%!PS-Adobe-2.0 %%Creator: dvips(k) 5.78 Copyright 1998 Radical Eye Software (www.radicaleye.com) %%Title: p.dvi %%Pages: 8 %%PageOrder: Ascend %%BoundingBox: 0 0 596 842 %%EndComments %DVIPSCommandLine: dvips -o p.ps p.dvi %DVIPSParameters: dpi=600, compressed %DVIPSSource: TeX output 1999.11.15:1421 %%BeginProcSet: texc.pro %! /TeXDict 250 dict def TeXDict begin /N{def}def /B{bind def}N /S{exch}N /X{S N}B /TR{translate}N /isls false N /vsize 11 72 mul N /hsize 8.5 72 mul N /landplus90{true}def /@rigin{isls{[0 landplus90{1 -1}{-1 1} ifelse 0 0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div hsize mul 0}ifelse TR}if Resolution VResolution vsize -72 div 1 add mul TR[matrix currentmatrix{dup dup round sub abs 0.00001 lt{round}if} forall round exch round exch]setmatrix}N /@landscape{/isls true N}B /@manualfeed{statusdict /manualfeed true put}B /@copies{/#copies X}B /FMat[1 0 0 -1 0 0]N /FBB[0 0 0 0]N /nn 0 N /IE 0 N /ctr 0 N /df-tail{ /nn 8 dict N nn begin /FontType 3 N /FontMatrix fntrx N /FontBBox FBB N string /base X array /BitMaps X /BuildChar{CharBuilder}N /Encoding IE N end dup{/foo setfont}2 array copy cvx N load 0 nn put /ctr 0 N[}B /df{ /sf 1 N /fntrx FMat N df-tail}B /dfs{div /sf X /fntrx[sf 0 0 sf neg 0 0] N df-tail}B /E{pop nn dup definefont setfont}B /ch-width{ch-data dup length 5 sub get}B /ch-height{ch-data dup length 4 sub get}B /ch-xoff{ 128 ch-data dup length 3 sub get sub}B /ch-yoff{ch-data dup length 2 sub get 127 sub}B /ch-dx{ch-data dup length 1 sub get}B /ch-image{ch-data dup type /stringtype ne{ctr get /ctr ctr 1 add N}if}B /id 0 N /rw 0 N /rc 0 N /gp 0 N /cp 0 N /G 0 N /sf 0 N /CharBuilder{save 3 1 roll S dup /base get 2 index get S /BitMaps get S get /ch-data X pop /ctr 0 N ch-dx 0 ch-xoff ch-yoff ch-height sub ch-xoff ch-width add ch-yoff setcachedevice ch-width ch-height true[1 0 0 -1 -.1 ch-xoff sub ch-yoff .1 sub]/id ch-image N /rw ch-width 7 add 8 idiv string N /rc 0 N /gp 0 N /cp 0 N{rc 0 ne{rc 1 sub /rc X rw}{G}ifelse}imagemask restore}B /G{{id gp get /gp gp 1 add N dup 18 mod S 18 idiv pl S get exec}loop}B /adv{cp add /cp X}B /chg{rw cp id gp 4 index getinterval putinterval dup gp add /gp X adv}B /nd{/cp 0 N rw exit}B /lsh{rw cp 2 copy get dup 0 eq{pop 1}{ dup 255 eq{pop 254}{dup dup add 255 and S 1 and or}ifelse}ifelse put 1 adv}B /rsh{rw cp 2 copy get dup 0 eq{pop 128}{dup 255 eq{pop 127}{dup 2 idiv S 128 and or}ifelse}ifelse put 1 adv}B /clr{rw cp 2 index string putinterval adv}B /set{rw cp fillstr 0 4 index getinterval putinterval adv}B /fillstr 18 string 0 1 17{2 copy 255 put pop}for N /pl[{adv 1 chg} {adv 1 chg nd}{1 add chg}{1 add chg nd}{adv lsh}{adv lsh nd}{adv rsh}{ adv rsh nd}{1 add adv}{/rc X nd}{1 add set}{1 add clr}{adv 2 chg}{adv 2 chg nd}{pop nd}]dup{bind pop}forall N /D{/cc X dup type /stringtype ne{] }if nn /base get cc ctr put nn /BitMaps get S ctr S sf 1 ne{dup dup length 1 sub dup 2 index S get sf div put}if put /ctr ctr 1 add N}B /I{ cc 1 add D}B /bop{userdict /bop-hook known{bop-hook}if /SI save N @rigin 0 0 moveto /V matrix currentmatrix dup 1 get dup mul exch 0 get dup mul add .99 lt{/QV}{/RV}ifelse load def pop pop}N /eop{SI restore userdict /eop-hook known{eop-hook}if showpage}N /@start{userdict /start-hook known{start-hook}if pop /VResolution X /Resolution X 1000 div /DVImag X /IE 256 array N 0 1 255{IE S 1 string dup 0 3 index put cvn put}for 65781.76 div /vsize X 65781.76 div /hsize X}N /p{show}N /RMat[1 0 0 -1 0 0]N /BDot 260 string N /rulex 0 N /ruley 0 N /v{/ruley X /rulex X V}B /V {}B /RV statusdict begin /product where{pop false[(Display)(NeXT) (LaserWriter 16/600)]{dup length product length le{dup length product exch 0 exch getinterval eq{pop true exit}if}{pop}ifelse}forall}{false} ifelse end{{gsave TR -.1 .1 TR 1 1 scale rulex ruley false RMat{BDot} imagemask grestore}}{{gsave TR -.1 .1 TR rulex ruley scale 1 1 false RMat{BDot}imagemask grestore}}ifelse B /QV{gsave newpath transform round exch round exch itransform moveto rulex 0 rlineto 0 ruley neg rlineto rulex neg 0 rlineto fill grestore}B /a{moveto}B /delta 0 N /tail{dup /delta X 0 rmoveto}B /M{S p delta add tail}B /b{S p tail}B /c{-4 M}B /d{ -3 M}B /e{-2 M}B /f{-1 M}B /g{0 M}B /h{1 M}B /i{2 M}B /j{3 M}B /k{4 M}B /w{0 rmoveto}B /l{p -4 w}B /m{p -3 w}B /n{p -2 w}B /o{p -1 w}B /q{p 1 w} B /r{p 2 w}B /s{p 3 w}B /t{p 4 w}B /x{0 S rmoveto}B /y{3 2 roll p a}B /bos{/SS save N}B /eos{SS restore}B end %%EndProcSet TeXDict begin 39158280 55380996 1000 600 600 (p.dvi) @start %DVIPSBitmapFont: Fa cmsy10 10 2 /Fa 2 4 df<0060150600F8150F6C151F007E153F6C157E6C6C14FC6C6CEB01F86C6CEB 03F06C6CEB07E06C6CEB0FC06C6CEB1F80017EEB3F006D137E6D6C5A90380FC1F8903807 E3F0903803F7E06DB45A6D5B6EC7FCA24A7E497F903803F7E0903807E3F090380FC1F890 381F80FC90383F007E017E7F49EB1F804848EB0FC04848EB07E04848EB03F04848EB01F8 4848EB00FC48C8127E007E153F48151F48150F00601506282874A841>2 DI E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fb cmtt10 10 30 /Fb 30 120 df<121FEA3F80EA7FC0EAFFE0A5EA7FC0EA3F80EA1F000B0B708A2C>46 D<1507ED0F80151FA2153F16005D157E15FE5D14015D14035DA214075D140F5D141F5D14 3F92C7FC5C147E14FE5CA213015C13035C13075C130F5C131F5CA2133F91C8FC5B137E13 FE5B12015B12035B12075BA2120F5B121F5B123F90C9FC5A127E12FE5AA25A127821417B B92C>I<121FEA3F80EA7FC0EAFFE0A5EA7FC0EA3F80EA1F00C7FCAE121FEA3F80EA7FC0 EAFFE0A5EA7FC0EA3F80EA1F000B2470A32C>58 D<02FF13700107EBE0F84913F9013F13 FD4913FFEBFF813901FE007F4848131FD807F0130F1507485A491303485A150148C7FCA2 5A007EEC00F01600A212FE5AAB7E127EA3007F15F06CEC01F8A26C7EA26C6C13036D14F0 6C6C130716E0D803FC131F6C6CEB3FC03A00FF81FF806DB512006D5B010F5B6D13F00100 138025357DB32C>67 D<007FB612F0B712F8A37E3903F00001A7ED00F01600A4EC01E04A 7EA490B5FCA5EBF003A46E5A91C8FCA5163C167EA8007FB612FEB7FCA36C15FC27337EB2 2C>69 D<007FB612F8B712FCA37ED803F0C7FCA716781600A515F04A7EA490B5FCA5EBF0 01A46E5A92C7FCAD387FFFE0B5FC805C7E26337EB22C>I<903901FC038090390FFF87C0 4913EF017F13FF90B6FC4813073803FC01497E4848137F4848133F49131F121F5B003F14 0F90C7FCA2127EED078092C7FCA212FE5AA8913803FFF84A13FCA27E007E6D13F8913800 0FC0A36C141FA27F121F6D133F120F6D137F6C7E6C6C13FF6D5A3801FF076C90B5FC6D13 EF011F13CF6DEB0780D901FCC7FC26357DB32C>I<007FB512F8B612FCA36C14F839000F C000B3B3A5007FB512F8B612FCA36C14F81E3379B22C>73 D75 D<387FFFE0B57EA36C5BD803F0C8FCB3AE16F0ED01F8 A8007FB6FCB7FCA36C15F025337DB22C>III<007FB512C0B612F88115FF6C15802603F00013C015 3FED0FE0ED07F0A2150316F81501A6150316F01507A2ED0FE0ED3FC015FF90B612801600 15FC5D15C001F0C8FCB0387FFF80B57EA36C5B25337EB22C>80 DI<90381FF8 0790B5EA0F804814CF000714FF5A381FF01F383FC003497E48C7FC007E147F00FE143F5A 151FA46CEC0F00007E91C7FC127F7FEA3FE0EA1FFCEBFFC06C13FC0003EBFFC06C14F06C 6C7F01077F9038007FFEEC07FF02001380153FED1FC0A2ED0FE0A20078140712FCA56CEC 0FC0A26CEC1F806D133F01E0EB7F009038FE01FF90B55A5D00F914F0D8F83F13C0D87007 90C7FC23357CB32C>83 D86 D89 D98 D<903803FFE0011F13F8017F13FE48B5FC48804848C6FCEA0FF0485A 49137E4848131890C9FC5A127EA25AA8127EA2127F6C140F6DEB1F806C7E6D133F6C6CEB 7F003907FE03FF6CB55A6C5C6C6C5B011F13E0010390C7FC21247AA32C>I103 DI<1307EB1FC0A2497EA36D5AA20107C7FC90C8FCA7387FFFC080B5FC7EA2 EA0007B3A8007FB512FCB612FEA36C14FC1F3479B32C>I<387FFFE0B57EA37EEA0003B3 B3A5007FB61280B712C0A36C158022337BB22C>108 D<3A7F83F007E09039CFFC1FF83A FFDFFE3FFCD87FFF13FF91B57E3A07FE1FFC3E01FCEBF83F496C487E01F013E001E013C0 A301C01380B33B7FFC3FF87FF0027F13FFD8FFFE6D13F8D87FFC4913F0023F137F2D2481 A32C>I<397FF01FE039FFF87FFC9038F9FFFE01FB7F6CB6FC00019038F03F80ECC01F02 807FEC000F5B5BA25BB3267FFFE0B5FCB500F11480A36C01E0140029247FA32C>I I<397FF01FE039FFF8FFF801FB13FE90B6FC6C158000019038F07FC09138801FE0913800 07F049EB03F85BED01FC491300A216FE167EA816FE6D14FCA2ED01F86D13036DEB07F015 0F9138801FE09138E07FC091B51280160001FB5B01F813F8EC3FC091C8FCAD387FFFE0B5 7EA36C5B27367FA32C>I<131E133FA9007FB6FCB71280A36C1500D8003FC8FCB1ED03C0 ED07E0A5EC800F011FEB1FC0ECE07F6DB51280160001035B6D13F89038003FE0232E7EAD 2C>116 D<3A7FFF01FFFCB514FE148314016C15FC3A03E0000F80A26D131F00011500A2 6D5B0000143EA26D137E017C137CA2017E13FC013E5BA2EB3F01011F5BA21483010F5BA2 14C701075BA214EF01035BA214FF6D90C7FCA26D5A147C27247EA32C>118 DI E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fc cmr5 5 1 /Fc 1 51 df50 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fd cmmi7 7 2 /Fd 2 59 df15 D<1238127C12FEA3127C123807077A8614>58 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fe cmr7 7 10 /Fe 10 112 df<140EB3A2B812E0A3C7000EC8FCB3A22B2B7DA333>43 D<13381378EA01F8121F12FE12E01200B3AB487EB512F8A215267BA521>49 D<13FF000313E0380E03F0381800F848137C48137E00787F12FC6CEB1F80A4127CC7FC15 005C143E147E147C5C495A495A5C495A010EC7FC5B5B903870018013E0EA018039030003 