Sorry to be a little pedantic as it’s at best auxiliary to your otherwise fascinating accounts. In my opinion it’s a bit of a miss to compare the retrograde motion (being the sum of two circular orbits) to decomposition by Fourier analysis. The sinusoidal basis functions are a rather special example of completeness and utility, and their rich applications in complex analysis also speak more to this. I am certainly not well versed in the virtues of the Ptolemaic model (though in other posts you rightfully point out given the set of available observations it made a compelling case) but referencing the resulting motion as being the sum of two other motions doesn’t even begin to describe the deep mathematical concepts underpinning Fourier analysis and it’s widespread applications.
This was an excellent and interesting presentation of the ptolemaic model and the point about having too many free parameters for an over constrained system was a nice treat. The requirement for the various radial vectors to be always parallel is only possible if the they share a common frequency. This quickly becomes obvious, and an explanation of this crucial observation is nowhere in the model. Knowledge of this could have driven Copernicus to keep searching until he found the appropriate solution. Though the Greek model was wrong it was still consistent with the scientific method as it kept appropriate questions open; it invited Copernicus to play.
The dogmatism of the church which found the explanation convenient was the one incentivized to cull further questionings.
I'm going to try to write up a more detailed response as a full post, but if you want a quick preview, the deferents and epicycles paradigm is essentially a 2D Fourier transform. More on that, here:
I think that the "culture wars" do cloud the perspectives of moderns who look back upon the medievals, for that is where the modern mythos leads one. Human nature also features a tendency towards pride and boastfulness, and this combined with the "evolutionary" analysis so typical of modernity also leads one to categorize oneself mistakenly as "more evolved" than predecessors. But the deepest problem is one of utility, of "what have you done for me lately?" which, in truth, really is shockingly the epistemological basis of modern science (the Scientific Method is a deceitful smoke-screen). If you take utility as your metric, which is what people are really doing, then science as we know it really began with Issac Newton, and everything before him winds up devalued.
I think it's a mistake to make judgments like this. But what do I know? One great disservice cemented by such a utilitarian approach is the masking of the central concern of natural philosophy, or science, in the Middle Ages. This concern was ethics. Realize that in the olden days the Line of Demarcation between Science and Magic were blurred. Throughout the Middle Ages always a tension existed around what was "good magic" or "bad magic". One of our heroes in this article, Roger Bacon, is a case in point. We see him through our filters as a Great Soul, a remarkable "proto-scientist". And this he was, there was no doubt. But also in his day Roger Bacon was perceived as a Magus, a sort of "wizard", who could be good or bad. Look to the figure of Nicolas of Cusa, who both admired Roger Bacon very much, but also at times labeled Bacon a heretic. For Bacon was not only a scientific pioneer, he was also the wizard who apparently conjured the Brazen Head. Now, of course moderns are going to scoff at these struggles against moralism and the "superstitions" of medieval authorities, but, again, the judgment of moderns are largely mistaken and self-inflated.
The key thing to realize, in my view, is that the "scientific" investigations were always tethered towards ethical purpose, and a very real danger was perceived about the mis-applications of knowledge. Newton's astounding success self-justified on the wide back of its utilitarian power, ushering in a sense of "moral Newtonism" that at once sheared science of every ethical tether. Of course, movements in this direction had already begun starting in the Renaissance. For example, you'd no doubt be appalled had you walked in upon Leonardo Da Vinci's lair, among all the strewn about cadaverous body parts. But, with Newton, the idea of grand "systems" governed by empirically discoverable laws became the guiding light of every species of analytical thought. And these grand systems were amoral.
We no longer had "evil wizards", they transmuted themselves into the form of "brave scientists". From rogues to heroes. And it became a DUTY of such figures to challenge ethics, in fact. So much for natural harmonies.
Good overview. Although I am missing the physics v metaphysics distinction. Medievals and Aristotle were great in metaphysics. The theology was the queen of sciences with philosophy and metaphysics above natural sciences. The appeal to authority was I think in this sense so the lower should not contradict the higher. Also for the passage from Moliere I remember Ed Feser defending it. In one of his books he's trying to make case for 'powers' within the thing itself as opposed to 'law of nature' pushing things from somewhete above which is, in a sense, quite platonic view of things.
