Abstract
For every young man of my background, the commitment to a religious (Orthodox) lifestyle and matters of sexual conduct, as well as the temptations presented by one’s surroundings, gave rise to a number of problems.
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Notes
- 1.
David Hoffmann, Das Buch Leviticus, trans. and explained, 2 vols. (Berlin: M. Poppelauer, 1905–1906). For an English translation of Hoffmann’s “Introduction” to Leviticus see Jenny Marmorstein, “David Hoffmann—Defender of the Faith,” Tradition 7–8 (1966): 91–101.**
- 2.
Emek may refer here to Emek Beit Shean, which has several religious kibbutzim. The kibbutzim in Emek Yizrael are secular.**
- 3.
Chwolson’s father Daniel (Joseph) [or Daniil (Iosif) Abramovich Khvol’son] (1819–1911), born in Vilnius (then Russia), studied the Torah in Russia, Breslau, and Leipzig, and became professor of Oriental Languages at the University of St. Petersburg after being baptized in 1855. He was one of the leading Orientalists of his time. He spoke out to the Russian government many times and sometimes successfully in defense of the Jews and even after his baptism he maintained ties to Russian rabbis. He took up the sentence in the main prayer of Yom Kippur (Day of Atonement), whose ambiguity made it difficult to translate:
עד שלא נוצרתי איני כדאי, ועכשו שנוצרתי כאילו לא נוצרתי
Its original meaning is: “Before I (that is, the person in prayer) was born I was nothing; now that I have been born, it is as if I had never been born.” As spoken by Chwolson it meant: Before I was baptized, I was a nothing, and now that I have been baptized, I conduct myself as if I had not been baptized.
- 4.
It was actually Friedrich Paulsen who wrote: “I have read this book with burning shame over the condition of the general and philosophical education of our people. It is painful that such a book was possible, that it could have been written, edited, sold, read, pondered, and believed by a people who possess a Kant, a Goethe, and a Schopenhauer.” F. Paulsen, Philosophie militans: Gegen Klerikalismus und Naturalismus (Berlin: Reuther & Reichard, 1901), 187, as cited in Daniel Gasman, The Scientific Origins of National Socialism (London/New York: MacDonald/American Elsevier, 1971), 14. Similar in meaning, what Chwolson actually said was: “What feelings should these lines arouse in an expert of physics? Contempt or bitterness? What should one do? Should he laugh or weep?” and that Haeckel revealed “a scarcely believable lack of knowledge of the most elementary questions.” See Armin Hermann, Wie die Wissenschaft ihre Unschuld verlor (Stuttgart: DVA, 1982), 78–79; cited with the English translation from Stefano Fait’s Ph.D. dissertation in Social Anthropology at the University of St. Andrews (2004), and Chwolson, Hegel, Haeckel, Kossuth und das zwölfte Gebot (Braunschweig: Vieweg, 1906), cited in Helge Kragh, Entropic Creation: Religious Contexts of Thermodynamics and Cosmology (Hampshire/Burlington: Ashgate, 2008), 148.**
- 5.
The “three weeks” between the 17th of Tammuz and the 9th of Av, observed as a time of quasi mourning, especially the last nine days.**
- 6.
This common name for (Shemini) Atzeret led in my final year of school to the following conversation. The Jewish New Year fell on Thursday and Friday, so that also in the subsequent weeks, except for the one immediately following the New Year, Thursday and Friday were holidays. In the last of these three weeks I said to the teacher on Wednesday that I would not be coming the next two days, whereupon he asked me: “Again? What holiday are you having now?” My answer was “the end of the festival.” His retort: “Well it is high time that your festivals finally come to an end!”
- 7.
Die Familie Mendelssohn 1729–1847, nach Briefen und Tagebüchern (Berlin: B. Behr’s, 1879); English: The Mendelssohn Family, trans. Carl Klingemann (New York: Harper, 1881).**
- 8.