0012065A001FB5FC5A485BB5FCA219267DA521>I<13FF000313E0380F01F8381C007C00 30137E003C133E007E133FA4123CC7123E147E147C5C495AEB07E03801FF8091C7FC3800 01E06D7E147C80143F801580A21238127C12FEA21500485B0078133E00705B6C5B381F01 F03807FFC0C690C7FC19277DA521>I<1230123C003FB512E0A215C0481480A239700007 000060130E140C48131C5C5CC75A5C1301495AA249C7FC5B130E131EA3133E133CA2137C A413FCA813781B287DA621>55 D<137F3803FFE0380781F8380E007C48131E5A801278A3 127C007E131EEA3F80EBE03C6C6C5A380FFCF03807FFC06C5BC613E0487F38079FFC380F 07FEEA1E0348C67E48133FEC1F8048130FA21407A315001278140E6C5B6C5B380F80F038 03FFE0C66CC7FC19277DA521>I<137F3801FFC03807C1E0380F0070001E1378003E7F00 3C133E007C131EA200FC131FA41580A4007C133FA2123C003E137F121E380F01DF3807FF 9F3801FE1FD8001013001300A2143E123C007E133CA25C5C007C5B383003C0381C0780D8 0FFFC7FCEA03F819277DA521>I<90387E03E03901FF9FF03807C3FC380F00F048EBF800 001E1378003E137CA6001E1378001F13F86C5BEBC3E0380DFF80D81C7EC7FC90C8FCA312 1E380FFFF014FC6C13FF001F1480393E001FC000781307EC03E0481301A40078EB03C000 7C13076CEB0F80390FC07E003803FFF838007FC01C277E9921>103 D108 D111 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Ff cmmi10 10 5 /Ff 5 80 df11 D15 D<126012FCB4FCEA7FC0EA1FF0EA07FC EA01FF38007FC0EB1FF0EB07FCEB01FF9038007FC0EC1FF0EC07FCEC01FF9138007FC0ED 1FF0ED07FCED01FF9238007FC0EE1FF0EE07FCEE01FF9338007F80EF1FC0A2EF7F809338 01FF00EE07FCEE1FF0EE7FC04B48C7FCED07FCED1FF0ED7FC04A48C8FCEC07FCEC1FF0EC 7FC04948C9FCEB07FCEB1FF0EB7FC04848CAFCEA07FCEA3FF0EA7FC048CBFC12FC127032 3279AD41>62 D<902603FFF891381FFFF8496D5CA2D90007030113006FEC007C02061678 DA0EFF157081020C6D1460A2DA1C3F15E0705CEC181F82023815016F6C5C143015070270 6D1303030392C7FC02607FA2DAE0015C701306ECC0008201016E130EEF800C5C163F0103 EDC01C041F131891C713E0160F49EDF03818300106140717F8010E02031370EFFC60130C EE01FE011C16E004005B011815FF177F1338600130153FA20170151F95C8FC01F081EA07 FCB512E01706A245397DB843>78 D<4BB4FC031F13F09238FE01FC913903F0007EDA07C0 EB1F80DA1F80EB0FC0023EC7EA07E002FCEC03F0495A4948EC01F8495A4948EC00FC495A 49C912FE49167E13FE49167F1201485AA2485AA2120F5B001F17FFA2485AA34848ED01FE A400FFEE03FC90C9FCA2EF07F8A2EF0FF0A218E0171F18C0EF3F806C167F180017FE4C5A 6C6C5D1603001F4B5A6D4A5A000FED1F806C6C4AC7FC6D147E0003EC01F8D801FC495AD8 007EEB0FC090263F807FC8FC903807FFF801001380383D7CBA3F>I E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fg cmr10 10 81 /Fg 81 125 df11 DIII<121C127FEAFF80A8EA7F00AB123EAB121CABC7FCA8121C12 7FEAFF80A5EA7F00121C093C79BB17>33 D<001C131C007F137F39FF80FF80A26D13C0A3 007F137F001C131C00001300A40001130101801380A20003130301001300485B00061306 000E130E485B485B485B006013601A197DB92A>I36 D<121C127FEAFF80A213C0A3127F121C1200A412011380A2120313005A1206120E5A5A5A 12600A1979B917>39 D<146014E0EB01C0EB0380EB0700130E131E5B5BA25B485AA2485A A212075B120F90C7FCA25A121EA2123EA35AA65AB2127CA67EA3121EA2121F7EA27F1207 7F1203A26C7EA26C7E1378A27F7F130E7FEB0380EB01C0EB00E01460135278BD20>I<12 C07E12707E7E7E120F6C7E6C7EA26C7E6C7EA21378A2137C133C133E131EA2131F7FA214 80A3EB07C0A6EB03E0B2EB07C0A6EB0F80A31400A25B131EA2133E133C137C1378A25BA2 485A485AA2485A48C7FC120E5A5A5A5A5A13527CBD20>II<121C127FEAFF80A213C0A3127F121C 1200A412011380A2120313005A1206120E5A5A5A12600A19798817>44 DI<121C127FEAFF80A5EA7F00121C0909798817>I<150C151E15 3EA2153C157CA2157815F8A215F01401A215E01403A215C01407A21580140FA215005CA2 141E143EA2143C147CA2147814F8A25C1301A25C1303A2495AA25C130FA291C7FC5BA213 1E133EA2133C137CA2137813F8A25B1201A25B1203A25B1207A25B120FA290C8FC5AA212 1E123EA2123C127CA2127812F8A25A12601F537BBD2A>IIIII<1538A2157815F8A2140114031407A2140F141F 141B14331473146314C313011483EB030313071306130C131C131813301370136013C012 01EA038013005A120E120C5A123812305A12E0B712F8A3C73803F800AB4A7E0103B512F8 A325397EB82A>I<0006140CD80780133C9038F003F890B5FC5D5D158092C7FC14FC3806 7FE090C9FCABEB07F8EB3FFE9038780F803907E007E090388003F0496C7E12066E7EC87E A28181A21680A4123E127F487EA490C71300485C12E000605C12700030495A00385C6C13 03001E495A6C6C485A3907E03F800001B5C7FC38007FFCEB1FE0213A7CB72A>II<12301238123E003FB612E0A316C05A168016000070C71206 0060140E5D151800E01438485C5D5DC712014A5A92C7FC5C140E140C141C5CA25CA214F0 495AA21303A25C1307A2130FA3495AA3133FA5137FA96DC8FC131E233B7BB82A>III<121C127FEAFF80A5EA7F00121CC7FC B2121C127FEAFF80A5EA7F00121C092479A317>I<121C127FEAFF80A5EA7F00121CC7FC B2121C127F5A1380A4127F121D1201A412031300A25A1206A2120E5A121812385A126009 3479A317>I63 D<1538A3157CA315FEA34A7EA34A6C7EA202077FEC063FA2020E7FEC0C1FA202 1C7FEC180FA202387FEC3007A202707FEC6003A202C07F1501A2D901807F81A249C77F16 7FA20106810107B6FCA24981010CC7121FA2496E7EA3496E7EA3496E7EA213E0707E1201 486C81D80FFC02071380B56C90B512FEA3373C7DBB3E>65 DI<913A 01FF800180020FEBE003027F13F8903A01FF807E07903A03FC000F0FD90FF0EB039F4948 EB01DFD93F80EB00FF49C8127F01FE153F12014848151F4848150FA248481507A2485A17 03123F5B007F1601A35B00FF93C7FCAD127F6DED0180A3123F7F001F160318006C7E5F6C 7E17066C6C150E6C6C5D00001618017F15386D6C5CD91FE05C6D6CEB03C0D903FCEB0F80 902701FF803FC7FC9039007FFFFC020F13F002011380313D7BBA3C>IIIIII< B612C0A3C6EBC0006D5AB3B3AD497EB612C0A31A397EB81E>I<013FB512E0A39039001F FC00EC07F8B3B3A3123FEA7F80EAFFC0A44A5A1380D87F005B0070131F6C5C6C495A6C49 C7FC380781FC3801FFF038007F80233B7DB82B>IIIIIII82 DI<003FB812E0A3D9C003EB001F 273E0001FE130348EE01F00078160000701770A300601730A400E01738481718A4C71600 B3B0913807FF80011FB612E0A335397DB83C>IIII<007FB590383FFFFCA3 C601F801071380D97FE0D903FCC7FC013FEC01F06D6C5C5F6D6C5C6D6C13034CC8FC6D6C 1306160E6D6C5B6DEB8018163891387FC0306E6C5A16E06E6C5A91380FF18015FB6EB4C9 FC5D14036E7EA26E7F6F7EA24B7E15DF9138019FF09138038FF8150F91380607FC91380E 03FE140C4A6C7EEC38000230804A6D7E14E04A6D7E49486D7E130391C76C7E01066E7E13 0E010C6E7E011C1401013C8101FE822607FF80010713E0B500E0013FEBFF80A339397EB8 3E>II<390180018000031303390700 0700000E130E485B0018131800381338003013300070137000601360A200E013E0485BA4 00CE13CE39FF80FF806D13C0A3007F137FA2393F803F80390E000E001A1974B92A>92 D97 DIIII<147E903803FF8090380FC1E0EB1F8790 383F0FF0137EA213FCA23901F803C091C7FCADB512FCA3D801F8C7FCB3AB487E387FFFF8 A31C3B7FBA19>IIII< EB01C0EB07F0EB0FF8A5EB07F0EB01C090C7FCAAEB01F813FFA313071301B3B3A2123C12 7E00FF13F01303A214E038FE07C0127C383C0F00EA0FFEEA03F8154984B719>III<2703F00FF0EB1FE000FFD93FFCEB7FF8913AF03F01E0 7E903BF1C01F83803F3D0FF3800FC7001F802603F70013CE01FE14DC49D907F8EB0FC0A2 495CA3495CB3A3486C496CEB1FE0B500C1B50083B5FCA340257EA445>I<3903F00FF000 FFEB3FFCECF03F9039F1C01F803A0FF3800FC03803F70013FE496D7EA25BA35BB3A3486C 497EB500C1B51280A329257EA42E>II<3903F01FE000FFEB7FF89038 F1E07E9039F3801F803A07F7000FC0D803FEEB07E049EB03F04914F849130116FC150016 FEA3167FAA16FEA3ED01FCA26DEB03F816F06D13076DEB0FE001F614C09039F7803F0090 38F1E07E9038F0FFF8EC1FC091C8FCAB487EB512C0A328357EA42E>II<3807E01F00 FFEB7FC09038E1E3E09038E387F0380FE707EA03E613EE9038EC03E09038FC0080491300 A45BB3A2487EB512F0A31C257EA421>II<1318A51338A31378A313F8120112031207001FB5FCB6FC A2D801F8C7FCB215C0A93800FC011580EB7C03017E13006D5AEB0FFEEB01F81A347FB220 >IIIIII<003FB512FCA2EB8003D83E0013F8003CEB07F00038EB0FE012300070EB1FC0 EC3F800060137F150014FE495AA2C6485A495AA2495A495A495AA290387F000613FEA248 5A485A0007140E5B4848130C4848131CA24848133C48C7127C48EB03FC90B5FCA21F247E A325>III E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fh cmti10 10 63 /Fh 63 125 df<04FFEB03F003039038E00FFC923A0FC0F01F1E923A3F00783E0F923A7E 01F87C3FDB7C03EBFC7F03FC14F8DA01F813F905F1137EDC01E1133C913B03F00003F000 A314074B130760A3140F4B130F60A3010FB812C0A3903C001F80001F8000A3023F143F92 C790C7FCA44A5C027E147EA402FE14FE4A5CA413014A13015FA313034A13035FA313074A 495AA44948495AA44948495AA3001CD9038090C8FC007E90380FC03F013E143E00FE011F 5B133C017C5C3AF8780F01E0D878F0EB07C0273FE003FFC9FC390F8000FC404C82BA33> 11 DI< EE7FE0923903FFFC7E92380FC03E92381F000F033EEB3FFE4B137F03FC14FC5D1401173D 4A48EB01F8A21703A24A4814F0A21707A2020F15E05D170FA218C0010FB7FCA3903B001F 80001F80A2173F143F92C71300A25FA24A147E147E17FEA25F14FE4A1301A25FA2010114 035CEFF070A21607010316F04AECE0E0A3EFE1C013074A14C3933803E380EE01E7933800 FF004948143C94C7FCA3495AA3001C90CAFC127E133E12FE133C137CEAF878EA78F0EA3F E0EA0F80374C82BA31>I<14F0EB03FCA21307A3EB0FF8A314F0A3EB1FE0A314C0A3EB3F 80A31400A3137EA3137CA35BA35BA3485AA45B1203A2C8FCA8120EEA3F80127F12FFA390 C7FC127E123C163C77BB19>33 D<3901E003C03907F00FE0000F131F01F813F0001F133F A3000F131F3907B00F6038003000A2017013E0016013C0EBE00101C01380000113030180 130000035B3807000E000E5B485B485B485B48485A00C05B1C1971B92B>I39 D44 D<387FFFF8A2B5FCA214F0150579941E>I<120EEA3F80127F12FFA31300127E123C0909 778819>I48 D<15181538157815F0140114031407EC0FE0141F147FEB03FF90383FEFC0148FEB1C 1F13001580A2143FA21500A25CA2147EA214FEA25CA21301A25CA21303A25CA21307A25C