In 2014 and 2018 I challenged the common view that Copernicus stole ideas from Maragha astronomers. My arguments were discussed by Nikfahm-Khubravan & Ragep (2019), who are believers in the “influence thesis” that I was challenging. Some people have asked me what I think of their take.
Nikfahm-Khubravan & Ragep do not try to refute me on any significant point.
The agree with my main point, e.g.: “as Blåsjö has recently shown, Swerdlow based his assessment on a misunderstanding of what Copernicus was saying regarding the behavior of the Mercury model” (35).
In other words, they agree that I refuted what Swerdlow called the “perhaps strongest evidence” for influence, and what Saliba said “elevates the discussion of the similarities to a whole new level”.
The following comment by Nikfahm-Khubravan & Ragep is ridiculous and nonsensical:
“Blåsjö also wishes us to believe that by showing that Swerdlow misunderstood what Copernicus was saying, this somehow disproves Swerdlow’s conclusion that Copernicus was copying Ibn al-Šāṭir’s model. … This is an unwarranted leap on Blåsjö’s part.” (40)
Obviously I never made such a “leap”. Obviously refuting what Swerdlow called the “perhaps strongest evidence” and what Saliba said “elevates the discussion of the similarities to a whole new level” is very significant. But obviously this in itself does not conclusively settle the question of influence one way or the other. The notion that I maintain that my argument “somehow” (sic) conclusively disproves influence altogether is obviously a ridiculous fabrication.
The following are just empty words:
“Viktor Blåsjö … insists that similarities between models can be explained by there being ‘natural’ solutions that would lead Copernicus and Ibn al-Šāṭir to come to similar conclusions without the necessity of assuming influence.” (3) “Blåsjö’s arguments about ‘naturalness’ are generally lacking in historical evidence.” (27)
Obviously questions of “naturalness” are inherently debatable and cannot be settled one way or the other from historical evidence. The suggestion of “naturalness” is no more “lacking in historical evidence” than its converse. The influence thesis itself is obviously “lacking in historical evidence,” which is why the whole discussion exists in the first place.
Note that my article is called “A Critique of the Arguments for Maragha Influence on Copernicus”, not “proof of the naturalness of Copernicus’s theory.” I use the prima facie plausibility of the naturalness thesis to motivate a critical look at the arguments for influence, but I do not try to prove the naturalness thesis itself.
Nikfahm-Khubravan & Ragep attack a very insignificant side remark in my article:
“Blåsjö thinks that it was not necessary for Copernicus to mention the maximum elongations at the trines ‘since his intended readership would of course be very familiar with Ptolemaic theory and realize at once that this corollary carries over directly insofar as the two theories are equivalent’. But … it is highly unlikely that Copernicus’ ‘intended readership’, or anyone else for that matter, would have seen the greatest elongations at the trines as somehow a ‘corollary’ to the effect of the Ṭūsī-couple.” (40, further elaborated in Appendix 1)
They even call this “Blåsjö’s main contention” (46), which is completely ludicrous. No sane person could read my article and come to the conclusion that this was my “main contention.”
Let’s read what I say in my article:
“It is not at all strange that Copernicus omits any mention of the ±120° case [= maximum elongations at the trines]. For one thing, the radius in Copernicus’s model is R − e cos(2α), where α is the Earth’s angular distance from Mercury’s apsis. Mathematically, the most natural way to specify this formula is to describe the cases t = 0°, ±90°, where it takes its extreme values, and this is precisely what Copernicus does. So the reason for Copernicus’s mode of description could very well be a concern with mathematical clarity rather than ignorance of the significance of the ±120° case. Indeed, it is evident throughout the Commentariolus that Copernicus’s goal is to define his models briefly and clearly, not to explain the heuristic reasoning behind them. Only for the latter goal, which Copernicus never sets himself, would the ±120° case be of any use.” (193)
“Copernicus’s statement should be seen for what it is: a statement that a radius correction will be introduced, and how it will operate, not why the model has such a component in it. As such it is admirably clear, completely correct, and could hardly be improved upon. It looks “very curious” only if one misconstrues it as a didactical account of how the model, and Ptolemy’s equivalent one, came to be. Such a misconstrual is all the less reasonable since such a didactical explanation would be completely out of place in the Commentariolus — indeed, Copernicus never includes any explanation of this sort for any of the other components of his planetary models.” (193)
This is obviously my main argument for why nothing at all can be concluded from the absence of any mention of maximum elongations. Nikfahm-Khubravan & Ragep do nothing to question this argument, even though this argument alone has already shown that the issue maximum elongations is completely immaterial to the influence thesis.