Cohen was on friendly terms with Kurt Hensel’s brother Paul, a professor of philosophy at the University of Erlangen. He sometimes allowed Paul to tell him the latest Jewish jokes when he was visiting in Marburg.
- 9.
For a largely scientific appraisal see H. Hasse’s 1949 article: “Kurt Hensel zum Gedächtnis” (In Memory of Kurt Hensel), in volume 187 of the Journal für die reine und angewandte Mathematik (“Crelle’s Journal”). The word Jude (“Jew”) is not mentioned in the article!
- 10.
The system R of rational numbers \( \frac{m}{n} \) has the property that the four elementary arithmetic operations (addition, multiplication, and their inverses: subtraction and division) can be applied without any limitations within the system, except for division by zero. R is therefore referred to as a field. Moreover, R is the smallest (infinite) field of numbers that is contained within a larger one, for example, in the field of all real (or complex) numbers.
However, there are also finite fields. Here as well, as in every field, it holds that a product is zero if and only if (at least) one of the factors is zero.
Already in the nineteenth century, more general fields had been considered, for example those whose elements are not numbers, but functions. An analysis of the most general “abstract” field and its properties was not conducted until 1910 by Ernst Steinitz, in his now classic 143-page treatise. As Steinitz himself stated, his analysis was prompted in part by “p-adic numbers,” the innovative constructions (between numbers and functions), which were introduced by Kurt Hensel for very different objectives related to number theory and are too complex to explain here.
Such systems are called rings—especially when they contain zero divisors. “Abstract” rings were first examined in my dissertation and postdoctoral professorial qualification theses, and a short time later in a far more general sense by other researchers. Here too there is a connection to Hensel’s number theory analyses, namely, to the g-adic numbers that appear in his book on number theory (1913), in which g denotes a composite number.
- 11.
Ramot Hashavim was founded by German immigrants, largely academics without university positions and lacking agricultural skills, who thus started chicken farms.**
- 12.
Charlottenburg College was the precursor to the Technical University of Berlin.**
- 13.
Chorev was established in 1934 by German Jewish Orthodox immigrants to Land of Israel/Palestine. Founded with 16 boys and girls, it followed the religious philosophy of Samson Rafael Hirsch. Currently there are gender-segregated Chorev elementary and high schools.**
- 14.
This refers to a comment of Hermann Cohen to Franz Rosenzweig, criticizing Zionists of eudaemonism. Gershom Scholem said it was the “most profound remark that an opponent of Zionism ever made about the movement.”**
- 15.
In this context it is interesting that at the reopening of the Frankfurt Free Jewish School on November 19, 1933, Martin Buber spoke of the German-Jewish (re)encounter of history. See Achim von Borries, Selbstzeugnisse des deutschen Judentums 1870–1945, Fischer Library, no. 439 (Frankfurt am Main, 1962).
- 16.
This is a pun on the German idiom: to eliminate something “mit Stumpf und Stiel” (root and branch).**
- 17.
Robinson moved to Yale University in 1967, where he remained until his death in 1974.**
- 18.
Here I am referring to Paul Natorp’s book Die logischen Grundlagen der exakten Wissenschaften (1910) in order to promote understanding of the problem, not only because it is expressly based on Cohen’s books on the subject (including Dimitry Gawronsky’s Ph.D. dissertation), and follows them chronologically, but also because its presentation is much more understandable than Cohen’s main work Logik der reinen Erkenntnis (1902; hereinafter: Logik), which was preceded in 1883 by Das Prinzip der Infinitesimal-Methode.
I will only briefly touch on the concept of space here, especially because a number of different interpretations of its treatment by Kant still exist today. The crucial point, aside from three-dimensionality, is the assessment of Euclidean geometry—in other words the characterization of the parallel axiom as a synthetic judgment a priori. It shall suffice to cite Natorp (p. 312): Euclidean space is “a ‘necessary’ presupposition in the specific sense that it is a condition for ‘possible experience,’ more specifically: for the unique (eindeutige), law-governed determinability of existence in experience.” Even before the general theory of relativity, mathematicians and natural scientists had to reject this concept of space.