A2130FA25CA2131FA25CA2133FA291C7FC497EB61280A31D3877B72A>III<16E0ED01F01503A3150716E0A3150F16C0A2151F1680A2ED3F00A3 157EA2157C15FC5D14015D14035D14075D140F5D141F92C7FC143EA25CECF81C153E9038 01F07EEB03E014C090380780FE130F49485A133EEB7C01137801F05BEA01E03803C003EA 0FFE391FFFC3F04813FB267C01FF13403AF0003FFFE000601307C71400EC0FE05DA3141F 5DA3143F92C7FCA4143E141C24487DB72A>I<010314186E13F8903907F007F091B512E0 16C01600495B15F8010E13E0020CC7FC011EC8FC131CA3133C1338A313781370A2147F90 38F3FFC09038EF83E09038FC01F0496C7E485A497F49137CC8FC157EA315FEA41401000C 5C123F5A1403485C5A4A5A12F800E05C140F4A5A5D6C49C7FC0070137E00785B387C01F8 383E07F0381FFFC06C90C8FCEA01F8253A77B72A>I<157F913803FFC0020F13E0EC3F81 91387E00F002F81370903903F003F0903807E007EB0FC0EB1F80020013E04914C0017E90 C7FC13FE5B485AA21203485AA2380FE07E9038E3FF809038E783E0391FCE01F09038DC00 F813F84848137C5B49137EA2485AA290C7FC15FE5A5AA214015D5AA214035DA348495A5D 140F5D4A5A6C49C7FC127C147C6C485A6C485A6CB45A6C1380D801FCC8FC243A76B72A> III< EC01FCEC0FFF023F138091387E07C0903901F803E0EB03F0903907E001F0EB0FC0EB1F80 013F14F814005B137E13FEA2485AA2150312035BA2ED07F012075B150FA216E00003141F A2153FED7FC0120115FF6C6C5A90397803BF8090383C0F3FD91FFC1300903807F07F90C7 FC157E15FE5D14015D4A5AA2003E495A007F495A5D4AC7FC00FE5B48137E007013F83878 03F0387C0FE0383FFF806C48C8FCEA03F8253A78B72A>I65 D<0107B612FCEFFF8018C0903B000FF0001FF04BEB07F81703021F15 FC17014B14FEA2023F1400A24B1301A2147F18FC92C7120318F84A140718F04AEC0FE0EF 1FC00101ED3F80EF7F004AEB01FEEE07F849B612E05F9139F80007F0EE01FC01076E7E17 7F4AEC3F80A2010F16C0171F5CA2131F173F5CA2133FEF7F805C1800017F5D4C5A91C748 5A5F49140FEE1FE0494A5A00014AB45AB748C7FC16F816C037397BB83A>II<0103B612FEEFFF C018F0903B0007F8000FF84BEB03FCEF00FE020F157FF03F804B141F19C0021F150F19E0 5D1807143F19F05DA2147FA292C8FCA25C180F5CA2130119E04A151FA2130319C04A153F A201071780187F4A1600A2010F16FEA24A4A5A60011F15034D5A4A5D4D5A013F4B5A173F 4A4AC7FC17FC017FEC03F84C5A91C7EA1FC04949B45A007F90B548C8FCB712F016803C39 7CB83F>I<0107B712FEA3903A000FF000074B1300187C021F153CA25DA2143FA25D1838 147FA292C8FCEE03804A130718004A91C7FCA201015CA24A131E163E010314FE91B5FC5E A2903807F800167C4A1378A2130FA24A1370A2011F14F0A24A90C8FCA2133FA25CA2137F A291CAFCA25BA25B487EB6FCA337397BB836>70 D<0103B5D8F80FB512E0A390260007F8 C7381FE0004B5DA2020F153F615DA2021F157F96C7FC5DA2023F5D605DA2027F14016092 C7FCA24A1403605CA249B7FC60A202FCC712070103150F605CA20107151F605CA2010F15 3F605CA2011F157F95C8FC5CA2013F5D5F5CA2017F14015F91C7FC491403007FD9FE01B5 12F8B55BA243397CB83E>72 D<0103B512F8A390390007F8005DA2140FA25DA2141FA25D A2143FA25DA2147FA292C7FCA25CA25CA21301A25CA21303A25CA21307A25CA2130FA25C A2131FA25CA2133FA25CA2137FA291C8FC497EB6FCA25C25397CB820>I<0207B512F0A3 91390007FC006F5AA215075EA3150F5EA3151F5EA3153F5EA3157F93C7FCA35D5DA31401 5DA314035DA31407A25DA2140FA2003F5C5A141F485CA24A5A12FC00E049C8FC14FE0070 5B495A6C485A381E0FC06CB4C9FCEA01F82C3B78B82C>I<0107B512FCA25E9026000FF8 C7FC5D5D141FA25DA2143FA25DA2147FA292C8FCA25CA25CA21301A25CA21303A25CA213 07A25CA2130F170C4A141CA2011F153C17384A1478A2013F157017F04A14E01601017F14 0317C091C71207160F49EC1F80163F4914FF000102071300B8FCA25E2E397BB834>76 D<902607FFF8923807FFF0614F13E0D9000FEFF0004F5AA2021F167FF1EFC0141DDA1CFC EC01CF023C16DF9538039F800238ED071FA20278ED0E3F97C7FC0270151CA202F04B5AF0 707E14E0037E14E0010117FE4D485A02C0EC0380A20103ED0701610280140EA20107ED1C 0305385B14006F137049160705E05B010EEC01C0A2011E913803800F61011CEC0700A201 3C020E131F4C5C1338ED1FB80178163F04F091C8FC01705CA201F04A5B187E00015DD807 F816FEB500C09039007FFFFC151E150E4C397AB84A>I<902603FFF891B512E0A281D900 07923807F8006F6E5A61020F5E81DA0E7F5DA2021E6D1307033F92C7FC141C82DA3C1F5C 70130EEC380FA202786D131E0307141C147082DAF003143C70133814E0150101016E1378 030014705C8201036E13F0604A1480163F010715C1041F5B91C7FC17E149EC0FE360010E 15F31607011E15FF95C8FC011C80A2013C805F1338160013785F01F8157CEA03FC267FFF E0143CB51538A243397CB83E>II<0107B612F817FF1880903B000FF0003FE04BEB0FF0EF03F8 141FEF01FC5DA2023F15FEA25DA2147FEF03FC92C7FCA24A15F817074A15F0EF0FE01301 EF1FC04AEC3F80EFFE0001034A5AEE0FF091B612C04CC7FCD907F8C9FCA25CA2130FA25C A2131FA25CA2133FA25CA2137FA291CAFCA25BA25B1201B512FCA337397BB838>I<0007 B812E0A25AD9F800EB001F01C049EB07C0485AD900011403121E001C5C003C1780140312 3800785C00701607140700F01700485CA2140FC792C7FC5DA2141FA25DA2143FA25DA214 7FA292C9FCA25CA25CA21301A25CA21303A25CA21307A25CA2130FA25CEB3FF0007FB512 F8B6FCA2333971B83B>84 D<003FB539800FFFFEA326007F80C7EA7F8091C8EA3F00173E 49153CA2491538A20001167817705BA2000316F05F5BA2000715015F5BA2000F15035F5B A2001F150794C7FC5BA2003F5D160E5BA2007F151E161C90C8FCA2163C4815385A167816 70A216F04B5A5E1503007E4A5A4BC8FC150E6C143E6C6C5B15F0390FC003E03907F01FC0 0001B5C9FC38007FFCEB1FE0373B70B83E>I87 D89 D<01181330013813709038F001E03901C003800180130000035B3807000E000E5B000C13 18001C1338485B00301360A2007013E000605BA238EF01DE38FF81FFA66CC65A003C1378 1C196AB92B>92 D<14F8EB07FE90381F871C90383E03FE137CEBF801120148486C5A485A 120FEBC001001F5CA2EA3F801403007F5C1300A21407485C5AA2140F5D48ECC1C0A2141F 15831680143F1587007C017F1300ECFF076C485B9038038F8E391F0F079E3907FE03FC39 01F000F0222677A42A>97 D<133FEA1FFFA3C67E137EA313FE5BA312015BA312035BA312 07EBE0F8EBE7FE9038EF0F80390FFC07C013F89038F003E013E0D81FC013F0A21380A212 3F1300A214075A127EA2140F12FE4814E0A2141F15C05AEC3F80A215005C147E5C387801 F8007C5B383C03E0383E07C0381E1F80D80FFEC7FCEA01F01C3B77B926>I<147F903803 FFC090380FC1E090381F0070017E13784913383901F801F83803F003120713E0120FD81F C013F091C7FC485AA2127F90C8FCA35A5AA45AA3153015381578007C14F0007EEB01E000 3EEB03C0EC0F806CEB3E00380F81F83803FFE0C690C7FC1D2677A426>II<147F90 3803FFC090380FC1E090383F00F0017E13785B485A485A485A120F4913F8001F14F0383F 8001EC07E0EC1F80397F81FF00EBFFF891C7FC90C8FC5A5AA55AA21530007C1438157800 7E14F0003EEB01E0EC03C06CEB0F806CEB3E00380781F83803FFE0C690C7FC1D2677A426 >IIIII107 DIII<147F903803FFC090380FC1F090381F00F8017E137C5B4848 137E4848133E0007143F5B120F485AA2485A157F127F90C7FCA215FF5A4814FEA2140115 FC5AEC03F8A2EC07F015E0140F007C14C0007EEB1F80003EEB3F00147E6C13F8380F83F0 3803FFC0C648C7FC202677A42A>I<9039078007C090391FE03FF090393CF0787C903938 F8E03E9038787FC00170497EECFF00D9F0FE148013E05CEA01E113C15CA2D80003143FA2 5CA20107147FA24A1400A2010F5C5E5C4B5A131F5EEC80035E013F495A6E485A5E6E48C7 FC017F133EEC70FC90387E3FF0EC0F8001FEC9FCA25BA21201A25BA21203A25B1207B512 C0A3293580A42A>II<3903C003F0390FF0 1FFC391E783C0F381C7C703A3C3EE03F8038383FC0EB7F800078150000701300151CD8F0 7E90C7FCEAE0FE5BA2120012015BA312035BA312075BA3120F5BA3121F5BA3123F90C9FC 120E212679A423>I<14FE903807FF8090380F83C090383E00E04913F00178137001F813 F00001130313F0A215E00003EB01C06DC7FC7FEBFFC06C13F814FE6C7F6D13807F010F13 C01300143F141F140F123E127E00FE1480A348EB1F0012E06C133E00705B6C5B381E03E0 6CB45AD801FEC7FC1C267AA422>II<13F8D803FEEB01C0D8078FEB03E0390E0F8007121E121C0038140F131F0078 15C01270013F131F00F0130000E015805BD8007E133FA201FE14005B5D120149137EA215 FE120349EBFC0EA20201131E161C15F813E0163CD9F003133814070001ECF07091381EF8 F03A00F83C78E090393FF03FC090390FC00F00272679A42D>I<01F0130ED803FC133FD8 071EEB7F80EA0E1F121C123C0038143F49131F0070140FA25BD8F07E140000E08013FEC6 485B150E12015B151E0003141C5BA2153C000714385B5DA35DA24A5A140300035C6D48C7 FC0001130E3800F83CEB7FF8EB0FC0212679A426>I<01F01507D803FC903903801F80D8 071E903907C03FC0D80E1F130F121C123C0038021F131F49EC800F00701607A249133FD8 F07E168000E0ED000313FEC64849130718000001147E5B03FE5B0003160E495BA2171E00 070101141C01E05B173C1738A217781770020314F05F0003010713016D486C485A000190 391E7C07802800FC3C3E0FC7FC90393FF81FFE90390FE003F0322679A437>I<903907E0 07C090391FF81FF89039787C383C9038F03E703A01E01EE0FE3803C01F018013C0D80700 14FC481480000E1570023F1300001E91C7FC121CA2C75AA2147EA214FEA25CA21301A24A 1370A2010314F016E0001C5B007E1401010714C000FEEC0380010F1307010EEB0F003978 1CF81E9038387C3C393FF03FF03907C00FC027267CA427>I<13F0D803FCEB01C0D8071E EB03E0D80E1F1307121C123C0038140F4914C01270A249131FD8F07E148012E013FEC648 133F160012015B5D0003147E5BA215FE00075C5BA214015DA314035D14070003130FEBF0 1F3901F87FE038007FF7EB1FC7EB000F5DA2141F003F5C48133F92C7FC147E147C007E13 FC387001F8EB03E06C485A383C1F80D80FFEC8FCEA03F0233679A428>I123 DI E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fi cmtt10 12 14 /Fi 14 121 df46 D64 D<383FFFFE487FB6FCA27E6C5BC648C9 FCB3B3A2177017F8EE01FCA9003FB7FC5AB8FCA27E6C16F82E3D7EBC34>76 D78 D<003FB712F04816F8B8FCA43AFE001FC003A8007C ED01F0C791C7FCB3B3A4010FB57E49804980A26D5C6D5C2D3D7DBC34>84 D97 DII107 D<383FFFFE487FB6FCA27E7EC77EB3B3 AD003FB612FE4881B81280A26C16006C5D293D7BBC34>I<027FEB1FC03B3FE1FF807FE0 D87FF39038E0FFF8B612E303F77F6C91B57E6C01C313F000030181EBE07ED9FE01EB807F 6E80491400A2495BA3495BB3A53C3FFF03FFC0FFF048018701E113F8B500CF01F313FCA2 