Pictures at an Exhibition Karl Sigmund
I n 1965 Kurt Gödel wrote to his mother Mari-
雾霾天气的危害anne: “I am happy not to have to take part in the Vienne festivities, as I hate the things.”
So we must concede: the Vienne festivities planned for April 2006, on the occasion of his centenary, would probably have made him wince.
In April 2006 a large scientific congress will be held at the University of Vienna, organized by the International Kurt Gödel Society and generously sponsored by the Templeton Foundation (e www.logic.at/goedel2006/). It will be attended by the few scientists who had clo per-sonal exchanges with Gödel, such as Georg Kreil, Dana Scott, and Gaisi Takeuti. There will also be an exhibition on the life and times of Gödel, and this provides me, who rashly volunteered for the job, with a new t of experiences.
The University of Vienna is well-advid, of cour, to celebrate Kurt Gödel as much as it can. The game theorist Oskar Morgenstern, one of Gödel’s few friends in later years, was surely right when he wrote: “Among all tho who taught at the University of Vienna, there is probably nobody who name
outshines that of Gödel.” Gödel did most of his best work in Vienna. The university did not exactly pamper him, however. He remained a lowly Privatdozent(meaning he had the right to lec-ture, but no salary worth speaking of), and he even-tually had to escape, under hair-raising circum-stances, to the safety offered by Princeton. No place other than the Institute for Advanced Study (IAS) could have provided him with more peace and ea, or better intellectual companionship. Yet within a dozen years his productivity trickled off, although he certainly did not relax in either ambi-tion or hard work.
The city of Vienna cannot boast about the way it treated Gödel, but his centenary is a good occa-sion for making amends. The same applies to Mozart. And as luck will have it, Mozart’s 250th an-niversary also takes place in 2006. And Freud’s 150th. Some competition!
Exhibitions are costly. Aspiring to just one or two percent of the sum lavished by Berlin, for example, on its splendid Albert Einstein Exhibition 2005 is not a trivial matter. Fortunately, among officials in some ministries and magistrates I found veral dedicated enthusiasts, true crypto-Gödelians who were ready to help. I also encountered some who had never heard of him: but as soon as I men-tioned that Time magazine had listed Gödel among the hundred most important persons of the twen-tieth century, conversation flowed more easily. Whoever drew up that list derves an accolade!
Exhibitions also need space. Eventually, the list of possible locations boiled down to three candi-dates. One was the main building of the University of Vienna. During the Congress, in the week of Gödel’s birthday (April 28), hundreds of experts from t theory and mathematical logic will stroll its neo-Renaissance arcades, in addition to the daily stream of students; but many other Vienne will be reticent to cross the university’s entrance stairs. The cond location is Palais Pallfy, on the
Karl Sigmund is professor of mathematics at the Univer-sity of Vienna and a rearch scholar at the Institute for Applied Systems Analysis in Laxenburg, Austria. His email address is karl.sigmund@univie.ac.at.
Jofsplatz, the most beautiful piazza in town, just opposite the Hofburg of the Habsburgs. Since this will be the venue of many high-level confer-ences in the first half of 2006 (when Austria pre-sides over the council of the European Union), one hopes that some visitors will take a look at Gödel. But people around the Jofsplatz are usually busy. Finally, there is the beautiful MuumsQuarter, who baroque halls are available during the sum-mer months, when flocks of tourists throng be-tween the Muum for the History of Art, the Leopold Muum with its collections of Klimt and Schiele, and a lively scene of bars and restaurants. No drawback here, except that Gödel’s birthday does not fall in summer. It finally was decided that the exhibition will travel and visit all three spots in
different incarnations, from the end of April to mid-August 2006.
What can one show in an exhibition on Kurt Gödel? His work was abstract and his life with-drawn. There is nothing equivalent to, say, the couch of Sigmund Freud, or the fiddle of Albert Ein-stein. Gödel’s famous spectacles have not been prerved, so it ems, but his optometric pre-scription from 1925 has survived. For Gödel, who grew up as an avid stamp collector, was not one to throw things lightly away. He kept the bill for his wedding meal, for instance, as well as the testy re-minder, signed by Helmut Has, that he had not paid his membership dues for the German Mathe-matical Society. Gödel also kept the receipt for the purcha of Principia Mathematica, acquired dur-ing his student days. The Gödel Nachlass, which be-longs to the IAS and is kept at Princeton Univer-sity’s Firestone Library, is a gold mine of tidbits like the, but also of more rious information, and Gödel’s biographer John Dawson, who knows that Nachlass like no one el, has kindly agreed to co-curate the exhibition. He writes, in this issue of the Notices, about his experiences cataloguing the boxes of Nachlass material (e also Dawson 1997).
