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\fs20\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid5791173 Sioban Roberts, }{\rtlch\fcs1 \af0 \ltrch\fcs0 \b\i\insrsid7949726\charrsid5791173 King of Infinite Space: Donald Coxeter}{\rtlch\fcs1 \af0 \ltrch\fcs0 
\insrsid5791173 , 2006 }{\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid7949726 \tab ISBN 0-8027-1499-4
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KING OF INFINITE SPACE
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While awaiting news of the Lowndean chair appointment, Coxeter kept himself preoccupied. He took in a bad Laurel and Hardy film, and attended a lecture by Godfrey Hardy: "How to Write and How Not to Write a Math\-ematical Paper."}{\rtlch\fcs1 \af0 
\ltrch\fcs0 \super\insrsid7949726\charrsid7949726 8}{\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid7949726\charrsid7949726  And he resumed his often "painful" discussions with Aus\-trian philosopher, Ludwig Wittgenstein then at {\*\xmlopen\xmlns2{\factoidname City
}}{\*\xmlopen\xmlns2{\factoidname place}}Cambridge{\*\xmlclose}{\*\xmlclose}, who was among the twentieth century's most influential philosophers, alongside Bertrand Russell and Jean-Paul Sartre.
\par }\pard\plain \ltrpar\s17\qj \fi288\li0\ri0\sl273\slmult1\nowidctlpar\wrapdefault\faauto\adjustright\rin0\lin0\itap0 \rtlch\fcs1 \af0\afs20\alang1025 \ltrch\fcs0 \fs20\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\rtlch\fcs1 \af0 \ltrch\fcs0 
\cs20\insrsid7949726\charrsid7949726 The reclusive Wittgenstein had taken a li
king to Coxeter when he was a student, and they kept in touch. "I had tea with Wittgenstein yesterday," Coxeter recorded in his diary. "He talked very interestingly about blindness and deafness, and why you get seasick on a camel but not on a horse. He do
esn't seem any more abnormal than before."9
\par Coxeter had enrolled in Wittgenstein's "Philosophy for Mathematicians" lecture for the }{\rtlch\fcs1 \af41 \ltrch\fcs0 \cs20\f41\insrsid7949726\charrsid7949726 1}{\rtlch\fcs1 \af0 \ltrch\fcs0 \cs20\sub\insrsid7949726\charrsid7949726 933}{\rtlch\fcs1 \af0 
\ltrch\fcs0 \cs20\insrsid7949726\charrsid7949726 -}{\rtlch\fcs1 \af0 \ltrch\fcs0 \cs20\sub\insrsid7949726\charrsid7949726 4 }{\rtlch\fcs1 \af0 \ltrch\fcs0 \cs20\insrsid7949726\charrsid7949726 year. To Wittgenstein's horror, so did a total of forty stu\-
dents, far too many for the intimate lecture he was willing
 to deliver. "There are too many of you," the philosopher protested. "Will three or four please leave?" After only a few weeks, Wittgenstein informed his still too numerous students that the class would continue no longer. He deigned to lecture for only a
 chosen few. He would dictate his thoughts, and his select students were instructed to copy the notes and distribute them to the rest of the class in what became known as his Blue Books. The select group included Wittgenstein's five fa\-
vorite students: Francis Skinner (a promising mathematics student who be\-came Wittgenstein's constant companion, confidante, and collaborator); applied mathematician Louis Goodstein; philosopher }{\rtlch\fcs1 \af0 \ltrch\fcs0 
\cs20\highlight7\insrsid7949726\charrsid7949726 {\*\bkmkstart Masterman}Margaret Masterman {\*\bkmkend Masterman}(a pioneer in the field of computational ling
uistics, her beliefs about language processing by computers were ahead of their time and are now fundamental to the field of artificial intelligence);}{\rtlch\fcs1 \af0 \ltrch\fcs0 \cs20\insrsid7949726\charrsid7949726 
 philosopher Alice Ambrose (of the analytic school, who also wrote papers on pi, mathematics, and the mind); and Coxeter.10
\par }\pard \ltrpar\s17\qj \fi288\li0\ri0\sb36\sl271\slmult1\nowidctlpar\wrapdefault\faauto\adjustright\rin0\lin0\itap0 {\rtlch\fcs1 \af0 \ltrch\fcs0 \cs20\insrsid7949726\charrsid7949726 
For Coxeter, Wittgenstein was largely unintelligible and intellectually precious. Wittgenstein refused to lecture for the customary }{\rtlch\fcs1 \af0 \ltrch\fcs0 \cs20\sub\insrsid7949726\charrsid7949726 5}{\rtlch\fcs1 \af0 \ltrch\fcs0 
\cs20\insrsid7949726\charrsid7949726 o minutes, but ' required 1}{\rtlch\fcs1 \af0 \ltrch\fcs0 \cs20\sub\insrsid7949726\charrsid7949726 5}{\rtlch\fcs1 \af0 \ltrch\fcs0 \cs20\insrsid7949726\charrsid7949726 
