Peterson digs up neglected lectures by a young and ambitious Galileo, at the court of the Medici, on the topic of Dante’s Inferno where he weighed in on a contemporary dispute between a fellow Florentine & a rival Italian about the size & geography of Hell (then still considered a real place located within the Earth). Galileo, assuming scale-invariance, defended & mathematically improved his fellow’s approach.
The scaling research, then, grew out of his doubts about his naive extrapolations, and he eventually refuted himself. In Renaissance Italy, science, being a patronage/prestige-based endeavour heavily driven by entertainment value, Galileo would be incentivized to keep this research secret lest he embarrass himself, and to use as a weapon in the controversy. However, the dispute appears to have died out and he never had to reveal it, so, decades later, he then included it in Two New Sciences while sanitizing it of its embarrassing origins.]
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