Subject: The Goedel--Thirring Connection Date: Sun, 28 May 2000 13:27:50 -0700 From: "Eckehart Köhler" To: Robert.Jantzen@Villanova.Edu, John Casti , Werner DePauli CC: (Onkel Kay-Kay) Eckehart.Koehler@univie.ac.at, , Michael.Stoeltzner@sbg.ac.at, Kurt-Goedel-Society , Matthias Baaz , Regenfelder.Jane@Netway.At Dear Robert Jantzen, My friend Jimmy Schimanovich sent me copies of your e-Mail correspondence on Goedel. So far as I know, I was almost certainly the first one to publish the claim that Gödel was influenced by Thirring's work in the '20s on rotating universes. [None of the other Goedel biographers were aware of this, and the great master of the subject, G.F.R. Ellis: ("Contributions of K. Goedel to ralativity and Cosmology" in P. Hayek (ed.): "Goedel '96", Springer Lecture Notes in Logic 6) was very surprised when I mentioned it in a discussion after his lecture in Bruenn in 1996.] I began work on the life of Goedel in Princeton for a project Schimanovich and Peter Weibel started in Vienna in 1978 to commemorate Goedel, at which time I lived in New Hope PA near Princeton, and they asked me to help them from the US side. Shortly thereafter, Fritz Stadler in Vienna invited me to Vienna to work on a project on the Vienna Circle (mainly Carnap) starting in 1981. My first article on Goedel appeared as an early version of "Goedel und der Wiener Kreis" in Paul Kruntorad (ed.): Jour fixe der Vernunft, Hoelder-Pichler-Tempsky, Vienna 1991, where I quote from a letter from Thirring to Goedel (see below). This article will appear in full in the long, long, long-delayed volume(s) on "Kurt Goedel---Wahrheit und Beweisbarkeit" begun by Schimanovich and Weibel, now being shepherded by Michael Stoeltzner. I have no direct evidence that Goedel read the two articles by Hans Thirring in the '20s on rotating universes (one with Lense). Furthermore, Goedel and Thirring probably never talked about the subject either, because 1. Goedel was painfully shy, 2. it was not customary in Austria (or Germany) for "mere students" to talk with beings from such an elevated station as full professors. But the indirect evidence is crushingly strong that Goedel must have known about Thirring's rotating universes: from 1924 to the Winter- Semester 1927/28, Goedel was primarily a PHYSICS student, not a math student (although it wasn't necessary to distinguish the two that much, as most of the courses would overlap anyway, and the two departments were even located in the same building---the same one where the Vienna Circle met!), and would therefore have attended most of the lectures on the subject, especially Thirring's seminars on theoretical physics. Furthermore, Goedel customarily tracked all journals and monographs on subjects he was interested in, so he couldn't have missed Thirring's publications---which must have struck his attention immediately because of their exotic cosmological content, combined with exotic technical tools In one of his lectures on mechanics in the summer semester of 1925, "Mechanik deformierbarer Koerper mit Einleitung in die Tensoranalysis", Thirring included an introduction to tensor analysis; in a later lecture, he included eigen-value calculation; but his first lecture on Relativity was not until the summer semester of 1930. However, we may conjecture with high probability that General Relativity was treated in his very regularly scheduled (advanced, but otherwise untitled) Seminar fuer theoretische Physik, which was free and which Goedel presumably attended regularly. Thirring regularly lectured on "Mechanik" or "Theoretische Mechanik", which could conceivably have dealt with rotating mass-shells in empty space (the topic of Thirrings cosmological papers). It may be that Thirring's papers, presumably in the possession of his son, Walter, contains lecture notes and seminar report schedules from those years. I have not inquired, but it's a definite possibility, as Thirring very likely kept such records. Goedel's interest in logic and foundations of mathematics was only ignited when Carnap was awarded a Habilitation in 1926 and offered an Uebung "Einfuehrung in die Logistik". The material for this appeared in Carnap's "Abriss der Logistik" with Springer/Vienna in 1928, the first, and for a long time the only really solid and wide-ranging introduction to formal logic, concentrating on applications and aimed at philosophers and scientists; whereas Tarski's wonderfully didactic "Mathematische Logik", Springer/Vienna 1926 was more narrowly aimed at mathematicians (Both were of course translated and widely used in the US). But the real breakthrough, after an interlude on "Philosophie des Raumes (Grundlagen der Geometrie)" was Carnap's "Die