Far more characteristic for the Marburg school than the analysis of space tracing back to Kant is the emphasis on the meaning of the infinitesimal, that is, of “infinitely small” quantities, as first introduced by Cohen. Starting with Aristotle, and then in scholastic philosophy and theology, and more intensively since the seventeenth century, the infinite was discussed, but not until Georg Cantor’s set theory did it acquire a firm foundation, in order to later play a key role in mathematics and a number of its applications. The Marburg neo-Kantians thus explained: If following Cantor an infinitely large “number” is denoted as w and if the ratio 1:w = x:1 is formulated, then x must be an “infinitely small number.” Such infinitesimal numbers could then be seen as, for example, numerator and denominator in the Leibniz notation \( \frac{dy}{dx} \) for the differential quotient.
In reality, however, as science has indubitably recognized since the early nineteenth century, \( \frac{dy}{dx} \) is not a quotient at all, but the limit of a quotient, and the “differentials” dx and dy definitely do not have the independent meaning that Cohen ascribed to them. However, he based his “principle of origin” on this as the foundation of his logic, asserting that with the infinitesimal method the “precise question” and “decisive answer” are thus given for the meaning of thought as production of existence, and dx is the “true unit,” the absolute (Logik, 32, 109, 116, 123, etc.). In contrast, Cohen by all means rejects the limit method as the basis of the infinitesimal method—also for the integral. It is obvious that a mathematician must reject this view as false (or as meaningless).
- 19.
Memoiren einer Großmutter, with a foreword by Gustav Karpeles, 2 vols. (Berlin: Poppelauer, 1908 and 1910) [English: Memoirs of a Grandmother: Scenes from the Cultural History of the Jews of Russia in the Nineteenth Century, translated with an introduction, notes, and commentary by Shulamit S. Magnus, 2 vols. (Stanford, CA: Stanford University Press, 2010 [vol. 1] and 2014 [vol. 2])**].
- 20.
Kurt Hensel, Zahlentheorie (Berlin and Leipzig: G. J. Göschen, 1913).
- 21.
In Journal für die reine und angewandte Mathematik, vol. 1912, no. 141 (Jan. 1912): 43–76.**
- 22.
Alfred Loewy, Lehrbuch der Algebra, vol. 1: Grundlagen der Arithmetik (Berlin: Veit & Co., 1915).
- 23.
Entailed estates are estates which cannot legally be sold or divided when inherited. Such conditions on estate can result in unfair division among heirs, or in heirs being rich in land but otherwise poor. When Professor Troeltsch said he wanted to discuss “the nature” of entailed estates, he added the prefix “Un-,” his wordplay changing “nature” to “disaster,” thus demonstrating his rejection of the concept of entailed estates and his courage in opposing reactionary laws and customs intended to benefit the rich.**
- 24.
In the “three-class franchise” system of Prussian representation, those eligible to vote (men over the age of 24) were divided into three classes based on amount of taxes paid, giving far greater representation to the rich.**
- 25.
This refers to the lodge and restaurant at Friedrichstrasse 127, proprietor: Morris Fifar.**
- 26.
At the beginning of the century he turned down a position as a full professor at a small northern German university. He was later conferred the title Privy Government Councilor.
- 27.
Heller als tausend Sonnen: Das Schicksal der Atomforscher (Stuttgart: Scherz, 1956) [English: Brighter than a Thousand Suns: A Personal History of the Atomic Scientists, trans. James Cleugh (New York: Harcourt Brace, 1958)**].
- 28.
See Fraenkel family tree on page 204.**
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Fraenkel, A.A. (2016). As a Student at Prussian Universities. In: Cohen-Mansfield, J. (eds) Recollections of a Jewish Mathematician in Germany. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-30847-0_3
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