6C018701E113F86C010301C013F0362C81AB34>I<14FE903807FFC0011F13F0017F13FC 90B57E488048010113803A07FC007FC04848EB3FE049131F4848EB0FF0491307003F15F8 491303007F15FC90C71201A300FEEC00FEAA6C14016C15FCA26D1303003F15F86D1307A2 6C6CEB0FF06C6CEB1FE06D133F6C6CEB7FC03A03FF83FF806C90B512006C5C6D5B011F13 F0010713C0010190C7FC272E7AAC34>111 D117 D<3B3FFFE07FFFC0486DB512E0B515F0A26C16E06C 496C13C0C690390007F0006D495A6D6C485AEB1FC06E485A010F49C7FC903807F0FEEB03 F8903801F9FCECFFF86D5B147F6E5A5D6E5A81143F4A7E81ECFDF8EB01F9903803F8FCEC F07E903807E07F010F6D7E90381FC01F02807F013F6D7E49486C7E137E01FE6D7E3B7FFF C01FFFF0B56C4813F86E5AA24A7E6C496C13F02D2B7DAA34>120 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fj cmr10 12 27 /Fj 27 122 df<121FEA3F80EA7FC0EAFFE0A5EA7FC0EA3F80EA1F000B0B788A1C>46 D67 D76 D78 DI<003FB912F8A3903BF8003FF8003F01C06D48130790C71501007EEF00FC007C187CA2 0078183CA20070181CA648180EA5C81600B3B3A44B7EEDFFFE0107B712C0A33F437CC248 >84 DI97 D<13FE12FFA3120312011200B315FF020713E091381F01F8913878007E 4A7F6D48EB1FC04A6D7E4A6D7E91C77F16034981160183A28382A21880AB18005EA25FA2 4C5AA26D5D4C5A6E495A6E5C01F94A5AD9F8F049C7FCD9F07813FE91383E03F89039E00F FFC090260001FEC8FC31467EC437>I100 D<14FF010713E090381F81F890387E00FC49137F4848EB3F800003141F 484814C04848EB0FE0A2121F49EB07F0123FA2007F15F85BA200FF1403A390B6FCA20180 C8FCA6127FA37F123F1638121F6D1478000F15706C6C14F016E06C6C13016C6CEB03C0D8 007EEB07806DEB1F0090380FC07C903803FFF09038007F80252E7DAC2C>III<13FE12FFA31203120112 00B3ED7F80913803FFF091380781FC91381E00FE0238137F4A7F4A805C01FF6E7E5CA291 C7FCA35BB3A8486C4A7EB5D8FE1FB512C0A332457DC437>II<13FE 12FFA3120312011200B3B3B3A5487EB512FEA317457DC41C>108 DIII<01FE13FF00FF01 0713E091381F01F891387800FE000349137FC66C48EB3FC04A6D7E4A6D7E91C76C7EA249 6E7EA283160183A3701380AB4C1300A35F16035F16076D5D4C5A6E5C6E495A4C5AD9FEF0 49C7FC027813FE91383E03F891380FFFC0DA01FEC8FC91CAFCAE487EB512FEA3313F7EAB 37>I<3901FC01F800FFEB0FFEEC1E1F9138383F8000039038707FC0000113E0000013C0 13FD1480ED3F8001FFEB0E0091C8FCA45BB3A67F487FB6FCA3222C7EAB27>114 D<90381FF0183901FFFC383907E00F78390F8007F8381E00015A007C130000781478A212 F81538A27E7EA26C6C1300EA7FE013FE383FFFF06C13FE6CEBFF806C14E0000114F06C6C 13F8010F13FCEB007FEC07FE140100E0EB00FF157F153F7E151FA27EA2151E7E153E6C14 3C6C147C6D13F839FBC001F039F0F00FC039E07FFF0038C00FF8202E7DAC27>I<130EA6 131EA4133EA2137EA213FE120112031207001FB512F8B6FCA2C648C7FCB3A4150EAA017E 131E017F131CA26D133C90381F8038ECC070903807E0E0903801FFC09038007F001F3E7E BC27>I<01FEEC1FC000FFEC1FFFA30003EC007F0001153F0000151FB3A8163FA3167FA2 017E14FF017F14DF6D01017F913980039FF0903B1FC0071FFFC0903807F01E903801FFF8 9026003FE0EBC000322D7DAB37>II<277FFFF803B5FCA30003D9E00013F0C649EB7F806D 4891C7FC6D6C137C011F14786D6C5B6E5B903807F8010103495A6D6C485AD900FE90C8FC 6E5AEC7F1EEC3FBCEC1FF85D140F14076E7E4A7EA24A7EEC1E7F023C7F9138383FC0EC78 1F4A6C7ED901E07F49486C7EEC800301076D7ED90F007F496D7E013E80017E8148B48100 0F6DEBFFF0B5D8C003EBFFC0A3322B7FAA35>120 DI E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fk cmbx10 17.28 24 /Fk 24 122 df<94B5FC043F14E00303B612FC031F8192B87E0203DAE0077F4A49C76C7E 021F01F0EC1FF04A01C0EC7FF84A90C8487E4948485C4B4A7F49495C5B5D5B4B4A7F5B4B 6E5BA4725B725B725BF13FC096C9FCAA0503B6FCBCFCA7D8001F01E0C7120184B3B3AD00 7FB6D8F803B712C0A752657CE45C>12 D<95B56C15E0053F02FCEC03F00407B76C130704 3F04E0130F4BB800F8131F030705FE133F031F9438FF807F037F9126FC003FEBC1FF4AB6 0080010313F34A02F8C86CB5FC020F02C0151F4A91C91207027F01FC8291B548824902E0 707E494A83494A834991CB7E495B49498449865D90B5488448875D481C7F5D481C3F5D5A 1D1F4891CDFCA3481C0F5CA248F407E09AC7FCA35CA2B5FCB07EA280A47EF503E06EF207 F07EA36C801D0F7E6F1AE07E6F191F7E6FF13FC07E6D6DF17F80816DF3FF006D6D606D6D 4E5A6D6E17076D6E4D5A6D02F04D5A6D6E4D5A6E6D4D5A021F01FF4C485A6E02E003075B 020302F8DB1FFEC7FC6EDAFF80ECFFFC6E6C02FC011F13F0031F91B75A0307188003014D C8FCDB003F16F8040716C0DC003F4AC9FC05001480646677E377>67 D70 D78 D80 D83 D89 D<913803FFFE027FEBFFF0 0103B612FE010F6F7E013F16E049D9001F13F8D9FFE001077F486D01017F4801FC6D6D7E 717F486D8085717FA2717FA3856C4980A26C5B38007FE0EB1F8090C9FCA5040FB5FC030F B6FC4AB7FC141F91B8FC0103ECF807010F1480013FEBF80090B512E04814804891C7FC48 13FC485B5A485B5C5A5CB5FCA25CA25FA36E5CA26C5E6E5C6C6D02FD7F0401ECFFC06C6D D903F9ECFF806C01FED90FF015C000039039FFC07FE06C91B5EA807F6C6C4B7E011F02FC 130F010302F001011480D9001F018090C9FC4A437BC150>97 D<92380FFFF092B67E0207 15F0023F15FC91B8FC4917800107DA001F13C04901F8010313E04901E0010F13F0017F5B 90B5484913F84891C7FC5C5A485BA2485B5A7113F05C487013E005011380489338007E00 95C7FC5CA3B5FCAE7E80A37EA2806C18F8F001FC6C6D1503A26C6DED07F86C7FF00FF06C 6E141F6C6E15E06D6DEC7FC06D01F814FF6D01FE010313800107903AFFC01FFE006D91B5 5A01005E023F15E0020F1580020102FCC7FCDA000F13C03E437BC149>99 DI<92380FFF C04AB512FC020FECFF80023F15E091B712F80103D9FE037F499039F0007FFE011F49EB1F FF4901806D7F4990C76C7F90B56E7F48496E7F5C48707F485B8548177F4A825A183F4884 A2485BA21A8084A2B5FCA391B9FCA41A0002E0CBFCA57EA3807EA36C181F6EEE3F807E19 7F6C6D17006C606E5E6C6D15016C6E4A5A6D6D14076D6DEC1FF86D01F8EC7FF06D01FE49 485A01039026FFC01F5B6D91B6C7FC6D6C5D021F15F8020315E0DA007F91C8FC030713F0 41437BC14C>III105 D<902607FF80902607FFC0ED1FFFB6027F01FC 4AB512F04CB6020714FC040703C0011F14FF041F6F017F8193263FF81F6D9026FFE07F7F 9326FF80079028F803FE001F7F922781FE00039026FC07F86D7FC6DA83F89226FE0FE081 6DD987F04C5A6DD98FE06D6D48486D7F4C94C7FCDB9F80167E03BFC84A8003BE4D8215FE 4B5FA24B5FA24B5FA34B5FB3B1B7D8F803B7D8E00FB71280A781417AC08A>109 D<902607FF80903807FFC0B6027F13FC4CB6FC040715C0041F8193263FF81F7F9326FF80 077F922781FE00037FC6DA83F8816DEB87F06DD98FE06D7F5EED9F8003BFC8FC03BE8315 FE5DA25DA25DA35DB3B1B7D8F803B712E0A753417AC05C>I<923807FFC092B512FE0207 ECFFC0023F15F891B712FE4949C67F010701F0011F13C04901C001077F49496D7F4990C7 6C7F49486E7F49486F7E488448496F1380A248496F13C04819E0A24819F0A248496F13F8 A44819FCA4B518FEAD6C19FCA46C19F86E5DA26C19F0A26C19E06E5D6C19C06C6D4B1380 A26C6D92B512006C6D4A5B6D6D495B6D6D495B6D01F0011F5B010701FE90B512C06D90B7 5A01004CC7FC023F15F8020F15E0020192C8FCDA000F13E047437BC152>I<902607FFC0 EB7FFCB60107B512E0043F14F893B7FC03C316C003CF8203DF018014F89227FFF8001F7F C603E001077F6D02806D7F6D49C76C804B6E804B6F7F4B834B818785878587A28587A473 1480AE4F1400A46361A263616361636F4B5B6F5F96B5FC6F4A5C6F4A91C7FC6F6C4913FC 70495B04F0013F5B9226EFFE01B512C003E7B7C8FC03E115FCDBE07F14F0041F14800401 01F0C9FC93CCFCB3A2B712F8A7515D7BC05C>I<903A07FF8007FEB690381FFFC0047F13 F093B57E038314FE923987FC1FFFDCF07F1380ED8FC0C6DA9F80B512C07F6DEBBF0015BE 15FE5DA25D7113805D711300EF0FFCEF03F04B90C8FCA55DB3AEB712FCA73A417BC044> 114 D<913A3FFFC007800103B538FC1FC0011FECFF3F017F15FF9038FFF000000390C712 1FD807FC1407484880484880484880177F485A173FA212FF6D151FA27F7F6DED0F8001FF 92C7FC14E014FF15F86CECFFE016FC6C15FF17C06C16F06C826C16FE6C826C17806C6C16 C06D16E0130F010116F0EB003F020115F8EC0007DB003F13FC16071601007C8100FE167F 173F6C161FA36D150FA26D16F8A26D151F7F18F06D153F6DED7FE06D16C06D6C903801FF 8002E00107130002FCEB7FFE01DFB65A018715F0D8FE0315C048C66C91C7FC0070010713 E036437BC141>II<902603FFE092380FFF80B60203B6FCA7C6EE00036D826D82B3B260A360A3606D5E A26F5C6D4C6C7F067E806D6D02FCECFFE06D6DEB03F86D9039FF801FF06D91B512E0023F 15C0020F1500020114FCDA001F01E002FCC7FC53427AC05C>I119 D<007FB600E049B512FE A7D8003F01F0C8380FFE006DEF03F86F1507A26D6D4B5AA26D6D4B5AA26D6D5E193F6D6E 5D197F6D95C7FC705C6E5E701301A26E6D495AA26E6D495AA26E6D5C180F6E6D5C181F6E 5E70133F6E5EEF807FA26E6E48C8FCA26FEBE1FEA26FEBF1FC17F36FEBFBF817FF6F5CA2 6F5CA36F5CA26F5CA26F91C9FCA2705AA2705AA2705AA3705AA24C5AA25F163F5F167FD8 07F092CAFCD81FFC5C486C5C486C1301A2B56C485AA24B5A5E150F4B5A4A485A6C147F49 495A003F4990CBFC9038F807FE391FF01FFC6CB512F06C5C6C1480C649CCFCEB1FF04F5D 7DBF57>121 D E %EndDVIPSBitmapFont end %%EndProlog %%BeginSetup %%Feature: *Resolution 600dpi TeXDict begin %%PaperSize: a4 %%EndSetup %%Page: 1 1 1 0 bop 544 280 a Fk(Predictions)56 b(for)g(Scien)-5 b(ti\014c)57 b(Computing)1055 468 y(Fift)-5 b(y)56 b(Y)-14 b(ears)55 b(F)-14 b(rom)55 b(No)-5 b(w)1475 704 y Fj(Llo)m(yd)34 b(N.)e(T)-8 b(refethen)977 820 y(Oxford)34 b(Univ)m(ersit)m(y)e (Computing)g(Lab)s(oratory)1393 936 y Fi(LNT@comlab.ox.ac.uk)300 1303 y Fh(This)41 b(essay)f(is)f(adapte)l(d)i(fr)l(om)f(a)g(talk)g (given)g(June)e(17,)43 b(1998)e(at)f(the)f(c)l(onfer)l(enc)l(e)h (\\Numeric)l(al)300 1420 y(A)n(nalysis)27 b(and)g(Computers|50)h(Y)-6 b(e)l(ars)27 b(of)g(Pr)l(o)l(gr)l(ess")g(held)h(at)e(the)h(University)h (of)f(Manchester)h(in)300 1536 y(c)l(ommemor)l(ation)j(of)f(the)g(50th) h(anniversary)g(of)f(the)g(Mark)h(1)f(c)l(omputer.)466 1903 y Fg(Fift)n(y)22 b(y)n(ears)d(is)i(a)f(long,)i(long)e(time)i(in)f (an)n(y)f(tec)n(hnological)f(\014eld.)35 b(In)21 