\$B7G<(HD(B\$B!C(B\$B!X!VCN!W\$N5=bV!Y4XO">pJs(B\$B!C(BSB\$B%j%s%/=8(B

# \$B%9%Z%s%5!\$B9uLZ(B \$B8<(B\$B:G=*99?7!'(B2001\$BG/(B2\$B7n(B4\$BF|!!(B(\$B:n@.!'(B2000\$BG/(B10\$B7n(B19\$BF|(B)\$B4m\$J\$\$%9%Z%s%5!\$B!?(B\$B2VLnJs9p\$X\$N%3%a%s%H(B

## \$BHcH=A4BN\$NMWLs(B

A.\$B!!(BGeorge Spencer-Brown \$BCx\$N!X7A<0\$NK!B'!Y\$K\$*\$1\$k(B primary arithmetic \$B\$H(B primary algebra \$B\$NM}O@\$O8EE5L?BjO@M}\$b\$7\$/\$O%V!<%kBe?t\$NM}O@\$NIwJQ\$o\$j\$J5-9fK!\$K\$h\$k:F9=@.\$K2a\$.\$J\$\$!#!X7A<0\$NK!B'!Y\$K\$*\$1\$k(B re-entry \$B\$NF3F~\$O!"AH\$_9g\$o\$;O@M}2sO)(B (\$B%V!<%kBe?t\$NM}O@\$G07\$(\$k(B) \$B\$rFbIt\$K%U%#!<%I%P%C%/\$r4^\$`=g=xO@M}2sO)\$K0lHL2=\$9\$k\$3\$H\$KBP1~\$7\$F\$\$\$k!#!X7A<0\$NK!B'!Y\$K\$O\$=\$l\$,=PHG\$5\$l\$?Ev;~\$K\$*\$\$\$F\$b2?\$b?7\$7\$\$\$3\$H\$,4^\$^\$l\$F\$\$\$J\$+\$C\$?\$N\$@!#(B (cf. 1, 2)

B.\$B!!\$7\$+\$7!"(B Spencer-Brown \$B\$O!X7A<0\$NK!B'!Y\$N=xJ8\$G\$"\$?\$+\$b\$=\$&\$G\$J\$\$\$+\$N\$h\$&\$K1)

C.\$B!!!X7A<0\$NK!B'!Y\$G\$O!V6hJL\$H;X<(!W\$K4X\$9\$k

D.\$B!!!X7A<0\$NK!B'!Y\$NJd0d(B2\$B\$G(B Spencer-Brown \$B\$OL?BjO@M}\$NHO0O\$G=R8lO@M}\$r07\$&\$3\$H\$KD)@o\$7!"EvA3\$=\$&\$J\$k\$Y\$-7A\$G<:GT\$7\$F\$\$\$k!#\$H\$3\$m\$,!"\$=\$N<:GT\$K2?\$+;WA[E*\$J2ACM\$,\$"\$k\$+\$N\$h\$&\$J%G%?%i%a\$r(B Spencer-Brown \$B\$O=R\$Y\$F\$\$\$k!#(B

E.\$B!!!X7A<0\$NK!B'!Y\$N?7\$7\$\$HG(B (\$BFH8lHG(B) \$B\$NJd0d(B5\$B\$K\$OJ?LL>e\$NCO?^\$,(B4\$B?'\$GEI\$jJ,\$1\$i\$l\$k\$H\$\$\$&DjM}(B (\$B;M?'DjM}(B) \$B\$K4X\$9\$k(B1979\$BG/\$N869F\$NMWLs\$,<}\$a\$i\$l\$F\$\$\$k\$i\$7\$\$!#(B Spencer-Brown \$B\$N;M?'DjM}>ZL@<:GT\$K4X\$9\$k0oOC\$O(B Scientific American 1980.2 \$B\$N!V?t3X%2!<%`!W\$G>R2p\$5\$l\$F\$\$\$k!#(B (cf. 1, 2, 3)

3\$B%v7n7P\$C\$?\$"\$H!"%;%_%J!<\$K;22C\$7\$?@lLg2H\$?\$A\$O\$_\$J!"\$3\$N>ZL@\$K%\%m\$,\$?\$/\$5\$s\$"\$k\$H\$\$\$&0U8+\$K\$J\$j\$^\$7\$?\$,!"%9%Z%s%5!ZL@!I\$O\$^\$@=PHG\$5\$l\$F\$^\$;\$s!#(B (\$B!X%5%\$%(%s%9!!(BScientific American\$B!Y(B 1980\$BG/(B4\$B7n9f!"(B113\$BJG\$h\$j(B)

F.\$B!!0J>e\$N(B B \$B\$d(B E \$B\$+\$i!"(B Spencer-Brown \$B\$OCf?H\$N\$J\$\$C1\$J\$k;3;U\$K2a\$.\$J\$\$\$3\$H\$,\$o\$+\$k!#(B