In addition to this already completely clear and still unquestioned argument, I also added the following additional point:
“Moreover, Ptolemy’s proof for the ±120° case altogether eliminates the need for Copernicus to address the issue. For it is only after his model has been fixed by the observations for the 0°, ±90°, 180° cases that Ptolemy derives the property of maximal elongation at ±120° as a corollary. Therefore it must also be true in Copernicus’s model owing to its near-equivalence to Ptolemy. There is no need for Copernicus to mention this since his intended readership would of course be very familiar with Ptolemaic theory and realize at once that this corollary carries over directly insofar as the two theories are equivalent. This simple and plausible explanation eliminates the need to stipulate the highly unlikely hypothesis that Copernicus was somehow unaware of this very prominent aspect of Ptolemy’s Mercury theory.” (193)
It is obvious that even if we grant for the sake of argument that this additional point is unconvincing, then that does still not in any what whatsoever undermine anything else I said in my article, and indeed it still leaves my main argument for the exact same subconclusion that I spelled out just before still standing.
So Nikfahm-Khubravan & Ragep’s entire beef in Appendix 1 is a red herring that is almost entirely irrelevant even if they are right.
I find their argument in this appendix unconvincing, and indeed even they admit that “Mathematically speaking, there is some truth to” (44-45) what I say etc., so whatever point they are making is hardly clear-cut.
But who cares? Obviously nothing of significance rests on this. Obviously they have ignored my actual argument and attacked an insignificant side remark that doesn’t matter.
Even if their argument in Appendix 1 were right, it would still at best only remove one of my two arguments for why Copernicus didn’t mention the maximum elongations in the Commentariolus. For that matter, even if the first argument (which no one has questioned or ever will), was itself refuted (which it never will be) that would still not prove anything about influence, obviously.
As I have shown, and as Nikfahm-Khubravan & Ragep have conceded, Copernicus’s model is correct. For whatever reason, he did not mention that it has the correct maximum elongations, although it does. Clearly there can be any number of reasons for why Copernicus didn’t mention this. I suggested two possible such reasons, without pretending that this was an exhaustive list of the possibilities, of which Nikfahm-Khubravan & Ragep dubiously claim to have been able to undermine one.
Obviously the step from Copernicus’s not mentioning the maximum elongations to the conclusion that he therefore must have copied the model is itself ludicrous in the first place, regardless of whether one of my two alternative suggestions for why Copernicus might have chosen to do so is the right one or not.
Parenthetically, I can add a minor comment about this passage already quoted above:
“Blåsjö thinks that it was not necessary for Copernicus to mention the maximum elongations at the trines ‘since his intended readership would of course be very familiar with Ptolemaic theory and realize at once that this corollary carries over directly insofar as the two theories are equivalent’. But … it is highly unlikely that Copernicus’ ‘intended readership’, or anyone else for that matter, would have seen the greatest elongations at the trines as somehow a ‘corollary’ to the effect of the Ṭūsī-couple.” (40)
This appears to misconstrue my point. Obviously what I am saying that readers would have been able to do is to go from the two premisses:
- Copernicus’s model is essentially equivalent to that of Ptolemy. (Which is not proved in the Commentariolus but could conceivably have been taken as implied.)
- Ptolemy’s model implies the correct maximum elongation behaviour.
to the conclusion:
Copernicus’s model has the correct maximum elongation behaviour.
Clearly I was not saying that readers would necessarily have been able to see directly that Copernicus’s model including the Ṭūsī-couple implies the correct maximum elongation behaviour, as Nikfahm-Khubravan & Ragep seem to imply.