The only other place with a sizeable amount of information on Kurt Gödel is Vienna (Köhler at al, 2002). There are the archives of the university, containing much on his brilliant Ph.D. thesis, on his epochal Habilitation, and on the sinister corre-spondence between academic officials and high-level
Nazis after 1938. Gödel managed twice, after Hitler annexed Austria, to go on leave to visit the U.S., first at the height of the Munich crisis and again in the ten months of the “phony war”. More than a year after Gödel had ttled down for good in the U.S., the German ministry nt him (c/o University of Vienna) a lavishly emblazoned diploma with his promotion to “Dozent Neuer Ordnung” and the pompous guarantee of the Führer’s special pro-tection. The document was never collected, though, and the receipt still waits to be signed.
Next to the univer-
sity, the richest source
on Gödel is in City Hall:
the municipality
bought hundreds of let-
ters which he wrote to
his mother on every
other Sunday evening,
for the first twenty
years after the war.
They were bought,
thanks to Werner Schi-
manovich and Peter
Weibel (producers of a
documentary on
Gödel), from the heirs
of Gödel’s brother
Rudolf. Unfortunately,
there is no trace of the
letters Gödel must have
nt from Princeton
during his visits there
in the 1930s, and after
Gödel’s death his wife
Adele destroyed all let-
ters by her mother-in-
law.
The gist of Gödel’s
major discoveries can
中国达人秀朱晓明
be explained fairly eas-
ily to a large public: (a)
incompleteness, (b) the
consistency of the continuum hypothesis, and (c)
time travel in rotating univers. But I do not be-
lieve that an exhibition can explain the finer points
of “Gödel’s proof” at the level of detail which v-
eral trade books have achieved. Visitors stroll from
one spot to another. Exhibitions are meant for me-
andering around. This implies some superficiality.
Anyone wanting greater depth should sit down to
read or listen to a lecture. In contrast, the format
of an exhibition ems well suited to giving an idea
of Gödel’s intellectual surroundings. That is the
right topic for an easy stroll.
So let us take a stroll through Gödel’s Vienna,
even if that means walking in a Circle. Gödel was
an unusually quiet and withdrawn person, but by
no means a hermit in his Vienne years. He was
a member of the Vienna Circle. This shaped him
profoundly, but in an indirect, almost contrary
way. In a questionnaire that Gödel filled out much
2013年上海高考数学
later (but which he never nt off—Dawson exca-
vated it from the Nachlass), he states that the most
decisive influences on his intellectual development
长颈鹿英语怎么读
were the lectures by Heinrich Gomperz in philos-
ophy and Philipp Furtwängler in mathematics. One
would have expected the names of Moritz Schlick
and Hans Hahn instead, the professors of philos-
ophy and mathematics who had founded the Vienna
STAMP OF APPROVAL. “I replied very
gently to the magistrate, saying that I
owed my education to the University,”
wrote Gödel to his mother. He had
experienced superb teachers but
obnoxious administration. During his
time as Privatdozent, he mostly was
on leave, either in Princeton or in
sanatoria, and lectured only for three
mesters altogether.
Circle (and were certainly no
mean lecturers). But no: Gom-
perz and Furtwängler, who
held the introductory lec-
tures for Gödel’s cohort, im-
printed him for life. There is
little reason to doubt that
Gödel was a Platonist by the
age of nineteen and never wa-
vered in this conviction (Fe-
ferman 1984).
Karl Menger, the profes-
sor of geometry who was justmoment of truth
four years older than Kurt
Gödel and who became his
mentor for many years, de-
scribed how Gödel usually re-frained from speaking out,but when he disagreed with something he heard, showed his disagreement by a slight movement of his head (Menger 1994). The ssions of the Vienna Circle gave Gödel many opportunities to do so, during discussions on Wittgenstein or Ru
sll. Most of the younger members of the Circle em to have dis-played a healthy but discreet skepticism towards their more outspoken niors.
Gödel’s correspondence in-
dicates that his clost friends in tho days were
Marcel Natkin and Herbert Feigl, two students of
philosophy and mathematics who both did their
Ph.D. with Schlick. Both venerated their professor
but were not above poking gentle fun at him. “For
consolation, I’ll nd you Schlick’s essay, an ex-
ample that one can talk nsibly only about non-
n. Did you hear from Feigl,” wrote Marcel
Natkin to Kurt Gödel in the summer break of 1928,
“how Wittgenstein and Schlick enjoyed speaking for
hours about the unspeakable?”
memory意思
Hahn became Gödel’s thesis advir but did not
have to do much. A careful analysis of the Ph.D. the-
sis (as found in the university archives, reprinted
in the Collected Works ) and of the version pub-
lished in the Monatshefte , suggests that Gödel
slightly adapted the latter to better fit the “party
line” of Hahn (Feferman 1984). It was only twelve
years later, after having solved two and a half of
Hilbert’s problems, that Gödel started to express
his Platonism publicly. He then could argue that his
success was due to the firmness of his conviction
on the reality of abstract concepts.