G.\$B!!7kO@!#(B A \$B\$H(B C \$B\$h\$j!X7A<0\$NK!B'!Y\$O;2>H\$9\$k2ACM\$N\$J\$\$J88%\$G\$"\$k\$3\$H\$,\$o\$+\$k!#!X7A<0\$NK!B'!Y\$K\$O(B D \$B\$d(B E \$B\$N\$h\$&\$J%G%?%i%a\$5\$(=q\$\$\$F\$"\$k!#\$=\$7\$F!"(B F \$B\$H(B B \$B\$h\$j!"!X7A<0\$NK!B'!Y\$r2?\$NN1J]\$bL5\$7\$K9NDjE*\$K0zMQ\$7\$F\$\$\$k?M\$?\$A\$O!"C1\$J\$k;3;U\$r;}\$A>e\$2\$k\$3\$H\$K\$h\$C\$F3XLd\$N?.MQ\$r=}IU\$1!"5-9fO@M}3X\$N\$h\$&\$JB>\$NJ,Ln\$r4V@\E*\$K=}IU\$1\$F\$\$\$k\$3\$H\$K\$J\$k!#(B

H.\$B!!(BSpencer-Brown \$B\$r9NDjE*\$K0zMQ\$7\$F\$7\$^\$C\$??M\$?\$A\$O3XLdE*\$K@UG\$\$r

## \$B%,!<%I%J!<\$H%/%L!<%9\$H%3%s%&%'%\$\$K\$h\$k:GDc\$NI>2A(B

\$B;d<+?H\$N(B G. Spencer-Brown \$B\$N!X7A<0\$NK!B'!Y(B (\$B;38}>;:H4F=\$!"Bg_7??9,!&5\Bf??;JLu!"D+F|=PHG\$BI>2A(B\$B\$O0J2<\$N\$h\$&\$KMWLs\$G\$-\$^\$9!'(B

Spencer-Brown \$B\$N(B primary algebra \$B\$O8EE5L?BjO@M}(B(\$B\$b\$7\$/\$O(B Bool \$BBe?t(B)\$B\$NM}O@\$r4qL/\$JI=5-K!\$G=q\$-D>\$7\$?\$b\$N\$K2a\$.\$J\$\$\$7!"(B re-entry \$B\$H;~4V\$NF3F~\$O%G%8%?%k2sO)\$b\$I\$-\$NOC\$r\$d\$C\$F\$\$\$k\$K2a\$.\$J\$\$!#!VJd0d(B2\$B!W\$O%H%s%G%b\$G\$"\$k!#(B Spencer-Brown \$B\$K\$O??LLL\\$KAj

\$B:G6a!"\$3\$l\$H\$^\$C\$?\$/F1MM\$NI>2A\$,CY\$/\$H\$b(B1979\$BG/\$K\$O\$/\$@\$5\$l\$F\$\$\$k\$3\$H\$rCN\$j\$^\$7\$?!#;d\$N(B SB \$B\$X\$NH]DjE*I>2A\$O8D?ME*\$J\$b\$N\$G\$O\$J\$/!"@\$3&E*\$J>o<1\$H\$_\$J\$7\$F9=\$o\$J\$\$\$h\$&\$G\$9!#(B

\$B\$=\$l\$K\$b\$+\$+\$o\$i\$:!"!V%9%Z%s%5!Laws of Form)\$B!W(B (\$B0J2<\$r8+\$h(B) \$B\$,B8B3\$7\$F\$\$\$k\$h\$&\$K8+\$(\$k\$N\$O:\$\$C\$?\$3\$H\$G\$9\$M!#(B

\$B\$5\$F!"(B G. Spencer-Brown \$B\$N(B Martin Gardner (Scientific American \$B\$K!V?t3X%2!<%`!W\$NO":\\$r\$7\$F\$\$\$?\$3\$H\$GM-L>\$J%"%^%A%e%"?t3X(B) \$B\$H(B John Horton Conway (\$B?t3X2A\$O

Miller \$B\$O(B G. Spencer-Brown \$B\$N(B "Laws of Form" \$B\$N%O!<%I%+!<%P!H=\$N\$b\$H\$G\$=\$&\$7\$?\$N\$G\$9\$,!"7k6I1?\$,NI\$\$\$3\$H\$K(B Miller \$B\$O\$=\$NK\\$rFI\$_\$^\$;\$s\$G\$7\$?!#(B Miller \$B\$O\$=\$NK\\$,\$/\$@\$i\$J\$\$K\\$G\$"\$k\$3\$H\$r8e\$GCN\$k\$3\$H\$K\$J\$j\$^\$9!#(B Miller \$B\$O(B Gardner \$B\$K

"I once planned a column about Spencer-Brown, but Donald Knuth talked me out of it on the grounds that it would give valuable publicity to a charlatan! But I have some paragraphs about Brown and his flawed four-color proof, and his Laws of Form, coming up in my Feb column. Conway once described the book as beautifully written but "content free." I describe it as a "construction of the propositional calculus in eccentric notation." But it has a big cult following, and even a periodical devoted to it."