philosophischen Grundlagen der Arithmetik", winter semester 1928/29, the first time Carnap did his own research on foundations of mathematics. He was apparently motivated to do this by a direct request to work on the subject from Adolf (later Abraham) Fraenkel; but Hans Hahn (the actual creator of the Vienna Circle) presumably was also a strong motivating force. Here Goedel first heard about Hilbert's Program and associated problems of decidability and consistency, whereby Carnap presumably referred to the 3rd edition of Fraenkel's "Mengenlehre", whose later chapters contain classically good treatments of "formalism" vs. "logicism" vs. "intuitionism" and which Fraenkel had sent Carnap to comment on in proof, requesting guidance from the already reputable master of logical "Konsequenz". Hahn had offered a memorable two-semester seminar on Whitehead & Russell's "Principia mathematica" in the winter and summer semesters of 1924/25, but Goedel almost certainly didn't attend, because it was (of course) advanced, and Goedel had only started that year, and he certainly wouldn't have been sassy enough to request special permission to attend as a beginner (although Gödel already had mastered university-level analysis at his Gymnasium in Bruenn). Instead, Goedel first studied mathematical logic, ironically, with his beloved Schlick, who wasn't a master but who revered Russell almost as much as Hahn, and used the German translation of Russell's "Introduction to Mathematical Philosophy" (with an introduction by Hilbert!) in a free one-hour lecture in his big lecture hall no. 41 in the winter semester of 1925/26. As masterful as Russell wrote, this text is rather popularly oriented and in any case didn't seem to spark much with Goedel, who did not finally read the "Principia" in detail until 1929! It was Carnap who got Goedel rolling. (Dawson missed this entirely in his biography. I protest!) It may be possible to prove Goedel registered for Thirring's lectures from records at the University of Vienna; Goedel's own "Studienbuch", in which students themselves kept such a record together with receipts for paying the nominal registration fees ("Hoergeld") apparently disappeared (which is surprising, as Goedel took many trivial receipts and scraps of paper with him from Vienna to Princeton on his crazy trip through Siberia in Jan. 1940; however, a chest of belongings the Goedel's left with his wife's family in Vienna has disappeared). Among the scraps of paper are library lending slips indicating which books Goedel lent out and when; maybe there some proof can be found. (These are nice especially because Goedel owned few books and relied primarly on library copies for research. They are kept at the Princeton Univ. Library among Goedel's papers, which were "organized" by John Dawson, bless his heart.) Thirring's status was rather anomalous, as his real metier was experimental physics, where he did his most highly regarded work. Yet he had the less prestigious chair for theoretical physics, whereas the more prestigious chair for experimental physics was held by F. Ehrenhaft (NOT Ehrenfest!). [Until Relativity and Quantum Mechanics, theoretical physics was regarded as finished and uninteresting, whereas experimental physics involved a comparatively huge budget and staff.] The anomalies accumulated: when Einstein gave his famous lectures in Vienna in the early '20s, he was Ehrenhaft's guest, NOT Thirring's --- despite the fact that Thirring locally represented theoretical physics and had published a well-regarded little monograph on Relativity, "Die Idee der Relativitaetstheorie" in 1921 with Springer/Vienna. Thirring's general politics also had extremely much in common with Einstein (and Goedel!) in being a very vocal pacifist at a time when that was highly frowned upon (Schroedinger's teacher Hasenoehrl was also a pacifist, suffering the mortal irony of dying in combat in WW I). Thirring later became a charter-member of the Pugwash- Movement, toward which he presumably oriented his memoirs, in connection with he directed his letter of inquiry to Goedel. That Goedel had personal contact with Thirring is proved by a letter Thirring, in his old age, wrote to Goedel in 1972, rather pleadingly requesting confirmation that Thirring played a role (parallel to Szilard's?) in goading Einstein to write his famous letter to Roosevelt to start the Manhattan Project. It is interesting that Goedel paid a farewell visit to Thirring in Jan. 1940, after Thirring had been dismissed by the Nazis, demonstrating at least a modicum of courage, because for someone as risk-avoiding as Goedel it would have appeared provocative to the new masters to associate with "undesirable