Interesting. Aquinas in particular was quite sophisticated. It became much the fashion to trash Aristotle in part due to a hostility against the authority of the Church and in part due to the excesses of the Schoolmen. I first came across the Moliere passage in Park's The How and the Why where it was presented as a satire of the Schoolmen's syllogisms.
Great piece! Very interesting. Did later scientists try to claim credit for this obscured work? Strange that it got lost when it's documented in writing...
It's fascinating to read Whewell (who was very English) saying nothing of note happened in the Middle Ages, but wow wasn't the Englishman Roger Bacon remarkably ahead of his time. Nationalist pride (and objective truth) triumphing over the received historical wisdom about the "Dark Ages." Ivor Harte in Makers of Science takes a similar tack.
Historians use selective picking through of their sources to bolster the narrative they serve. Henry VIII's "Dissolution of the Monasteries" had to be defending and justified so his nobles who inherited the spoils could keep them. That's where we get the narrative of the dark ages when [Catholic] superstition reigned until the "winter of our discontent Made glorious summer by this sun of York." That's literally Richard praising his brother Edward who's seized the throne, but recall Henry VIII was the son of Elizabeth of York. We also have the adamant refusal to accept a Catholic sovereign which led to the Glorious Revolution. The English historical tradition is all about trash talking the medieval period so they can look better by comparison.
Francis Bacon, of course. I can't tell for sure if Lord Bacon was deliberately slighting his predecessors, or taking issue with the misinterpretations of the Schoolmen, or merely ignorant of those who preceded him. Hard to believe that last, as well read as Lord Bacon was. Where Newton ascribed success to having "stood on the shoulders of giants," Bacon declared the giants were all standing in his way, and he was shoving them aside. As a wise podcaster once told me, "The handmaiden of Bacon's secrecy was his mendacity."
Sorry to be a little pedantic as it’s at best auxiliary to your otherwise fascinating accounts. In my opinion it’s a bit of a miss to compare the retrograde motion (being the sum of two circular orbits) to decomposition by Fourier analysis. The sinusoidal basis functions are a rather special example of completeness and utility, and their rich applications in complex analysis also speak more to this. I am certainly not well versed in the virtues of the Ptolemaic model (though in other posts you rightfully point out given the set of available observations it made a compelling case) but referencing the resulting motion as being the sum of two other motions doesn’t even begin to describe the deep mathematical concepts underpinning Fourier analysis and it’s widespread applications.
Another note for my own reference... here's a really good if somewhat technical discussion of the Ptolemaic system: https://www.mathpages.com/home/kmath639/kmath639.htm
This was an excellent and interesting presentation of the ptolemaic model and the point about having too many free parameters for an over constrained system was a nice treat. The requirement for the various radial vectors to be always parallel is only possible if the they share a common frequency. This quickly becomes obvious, and an explanation of this crucial observation is nowhere in the model. Knowledge of this could have driven Copernicus to keep searching until he found the appropriate solution. Though the Greek model was wrong it was still consistent with the scientific method as it kept appropriate questions open; it invited Copernicus to play.
The dogmatism of the church which found the explanation convenient was the one incentivized to cull further questionings.
Thanks for the link!
I'm going to try to write up a more detailed response as a full post, but if you want a quick preview, the deferents and epicycles paradigm is essentially a 2D Fourier transform. More on that, here:
https://www.jezzamon.com/fourier/
Disappointing calumny against the noble schoolmen.
How so?
I think that the "culture wars" do cloud the perspectives of moderns who look back upon the medievals, for that is where the modern mythos leads one. Human nature also features a tendency towards pride and boastfulness, and this combined with the "evolutionary" analysis so typical of modernity also leads one to categorize oneself mistakenly as "more evolved" than predecessors. But the deepest problem is one of utility, of "what have you done for me lately?" which, in truth, really is shockingly the epistemological basis of modern science (the Scientific Method is a deceitful smoke-screen). If you take utility as your metric, which is what people are really doing, then science as we know it really began with Issac Newton, and everything before him winds up devalued.