Garder \$B\$N(B Spencer-Brown \$B\$K4X\$9\$k%3%i%`<9I.\$r;W\$\$N1\$^\$i\$;\$?(B Knuth \$B\$O(B Spencer-Brown \$B\$K4X\$7\$F!V(B\$B@lLgCN<1\$r\$b\$C\$?\$U\$j\$r\$7\$F\$\$\$k;3;U(B (charlatan) \$B\$J\$N\$GH`\$N@kEA\$K6(NO\$7\$F\$O\$\$\$1\$J\$\$(B\$B!W\$H7Y9p\$7!"(B Conway \$B\$O(B Spencer-Brown \$B\$N!X7A<0\$NK!B'!Y\$r!V(B\$Be:No\$K=q\$+\$l\$?K\\$@\$,FbMF\$,\$J\$\$(B (content free)\$B!W\$H9sI>\$7\$F\$\$\$^\$9!#\$=\$7\$F!"(B Gardner \$B<+?H\$O!"!X7A<0\$NK!B'!Y\$,\$d\$C\$F\$\$\$k\$3\$H\$O!V(B\$BL?BjO@M}\$rIwJQ\$o\$j\$JI=5-K!\$G9=@.\$7\$?\$K\$9\$.\$J\$\$(B\$B!W!"!V(B\$B\$=\$l\$K\$b\$+\$+\$o\$i\$:!"!X7A<0\$NK!B'!Y\$NG.68E*\$J?.Jt\$B!W\$H6l!9\$7\$/8l\$C\$F\$\$\$^\$9!#(B

Gardner \$B\$O(B1980\$BG/(B2\$B7n\$N!V?t3X%2!<%`!W\$NJ?LL>e\$NCO?^\$,(B4\$B?'\$GEI\$jJ,\$1\$i\$l\$k\$H\$\$\$&DjM}\$K4X\$9\$k%3%i%`\$r=q\$-!"\$=\$NCf\$K(B Spencer-Brown \$B\$rEP>l\$5\$;\$^\$7\$?!#\$=\$NE?Kv\$O0J2<\$NDL\$j!'(B

The February 1980 Mathematical Games column was devoted to the Four-Color Map Theorem. Gardner described Spencer-Brown as a maverick mathemetician. People at Stanford invited him to present his proof. He did, and went home convinced that his proof was correct. Three months later all (?) agreed his proof was laced with holes.

Stanford \$B\$G>ZL@\$rOC\$7\$?(B Spencer-Brown \$B\$O<+J,\$N>ZL@\$N@5\$7\$5\$r3N?.\$7\$F2HO)\$K\$D\$\$\$?\$N\$G\$9\$,!"(B \$B\$=\$N(B3\$B%v7n8e\$K\$OH`\$N>ZL@\$O7j\$@\$i\$1\$G\$"\$k\$3\$H\$K3'(B(?)\$B\$,;?@.\$7\$F\$\$\$?\$N\$G\$7\$?!#\$A\$c\$s\$A\$c\$s!#(B

\$BBg3X\$N?t3X2J\$K\$O\$H\$-\$I\$-!V%U%'%k%^!<\$N:G=*DjM}\$N=iEyE*>ZL@!W\$N\$h\$&\$J

## \$B?t3X%2!<%`\$+\$i\$NH4?h(B

\$B!X%5%\$%(%s%9!!(BScientific American\$B!Y(B 1980\$BG/(B4\$B7n9f(B (\$BJF9qHG\$NF1G/(B2\$B7n9f\$NK]Lu!"F|7P?7J9l\$7\$F\$\$\$^\$9!'(B

\$B!!(B1976\$BG/(B12\$B7n\$K1Q9q0lI\$O5E*\$J?t3XZL@\$r\$d\$C\$?\$H8@\$C\$FF1N=\$r6C\$+\$;\$^\$7\$?!#H`\$,@dBPE*\$J<+?.\$r;}\$A!"\$^\$??t3X@<\$,9b\$+\$C\$?\$?\$a!"%9%?%s%U%)!<%IBg3X\$OH`\$r\$=\$N>ZL@\$K4X\$9\$k%;%_%J!<\$K>7\$-\$^\$7\$?!#(B 3\$B%v7n7P\$C\$?\$"\$H!"%;%_%J!<\$K;22C\$7\$?@lLg2H\$?\$A\$O\$_\$J!"\$3\$N>ZL@\$K%\%m\$,\$?\$/\$5\$s\$"\$k\$H\$\$\$&0U8+\$K\$J\$j\$^\$7\$?\$,!"%9%Z%s%5!ZL@!I\$O\$^\$@=PHG\$5\$l\$F\$^\$;\$s!#(B