b(our)g(o)n(wn)f (\014eld)h(of)g(scien)n(ti\014c)300 2019 y(computing)39 b(or)g(n)n(umerical)g(analysis,)i(think)f(bac)n(k)f(to)g(1950.)71 b(Around)39 b(the)h(w)n(orld,)i(n)n(umerical)300 2135 y(problems)18 b(in)h(1950)e(w)n(ere)g(solv)n(ed)h(with)h(slide)f(rules) h(and)f(on)g(pap)r(er,)i(or)e(with)h(mec)n(hanical)f(calculators)300 2251 y(that)25 b(had)f(little)h(in)g(common)f(with)h(to)r(da)n(y's)f (computers.)35 b(Some)24 b(of)g(the)h(algorithms)e(w)n(e)h(use)h(to)r (da)n(y)300 2368 y(w)n(ere)34 b(in)h(existence)g(then,)i(but)f(on)e (the)i(whole,)g(the)f(last)g(\014ft)n(y)g(y)n(ears)e(ha)n(v)n(e)h(c)n (hanged)g(n)n(umerical)300 2484 y(computing)27 b(b)r(ey)n(ond)h (recognition.)35 b(The)28 b(next)g(\014ft)n(y)g(will)f(do)h(it)g (again.)466 2611 y(My)f(remarks)f(consist)g(of)h(t)n(w)n(elv)n(e)g (predictions.)36 b(I)27 b(did)h(not)f(aim)g(for)f(these)i(to)f(orbit)f (around)g(a)300 2727 y(unifying)i(theme,)g(but)g(that)g(is)g(nev)n (ertheless)e(what)i(happ)r(ened.)300 2944 y Fh(1.)60 b(We)30 b(may)g(not)g(b)l(e)g(her)l(e.)466 3106 y Fg(In)k(the)f(20th)g (cen)n(tury)-7 b(,)34 b(ev)n(erything)e(tec)n(hnological)g(seems)h(to)g (b)r(e)h(c)n(hanging)e(exp)r(onen)n(tially)-7 b(.)300 3223 y(This)27 b(raises)f(a)h(problem.)36 b(Exp)r(onen)n(tials)26 b(do)h(not)g(go)f(on)h(for)g(ev)n(er;)f(something)h(happ)r(ens)g(to)g (them.)300 3339 y(No)n(w)i(in)g(m)n(y)g(opinion,)h(man)n(y)f(of)g(the)h (exp)r(onen)n(tials)e(w)n(e)h(are)f(sitting)i(on)f(ha)n(v)n(e)f(not)h (y)n(et)g(started)g(to)300 3455 y(lev)n(el)34 b(o\013.)58 b(Here)34 b(at)h(the)g(b)r(eginning)f(of)h(the)f(third)h(millennium,)j (biology)33 b(is)h(just)h(b)r(eginning)g(its)300 3571 y(great)28 b(explosion,)g(and)g(although)g(electronics)g(got)g(a)g (head)h(start)f(of)g(a)h(few)g(decades,)f(it)h(is)g(hardly)300 3688 y(slo)n(wing)d(do)n(wn)h(y)n(et.)466 3815 y(The)39 b(presence)g(of)g(exp)r(onen)n(tials)f(all)h(around)g(us)g(o)n(v)n (ershado)n(ws)d(an)n(y)i(attempt)i(to)f(predict)300 3931 y(the)i(future.)76 b(I)41 b(feel)f(I)h(m)n(ust)g(dw)n(ell)f(for)g(a)g (momen)n(t)h(on)f(one)g(of)g(the)h(shado)n(ws,)i(one)d(that)h(has)300 4047 y(nothing)22 b(sp)r(eci\014cally)g(to)g(do)g(with)g(computing.)35 b(In)23 b(m)n(y)f(opinion,)g(our)g(p)r(osition)g(on)g(an)g(exp)r(onen)n (tial)300 4163 y(tra)5 b(jectory)20 b(is)h(evidence)h(that)f(tec)n (hnological)f(civilisations)h(do)g(not)g(last)h(v)n(ery)e(long.)34 b(I)22 b(do)f(not)g(claim)300 4279 y(that)29 b(our)f(civilisation)g(m)n (ust)h(end)g(within)g(\014ft)n(y)h(y)n(ears,)d(or)h(\014v)n(e)g(h)n (undred,)h(but)g(I)g(do)g(b)r(eliev)n(e)f(there)300 4396 y(is)f(reason)f(to)i(doubt)g(it)g(can)f(surviv)n(e)f(for,)h(sa)n(y)-7 b(,)27 b(ten)h(thousand)f(y)n(ears.)466 4523 y(My)j(reasoning)d(has)i (nothing)g(to)h(do)f(with)h(an)n(y)f(particular)f(cataclysm)h(that)g (ma)n(y)g(b)r(efall)h(us,)300 4639 y(suc)n(h)d(as)g(en)n(vironmen)n (tal)f(catastrophe)f(or)i(exhaustion)g(of)g(resources)e(or)i(asteroid)f (impact)h(or)g(bio-)300 4755 y(logical)f(or)g(n)n(uclear)g(w)n(ar.)36 b(The)27 b(argumen)n(t)f(is)h(more)f(abstract,)g(and)h(it)h(go)r(es)e (lik)n(e)h(this.)37 b(The)27 b(indus-)300 4871 y(trial)e(explosion)f (on)i(earth)e(b)r(egan)h(just)i(t)n(w)n(o)d(or)h(three)g(h)n(undred)g (y)n(ears)f(ago.)35 b(No)n(w)25 b(if)h(tec)n(hnological)300 4988 y(civilisations)31 b(can)g(last)h(tens)g(of)f(thousands)h(of)f(y)n (ears,)g(ho)n(w)h(do)f(y)n(ou)g(explain)h(the)g(extraordinary)300 5104 y(coincidence)20 b(that)h(y)n(ou)e(w)n(ere)h(b)r(orn)g(in)h(the)g (\014rst)f(few)h(generations)d(of)j(this)g(one?)34 b(|)20 b(in)h(the)g(v)n(ery)e(\014rst)300 5220 y(cen)n(tury)33 b(of)h(radio,)h(television,)g(ligh)n(t)e(bulbs,)j(telephones,)f (phonographs,)f(lasers,)g(refrigerators,)1869 5419 y(1)p eop %%Page: 2 2 2 1 bop 300 263 a Fg(automobiles,)26 b(airplanes,)f(spacecraft,)h (computers,)g(n)n(uclear)g(p)r(o)n(w)n(er,)f(n)n(uclear)h(w)n(eap)r (ons,)g(plastics,)300 379 y(an)n(tibiotics,)h(and)h(genetic)f (engineering?)466 502 y(I)d(b)r(eliev)n(e)g(that)h(the)f(explanation)f (of)h(our)g(sp)r(ecial)g(p)r(osition)g(in)g(history)f(ma)n(y)h(b)r(e)g (that)h(it)f(is)g(not)300 618 y(so)i(sp)r(ecial)g(after)g(all,)h(b)r (ecause)f(history)g(tends)h(not)f(to)h(last)f(v)n(ery)g(long.)35 b(This)27 b(argumen)n(t)f(has)g(b)r(een)300 734 y(called)h(the)h Fh(Cop)l(ernic)l(an)j(Principle)f Fg(b)n(y)d(J.)h(R.)g(Gott)f(of)h (Princeton)f(Univ)n(ersit)n(y)-7 b(.)466 857 y(There)29 b(is)g(a)g(second)g(line)h(of)f(evidence,)h(sometimes)f(kno)n(wn)g(as)g Fh(F)-6 b(ermi's)32 b(p)l(ar)l(adox,)f Fg(that)f(also)300 973 y(suggests)18 b(that)h(tec)n(hnological)f(civilisations)g(are)g (short-liv)n(ed.)33 b(The)19 b(h)n(uman)h(race)e(is)h(not)g(an)g(outp)r (ost)300 1090 y(of)29 b(a)g(galactic)f(so)r(ciet)n(y;)i(it)g(is)f(a)g (domestic)g(pro)r(duct.)42 b(Ho)n(w)29 b(can)f(w)n(e)h(explain)g(this)h (if)g(tec)n(hnological)300 1206 y(civilisations)h(last)g(tens)h(of)g (thousands)f(of)h(y)n(ears?)48 b(An)33 b(ages-old)d(tec)n(hnological)g (civilisation)h(will)300 1322 y(expand)19 b(across)e(its)i(galaxy)-7 b(,)19 b(simply)h(b)r(ecause)e(it)i(can.)34 b(\(Don't)20 b(ask)e(wh)n(y)-7 b(,)20 b(for)f(expanding)g(is)g(what)g(life)300 1438 y(do)r(es.)37 b(If)28 b(one)f(sp)r(ecies)h(do)r(esn't,)g(another)e (will)i(replace)f(it.\))56 b(Y)-7 b(et)28 b(in)g(100,000)d(y)n(ears)h (of)i(expanding)300 1555 y(at)h(one)g(h)n(undredth)h(the)g(sp)r(eed)g (of)f(ligh)n(t,)h(a)f(civilisation)g(can)g(spread)f(one)h(thousand)g (ligh)n(t)h(y)n(ears,)300 1671 y(a)e(distance)g(encompassing)f (millions)i(of)f(stars.)38 b(Is)29 b(it)f(plausible)h(that)f(tec)n (hnological)f(civilisations)300 1787 y(are)g(so)g(rare)f(as)h(to)g (arise)f(on)i(only)f(one)g(star)g(among)f(millions?)466 1910 y(I)h(b)r(eliev)n(e)f(that)h(the)g(explanation)f(of)g(the)h (emptiness)g(out)g(there)f(ma)n(y)g(b)r(e)h(that)g(tec)n(hnological)300 2026 y(civilisations)33 b(p)r(erish)h(b)r(efore)g(they)h(start)e(to)h (spread)g(across)e(their)i(galaxy|or)e(that)i(they)h(start)300 2142 y(spreading,)26 b(then)i(p)r(erish)g(in)g(a)f(cataclysm)g(so)f (great)h(as)g(to)g(tak)n(e)g(the)h(galaxy)e(with)i(them.)466 2265 y(Suddenly)d(the)f(problem)g(of)g(predicting)g(\014ft)n(y)g(y)n (ears)f(of)h(scien)n(ti\014c)g(computing)g(b)r(egins)g(to)g(lo)r(ok)300 2381 y(easy!)36 b(Let's)27 b(get)h(do)n(wn)f(to)g(it.)300 2594 y Fh(2.)46 b(We'l)t(l)24 b(talk)f(to)f(c)l(omputers)h(mor)l(e)g (often)g(than)f(typ)l(e)h(to)g(them,)h(and)f(they'l)t(l)i(r)l(esp)l (ond)e(with)g(pictur)l(es)433 2710 y(mor)l(e)30 b(often)g(than)g(numb)l (ers.)466 2864 y Fg(A)j(big)e(c)n(hange)g(in)i(the)f(last)g(t)n(w)n(en) n(t)n(y)g(y)n(ears)e(has)i(b)r(een)g(the)h(arriv)-5 b(al)30 b(of)i(graphical)f(in)n(terfaces.)300 2980 y(When)26 b(I)f(w)n(as)f(a)h(graduate)e(studen)n(t)j(at)f(Stanford)f(around)h (1980,)e(w)n(e)i(pla)n(y)n(ed)f(with)i(some)e(Alto)i(ma-)300 3097 y(c)n(hines)21 b(donated)f(b)n(y)h(Xero)n(x,)g(early)f(w)n (orkstations)f(featuring)h(windo)n(ws,)i(icons,)g(mice)f(and)g(p)r(oin) n(ters,)300 3213 y(but)26 b(I)f(though)n(t)f(these)h(w)n(ere)f(part)n (y)g(tric)n(ks,)h(to)r(o)f(gimmic)n(ky)h(to)f(catc)n(h)h(on.)35 b(T)-7 b(o)r(da)n(y)25 b(the)g(descendan)n(ts)300 3329 y(of)37 b(the)g(Altos)g(ha)n(v)n(e)e(driv)n(en)h(other)h(mac)n(hines)f (to)g(extinction.)65 b(It)37 b(tak)n(es)f(no)g(sp)r(ecial)h(insigh)n(t) f(to)300 3445 y(predict)24 b(that)g(so)r(on,)g(an)g(equally)g(great)e (c)n(hange)h(will)i(o)r(ccur)e(as)g(w)n(e)h(tak)n(e)f(to)h(in)n (teracting)f(with)i(com-)300 3562 y(puters)e(b)n(y)h(sp)r(eec)n(h.)35 b(It)24 b(has)f(b)r(een)h(a)f(long)g(time)h(coming,)g(but)g(this)g (transformation)e(is)h(no)n(w)g(around)300 3678 y(the)28 b(corner.)466 3801 y(It)d(is)f(go)r(o)r(d)f(fun)i(to)g(imagine)e(what)h (computer)g(graphics)f(will)i(b)r(e)f(lik)n(e)g(in)h(\014ft)n(y)f(y)n (ears.)35 b(I)24 b(hardly)300 3917 y(dare,)i(except)h(to)g(note)f(that) h(three-dimensional)f(virtual)g(realit)n(y)g(will)h(b)r(e)g(as)f (ordinary)g(as)g(V)-7 b(elcro.)466 4040 y(Curiously)g(,)26 b(though)h(the)g(dev)n(elopmen)n(t)g(of)f(sp)r(eec)n(h)h(and)g (graphics)e(will)j(mak)n(e)e(our)g(n)n(umerical)300 4156 y(w)n(ork)33 b(ev)n(er)h(more)f(h)n(uman)i(in)f(feel,)j(less)d(ob)n (viously)f(n)n(umerical,)j(the)f(underlying)f(computations)300 4272 y(will)d(con)n(tin)n(ue)f(to)g(b)r(e)h(based)f(on)g(n)n(um)n(b)r (ers)g(represen)n(ted)g(digitally)g(to)g(man)n(y)g(digits)h(of)f (precision.)300 4388 y(The)d(digital)f(idea)h(is)f(what)h(mak)n(es)f (ev)n(erything)f(p)r(ossible,)i(and)g(it)g(is)g(not)f(going)g(to)h(go)e (a)n(w)n(a)n(y)-7 b(.)35 b(This)300 4504 y(is)30 b(one)g(sense)g(in)h (whic)n(h)f(the)h(scien)n(tists)f(and)g(engineers)f(of)i(the)f(future)h (will)g(b)r(e)f(further)h(remo)n(v)n(ed)300 