0 minutes, partly because he needed an hour to warm up and partly due to his 
habit of stopping midsentence as he worked through his next point internally. Coxeter timed a pause at more than twenty minutes, after which Wittgenstein carried on where he left off, as if nothing was amiss. On another occasion, Wittgenstein complained t
he lecture hall was too formal. Coxeter offered the sitting room in his suite in {\*\xmlopen\xmlns2{\factoidname Street}}{\*\xmlopen\xmlns2{\factoidname address}}Great Court{\*\xmlclose}{\*\xmlclose}
, and Wittgenstein agreed to the new location. Of one lecture, Coxeter noted: "Found Wittgenstein really interesting for the first time (Locality of Tho
ught)," but shortly thereafter he ceased attending, judging his time better spent on his own mathematical research (nonetheless Wittgenstein continued using Coxeter's room)." Coxeter later remarked of his Wittgenstein excursion: "I
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\cs21\f0\fs20\insrsid7949726\charrsid7949726 07}{\rtlch\fcs1 \af40\afs16 \ltrch\fcs0 \cs21\f40\fs16\insrsid7949726\charrsid7949726 
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couldn't understand that kind of philosophy. I thought it was nonsense. It didn't appeal to me at all. The only thing I remember of his work is that his book }{\rtlch\fcs1 \ai\af0 \ltrch\fcs0 \cs20\i\insrsid7949726\charrsid7949726 
Tractatus-Logico-Philosophicus }{\rtlch\fcs1 \af0 \ltrch\fcs0 \cs20\insrsid7949726\charrsid7949726 began in chapter one with the propo\-sition, 'The world is everything that is the case,' and ended in the final chap\-
ter with the proposition [and the only sentence in that chapter], 'Whereof one cannot speak, thereof one must be silent.}{\rtlch\fcs1 \af42\afs10 \ltrch\fcs0 \cs20\f42\fs10\insrsid7949726\charrsid7949726 5}{\rtlch\fcs1 \af0 \ltrch\fcs0 
\cs20\insrsid7949726\charrsid7949726  }{\rtlch\fcs1 \af41\afs12 \ltrch\fcs0 \cs20\f41\fs12\insrsid7949726\charrsid7949726 "12
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\cs20\insrsid7949726\charrsid7949726 4 0 
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\cs20\insrsid7949726\charrsid7949726 The {\*\xmlopen\xmlns2{\factoidname City}}Cambridge{\*\xmlclose} professorial elections were held on February z8, and disap\-}{\rtlch\fcs1 \af0 \ltrch\fcs0 \cs20\super\insrsid7949726\charrsid7949726 p}{\rtlch\fcs1 
\af0 \ltrch\fcs0 \cs20\insrsid7949726\charrsid7949726 ointingly Coxeter lost the Lowndean chair to William Hodge, winner of }{\rtlch\fcs1 \af0 \ltrch\fcs0 \cs20\super\insrsid7949726\charrsid7949726 {\*\xmlopen\xmlns2{\factoidname City}}
{\*\xmlopen\xmlns2{\factoidname place}}C}{\rtlch\fcs1 \af0 \ltrch\fcs0 \cs20\insrsid7949726\charrsid7949726 ambridge{\*\xmlclose}{\*\xmlclose}'s Adams Prize. Never before had the biannual Adams Prize com\-}{\rtlch\fcs1 \af0 \ltrch\fcs0 
\cs20\super\insrsid7949726\charrsid7949726 p}{\rtlch\fcs1 \af0 \ltrch\fcs0 \cs20\insrsid7949726\charrsid7949726 etition, since its inception in 18}{\rtlch\fcs1 \af0 \ltrch\fcs0 \cs20\sub\insrsid7949726\charrsid7949726 4}{\rtlch\fcs1 \af0 \ltrch\fcs0 
\cs20\insrsid7949726\charrsid7949726 8, been on a geometrical topic. Usually it }{\rtlch\fcs1 \af0 \ltrch\fcs0 \cs20\super\insrsid7949726\charrsid7949726 a}{\rtlch\fcs1 \af0 \ltrch\fcs0 \cs20\insrsid7949726\charrsid7949726 
ddressed natural philosophy or physics. The {\*\xmlopen\xmlns2{\factoidname place}}Adams{\*\xmlclose} question this time called for an advance in existing geometrical theory." Coxeter's groups gen\-
erated by reflections would have qualified (there is no record as to whether he made a submission), but Hodge, backed by none other than Weyl and }{\rtlch\fcs1 \af0 \ltrch\fcs0 \cs20\super\insrsid7949726\charrsid7949726 Lef}{\rtlch\fcs1 \af0 \ltrch\fcs0 
\cs20\insrsid7949726\charrsid7949726 schetz," won for work developing the relationship between geometry, }{\rtlch\fcs1 \af0 \ltrch\fcs0 \cs20\super\insrsid7949726\charrsid7949726 an}{\rtlch\fcs1 \af0 \ltrch\fcs0 \cs20\insrsid7949726\charrsid7949726 
alysis, and topology\emdash a contribution described as ". . one of the great }{\rtlch\fcs1 \af0 \ltrch\fcs0 \cs20\super\insrsid7949726\charrsid7949726 land}{\rtlch\fcs1 \af0 \ltrch\fcs0 \cs20\insrsid7949726\charrsid7949726 marks in the history of s
cience in the present century?"
\par }}