I think it's a mistake to make judgments like this. But what do I know? One great disservice cemented by such a utilitarian approach is the masking of the central concern of natural philosophy, or science, in the Middle Ages. This concern was ethics. Realize that in the olden days the Line of Demarcation between Science and Magic were blurred. Throughout the Middle Ages always a tension existed around what was "good magic" or "bad magic". One of our heroes in this article, Roger Bacon, is a case in point. We see him through our filters as a Great Soul, a remarkable "proto-scientist". And this he was, there was no doubt. But also in his day Roger Bacon was perceived as a Magus, a sort of "wizard", who could be good or bad. Look to the figure of Nicolas of Cusa, who both admired Roger Bacon very much, but also at times labeled Bacon a heretic. For Bacon was not only a scientific pioneer, he was also the wizard who apparently conjured the Brazen Head. Now, of course moderns are going to scoff at these struggles against moralism and the "superstitions" of medieval authorities, but, again, the judgment of moderns are largely mistaken and self-inflated.
The key thing to realize, in my view, is that the "scientific" investigations were always tethered towards ethical purpose, and a very real danger was perceived about the mis-applications of knowledge. Newton's astounding success self-justified on the wide back of its utilitarian power, ushering in a sense of "moral Newtonism" that at once sheared science of every ethical tether. Of course, movements in this direction had already begun starting in the Renaissance. For example, you'd no doubt be appalled had you walked in upon Leonardo Da Vinci's lair, among all the strewn about cadaverous body parts. But, with Newton, the idea of grand "systems" governed by empirically discoverable laws became the guiding light of every species of analytical thought. And these grand systems were amoral.
We no longer had "evil wizards", they transmuted themselves into the form of "brave scientists". From rogues to heroes. And it became a DUTY of such figures to challenge ethics, in fact. So much for natural harmonies.
Good overview. Although I am missing the physics v metaphysics distinction. Medievals and Aristotle were great in metaphysics. The theology was the queen of sciences with philosophy and metaphysics above natural sciences. The appeal to authority was I think in this sense so the lower should not contradict the higher. Also for the passage from Moliere I remember Ed Feser defending it. In one of his books he's trying to make case for 'powers' within the thing itself as opposed to 'law of nature' pushing things from somewhete above which is, in a sense, quite platonic view of things.
Interesting. Aquinas in particular was quite sophisticated. It became much the fashion to trash Aristotle in part due to a hostility against the authority of the Church and in part due to the excesses of the Schoolmen. I first came across the Moliere passage in Park's The How and the Why where it was presented as a satire of the Schoolmen's syllogisms.
Great piece! Very interesting. Did later scientists try to claim credit for this obscured work? Strange that it got lost when it's documented in writing...
It's fascinating to read Whewell (who was very English) saying nothing of note happened in the Middle Ages, but wow wasn't the Englishman Roger Bacon remarkably ahead of his time. Nationalist pride (and objective truth) triumphing over the received historical wisdom about the "Dark Ages." Ivor Harte in Makers of Science takes a similar tack.
Historians use selective picking through of their sources to bolster the narrative they serve. Henry VIII's "Dissolution of the Monasteries" had to be defending and justified so his nobles who inherited the spoils could keep them. That's where we get the narrative of the dark ages when [Catholic] superstition reigned until the "winter of our discontent Made glorious summer by this sun of York." That's literally Richard praising his brother Edward who's seized the throne, but recall Henry VIII was the son of Elizabeth of York. We also have the adamant refusal to accept a Catholic sovereign which led to the Glorious Revolution. The English historical tradition is all about trash talking the medieval period so they can look better by comparison.
HAHA! - true story about that trash talking going all the way to Shakepseare
"The Lost King"
https://www.youtube.com/watch?v=USm64dSkd48
Francis Bacon, of course. I can't tell for sure if Lord Bacon was deliberately slighting his predecessors, or taking issue with the misinterpretations of the Schoolmen, or merely ignorant of those who preceded him. Hard to believe that last, as well read as Lord Bacon was. Where Newton ascribed success to having "stood on the shoulders of giants," Bacon declared the giants were all standing in his way, and he was shoving them aside. As a wise podcaster once told me, "The handmaiden of Bacon's secrecy was his mendacity."
Wow. What a low life...!