\$B!!%9%Z%s%5!Laws of Form)\$B!I\$H\$\$\$&IwJQ\$o\$j\$JGv\$\$K\\$r=q\$\$\$F\$\$\$^\$9!#\$3\$l\$O4qL/\$J5-K!\$GL?BjO@M}\$r:F9=@.\$7\$?\$H\$\$\$(\$kK\\$G\$9\$,!"1Q9q\$N?t3X\$7\$F!"H~\$7\$/=q\$+\$l\$F\$\$\$k\$,!HL5FbMF(B (content free)\$B!I\$G\$"\$k\$H8@\$C\$F\$^\$9!#\$7\$+\$7!"\$3\$NK\\$K\$O0lCD\$NH?J82=ZL@\$7\$?\$HH/I=\$7\$?\$H\$\$\$&5-;v\$,=P\$?\$H\$-!"%P%s%/!<%P!ZL@\$G\$-\$k\$O\$:\$,\$J\$\$!#\$J\$<\$J\$i(B SCIENTIFIC AMERICAN 1975\$BG/(B4\$B7n9f(B (\$BK\;oF1G/(B6\$B7n9f(B) \$B\$K(B5\$B?'I,MW\$JCO?^\$,=P\$F\$\$\$k!D!#\$J\$s\$HH`=w\$O\$3\$N%3!<%J!<\$K(B4\$B7nGOiCL\$NCO?^\$r;2>H\$7\$F\$\$\$?\$N\$G\$9!*(B

(\$B%^!<%A%s!&%,!<%I%J!

\$B\$b\$A\$m\$s\$N\$3\$H\$G\$9\$,!"%,!<%I%J!<<+?H\$O%9%Z%s%5!@<\$,9b\$+\$C\$?!W\$3\$H\$r\$^\$K\$&\$1\$F\$\$\$k\$o\$1\$G\$O\$"\$j\$^\$;\$s!#(B\$B>e\$K=q\$\$\$F\$*\$\$\$?\$h\$&\$K(B\$B%I%J%k%I!&%/%L!<%9\$,!V@lLgCN<1\$r\$b\$C\$?\$U\$j\$r\$7\$F\$\$\$k;3;U(B (charlatan) \$B\$J\$N\$GH`\$N@kEA\$K6(NO\$7\$F\$O\$\$\$1\$J\$\$!W\$H7Y9p\$7\$F\$/\$l\$?\$3\$H\$r%,!<%I%J!<\$O1#\$7\$F\$\$\$^\$9!#\$=\$N\$h\$&\$J\$3\$H\$r=q\$/\$N\$O!V?t3X%2!<%`!W\$NJ70O5\$\$K9g\$o\$J\$\$\$7!">P\$\$\$re\$N\$3\$H\$r=q\$/\$N\$r;_\$a\$?\$N\$G\$7\$g\$&!#8m2r\$;\$:\$KFI\$a\$P%9%Z%s%5!2A\$,\$o\$+\$k@dL/\$NI.CW\$K\$J\$C\$F\$\$\$k\$H;W\$\$\$^\$9!#(B

\$B%A%'%C%/\$7\$F\$J\$\$\$N\$G\$9\$,!"!V\$7\$+\$7!"\$3\$NK\\$K\$O0lCD\$NH?J82=\$B>e\$r8+\$h(B)\$B!#(B

\$B0J2<\$N!V(B\$B%3%s%&%'%\$\$N%3%a%s%H(B\$B!W\$r8+\$l\$P\$o\$+\$k\$h\$&\$K!"%9%Z%s%5!

## \$B%3%s%&%'%\$\$N%3%a%s%H(B

\$B%3%s%&%'%\$\$K\$h\$k%9%Z%s%5!\$O(B Looking for Info on G. Spencer-Brown (1995, in Math Forum: geometry-puzzles) \$B\$GFI\$a\$^\$9!#(B

Does anyone know where I can find more information on the mathematical work of G. Spencer-Brown? He wrote a book entitled THE LAWS OF FORM that dealt with the fundamental arithmetic underlying boolean algebra.

G. Spencer-Brown was a contemporary of Bertrand Russell as well as Wittgenstein. His arithemetic if I understand it correctly removes some of the paradoxes that arise in formal logic in the same way that doing problems in the complex plane (with i) makes much easier calculation that in a real plane are intractable. I believe he used his arithemetic to do a first proof of the MAP THEOREM sometime around 1977-78.