In unison with Menger, Gödel drifted away from
the Vienna Circle and became a member of an-
other circle, this time of younger mathematicians,including Georg Nöbeling, Franz Alt, and Abraham Wald. It was to this group that Gödel lectured first on incompleteness. “That’s very interesting,” said a voice in the awestruck silence ending Gödel’s lecture. “You should publish that.” (Alt, 1998) “I am consumed with unjustifiable pride,” wrote Natkin from Paris. “So you have proved that Hilbert’s sys-tem of axioms contains unsolvable problems—why, this is not a trifling matter.”The young prodigy was soon pointed out by Karl Menger and John von Neumann to Oswald Ve-blen, who toured Europe as talent scout for the IAS.The newly founded institute invited Gödel to be among the first group of visiting scholars. Feigl, who had been the first member of the Vienna Circle to emigrate to the U.S., wrote from Iowa: “So you too,my son, like Einstein and all other celebrities, could not help it and had to cross the great water. Well then, probably a permanent position will come out of it in the end, and the Germans and Austrians will again have lost a scientist (racially pure, this time).”The wor
ds of Feigl were prophetic. The Circle of Vienna disbanded rapidly. Menger was one of tho who left for the U.S. In 1937 he wrote to Alt,
who was still in Vienna: “I believe you should get RIPE IDEALS. Philipp Furtwängler, a cousin of the famous conductor, was a first-rate number theorist. He was partially paralyzed from the neck down and had to be carried into the lecture hall in his chair.His greatest achievement came in 1929 (the year of Gödel’s completeness theorem), when he proved another conjecture of Hilbert, the Hauptidealsatz (principal ideal theorem) for class fields, at the respectable
age of sixty.CLASSICAL TASTE. Heinrich Gomperz,philosopher, in a drawing by Egon Schiele. An intriguing literary vignette of Gomperz can be found in the autobiography of Elias Canetti,who studied chemistry in the same building and at the same time as Gödel and who later
won a Nobel Prize in literature.
together from time to time, and especially e that Gödel takes part in the Kolloquium. It would not only be of greatest benefit for all other partici-pants, but also for himlf, though he might not realize it. Heaven knows into what he could entangle himlf if he does not talk to you and the other friends in Vienna from time to time. If necessary, be pushy, on my say-so.” But by the time that let-ter reache
d him, Alt had to work urgently on his own escape.
Menger would later ruminate that Gödel needed to move within a sympathetic group, which would stimulate him to lecture frequently and gently re-mind him to write things down, and even push him a little to do so, if necessary (Menger 1994). This is what Vienna had been able to provide, for a few blesd years. Hahn and Schlick had managed to create a critical mass (as one says nowadays) of young people studying both philosophy and math-ematics. But in tho Vienne days the two top-ics were in the air. The writers Hermann Broch and Robert Musil, and the philosophers Ludwig Wittgen-stein and Karl Popper had the same twin interests. Their opinions were widely divergent (as were opin-
ions within the Circle); but that heterogeneity was also probably an advantage for Kurt Gödel. He could have found splendid teachers in Göttingen
or Cambridge, but probably nowhere el a simi-
lar variety of views. For someone who was per-
fectly aware that his opinions were unfashionable
to the extreme, and who wished to explore a com-
pletely new approach, this must have been en-
couraging.
The main contribution of the Vienna Circle, then,
might have been to give everyone some clear state-
ments to clearly disagree with. Karl Popper is a ca
in point. For the last sixty years of his life he kept
repeating that he did not mind at all never having
been invited to a meeting of the Vienna Circle. But
his huge first book, Die Logik der Forschung, ap-
peared in the ries edited by Frank and Schlick,
and Hahn had gently said “as kind words as I could
have wished”. (Popper 1995) Nevertheless, Popper
took an almost oedipal pleasure in claiming, later,
that the Vienna Circle was dead. “Who killed it? …I
am afraid I did it.” (Stadler 1997)
Popper was as vehemently anti-Plato as Gödel
was Platonist. The two met but never were clo.