elements". (In the Fall of 1938, Goedel had been roughed up by Nazi hooligans, who identified him as a member of that notorious gang of Jews and liberals: the Vienna Circle. In contrast, according to his acceptance as a "Dozent neuer Ordnung" by the new Nazi administration at the University of Vienna after Goedel had left, the Nazis had no evidence any involvement in politics, and they didn't mention his membership in the highly suspect Vienna Circle.) However, Goedel was very mindful of good manners, and Thirring was probably the last of his teachers and friends from the '20s who was still in Vienna, and by that time Goedel was already world famous and his status had risen to a level comparable to that of Thirring. Thirring's inquiry (in his letter of 1972, among Goedel's papers) was whether Goedel relayed Thirring's news of Jan. 1940 that, based on hot developments with Hahn & Meitner, an atomic bomb was feasible, to Einstein, as Thirring claimed he suggested in the farewell conversation. Goedel replied that he indeed relayed Thirring's greetings to Einstein in 1940, but he had no recollection about uranium or atomic bombs. [Anyone who knew Goedel would have laughed at the very idea that Goedel would ever relay anything which could possibly change history, especially concerning anything so highly dangerous.] Thirring of course knew that Einstein was at the IAS and assumed it was easy for Goedel to see Einstein there---but as your oral history has already revealed, that was easier said than done. By the way, Goedel's reply to Thirring refutes Oppenheimer's suggestion [which I first heard from Stavan Harnad, who had lived at Oppenheim's house] that he had not met Einstein until Oppenheim virtually held their hands together. Rather, knowing Goedel's personality, we may conjecture that he dutifully and politely relayed Thirring's greetings to Einstein, that he suppressed relaying anything that could cause hideous destruction (although Goedel hated the Nazis as much as Einstein, he was, unlike the casuist pacifists Einstein and Russell, an absolute pacifist who would refuse to pull the trigger of a gun he held even if Satan were right before him raping and pillaging). But once he executed his duty, Goedel would not otherwise want to pester the great man, and simply ignored his presence. However, Goedel did indeed report on Einstein's publicly known activities numerous times in the frequent letters to his mother in Vienna, beginning around 1946, who specifically inquired about the great Einstein's movements (proud that her son was at the same institute), and these should be consulted. They were bought by Schimanovich from Goedel's older brother Rudolf (now deceased) and stored in Vienna's City Hall. (I have copies.) Wang quotes a lot from these letters in his "Reflections on Kurt Goedel" and "A Logical Journey". I hope this information is of use to you, and I apologize for my occasional use of conjecture rather than documented facts. But the conjectures are at least based on documents, especially the university course catalogs, of which I have copies. And letters. Also, the conjectures guide search for documentary proof. Yours Eckehart Koehler PS: Here's a footnote on Thirring from my unpublished article, scheduled to appear in the still mythical collection mentioned above, "Goedel in Princeton" (if you read German, I can attach the whole article): Thirring war Ordinarius für theoretische Physik an der Wiener Universität (seine eigentliche Forschung betraf allerdings hauptsächlich technische und Experimental-Physik). Er wurde wegen seines Pazifismus zwangsweise pensioniert, worauf er eine Konsulententätigkeit ausübte. Nach dem Krieg kam er wieder auf seinen alten Posten zurück, beschäf-tigte sich aber intensiv im pazifistischen Sinn mit politischer Psychologie und der Motivation hinter Aggression und Krieg. Insbesondere wirkte er führend, gemeinsam mit Russell und Einstein, in der “Pugwash-Bewegung” von Naturwissenschaftlern gegen Atomrüstung mit. Er hatte eine der frühesten allgemeinverständlichen, aber trotzdem exakten Darstel-lungen der allgemeinen Relativitätstheorie verfaßt: Die Idee der Relativitätstheorie, Springer-Verlag, Wien 1921, 31948. Schon gegen Ende des ersten Weltkrieges arbeitete er im Rahmen der allgemeinen Relativitätstheorie über das Verhalten von rotierenden Massenschalen im Weltraum, was offenbar die Grundlage für Gödels spätere Arbeit über rotierende Universen werden sollte (siehe §3.3). Siehe H. Thirring: Physikalische Zeit- schrift 19(1918) 33; 22(1921) 29; und gemeinsam mit J. Lense (einem Mathematiker-Kollegen Hans Hahns): ebenda 19(1918) 156. Univ.-Doz. Dr. Eckehart Koehler Lichtenauergasse 9 / 6 A - 1020 Vienna, Austria