\$B\$I\$J\$?\$+(B G. \$B%9%Z%s%5!pJs\$,\$"\$k>l=j\$r8fB8\$8\$"\$j\$^\$;\$s\$+!)!!H`\$O!"%V!<%kBe?t\$N4pAC\$H\$J\$k4pACE*\$J;;=Q\$r07\$C\$?!X7A<0\$NK!B'!Y\$H\$\$\$&BjL>\$NK\\$r=q\$-\$^\$7\$?!#(B

G. \$B%9%Z%s%5!ZL@\$G(B1977-1978\$BG/:"\$KMQ\$\$\$^\$7\$?!#(B

\$B\$3\$l\$K4X\$7\$F!"(B John Conway (conway@math.Princeton.EDU) \$B\$O(B1995\$BG/(B6\$B7n(B29\$BF|\$K

George Spencer-Brown is an old acquaintance of mine. It's true that Bertrand Russell wrote a brief preface to his "Laws of Form", but it's hardly fair to call him a contemporary of Russell, still less of Wittgenstein.

In his "Laws of Form" he recasts some of logic in a very elegant new way, but it can't really be said that this removes the paradoxes form formal logic. I don't believe his "proof" of the 4-color theorem (and don't know any other professional mathematician who does). When he first made this claim, I bet him 10 pounds that his proof wasn't valid. At that time, it wasn't written down, but he spent a good few hours describing it. I told him that I certainly wasn't going to pay up without having seen a written copy of the proof, and I'm still waiting to do so!

\$B%8%g!<%8!a%9%Z%s%5!

\$BH`\$N!X7A<0\$NK!B'!Y\$NCf\$G!"H`\$O!"e:No\$J?7\$7\$\$\$d\$jJ}\$GO@M}3X\$N0lIt\$r:n\$jD>\$7\$F\$^\$9\$,!"ZL@!I\$r?.MQ\$7\$F\$^\$;\$s(B (\$BH`\$N>ZL@\$r?.MQ\$7\$F\$\$\$kB>\$N@lLg\$N?t3XZL@\$G\$-\$?\$H8@\$C\$?\$H\$-\$K!";d\$OH`\$K\$=\$N>ZL@\$,@5\$7\$/\$J\$\$J}\$K==%]%s%IER\$1\$k\$H8@\$\$\$^\$7\$?!#\$=\$N\$H\$->ZL@\$O=q\$-2<\$5\$l\$F\$J\$+\$C\$?\$N\$G\$9\$,!"H`\$O2?;~4V\$b\$+\$1\$F8}F,\$G\$=\$l\$r@bL@\$7\$F\$/\$l\$^\$7\$?!#;d\$OH`\$K8@\$\$\$^\$7\$?!#!V;f\$K=q\$+\$l\$?>ZL@\$r8+\$k\$^\$G!"\$*%+%M\$rJ'\$&\$D\$b\$j\$O\$J\$\$\$h!#\$=\$&\$J\$k\$N\$r\$:\$C\$HBT\$C\$F\$\$\$k\$s\$@\$1\$I\$M!*!W(B

\$B?M\$N0-\$\$%3%s%&%'%\$\$O%9%Z%s%5!\$B\$h\$&\$G\$9\$M!#(B`:-)`

\$B0J2<\$O;d\$N%3%a%s%H\$G\$9!#(B

\$B%9%Z%s%5!

\$B!V%V!<%kBe?t\$N4pAC\$H\$J\$k4pACE*\$J;;=Q\$r07\$C\$?!X7A<0\$NK!B'!Y\$H\$\$\$&BjL>\$NK\(B (a book entitled THE LAWS OF FORM that dealt with the fundamental arithmetic underlying boolean algebra)\$B!W\$H\$\$\$&8@\$\$J}\$b8m2r\$r>7\$-\$+\$M\$J\$\$\$N\$GMWCm0U\$G\$9!#(B

\$B%9%Z%s%5!

\$B%9%Z%s%5!\$9\$H\$\$\$&\$D\$^\$i\$J\$\$;E;v\$r9T\$J\$\$\$^\$7\$?!#H`\$O!"(B OR \$B\$rC1\$J\$kJ8;z\$NJBCV(B ab \$B\$GI=\$o\$7!"(B 0 \$B\$r6uJ8;z\$G=q\$-!"(B NOT \$B\$r!V0O\$\$!W\$N5-9fK!(B

```---+
a |```

\$B\$GI=\$o\$7\$^\$7\$?!#(B

\$B8+\$+\$1>e\$3\$N0O\$\$\$N5-9f\$@\$1\$G%V!<%kBe?t\$HF1Ey\$NM}O@\$,e5-9f\$N8D?t\$,>/\$J\$/\$J\$C\$F\$\$\$k\$@\$1\$G\$9!#(B

\$BNc\$(\$P!"(B `1 = NOT 0` \$B\$H=q\$/\$H\$-!"%9%Z%s%5!