4621 y(from)24 b(the)h(details)g(of)f(computing)h(than)f(w)n(e)h(are,)f(just)h(as)f(w) n(e)g(are)g(further)g(remo)n(v)n(ed)f(than)i(w)n(ere)f(our)300 4737 y(paren)n(ts.)300 4950 y Fh(3.)83 b(Numeric)l(al)41 b(c)l(omputing)g(wil)t(l)h(b)l(e)f(adaptive,)46 b(iter)l(ative,)f (explor)l(atory,)h(intel)t(ligent|and)c(the)433 5066 y(c)l(omputational)31 b(p)l(ower)f(wil)t(l)h(b)l(e)f(b)l(eyond)h(your)f (wildest)h(dr)l(e)l(ams.)466 5220 y Fg(Adaptiv)n(e)37 b(n)n(umerical)f(computing)g(is)h(one)f(of)h(the)g(glories)e(of)i(the)g (computer)f(age.)64 b(Gauss)1869 5419 y(2)p eop %%Page: 3 3 3 2 bop 300 263 a Fg(quadrature)27 b(w)n(as)h(in)n(v)n(en)n(ted)h(t)n (w)n(o)f(cen)n(turies)h(ago,)f(but)h(adaptiv)n(e)f(quadrature)g(didn't) i(arriv)n(e)d(un)n(til)300 379 y(the)e(1960s.)34 b(Adaptiv)n(e)24 b(ODE)h(solv)n(ers)d(came)j(so)r(on)f(after,)g(and)h(turned)g(the)g (solution)f(of)h(most)f(ordi-)300 495 y(nary)j(di\013eren)n(tial)g (equations)g(in)n(to)g(the)h(use)g(of)f(a)h(blac)n(k)e(b)r(o)n(x.)37 b(P)n(artial)26 b(di\013eren)n(tial)h(equations)g(are)300 612 y(not)k(y)n(et)g(b)r(o)n(xed)f(in)h(blac)n(k,)h(but)f(the)h(trend)f (is)f(in)i(that)f(direction.)46 b(As)32 b(time)f(go)r(es)f(b)n(y)-7 b(,)32 b(adaptivit)n(y)300 728 y(managed)21 b(b)n(y)h(the)g(computer's) g(in)n(telligence)f(b)r(ecomes)h(more)f(and)h(more)g(widespread.)34 b(Computers)300 844 y(are)e(not)h(as)g(wise)g(as)f(p)r(eople,)j(but)e (they)h(can)e(explore)g(a)h(forest)g(of)g(p)r(ossibilities)g(faster)f (than)h(w)n(e)300 960 y(can.)39 b(In)28 b(\014ft)n(y)h(y)n(ears,)e (this)h(is)h(ho)n(w)e(most)h(n)n(umerical)g(problems)f(will)i(b)r(e)g (solv)n(ed.)38 b(W)-7 b(e)28 b(will)h(tell)g(the)300 1077 y(mac)n(hine)i(what)h(w)n(e)f(w)n(an)n(t,)h(and)f(the)h(mac)n (hine,)g(an)g(in)n(telligen)n(t)f(con)n(trol)f(system)i(sitting)f(atop) g(an)300 1193 y(encyclopaedia)25 b(of)h(n)n(umerical)g(metho)r(ds,)h (will)f(juggle)g(computational)g(options)g(at)g(incomprehen-)300 1309 y(sible)f(sp)r(eed)h(un)n(til)g(it)g(has)f(solv)n(ed)f(the)i (problem)f(to)g(the)h(accuracy)d(required.)36 b(Then)25 b(it)h(will)g(giv)n(e)e(us)300 1425 y(the)k(answ)n(er;)e(and)i(if)g(w)n (e)f(insist,)h(it)g(ma)n(y)f(ev)n(en)g(tell)h(us)f(something)g(of)h(ho) n(w)f(it)h(got)f(there.)466 1551 y(The)c(p)r(o)n(w)n(er)f(unleashed)h (b)n(y)g(this)h(kind)g(of)f(computing)g(will)g(b)r(e)h(v)-5 b(ast.)35 b(Large)22 b(parts)h(of)g(ph)n(ysical)300 1667 y(realit)n(y)g(will)i(b)r(e)g(sim)n(ulated)f(in)h(real)e(time)i(b)r (efore)g(our)e(ey)n(es,)i(with)g(e\013ects)f(so)g(far)g(b)r(ey)n(ond)g (what)h(the)300 1784 y(men)19 b(of)g(1950)f(could)h(en)n(vision)f(that) h(the)h(w)n(ord)e(\\computation")g(ma)n(y)g(b)r(egin)h(to)g(seem)g (old-fashioned)300 1900 y(and)27 b(drop)g(out)h(of)g(use.)466 2026 y(When)35 b(computations)e(are)g(all)h(in)n(telligen)n(t,)h(when)f (ev)n(erything)f(is)h(em)n(b)r(edded)h(in)f(a)f(con)n(trol)300 2142 y(lo)r(op,)c(the)g(mathematical)f(landscap)r(e)g(will)h(c)n (hange.)40 b(One)28 b(distinction)h(that)g(means)f(a)h(great)e(deal)300 2258 y(to)34 b(us)h(to)r(da)n(y)e(is)h(that,)j(broadly)c(sp)r(eaking,)i (linear)f(problems)g(can)f(b)r(e)i(solv)n(ed)f(in)g(one)g(pass,)h(but) 300 2374 y(nonlinear)40 b(ones)f(require)h(iteration.)75 b(In)40 b(\014ft)n(y)h(y)n(ears,)h(when)f(ev)n(erything)e(is)i(em)n(b)r (edded)g(in)f(an)300 2491 y(iterativ)n(e)25 b(lo)r(op)g(an)n(yw)n(a)n (y)-7 b(,)24 b(this)i(di\013erence)g(will)g(ha)n(v)n(e)e(diminished.)37 b(F)-7 b(or)25 b(the)h(same)f(reason,)g(to)r(da)n(y's)300 2607 y(big)i(distinction)h(b)r(et)n(w)n(een)g(forw)n(ard)e(and)h(in)n (v)n(erse)f(problems)h(will)h(ha)n(v)n(e)e(faded)i(to)r(o.)466 2733 y(My)g(next)f(prediction)h(is)f(a)g(corollary)-7 b(.)300 2948 y Fh(4.)60 b(Determinism)30 b(in)g(numeric)l(al)g(c)l (omputing)g(wil)t(l)h(b)l(e)f(gone.)466 3109 y Fg(Recen)n(tly)h(our)f (family)h(ren)n(ted)f(a)h(car)f(for)g(a)g(holida)n(y)-7 b(.)46 b(One)31 b(ev)n(ening)f(w)n(e)g(w)n(an)n(ted)g(to)h(lo)r(ok)f (at)300 3225 y(the)f(stars,)e(whic)n(h)h(mean)n(t)g(turning)g(o\013)h (the)f(dome)g(ligh)n(t.)39 b(W)-7 b(e)29 b(couldn't)f(\014gure)g(out)g (ho)n(w)f(to)i(do)f(it!)300 3341 y(A)c(decade)f(ago,)f(closing)h(the)g (do)r(ors)g(and)g(\015ipping)g(a)g(switc)n(h)g(w)n(ould)g(ha)n(v)n(e)f (su\016ced,)j(but)f(no)n(w)n(ada)n(ys,)300 3457 y(cars)30 b(are)h(more)f(in)n(telligen)n(t.)48 b(In)32 b(some,)g(the)g(ligh)n(t)f (sta)n(ys)f(on)h(for)g(a)g(\014xed)h(p)r(erio)r(d)f(after)g(y)n(ou)g (close)300 3574 y(the)25 b(do)r(ors,)f(and)g(in)h(ours,)f(the)h (situation)f(w)n(as)f(ev)n(en)h(more)g(complicated.)36 b(There)24 b(w)n(as)f(an)h(in)n(terlo)r(c)n(k)300 3690 y(with)33 b(the)f(engine,)h(plus)g(some)e(additional)h(in)n(telligence) g(that)g(w)n(e)g(nev)n(er)f(got)h(to)g(the)h(b)r(ottom)f(of.)300 3806 y(Ev)n(en)n(tually)26 b(w)n(e)g(got)h(the)g(ligh)n(t)g(o\013,)h (but)f(w)n(e)g(w)n(ere)f(not)h(quite)h(sure)e(ho)n(w)h(w)n(e)f(had)h (done)g(it,)h(or)e(if)h(w)n(e)300 3922 y(could)g(do)h(it)g(the)g(same)f (w)n(a)n(y)f(again.)466 4048 y(Ha)n(v)n(e)c(y)n(ou)g(noticed)h(ho)n(w)g (man)n(y)f(of)h(our)f(mac)n(hines)g(b)r(eha)n(v)n(e)h(this)g(w)n(a)n (y?)34 b(Photo)r(copiers)21 b(used)i(to)300 4164 y(b)r(e)g (deterministic,)h(but)f(no)n(w)n(ada)n(ys)d(they)j(ha)n(v)n(e)f (complicated)g(arra)n(ys)e(of)j(in)n(ternal)f(states.)35 b(The)22 b(\014rst)300 4281 y(cop)n(y)28 b(ma)n(y)f(come)h(out)h(in)f (landscap)r(e)g(orien)n(tation,)g(but)h(the)f(second)g(in)h(p)r (ortrait,)f(if)h(the)g(mac)n(hine)300 4397 y(decides)i(in-b)r(et)n(w)n (een)f(that)i(it)f(ough)n(t)f(to)h(c)n(hange)e(mo)r(des.)47 b(T)n(yp)r(ewriters)30 b(used)g(to)h(b)r(e)g(predictable)300 4513 y(to)r(o:)56 b(y)n(ou)37 b(knew)g(what)g(w)n(ould)g(happ)r(en)h (when)f(y)n(ou)g(pressed)f(a)h(k)n(ey)-7 b(.)66 b(No)n(w)n(ada)n(ys,)37 b(in)h(W)-7 b(ord)37 b(or)300 4629 y(LaT)-7 b(eX,)23 b(c)n(hanging)f(one)h(c)n(haracter)e(of)i(input)h(ma)n(y)f(alter)f(the) i(whole)f(do)r(cumen)n(t)h(in)f(startling)g(w)n(a)n(ys.)300 4745 y(Wh)n(y)-7 b(,)38 b(at)d(motorw)n(a)n(y)f(rest)h(stops,)i(ev)n (en)e(toilets)h(are)e(in)n(telligen)n(t)i(devices)f(no)n(w)g(whose)g (states)g(of)300 4862 y(mind)28 b(w)n(e)f(don't)h(fully)g(understand,)g (and)f(when)h(y)n(ou're)f(\014nished)g(with)i(the)f(toilet,)g(y)n(ou)e (ha)n(v)n(e)h(t)n(w)n(o)300 4978 y(further)d(negotiations)f(to)h (undertak)n(e)f(with)i(the)f(in)n(telligen)n(t)g(sink)g(and)g(the)h(in) n(telligen)n(t)f(hand)g(drier!)466 5104 y(What's)h(true)g(of)g(toilets) g(will)h(b)r(e)f(true)g(of)g(n)n(umerical)f(computations.)36 b(In)25 b(\014ft)n(y)g(y)n(ears,)f(though)300 5220 y(the)34 b(answ)n(ers)d(y)n(ou)i(get)g(will)h(b)r(e)f(accurate)g(without)g(fail) h(to)f(the)h(prescrib)r(ed)e(precision,)i(y)n(ou)f(will)1869 5419 y(3)p eop %%Page: 4 4 4 3 bop 300 263 a Fg(not)34 b(exp)r(ect)g(to)f(duplicate)h(them)g (exactly)f(if)h(y)n(ou)f(solv)n(e)f(the)i(problem)g(a)f(second)g(time.) 55 b(I)34 b(don't)300 379 y(see)e(ho)n(w)g(this)g(loss)g(of)g (determinism)g(can)g(b)r(e)h(stopp)r(ed.)51 b(Of)33 b(course,)f(from)g (a)g(tec)n(hnical)g(p)r(oin)n(t)g(of)300 495 y(view,)24 b(it)h(w)n(ould)e(b)r(e)h(easy)f(to)h(mak)n(e)f(our)g(mac)n(hines)g (deterministic)h(b)n(y)g(simply)g(lea)n(ving)e(out)i(all)g(that)300 612 y(in)n(telligence.)37 b(Ho)n(w)n(ev)n(er,)25 b(w)n(e)i(will)h(not)g (do)f(this,)h(for)f(in)n(telligence)g(is)h(to)r(o)f(p)r(o)n(w)n(erful.) 466 737 y(In)j(the)g(last)f(\014ft)n(y)h(y)n(ears,)f(the)h(great)e (message)h(comm)n(unicated)g(to)g(scien)n(tists)h(and)f(engineers)300 853 y(w)n(as)g(that)h(it)g(is)f(unreasonable)f(to)i(ask)f(for)g (exactness)f(in)i(n)n(umerical)f(computation.)43 b(In)30 b(the)g(next)300 969 y(\014ft)n(y)-7 b(,)28 b(they)g(will)g(learn)f (not)g(to)h(ask)e(for)h(rep)r(eatabilit)n(y)-7 b(,)27 b(either.)300 1184 y Fh(5.)60 b(The)31 b(imp)l(ortanc)l(e)g(of)f(\015o) l(ating)g(p)l(oint)g(arithmetic)h(wil)t(l)g(b)l(e)f(undiminishe)l(d.) 466 1342 y Fg(So)25 b(m)n(uc)n(h)g(will)g(c)n(hange)f(in)h(\014ft)n(y)h (y)n(ears)d(that)j(it)f(is)g(refreshing)f(to)h(to)g(predict)g(some)f (con)n(tin)n(uit)n(y)-7 b(.)300 1459 y(One)27 b(thing)h(that)f(I)h(b)r (eliev)n(e)f(will)h(last)f(is)g(\015oating)g(p)r(oin)n(t)g(arithmetic.) 