In my post An Infinite Sphere Whose Centre is Everywhere and Whose Circumference is Nowhere, I wrote that I had found references to a book by Dietrich Mahnke (1884-1939) entitled Unendliche Sphäre und Allmittelpunkt. Beiträge zur Genealogie der mathematischen Mystik1 [Infinite Sphere and Centre of the Universe. Contributions to the Genealogy of Mathematical Mysticism].
Mahnke’s book had been referred to by Max Caspar (1880-1956), in his notes on Johannes Kepler’s (1571-1630) De Stella Nova [On the New Star] and Epitomes Astronomiae Copernicae [Epitome of Copernican Astronomy], by Alexandre Koyré (1892-1964) in his From the Closed World to the Infinite Universe, and by E.J. Aiton (1920-) in his notes to the English-language translation of Kepler’s Mysterium Cosmographicum. It was in Mahnke’s book that I found the reference to La “Sphère infinie” de Pascal [Pascal’s “Infinite Sphere”] by Ernest Jovy (1859-1933), which formed the basis for the above-mentioned post.
I first looked at Mahnke’s book when I was preparing my post Johannes Kepler Views an Infinite Universe with Horror. Mahnke explains why he thinks that Kepler had rejected the idea of an infinite universe, despite the latter’s high praise for Nicholas of Cusa (1401-1464). Mahnke writes that notwithstanding his praise for Cusa, Kepler read neither Cusa’s De quadratura circuli nor De docta ignorantia. Here is a translation of the German into English, with the help of Deepl:
Even in his youthful Mysterium Cosmographicum, in which he attempts to elucidate the “mystery” of the definite number, size and movement of the celestial spheres with the help of the five regular bodies, Kepler expressly refers to Cusa and calls him downright “divine, because he attached such great importance to the relationship between the straight and the crooked and dared to compare the crooked to God and the straight to creatures”. Then, in a letter from 1608, he quotes Cusa’s words that “an infinite circle is a straight line”, thus paralleling his own description of the straight line as the “most obtuse hyperbola” and the “most acute parabola” as well as the point as the smallest condensation of the most diverse geometric bodies. Finally, he mentions in his Kepler's Conversation with Galileo’s Sidereal Messenger the “Thoughts of Cardinal Cusanus and Jordanus Brunus on the infinity of the world”. However, Kepler's closer acquaintance with Cusa’s writings De quadratura circuli and De docta ignorantia has been wrongly inferred from this. The last quotation certainly refers to the cosmological chapters of Cusa’s first philosophical treatise, but Kepler only knew about these from hearsay. And the two earlier quotations, as I will show, actually refer to two later writings, the Complementum theologicum and De mathematica perfectione, which form the conclusion of the mathematical part of the Paris Cusa edition. [pp.129-130, my emphasis]
According to Mahnke, if Kepler had read the astronomical chapters of De docta ignorantia, he would have classified Cusa as being among those who supported an infinite universe, as I wrote in my post Nicholas of Cusa Writes that the Universe is Privately Infinite.
In the essay on Galileo's astronomical discoveries, Kepler says that the Imperial Councillor Wackher first told him about the four newly discovered planets and added that they were certainly satellites of fixed stars; Wackher, following Cusa and Bruno, had already thought of such a possibility earlier, in contrast to himself, and now found in the actual discovery of unknown planets a confirmation of his opinion that either this world of ours was infinite, as Melissos and William Gilbert had already assumed, or that countless other worlds existed besides it, as Leucippus, Democritus, Bruno and Edmund Bruce believed. From these words it is clear that Kepler was not exactly familiar with the astronomical chapters of the Docta ignorantia; otherwise he would certainly have expressly included Cusa in one of the two classes, namely Gilbert’s…. If Kepler had read the Docta ignorantia himself, he would perhaps have allowed himself to be converted to the belief in the infinity of the world by the geometric-mystical reasons of Cusa rather than by the supposedly irreligious Bruno. [pp.130-131, my emphasis]
So that was my introduction to Mahnke. But that was not the end of the story. I went to look at the Wikipedia entry for Dietrich Mahnke, and there found that “Mahnke was killed in a car accident”. Furthermore,
At the time of his death, Mahnke was editing a volume of Leibniz's mathematical correspondence. This project was then taken over by Joseph Ehrenfried Hofmann.
The project that Joseph Hofmann (1900-1973) took over led to the latter’s book Leibniz in Paris2, which formed the basis for my previous post Joseph Ehrenfried Hofmann Demonstrates that Gottfried Wilhelm Leibniz Did Not Plagiarize Isaac Newton.
But it turns out that Hofmann was also an expert on Cusa: he wrote the introduction and notes to the German translation3 of Cusa’s mathematical writings undertaken by his wife, Josepha Hofmann.
Continuing on, I looked at the Wikipedia entry for Joseph Ehrenfried Hofmann, and there found that “Out for a morning walk, he was killed by a vehicular hit and run.” This is confirmed in the Preface to Leibniz in Paris, which ends with the following paragraph:
Early in October 1972 Professor Hofmann sent a last addition to his notes for this book incorporating one of his most recent finds in the Leibniz manuscripts. On 9 November he was knocked down by a motorcar while on his early morning walk and some six months later he died—on 7 May 1973, two months after his 73rd birthday. [p.xi]
So we have two successive German experts on the writings of Nicholas of Cusa and of Gottfried Wilhelm Leibniz, namely Dietrich Mahnke and Joseph Ehrenfried Hofmann, both dying in car accidents, the latter a hit-and-run. What an unfortunate coincidence!
If these accidents had taken place earlier, we might not have today the results of Hofmann’s work, demonstrating that Leibniz did not plagiarize Newton on the invention of the infinitesimal calculus.
Dietrich Mahnke. Unendliche Sphäre und Allmittelpunkt. Beiträge zur Genealogie der mathematischen Mystik. Haale/Saale: Max Niemeyer Verlag, 1937.
Joseph E. Hofmann. Leibniz in Paris 1672-1676: His Growth to Mathematical Maturity. Cambridge University Press, 1974. Revised translation of Die Entwicklungsgeschichte der Leibnizschen Mathematik während des Aufenthalts in Paris (1672-1676). Munich: R. Oldenbourg Verlag, 1949.
Nikolaus von Kues. Die Mathematischen Schriften. Übersetzt von Josepha Hofmann mit einer Einführung und Anmerkungen versehen von Joseph Ehrenfried Hofmann. Hamburg: Felix Meiner Verlag, 1980.
The beasts. Thank you for this.
Thanks John, that is interesting.