```---+ ---+   ---+
|    | =    |,

-----+
---+ |
| | = ```

\$B\$O\$=\$l\$>\$l(B

```1 OR 1 = 1,
NOT 1 = 0```

\$B\$KBP1~\$7\$F\$\$\$^\$9!#%9%Z%s%5!\$7\$?\$b\$N\$K2a\$.\$^\$;\$s!'(B

```NOT 0 = 1,  NOT 1 = 0,
0 OR 0 = 0,  0 OR 1 = 1,  1 OR 0 = 1,  1 OR 1 = 1.```

\$B\$3\$l\$G!"%9%Z%s%5!

\$B\$=\$7\$F!">\\$7\$\$@bL@\$O>JN,\$7\$^\$9\$,!"%9%Z%s%5!

(\$B0lHL\$N%V!<%kBe?t\$NE57?Nc\$OG\$0U\$N=89g(B X \$B\$NItJ,=89gA4BN\$N=89g(B P(X) \$B\$K(B AND, OR, NOT, 0, 1 \$B\$r(B a AND b = a\$B"A(Bb\$B!"(B a OR B = a\$B"@(Bb\$B!"(B NOT a = X - a\$B!"(B 0 = \$B&U!"(B 1 = X \$B\$HDj5A\$7\$?\$b\$N\$G\$"\$k!#(B \$BNc\$(\$P!"(B X = {\$B&U(B} \$B\$G\$"\$k\$H\$-(B P(X) = {0, 1} (0 = \$B&U!"(B 1 = X) \$B\$G\$"\$j!"(B 0 \$B\$H(B 1 \$B\$@\$1\$+\$i\$J\$k%V!<%kBe?t\$,F@\$i\$l\$k!#(B)

\$B%9%Z%s%5!O\$G:F;2F~(B (re-entry) \$B\$H;~4V\$N35G0\$rF3F~\$7\$^\$7\$?!#\$3\$l\$O0l8+?7\$7\$\$35G0\$K8+\$(\$k\$N\$G\$9\$,!"\$=\$NFbMF\$O\$h\$/CN\$i\$l\$F\$\$\$k\$b\$N\$G\$9!#(B

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\$B%9%Z%s%5!\$7\$K2a\$.\$J\$\$%9%Z%s%5!\$B%U%#!<%I%P%C%/\$H<+8J8@5Z\$O0[\$J\$k35G0(B\$B\$J\$N\$G!"FbIt\$K%U%#!<%I%P%C%/\$r;}\$D%G%8%?%k2sO)\$NOC\$r\$7\$F\$b!"7A<0O@M}\$N%Q%i%I%C%/%9\$,2r>C\$5\$l\$k\$O\$:\$,\$"\$j\$^\$;\$s!#(B

\$B;M?'LdBj(B (\$BJ?LLCO?^\$,(B4\$B?'\$KEI\$jJ,\$1\$i\$l\$k\$+\$H\$\$\$&LdBj(B) \$B\$O!"(B1976\$BG/\$K(B Kenneth Appel\$B!"(B Wolfgang Haken\$B!"(B John Koch \$B\$K\$h\$C\$F9NDjE*\$K2r7h\$5\$l!"DjM}\$K\$J\$j\$^\$7\$?!#@lLgCN<1\$r;}\$C\$?\$U\$j\$r\$7\$?;3;U\$N%9%Z%s%5!ZL@\$N<:GT\$O!"(B\$B%^!<%A%s!&%,!<%I%J!<\$N!V?t3X%2!<%`!W\$G(B1980\$BG/(B2\$B7n\$K%M%?\$K\$5\$l\$F\$\$\$^\$9(B\$B!#(B

## 1970\$BG/Be\$N%9%Z%s%5!

\$B;3;U%9%Z%s%5!

\$B\$B<+8JAH?%2=\$K4X\$9\$k\$H\$"\$k%&%'%V%5%\$%H(B\$B\$K\$"\$k(B Self-organization: Portrait of a Scientific Revolution. Edited by W. Krohn, G. Kppers, and H. Novotny, Dordrecht: Kluwer Academic Publishers (1990) Pages 1-12 \$B\$NH4?h\$K\$h\$l\$P!"(B

The relevance of the intellectual and social climate of the 1970s, which was characterized by students riots, the Vietnam crisis, and the zodiacal sign of Aquarius for a New Age, is evident. Alan Watts and John C. Lilly suggested, for instance, organizing a conference on Spencer-Brown's book Laws of Forms. It took place at the Esalen Institute (Big Sur) in 1973. Among the participants were Bateson, von Foerster, Pribram, Brand, and Tart.(15) Similar meetings took place with Ivan Illich in Cuernavaca (Mexico). The summer camps for intellectuals in the alternative Lindisfarne Association (USA) attracted representatives from artistic, esoteric-psychological, ecological, alternative, and techno-scientific circles. Among them were Bateson, E. F. Schuhmacher, J. Salk, W.J. Thompson, P. Saleri, S. Mendlovitz, and F. Varela.(16)

15. See J. and A. Lilly, The Dyadic Cyclone, Mallbu: Human Software Ing., 1976. J. Brockman (ed.), About Bateson, London: Wildwood House, 1978.

