The Political Perfection of Original Judaism: Pedagogical Governance and Ecclesiastical Power in Mendelssohn's Jerusalem
Moses Mendelssohn famously penned his Jerusalem; or, On Religious Power and Judaism in response to a public challenge. Mendelssohn had declared “ecclesiastical power” to be a contradiction in terms, and had thus come out strongly against the use of coercion in religious life, and against the ban of excommunication by rabbinic authorities, in particular. In the anonymously published The Search for Light and Right, August Cranz defies Mendelssohn to explain how he could reconcile this liberal view of religion with his continued commitment to—and his insistence that Jews were still obligated to observe—Jewish law. “As reasonable as all you say [about religious power] may be, to just that degree it contradicts the faith of your fathers . . . and the principles of its church . . . expressly set down in the books of Moses,” Cranz argues. “The theocratic ruling staff drove the whole people . . . with force and punishment.” True, Cranz concedes, exile reduced the capacity of Jewish authorities to enforce Jewish law, “but these ecclesiastical laws are there even if their exercise is no longer a must.” Cranz challenges Mendelssohn to explain his apparently irreconcilable commitments: “How can you persist in the faith of your fathers and shake the whole structure by clearing away its cornerstones, dear Mr. Mendelssohn, when you contest the ecclesiastical law given as divine revelation through Moses?”
Between Judaism and German Enlightenment: Recent Work on Moses Mendelssohn in English
Moses Mendelssohn (1729–1786) is generally recognized as the first German-Jewish philosopher. The past forty years have witnessed the appearance of five major book-length interpretations of Moses Mendelssohn in English: Michael Meyer’s The Origins of the Modern Jew: Jewish Identity and European Culture in Germany 1749–1824 (1967); Alexander Altmann’s Moses Mendelssohn: A Biographical Study (1973); Allan Arkush’s Mendelssohn and the Enlightenment (1994); David Sorkin’s Moses Mendelssohn and the Religious Enlightenment (1996) and Edward Breuer’s The Limits of Enlightenment: Jews, Germans, and the Eighteenth-Century Study of Scripture (1996). These works have generally been guided by a single interpretive question namely whether or not Mendelssohn was able to harmonize his commitment to Judaism with his commitment to Enlightenment. I review these five interpretations of Mendelssohn.
Rubik's for cryptographers
Hard mathematical problems are at the core of security arguments in cryptography. In this paper, we study mathematical generalizations of the famous Rubik’s cube puzzle, namely the factorization, representation and balance problems in non-Abelian groups. These problems arise naturally when describing the security of Cayley hash functions, a class of cryptographic hash functions with very interesting properties. The factorization problem is also strongly related to a famous long-standing conjecture of Babai, at the intersection of group theory and graph theory. A constructive proof of Babai’s conjecture would make all Cayley hash functions insecure, but on the other hand it would have many positive applications in graph theory and computer science. In this paper, we classify existing attacks against Cayley hash functions and we review known results on Babai’s conjecture. Despite recent cryptanalytic progress on particular instances, we show that the factorization, representation and balance problems presumably remain good sources of cryptographic hard problems. Our study demonstrates that Cayley hash functions deserve further interest by the cryptography community.