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I have finished reading the paper for the third time and in doing so I have noticed a very curious coincidence: at the end of one of my earlier posts in this thread, post #47, I linked to a biographical memoir written by Atiyah about Hermann Weyl I had come across a few years ago when I was reading up on Weyl. In it, on page 328, Atiyah says the following about Weyl:
historical continuity and especially the non-linear nature of a text which has to be read and reread again many times in order to be properly understood seem to be eerily reflected in the way Atiyah's preprint 'The Fine Structure Constant' was written; on the face of it, the numbered paragraph format is also somewhat reminiscent of Wittgenstein's Tractatus Logico-Philosophicus.
Did Atiyah write the paper this way on purpose, knowing it would probably only be understandable by the older readers? As I have argued in my earlier posts including #68 in this thread, much of the controversy seems to stem from the way this paper is written. I haven't tracked down Weyl's book yet, so this remains speculation. In either case, more and more, it seems to be the case that emulating this style was exactly his intent.
For example, in my first and second reading of the paper, both times I thought his remarks about the Axiom of Choice in 6.6 were clearly erroneous and that he was confusing the axiom with the school of Brouwerian intuitionism and its rejection of the law of the excluded middle; upon my third reading however I decided to read up on the historical matter regarding the axiom of choice a bit more and learned that I just wasn't aware that the law of the excluded middle is directly derivable from the axiom of choice. In other words, during a third careful reread I realized it was in fact I who was mistaken about something based on my prior knowledge of some fact being incomplete and therefore incorrect, while he was correct all along!
As for the faulty equations, especially 1.1 and possibly 7.1 as well, it seems very clear that these bits were written later than the other parts of the text as they seemingly come from thin air. With regard to 7.1, where does this equation come from exactly if not derived from the equations in section 8? I'm beginning to fear that these bits were written (much) later than most of the other parts, perhaps after his wife had already passed or after his cognitive decline had begun/worsened, and that perhaps there are even mistakes lurking in 7.1 which are extremely difficult to even identify, let alone correct without explicitly rederiving such an expression based on the equations in section 8.
Most of these points are actually rebutted by Lipton & Regan to which @martinbn linked to in post #62. Here again we see that professionals and experts have a very different grasp of matters compared to non-experts.
Moreover, I tracked down Hirzebruch's book which was referenced in the paper, in particular chapter 3. This chapter is a mere 23pp read instead of 250pp. I will see what can be found in it. If anyone wants a link to the chapter I will provide it.
These ideas of the unity of mathematics,Michael Atiyah said:
historical continuity and especially the non-linear nature of a text which has to be read and reread again many times in order to be properly understood seem to be eerily reflected in the way Atiyah's preprint 'The Fine Structure Constant' was written; on the face of it, the numbered paragraph format is also somewhat reminiscent of Wittgenstein's Tractatus Logico-Philosophicus.
Did Atiyah write the paper this way on purpose, knowing it would probably only be understandable by the older readers? As I have argued in my earlier posts including #68 in this thread, much of the controversy seems to stem from the way this paper is written. I haven't tracked down Weyl's book yet, so this remains speculation. In either case, more and more, it seems to be the case that emulating this style was exactly his intent.
For example, in my first and second reading of the paper, both times I thought his remarks about the Axiom of Choice in 6.6 were clearly erroneous and that he was confusing the axiom with the school of Brouwerian intuitionism and its rejection of the law of the excluded middle; upon my third reading however I decided to read up on the historical matter regarding the axiom of choice a bit more and learned that I just wasn't aware that the law of the excluded middle is directly derivable from the axiom of choice. In other words, during a third careful reread I realized it was in fact I who was mistaken about something based on my prior knowledge of some fact being incomplete and therefore incorrect, while he was correct all along!
As for the faulty equations, especially 1.1 and possibly 7.1 as well, it seems very clear that these bits were written later than the other parts of the text as they seemingly come from thin air. With regard to 7.1, where does this equation come from exactly if not derived from the equations in section 8? I'm beginning to fear that these bits were written (much) later than most of the other parts, perhaps after his wife had already passed or after his cognitive decline had begun/worsened, and that perhaps there are even mistakes lurking in 7.1 which are extremely difficult to even identify, let alone correct without explicitly rederiving such an expression based on the equations in section 8.
Regarding the third comment there, quoted here for convenience here:mathman said:
m00n said:
Moreover, I tracked down Hirzebruch's book which was referenced in the paper, in particular chapter 3. This chapter is a mere 23pp read instead of 250pp. I will see what can be found in it. If anyone wants a link to the chapter I will provide it.
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