16. One of the sources for this information is the Lindisfarne book Earth's Answer, New York: Harper & Row, 1977. We wish to thank Rainer Paslack for this information.

\$BM-L>?M\$?\$A\$NL>A0\$,BgNL\$K5s\$,\$C\$F\$\$\$^\$9!'(B Alan Watts, John C. Lilly, Gregory Bateson, Heinz von Foerster, Karl H. Pribram, Stewart Brand, and Charles T. Tart, Ivan Illich, E. F. Schuhmacher, J. Salk, W. J. Thompson, P. Saleri, S. Mendlovitz, Francisco J. Varela, John Brockman.

\$BFC\$K(B H. von Foerster \$B\$H(B F. Varela \$B\$NL>\$,\$"\$k\$3\$H\$KCmL\!#\$^\$:!"(B von Foerster \$B\$O(B"second-order cybernetics" \$B\$rH/E8\$5\$;\$??MJ*\$H\$7\$FM-L>\$G\$"\$k\$H\$\$\$&\$3\$H\$K\$J\$C\$F\$*\$j!"(B 1969\$BG/\$K!X7A<0\$NK!B'!Y\$N9%0UE*\$J=qI>\$r=q\$-(B (cf. Bibliography of Heinz von Foerster 1943-1999)\$B!"(B Spencer-Brown \$B\$,%5%\$%P%M%F%#%/%9\$*\$h\$S%7%9%F%`O@\$K'\$7\$?\$3\$H\$GM-L>\$@\$H\$\$\$&\$3\$H\$K\$J\$C\$F\$*\$j!"(B Spencer-Brown \$B\$N!X7A<0\$NK!B'!Y\$r@Q6KE*\$K1~MQ\$7\$^\$7\$?!#\$3\$NFs?M\$O(B Niklas Luhmann \$B\$N!VH\$7\$F\$\$\$^\$9!#(B

\$B\$5\$i\$K!"%"%\$%=%l!<%7%g%s!&%?%s%/(B (\$B463P\$J(B Lilly \$B\$K4X\$7\$F\$O!"!V(Bserial experiments lain \$BMQ8l<-E5(B\$B!W\$N!V(B\$B%8%g%s!&(BC\$B!&%j%j!<(B/John C. Lilly\$B!W\$*\$h\$S(B AltCulture Japan \$B\$N(B\$B!N\$7(B-027\$B!O(B\$B\$r8+\$F2<\$5\$\$!#\$5\$i\$K>\\$7\$\$>pJs\$rCN\$j\$?\$\$?M\$O(B John C. Lilly Homepage \$B\$r8+\$F2<\$5\$\$!#(B VORTEX of Knowledge: John's Teachers \$B\$K\$O(B Lilly \$B\$K1F6A\$rM?\$(\$??M\$?\$A\$N%j%9%H\$,\$"\$j!"\$=\$NCf\$K(B Spencer-Brown \$B\$bEP>l\$7\$^\$9!#(B

Rudolf Maresch \$B\$K\$h\$l\$P(B\$B!"!X7A<0\$NK!B'!Y\$O(B von Foerster \$B\$N9%0UE*\$J=qI>(B (1969\$BG/(B) \$B\$N\$*\$+\$2\$G!V%5%\$%P%M%F%#%/%9\$d?@7P@8M}3X\$d@8J*3X\$d%\$%k%+8&5f\$N3X\$B!X7A<0\$NK!B'!Y\$B!W\$r;2>H\$;\$h!#(B)\$B!!\$=\$N\$*\$+\$2\$G(B Spencer-Brown \$B\$O(B1973\$BG/\$K8&5f2q\$r3+\$\$\$F\$b\$i\$(\$?!#(B Maresch \$B\$K\$h\$l\$P\$=\$l\$K\$h\$C\$F(B Spencer-Brown \$B\$O!V9-\$\$HO0O\$NFI

\$B\$7\$+\$7!"\$=\$N8&5f2q\$N3+:E\$K\$h\$C\$F!"(B 1970\$BG/Be\$N%"%a%j%+\$K\$*\$1\$kM-L>?M\$?\$A\$,(B Spencer-Brown \$B\$K3X\$\\$&\$H\$7\$?\$3\$H\$,@kEA\$5\$l!"\$=\$N<~0O\$K72\$,\$k8"0R\$K

\$B\$5\$i\$K!"(B John Brockman \$B\$X\$N%\$%s%?%S%e!<(B\$B\$K\$h\$l\$P!"(B

John Brockman (JB): ...... Years ago, I had written "By the Late John Brockman", was invited by Alan Watts John Lilly to a conference which they called the American University of Masters, which was a joke because if you spell out the initials it's "AUM". The idea was that these masters were people whose authority was derived from their persona and their ideas, not from their institutions. It included Heinz von Foerster, Gregory Bateson, Stewart Brand among others.

