Thinking of the whole “pursuit of knowledge” process in terms of “retriveing what the ancients knew”, something in which the concept of “experiment” doesn’t feature
(possibly) a religious context in which truth == revealed truth. By definition, what’s true is what the ancients wrote.
No concept of paraboles—it seems “right” (per Occam’s Razor) that nature should only use simple shapes like circles and straight lines. Any observation that didn’t seem to be an exact circle could be considered an “imperfect circle”, distorted by things like wind.
Not that many occasions to actually witness a parabola, at least until fountains shooting water became widespread (yes, OK, men can regularly observe streams of liquid, but not from an angle that gives you a good view of the trajectory.
(Possibly) a social context that doesn’t reward improvements to theory; if an apprentice to an engineer noticed that Aristotle was kinda wrong, what would he get by pointing that out to his master? If two rival engineers are vying for a juicy catapult contract, and one of them was known for criticizing Aristotle,who would the Lord choose? (Situations like that haven’t disappeared, it’s just that now Aristotle lost his prestige)
Note that the ancient Greeks studied parabolas in detail. They were consider the next most nice shape after circles (essentially tied with the other conic sections, ellipses and hyperbolas). So your third suggestion doesn’t hold water. I suspect that Constanza’s remark above is closer to the truth; there’s a fair bit of hindsight bias in seeing the impetus theory as obviously incorrect.
Note how this obsession with “perfect shapes” led the ancient Greeks to postulate hypotheses that were, in fact, not empirically founded and ran contrary to Occam’s Razor (which, granted, was not explicitly formulated back then):
Philolaus’ cosmology predicting an unobservable tenth celestial body, “Counter-Earth”, just because ten was considered a “perfect number”.
Plato’s association of the five classic elements (fire, water, air, earth, aether) with the five regular polyhedra, again with no experimental basis other then that there were five of each and the polyhedra were “perfect shapes”.
Aristotle’s division of the world into “under the moon” and “over the moon”, postulating that “natural” trajectories for bodies were downward lines towards the center of the universe (coinciding with the Earth’s center) in the former and circles with the latter. While it admittedly did explain the experimental data, it was still based on the iffy premise of nature “preferring” certain paths and impeded the development of competing heliocentric theories, such as that of Aristarchus.
Seems analogous to the concept of elegance in modern math and science. I’m not sure if we should interpret the characteristic Greek speculation about symmetries as a violation of Occam’s Razor—it’s certainly not empirically founded, but it’s not clear to me that it’d increase the K-complexity or any of the other usual complexity measures when applied to the rather fuzzily defined Greek models of the world.
The addition of an extra planet, empirically unobserved and claimed to be hidden from observers, just to have the celestial body count add up to a “good” number, seems like a pretty clear Occam’s Razor violation to me.
Conceded, but only because the specific mechanics of the Counter-Earth proposal were rather far-fetched.
In Classical times, so little was known about the actual mechanics underlying natural phenomena that an emphasis on fitting those phenomena into mathematical symmetries would be productive, even if there were some holes in the data. There simply wasn’t that much rigorous data to study, and even fewer well-understood analytical tools to do it with, so I’d expect some real symmetries to look awkward in practice thanks to sampling bias. I think the Greek philosophers had some idea of this, too.
Some factors:
Thinking of the whole “pursuit of knowledge” process in terms of “retriveing what the ancients knew”, something in which the concept of “experiment” doesn’t feature
(possibly) a religious context in which truth == revealed truth. By definition, what’s true is what the ancients wrote.
No concept of paraboles—it seems “right” (per Occam’s Razor) that nature should only use simple shapes like circles and straight lines. Any observation that didn’t seem to be an exact circle could be considered an “imperfect circle”, distorted by things like wind.
Not that many occasions to actually witness a parabola, at least until fountains shooting water became widespread (yes, OK, men can regularly observe streams of liquid, but not from an angle that gives you a good view of the trajectory.
(Possibly) a social context that doesn’t reward improvements to theory; if an apprentice to an engineer noticed that Aristotle was kinda wrong, what would he get by pointing that out to his master? If two rival engineers are vying for a juicy catapult contract, and one of them was known for criticizing Aristotle,who would the Lord choose? (Situations like that haven’t disappeared, it’s just that now Aristotle lost his prestige)
Note that the ancient Greeks studied parabolas in detail. They were consider the next most nice shape after circles (essentially tied with the other conic sections, ellipses and hyperbolas). So your third suggestion doesn’t hold water. I suspect that Constanza’s remark above is closer to the truth; there’s a fair bit of hindsight bias in seeing the impetus theory as obviously incorrect.
Note how this obsession with “perfect shapes” led the ancient Greeks to postulate hypotheses that were, in fact, not empirically founded and ran contrary to Occam’s Razor (which, granted, was not explicitly formulated back then):
Philolaus’ cosmology predicting an unobservable tenth celestial body, “Counter-Earth”, just because ten was considered a “perfect number”.
Plato’s association of the five classic elements (fire, water, air, earth, aether) with the five regular polyhedra, again with no experimental basis other then that there were five of each and the polyhedra were “perfect shapes”.
Aristotle’s division of the world into “under the moon” and “over the moon”, postulating that “natural” trajectories for bodies were downward lines towards the center of the universe (coinciding with the Earth’s center) in the former and circles with the latter. While it admittedly did explain the experimental data, it was still based on the iffy premise of nature “preferring” certain paths and impeded the development of competing heliocentric theories, such as that of Aristarchus.
I see a pattern here....
Seems analogous to the concept of elegance in modern math and science. I’m not sure if we should interpret the characteristic Greek speculation about symmetries as a violation of Occam’s Razor—it’s certainly not empirically founded, but it’s not clear to me that it’d increase the K-complexity or any of the other usual complexity measures when applied to the rather fuzzily defined Greek models of the world.
The addition of an extra planet, empirically unobserved and claimed to be hidden from observers, just to have the celestial body count add up to a “good” number, seems like a pretty clear Occam’s Razor violation to me.
Conceded, but only because the specific mechanics of the Counter-Earth proposal were rather far-fetched.
In Classical times, so little was known about the actual mechanics underlying natural phenomena that an emphasis on fitting those phenomena into mathematical symmetries would be productive, even if there were some holes in the data. There simply wasn’t that much rigorous data to study, and even fewer well-understood analytical tools to do it with, so I’d expect some real symmetries to look awkward in practice thanks to sampling bias. I think the Greek philosophers had some idea of this, too.