“I recently met a Mr. Popper (philosopher),” wrote
Gödel to Menger in 1934. “He has just finished a
huge book in which, so he claims, all phil. problems
are solved. —Do you think he is any good?” (Gödel,
Collected Works, 1986–2002)
The novelist Hermann Broch also turned away
from logical empiricism, but for entirely different
reasons. In the 1920s, Broch was a minor celebrity
in the Vienne coffee-hou scene, the well-off heir
to a textile firm and a womanizer of renown. He
decided, at the age of forty, to study mathematics
and philosophy and sat through many of the same
SKEPTICAL ATTITUDE. Marcel Natkin, a young philosopher and student friend of Gödel, eventually became one of the most eminent photographers in Paris. When Natkin, Feigl, and Gödel met in New York thirty years later, Gödel wrote to his mother: “The two have hardly changed. I do not know whetherroad tour
the same thing can be said of me.”
PHILOSOPHICAL CONFIDENCE. Herbert Feigl
(with bare feet) and Moritz Schlick (without) on
the shores of Lake Millstaedter. Feigl, a student
friend of Gödel, later became professor of
philosophy at the universities of Iowa and
Minnesota, and president of the American
Philosophical Association.
lectures as Kurt Gödel, his junior by twenty years.
Thirty of Broch’s notebooks covering the lec-
tures are kept at Duke University. Broch was dis-
atedappointed by the anti-metaphysical bent of the
philosophers of the Vienna Circle, but acknowl-
edged that they had one saving grace: Krankheit-
insicht (meaning that they knew how sick they
were). In the end, Broch became a major figure in
German literature. His cond novel, The Unknown
Quantity , is about a young mathematician who
dreams of finding “a logic without axioms”. Musil’s
“Man without Qualities” is also a rearch mathe-
matician, but Musil’s attempt at a “crystal-clear
mysticism” is literally worlds apart from the pos-
itivism of his friend Richard von Mis, another Vi-
enne who combined mathematics with philoso-
phy.
Hans Nelböck, the man who shot Schlick on the
stairs of the university in 1936, and who thus re-
ally murdered the Vienna Circle, had studied math-
ematics and philosophy at the same time as Gödel
and Broch and had written his Ph.D. thesis with
Schlick, just as Natkin and Feigl had done. In the
1930s, both Nelböck and Gödel were confined for
veral periods in psychiatric institutions. Both
had been living in the same street, the Lange Gas.
At that time, in 1929, Gödel’s attention was taken
up by another neighbor, who had just moved in, a
young masu named Adele Nimbursky. He
would marry her ten years later. It is not certain
that Gödel ever met Schlick’s murderer. But nov-
elists with a n for the bizarre will recognize the
leitmotiv of the Doppelgänger (the double). Vi-
enna’s golden autumn, so full of radiance, was also
filled with violence and hate.
Gödel had no wish to return to Vienna after the
war. “I am so happy to have escaped from beauti-
ful Europe,” he would write to his mother. But if
you happen, between May and August, to stop-
over in beautiful Europe, do come and visit the
Gödel exhibition. It is free!
Acknowledgments
The author wishes to acknowledge gratefully the
传宗接代英文
u of material from the Gödel Nachlass kept at the
北京雅思学校Firestone Library for Rare Manuscripts at Prince-
ton University, the archives of the IAS and the Uni-
versity of Vienna, the Handschriftensammlung of
the Wiener Stadt- und Landesbibliothek and the Vi-
enna Circle Foundation in Amsterdam, in particu-
lar Monika Cliburn (-Schlick) and G. M. H. van de
Velde (-Schlick). Friedrich Stadler and John Dawson
helped generously.
References
[1]F RANZ A LT , Afterword to Karl Menger, Ergebnis eines mathematischen Kolloquiums , E. Dierker and K. Sig-mund (eds.), Springer Vienna, 1998.[2]J OHN D. D AWSON , Logical Dilemmas: The life and work of Kurt Gödel , A. K. Peters, 1997.[3]K URT G ÖDEL , Collected Works Vol I–V, S. Feferman et al (eds.), Oxford University Press, 1986–2003.[4]S OLOMON F EFERMAN , Kurt Gödel: Conviction and cau-tion, Philosophia Naturalis 21(1984), 546–562.[5]K ARL M ENGER , Reminiscences of the Vienna Circle and the Mathematical Colloquium , Kluwer, 1994.[6]F RIEDRICH S TADLER , Studien zum Wiener Kreis , Suhrkamp,Frankfurt, 1997.[7]K ARL P OPPER , In memory of Hans Hahn, in Hans Hahn,Collected Works , (L. Schmetterer and K. Sigmund, eds.)vol.
1, pp.1–19, Springer Vienna,1995.[8]E KKEHARD K ÖHLER et al (eds), Wahrheit und Beweis-barkeit
, Hölder-Pichler-Tempsky, Wien, 2002.STAIRS TO PERDITION. Schlick’s murder on the stairca of the university became a cau célèbre in the Vienna of 1936.The murderer was relead from prison in the fall of 1938.