HUO: When did this conference take place?

JB: 1973. We were all brought together to spend a week studying laws of form ... Spencer Brown's mathematical formulations. I was a late invitee. I went because I wanted to hear Richard Feynman, the keynote speaker. When I arrived and asked when he was scheduled to speak, the person at the desk showed me the schedule: his name was crossed out and mine written in pencil next to it. He had become ill and was unable to attend. I never did get to meet him. The point is you don't have to ask permission in America, and that allows people to be wild, at least in their heads, and that's where you get your breakthroughs.

## \$B!X7A<0\$NK!B'!Y

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(3)\$B!!(BGeorge Spencer-Brown, Laws of Form, 1969.\$B!!%k!<%^%s\$,!XZL@!W(B (\$B<76eG/\$K<9I.\$5\$l\$?869F\$r!"Cx

\$B!!%9%Z%s%5!<(B-\$B%V%i%&%s\$O0l6eFs;0G/\$K%j%s%+%s%7%c!<\$N%0%j%9%S!<\$K@8\$^\$l!"?t3X\$r3X\$s\$@8e%*%C%/%9%U%)!<%I\$GO@M}3X\$r65\$(\$?\$3\$H\$b\$"\$C\$?\$,!"%m%s%I%s\$K0\\$C\$F!"%3%s%T%e!<%?!<\$N\$?\$a\$N%H%i%s%8%9%?!<2sO)\$N@_7W\$K7H\$o\$C\$?!#\$=\$N\$5\$\$8EE5E*\$JO@M}3X\$G\$O2r\$1\$J\$\$J#;(\$JLdBj\$H8e\$K0lE>\$7\$F!"=w;R3X@8\$NN>?F\$NH?BP\$K\$h\$C\$F:C@^\$7\$?Nx\$r8l\$k!X\$3\$N%2!<%`\$,\$G\$-\$k\$N\$OFs?M\$@\$1!Y(B (Only Two Can Play This Game, 1971) \$B\$r%8%'!<%`%:!&%-!<%:(B (James Keys) \$B\$H\$\$\$&I.L>\$GH/I=\$7!"!X7A<0\$NK!B'!Y\$+\$i0lC6N%\$l\$k(B (\$B0J>e\$K\$D\$\$\$F\$O(B Rudolf Maresch, Ariadne hat sich umsonst erh\"angt, http://wwwdb.ix.de/tp/deutch/inhalt/buch/2311/1.html \$B\$*\$h\$S(B G\'abol Pa\'al, Logik des Unsinns, aus der Reihe: Paradoxien, SWR2 Wissen, http://www.swr2.de/wissen/manuskripte/paradoxien_1.html \$B\$r;2>H\$7\$?(B)\$B!#\$7\$+\$7!"\$=\$N8e%9%Z%s%5!<(B-\$B%V%i%&%s\$O!"!XFs?M\$@\$1!Y\$K\$h\$C\$FF@\$i\$l\$?!VL5\$OL5<+3P\$K\$h\$C\$F\$7\$+JQ\$o\$i\$J\$\$!W\$H\$\$\$&G'<1\$K\$h\$C\$F!"!VL5\$,2?\$bJQ\$(\$k\$3\$H\$,\$G\$-\$J\$\$\$J\$i!R:G=i\$N6hJL!S\$,0J8e\$N0l@Z\$r=P8=\$5\$;\$k!W\$H\$\$\$&!X7A<0\$NK!B'!Y\$N;W9M\$r:F3NG'\$7!"!XFs?M\$@\$1!Y\$N%I%\$%D8lHG(B (Dieses Spiel geht nur zu zweit, 1994) \$B\$K4s\$;\$?!V%I%\$%D8lBh0lHG\$X\$N\$O\$7\$,\$-!W\$K\$*\$\$\$F!"!VEv;~\$OCN\$i\$J\$+\$C\$?\$,!"\$b\$"\$C\$F!"%5%\$%P%M%F%#%/%9\$d?@7P@8M}3X\$d@8J*3X\$d%\$%k%+8&5f\$N3X\$J%A%j\$N@8J*3XJ}\$H\$b:\\$;\$k\$h\$&\$KMW5a\$7\$?\$?\$a!"\$=\$N7W2h\$OF\:C\$7\$?\$H\$\$\$&!#FHLuHG\$X\$N!V\$O\$7\$,\$-!W\$,\$9\$G\$K0l6eH,8^G/\$K<9I.\$5\$l\$F\$\$\$k\$N\$O!"\$3\$&\$7\$?;v>p\$K\$h\$k\$b\$N\$G\$"\$m\$&!#(B

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