37 b(Of)28 b(course,)e(the)i(details)f(will)300 1575 y(c)n(hange,)37 b(and)f(in)g(particular,)h(w)n(ord)d(lengths)i(will)g (con)n(tin)n(ue)g(their)f(progression)f(from)h(16)g(to)h(32)300 1691 y(to)30 b(64)e(to)i(128)e(bits)i(and)f(b)r(ey)n(ond,)h(as)f (sequences)g(of)h(computations)f(b)r(ecome)g(longer)g(and)g(require)300 1807 y(more)36 b(accuracy)f(to)h(con)n(tain)g(accum)n(ulation)g(of)h (errors.)61 b(Conceiv)-5 b(ably)36 b(w)n(e)g(migh)n(t)h(ev)n(en)f (switc)n(h)300 1924 y(to)d(hardw)n(are)f(based)h(on)g(a)g(logarithmic)f (represen)n(tation)g(of)h(n)n(um)n(b)r(ers.)54 b(But)34 b(I)g(b)r(eliev)n(e)f(the)h(t)n(w)n(o)300 2040 y(de\014ning)e(features) f(of)g(\015oating)g(p)r(oin)n(t)h(arithmetic)f(will)h(p)r(ersist:)44 b(relativ)n(e)31 b(rather)f(than)i(absolute)300 2156 y(magnitudes,)27 b(and)h(rounding)f(of)g(all)g(in)n(termediate)h(op)r (erations.)466 2281 y(Outside)41 b(the)g(n)n(umerical)e(analysis)h (comm)n(unit)n(y)-7 b(,)43 b(some)e(p)r(eople)f(feel)h(that)g (\015oating)f(p)r(oin)n(t)300 2397 y(arithmetic)20 b(is)h(an)f(anac)n (hronism,)g(a)g(1950s)f(kludge)h(that)h(is)f(destined)h(to)g(b)r(e)g (cast)f(aside)g(as)g(mac)n(hines)300 2513 y(b)r(ecome)31 b(more)e(sophisticated.)46 b(Computers)30 b(ma)n(y)g(ha)n(v)n(e)f(b)r (een)i(b)r(orn)f(as)g(n)n(um)n(b)r(er)h(crunc)n(hers,)f(the)300 2630 y(feeling)d(go)r(es,)f(but)h(no)n(w)f(that)h(they)g(are)e(fast)i (enough)f(to)g(do)h(arbitrary)d(sym)n(b)r(olic)j(manipulations,)300 2746 y(w)n(e)32 b(m)n(ust)h(mo)n(v)n(e)f(to)g(a)h(higher)f(plane.)52 b(In)33 b(truth,)h(no)f(amoun)n(t)f(of)g(computer)h(p)r(o)n(w)n(er)e (will)i(c)n(hange)300 2862 y(the)25 b(fact)g(that)g(most)g(n)n (umerical)f(problems)g(cannot)g(b)r(e)h(solv)n(ed)f(sym)n(b)r(olically) -7 b(.)35 b(Y)-7 b(ou)25 b(ha)n(v)n(e)e(to)i(mak)n(e)300 2978 y(appro)n(ximations,)d(and)h(\015oating)g(p)r(oin)n(t)g (arithmetic)g(is)h(the)f(b)r(est)h(general-purp)r(ose)d(appro)n (ximation)300 3095 y(idea)27 b(ev)n(er)g(devised.)36 b(It)28 b(will)g(p)r(ersist,)g(but)g(get)f(hidden)h(deep)r(er)g(in)g (the)g(mac)n(hine.)300 3309 y Fh(6.)60 b(Line)l(ar)31 b(systems)e(of)i(e)l(quations)f(wil)t(l)h(b)l(e)e(solve)l(d)i(in)f Ff(O)r Fg(\()p Ff(N)2236 3279 y Fe(2+)p Fd(\017)2353 3309 y Fg(\))g Fh(\015ops.)466 3468 y Fg(Matrix)d(computations)h(as)f (p)r(erformed)h(on)f(mac)n(hines)h(around)f(the)h(w)n(orld)f(t)n (ypically)g(require)300 3584 y Ff(O)r Fg(\()p Ff(N)473 3554 y Fe(3)511 3584 y Fg(\))36 b(\015oating)f(p)r(oin)n(t)h(op)r (erations|\\\015ops"|where)c Ff(N)45 b Fg(is)36 b(the)g(dimension)g(of) f(the)i(problem.)300 3700 y(This)e(statemen)n(t)f(applies)g(exactly)g (for)h(computing)f(in)n(v)n(erses,)h(determinan)n(ts,)h(and)e (solutions)g(of)300 3817 y(systems)d(of)g(equations,)g(and)g(it)g (applies)g(appro)n(ximately)e(for)i(eigen)n(v)-5 b(alues)30 b(and)h(singular)e(v)-5 b(alues.)300 3933 y(But)33 b(all)f(of)h(these)f (problems)g(in)n(v)n(olv)n(e)f(only)h Ff(O)r Fg(\()p Ff(N)1912 3903 y Fe(2)1950 3933 y Fg(\))h(inputs,)h(and)f(as)f(mac)n (hines)g(get)g(faster,)h(it)g(is)300 4049 y(increasingly)26 b(aggra)n(v)-5 b(ating)25 b(that)j Ff(O)r Fg(\()p Ff(N)1556 4019 y Fe(3)1593 4049 y Fg(\))g(op)r(erations)f(should)g(b)r(e)h (needed)g(to)f(solv)n(e)g(them.)466 4174 y(Strassen)k(sho)n(w)n(ed)g (in)h(1968)e(that)i(the)h Ff(O)r Fg(\()p Ff(N)1894 4144 y Fe(3)1931 4174 y Fg(\))g(barrier)d(could)i(b)r(e)g(breac)n(hed.)49 b(He)32 b(devised)f(a)300 4290 y(recursiv)n(e)i(algorithm)h(whose)g (running)g(time)h(w)n(as)f Ff(O)r Fg(\()p Ff(N)2156 4260 y Fe(log)2242 4275 y Fc(2)2274 4260 y Fe(7)2312 4290 y Fg(\),)j(appro)n(ximately)32 b Ff(O)r Fg(\()p Ff(N)3130 4260 y Fe(2)p Fd(:)p Fe(81)3254 4290 y Fg(\),)37 b(and)300 4406 y(subsequen)n(t)31 b(impro)n(v)n(emen)n(ts)f(b)n(y)h(Copp)r (ersmith,)h(Winograd)e(and)h(others)g(ha)n(v)n(e)f(brough)n(t)g(the)i (ex-)300 4523 y(p)r(onen)n(t)h(do)n(wn)f(to)g(2.376.)50 b(Ho)n(w)n(ev)n(er,)32 b(the)h(algorithms)e(in)i(question)f(in)n(v)n (olv)n(e)f(constan)n(ts)h(so)g(large)300 4639 y(that)e(they)g(are)f (impractical,)h(and)g(they)g(ha)n(v)n(e)f(had)g(little)i(e\013ect)f(on) g(scien)n(ti\014c)g(computing.)43 b(As)30 b(a)300 4755 y(result,)k(the)g(problem)f(of)g(sp)r(eeding)g(up)g(matrix)g (computations)g(is)g(view)n(ed)f(b)n(y)h(man)n(y)g(n)n(umerical)300 4871 y(analysts)26 b(as)h(a)g(theoretical)f(distraction.)36 b(This)27 b(is)g(a)g(strange)f(attitude)i(to)f(tak)n(e)g(to)g(the)h (most)f(con-)300 4988 y(spicuous)h(unsolv)n(ed)g(problem)h(in)g(our)f (\014eld!)58 b(Of)29 b(course,)f(it)h(ma)n(y)g(b)r(e)g(that)g(there)g (is)f(some)h(reason)300 5104 y(wh)n(y)c(no)h(practical)f(algorithm)f (can)i(ev)n(er)f(b)r(e)h(found,)g(but)h(w)n(e)e(certainly)g(do)h(not)g (kno)n(w)f(that)h(to)r(da)n(y)-7 b(.)300 5220 y(A)31 b(\\fast)g(matrix)g(in)n(v)n(erse")e(ma)n(y)h(b)r(e)i(p)r(ossible,)f(p) r(erhaps)g(one)g(with)g(complexit)n(y)g Ff(O)r Fg(\()p Ff(N)3094 5190 y Fe(2)3146 5220 y Fg(log)14 b Ff(N)9 b Fg(\))31 b(or)1869 5419 y(4)p eop %%Page: 5 5 5 4 bop 300 263 a Ff(O)r Fg(\()p Ff(N)473 233 y Fe(2)525 263 y Fg(log)632 226 y Fe(2)683 263 y Ff(N)9 b Fg(\),)28 b(and)f(disco)n(v)n(ering)f(it)i(w)n(ould)f(c)n(hange)f(ev)n(erything.) 466 387 y(In)36 b(1985)f(I)h(made)g(a)f(b)r(et)i(with)g(P)n(eter)e (Alfeld)i(of)f(the)g(Univ)n(ersit)n(y)f(of)h(Utah)h(that)f(a)g(matrix) 300 503 y(algorithm)22 b(with)i(complexit)n(y)f(0\()p Ff(N)1427 473 y Fe(2+)p Fd(\017)1542 503 y Fg(\))h(for)e(an)n(y)h Ff(\017)f(>)h Fg(0)g(w)n(ould)g(b)r(e)g(found)h(within)g(ten)g(y)n (ears.)33 b(None)300 620 y(w)n(as,)c(and)g(I)g(ga)n(v)n(e)e(Alfeld)j(a) f(c)n(hec)n(k)f(for)h($100.)39 b(W)-7 b(e)30 b(renew)n(ed)e(our)g(b)r (et,)j(ho)n(w)n(ev)n(er,)c(to)i(2005,)f(and)h(in)300 736 y(that)i(y)n(ear)d(I)j(will)f(renew)g(it)g(again)f(if)i(necessary) -7 b(.)43 b(One)30 b(morning,)g(with)h(luc)n(k,)f(the)h(headlines)f (will)300 852 y(app)r(ear.)36 b(I)28 b(think)g(\014ft)n(y)g(y)n(ears)e (should)h(b)r(e)h(long)f(enough.)300 1066 y Fh(7.)60 b(Multip)l(ole)31 b(metho)l(ds)g(and)f(their)g(desc)l(endants)g(wil)t (l)h(b)l(e)f(ubiquitous.)466 1223 y Fg(The)37 b(conjugate)g(gradien)n (t)f(and)h(Lanczos)f(algorithms)f(w)n(ere)i(in)n(v)n(en)n(ted)f(around) g(1950,)i(and)300 1339 y(their)29 b(story)e(is)i(a)f(curious)g(one.)39 b(No)n(w)n(ada)n(ys)26 b(w)n(e)j(ha)n(v)n(e)e(no)i(doubt)f(as)g(to)h (what)g(these)f(metho)r(ds)h(are)300 1455 y(go)r(o)r(d)h(for:)44 b(they)31 b(are)f(matrix)h(iterations,)g(whic)n(h)g(for)f(certain)h (structured)g(matrices)f(bring)g(those)300 1571 y Ff(O)r Fg(\()p Ff(N)473 1541 y Fe(3)511 1571 y Fg(\))36 b(op)r(eration)f(coun) n(ts)g(do)n(wn)g(to)h Ff(O)r Fg(\()p Ff(N)1738 1541 y Fe(2)1776 1571 y Fg(\))g(or)f(ev)n(en)g(b)r(etter.)62 b(Though)36 b(there)f(are)g(constan)n(ts)300 1688 y(hidden)29 b(in)f(the)g(\\O",)f(these)h(metho)r(ds)g(are)f(often)i(m)n(uc)n(h)f (faster)f(than)h(Gaussian)f(elimination)h(and)300 1804 y(its)g(relativ)n(es)e(when)i Ff(N)36 b Fg(is)28 b(large.)466 1928 y(What)21 b(is)f(curious)f(is)i(that)f(Hestenes,)i(Stiefel,)h (Lanczos)c(and)h(the)h(rest)f(didn't)h(see)f(this)h(coming.)300 2044 y(In)i(the)f(1950s,)g Ff(N)31 b Fg(w)n(as)21 b(to)r(o)h(small)g (for)g(conjugate)g(gradien)n(ts)f(and)h(Lanczos)f(y)n(et)h(to)g(b)r(e)h (comp)r(etitiv)n(e,)300 2160 y(but)h(all)f(the)h(mathematical)f(pieces) g(w)n(ere)g(in)h(place.)35 b(These)23 b(men)h(knew)f(something)g(of)g (the)h(con)n(v)n(er-)300 2277 y(gence)h(prop)r(erties)g(of)h(their)g (iterations,)g(enough)f(to)h(ha)n(v)n(e)f(b)r(een)h(able)g(to)g (predict)g(that)g(ev)n(en)n(tually)-7 b(,)300 2393 y(as)33 b(mac)n(hines)g(grew)g(faster,)i(they)f(m)n(ust)g(b)r(eat)g(the)g(comp) r(etition.)56 b(Y)-7 b(et)34 b(they)g(seem)g(not)g(to)f(ha)n(v)n(e)300 2509 y(made)c(this)h(prediction.)43 b(A)30 b(n)n(umerical)e(analyst)h (writing)g(an)g(essa)n(y)f(lik)n(e)i(this)f(one)h(in)f(1960)f(migh)n(t) 300 2625 y(not)g(ha)n(v)n(e)e(men)n(tioned)i(conjugate)e(gradien)n(ts)h (at)g(all.)466 2749 y(It)i(is)f(with)h(this)f(history)g(in)h(mind)g (that)f(I)h(men)n(tion)f(m)n(ultip)r(ole)h(metho)r(ds,)g(b)n(y)f(whic)n (h)g(I)g(mean)300 2866 y(metho)r(ds)21 b(related)g(to)g(the)g(recen)n (t)g(algorithms)e(of)i(Rokhlin)g(and)g(Greengard)f(for)g Ff(N)9 b Fg(-b)r(o)r(dy)21 b(problems)300 2982 y(and)39 b(in)n(tegral)f(equations.)70 b(Times)39 b(ha)n(v)n(e)f(c)n(hanged,)j (and)e(w)n(e)g(are)f(all)g(asymptotic)n(k)n(ers.)70 b(When)300 3098 y(m)n(ultip)r(ole)32 b(metho)r(ds)g(w)n(ere)f(b)r(eing)h(in)n(v)n (en)n(ted)g(in)g(the)g(1980s,)f(they)h(w)n(ere)f(comp)r(etitiv)n(e)h (in)h(2D)e(but)300 3214 y(not)36 b(3D.)73 b(Y)-7 b(et)37 b(Rokhlin)f(and)g(Greengard)e(sa)n(w)h(immediately)i(that)f(these)g (tec)n(hniques)g(reduced)300 3330 y(op)r(eration)29 b(coun)n(ts)g(from) h Ff(O)r Fg(\()p Ff(N)1309 3300 y Fe(2)1347 3330 y Fg(\))g(to)g Ff(O)r Fg(\()p Ff(N)9 b Fg(\),)31 b(giv)n(e)e(or)g(tak)n(e)g(a)h (logarithmic)e(factor,)i(so)f(ho)n(w)g(could)300 3447 y(they)f(not)f(win)h(in)g(the)g(long)f(run?)37 b(And)28 b(so)f(they)h(will.)466 3571 y(The)h(success)f(of)h(m)n(ultip)r(ole)h (metho)r(ds)f(will)g(exemplify)h(a)e(general)g(trend.)41 b(As)30 b(time)f(go)r(es)f(b)n(y)-7 b(,)300 3687 y(large-scale)22 b(n)n(umerical)h(computations)h(rely)g(more)g(on)g(appro)n(ximate)f (algorithms,)g(ev)n(en)h(for)g(prob-)300 3803 y(lems)j(that)h(migh)n(t) f(in)h(principle)f(b)r(e)h(solv)n(ed)e(exactly)h(in)h(a)f(\014nite)h(n) n(um)n(b)r(er)f(of)g(steps.)37 b(Appro)n(ximate)300 3919 y(algorithms)26 b(are)h(more)g(robust)g(than)g(exact)g(ones,)g(and)h (they)g(are)e(also)h(often)h(faster.)300 4133 y Fh(8.)77 b(Br)l(e)l(akthr)l(oughs)40 b(wil)t(l)f(have)h(o)l(c)l(curr)l(e)l(d)e (in)g(matrix)g(pr)l(e)l(c)l(onditioners,)43 b(sp)l(e)l(ctr)l(al)38 b(metho)l(ds,)j(and)433 4250 y(time)30 b(stepping)g(for)h(p)l(artial)g (di\013er)l(ential)g(e)l(quations.)466 4406 y Fg(It)20 b(is)f(hard)f(not)h(to)g(b)r(e)h(optimistic)f(ab)r(out)h(merely)e(tec)n (hnical)h(h)n(urdles.)33 b(The)20 b(business)e(of)i(matrix)300 4523 y(preconditioners)26 b(is)i(vitally)f(imp)r(ortan)n(t,)h(but)g(it) h(is)e(a)h(jungle)g(these)g(da)n(ys|surely)e(impro)n(v)n(emen)n(ts)300 4639 y(are)20 b(in)i(store!)41 b(Sp)r(ectral)21 b(metho)r(ds)g(for)g (PDEs)g(are)f(in)h(a)g(similar)f(state|remark)-5 b(ably)20 b(p)r(o)n(w)n(erful,)h(but)300 4755 y(v)-5 b(arying)30 b(a)n(wkw)n(ardly)e(from)i(one)h(application)f(to)g(the)i(next.)46 b(Order)30 b(is)g(needed)h(here,)g(and)g(it)g(will)300 4871 y(come.)36 b(As)25 b(for)g(time-stepping,)h(this)f(is)g(the)h(old) f(problems)f(of)i(sti\013ness,)f(reasonably)f(w)n(ell)h(in)g(hand)300 4988 y(for)g(ODEs)g(but)i(still)f(unsolv)n(ed)e(in)i(a)g(general)e(w)n (a)n(y)h(for)g(PDEs.)35 b(T)-7 b(o)26 b(this)g(da)n(y)-7 b(,)25 b(the)h(CFL)g(restriction)300 5104 y(constrains)37 b(our)h(computations)g(all)h(across)d(the)j(range)f(of)g(science)h(and) f(engineering.)69 b(T)-7 b(o)38 b(get)300 5220 y(around)31 b(this)i(constrain)n(t,)g(time)g(steps)f(are)f(tak)n(en)h(smaller)g (than)g(w)n(e)g(w)n(ould)g(wish,)i(h)n(uge)e(matrix)1869 5419 y(5)p eop %%Page: 6 6 6 5 bop 300 263 a Fg(problems)26 b(are)g(solv)n(ed)g(at)h(great)e (cost,)i(and)g(ph)n(ysically)e(imp)r(ortan)n(t)i(terms)g(are)e(thro)n (wn)i(a)n(w)n(a)n(y)d(just)300 379 y(b)r(ecause)e(they)i(are)d(to)r(o)i (hard)f(to)h(implemen)n(t.)36 b(The)23 b(CFL)g(condition)g(will)g(not)g (disapp)r(ear,)g(but)g(new)300 495 y(w)n(eap)r(ons)k(will)g(b)r(e)h (devised)g(to)f(help)h(us)g(in)f(the)h(da)n(y-to-da)n(y)e(struggle)g (against)g(it.)300 710 y Fh(9.)60 b(The)31 b(dr)l(e)l(am)f(of)h(se)l (amless)f(inter)l(op)l(er)l(ability)i(wil)t(l)f(have)g(b)l(e)l(en)e (achieve)l(d.)466 869 y Fg(Users)h(and)g(onlo)r(ok)n(ers)e(complain)i (y)n(ear)f(after)i(y)n(ear,)e(wh)n(y)h(is)h(so)f(m)n(uc)n(h)g(h)n(uman) g(in)n(terv)n(en)n(tion)300 985 y(needed)i(to)g(get)g(from)g(the)g (whiteb)r(oard)g(to)g(the)g(solution?)50 b(Wh)n(y)32 b(do)r(es)g(one)f(computer)h(program)300 1101 y(ha)n(v)n(e)25 b(to)h(b)r(e)g(written)g(for)g(the)g(grid)f(generator,)g(another)g(for) g(the)h(discretisation,)g(and)g(another)f(for)300 1218 y(the)i(linear)e(algebra,)g(requiring)g(in)n(terfaces)g(all)h(along)f (the)h(w)n(a)n(y)f(with)i(rep)r(eated)f(opp)r(ortunities)g(for)300 1334 y(h)n(uman)32 b(error?)49 b(Wh)n(y)33 b(are)e(sym)n(b)r(olic)h (and)g(n)n(umerical)f(calculations)h(separate?)49 b(Wh)n(y)33 b(can't)f(our)300 1450 y(ideas)i(and)h(to)r(ols)f(blend)h(together)f (in)n(to)g(a)h(seamless)e(in)n(terop)r(erable)g(system?)59 b(W)-7 b(ell,)37 b(of)d(course,)300 1566 y(they)26 b(can,)g(and)f (getting)h(there)f(is)h(merely)f(an)g(engineering)g(problem.)36 b(Fift)n(y)26 b(y)n(ears)e(from)h(no)n(w,)h(the)300 1682 y(grids)33 b(and)h(the)h(solv)n(ers)d(will)j(ha)n(v)n(e)e(b)r(een)i (coupled|and)e(h)n(umans)h(will)h(more)e(and)h(more)g(rarely)300 1799 y(catc)n(h)27 b(sigh)n(t)g(of)h(actual)f(n)n(um)n(b)r(ers)g(in)h (the)g(course)e(of)i(doing)f(science.)300 2014 y Fh(10.)69 b(The)41 b(pr)l(oblem)f(of)h(massively)g(p)l(ar)l(al)t(lel)h(c)l (omputing)d(wil)t(l)i(have)g(b)l(e)l(en)e(blown)i(op)l(en)f(by)g(ide)l (as)483 2130 y(r)l(elate)l(d)30 b(to)g(the)g(human)f(br)l(ain.)466 2288 y Fg(The)k(information)f(rev)n(olution)g(is)h(w)n(ell)g(underw)n (a)n(y)-7 b(,)33 b(but)g(the)h(rev)n(olution)d(in)j(understanding)300 2404 y(the)28 b(h)n(uman)f(brain)g(has)g(not)h(arriv)n(ed)e(y)n(et.)37 b(Some)27 b(k)n(ey)g(idea)g(is)h(missing.)466 2529 y(Another)34 b(fact)h(of)f(scien)n(ti\014c)g(life)h(is)f(that)g(the)h(problem)f(of)g (massiv)n(ely)f(parallel)g(computing)300 2646 y(is)g(stalled.)52 b(F)-7 b(or)32 b(decades)g(it)h(has)g(seemed)f(plain)h(that)g(ev)n(en)n (tually)-7 b(,)33 b(serial)f(computers)g(m)n(ust)h(run)300 2762 y(up)h(against)f(the)h(constrain)n(ts)f(of)h(the)g(sp)r(eed)g(of)g (ligh)n(t)g(and)g(the)g(size)f(of)h(atoms,)h(at)f(whic)n(h)g(p)r(oin)n (t)300 2878 y(further)24 b(increases)e(in)i(p)r(o)n(w)n(er)f(m)n(ust)h (come)f(ab)r(out)h(through)f(parallelism.)35 b(Y)-7 b(et)24 b(parallel)f(computing)300 2994 y(no)n(w)n(ada)n(ys)h(is)i(a)g(clumsy)g (business,)g(b)r(ogged)g(do)n(wn)g(in)g(comm)n(unication)g(problems,)g (no)n(where)f(near)300 3111 y(as)i(adv)-5 b(anced)27 b(as)g(ev)n(ery)n(one)e(exp)r(ected)j(a)g(decade)f(ago.)466 3235 y(I)40 b(b)r(eliev)n(e)f(that)h(the)g(dream)e(of)i(parallel)e (computing)h(will)h(b)r(e)g(ful\014lled.)73 b(And)40 b(it)g(is)g(hard)300 3352 y(to)33 b(a)n(v)n(oid)f(the)h(though)n(t)g (that)g(if)h(parallel)e(computing)h(and)f(the)i(h)n(uman)f(brain)f(are) g(b)r(oth)i(on)f(the)300 3468 y(agenda,)23 b(the)h(t)n(w)n(o)f(rev)n (olutions)f(in)i(store)e(will)i(someho)n(w)e(b)r(e)i(link)n(ed.)36 b(Brain)22 b(researc)n(hers)f(will)j(mak)n(e)300 3584 y(disco)n(v)n(eries)d(that)i(transform)e(our)h(metho)r(ds)h(of)g (parallel)f(computing;)i(or)e(computer)g(scien)n(tists)h(will)300 3700 y(mak)n(e)h(disco)n(v)n(eries)e(that)j(unlo)r(c)n(k)f(the)g (secrets)g(of)g(the)h(brain;)g(or,)f(just)h(as)f(lik)n(ely)-7 b(,)25 b(the)g(t)n(w)n(o)e(\014elds)i(will)300 3817 y(c)n(hange)k(in)i (tandem,)h(p)r(erhaps)e(during)g(an)h(astonishing)e(ten)i(y)n(ears)e (of)i(uphea)n(v)-5 b(al.)45 b(The)31 b(uphea)n(v)-5 b(al)300 3933 y(could)24 b(b)r(egin)h(tomorro)n(w,)e(or)g(it)i(migh)n(t)f(tak)n (e)g(another)g(generation,)f(but)i(it)g(will)g(come)f(b)r(efore)g (2050.)466 4058 y(Mean)n(while,)29 b(another)g(rev)n(olution)f(in)h (biology)f(is)h(already)f(happ)r(ening:)i(the)f(w)n(orking)f(out)h(of) 300 4174 y(DNA/RNA)g(genomes)d(and)h(their)g(implications.)37 b(Ev)n(ery)25 b(organism)h(from)h(virus)g(to)g(man)g(is)g(sp)r(ec-)300 4290 y(i\014ed)i(b)n(y)f(a)g(program)f(written)i(in)g(the)g(alphab)r (et)f(of)h(the)g(n)n(ucleotides.)39 b(Since)29 b(W)-7 b(atson)29 b(and)f(Cric)n(k,)300 4406 y(w)n(e)k(ha)n(v)n(e)f(kno)n(wn)g (this)h(m)n(ust)g(b)r(e)h(true,)g(and)f(in)g(1995,)f(the)i(\014rst)f (genome)f(of)h(a)f(free-standing)g(or-)300 4523 y(ganism)c(w)n(as)f (sequenced.)36 b(Since)28 b(then,)g(dozens)f(more)f(ha)n(v)n(e)h(follo) n(w)n(ed,)f(with)i(the)g(h)n(uman)f(genome)300 4639 y(itself)g(no)n(w)f (nearly)f(complete,)i(and)f(ev)n(erything)f(in)i(biology)-7 b(,)25 b(from)i(dev)n(elopmen)n(t)e(to)i(drug)e(design,)300 4755 y(is)37 b(b)r(eing)g(rein)n(v)n(en)n(ted)e(as)i(w)n(e)f(w)n(atc)n (h.)64 b(If)37 b(I)g(giv)n(e)f(y)n(ou)g(the)h(sequence)f Fb(KPSGCGEQNMINFYPNV)o(L)31 b Fg(in)300 4871 y(the)38 b(standard)e(co)r(de)h(for)g(the)g(amino)g(acids,)i(this)e(is)g(enough) g(for)g(y)n(ou)f(to)h(determine)h(in)f(a)g(few)300 4988 y(seconds)30 b(that)i(I)f(am)f(sp)r(eaking)h(of)g(an)f Ff(\013)p Fg(-macroglobulin)g(proteinase)g(inhibitor)h(of)g Fh(Octopus)h(vul-)300 5104 y(garis)p Fg(,)37 b(and)d(to)g(lo)r(cate)g (related)g(enzymes)g(in)g(ten)h(other)f(sp)r(ecies.)56 b(Just)34 b(p)r(oin)n(t)h(y)n(our)e(bro)n(wser)f(to)300 5220 y Fb(http://www.ncbi.)o(nlm)o(.n)o(ih)o(.go)o(v)22 b Fg(and)27 b(run)g Fh(blastp)p Fg(.)1869 5419 y(6)p eop %%Page: 7 7 7 6 bop 466 263 a Fg(I)28 b(b)r(eliev)n(e)f(that)h(this)g(drama)e(has)h (implications)h(for)f(computing.)300 469 y Fh(11.)39 b(Our)29 b(metho)l(ds)h(of)g(pr)l(o)l(gr)l(amming)g(wil)t(l)h(have)g(b) l(e)l(en)e(blown)h(op)l(en)g(by)g(ide)l(as)g(r)l(elate)l(d)g(to)f (genomes)483 585 y(and)h(natur)l(al)f(sele)l(ction.)466 727 y Fg(Genetic)f(programs)d(and)j(computer)f(programs)f(are)g (strangely)h(analogous.)34 b(Both)28 b(are)e(abso-)300 843 y(lutely)k(precise)f(digital)g(co)r(des,)h(and)g(no)f(other)g(co)r (des)h(that)g(w)n(e)f(kno)n(w)g(of)h(ha)n(v)n(e)e(an)n(ything)h(lik)n (e)h(the)300 959 y(complexit)n(y)18 b(of)h(these)g(t)n(w)n(o,)h(with)g (the)f(size)g(of)g(a)f(genome)g(b)r(eing)h(of)g(roughly)f(the)h(same)g (order)e(of)i(mag-)300 1075 y(nitude)24 b(\(3)10 b Fa(\002)g Fg(10)797 1045 y Fe(9)857 1075 y Fg(n)n(ucleotides)23 b(for)g Fh(Homo)k(sapiens)7 b Fg(\))25 b(as)e(the)h(size)f(of)g(an)h (op)r(erating)e(system)i(\(2)10 b Fa(\002)g Fg(10)3444 1045 y Fe(9)300 1192 y Fg(bits)33 b(for)f(Windo)n(ws)h(98\).)52 b(As)32 b(a)h(generation)e(of)i(engineers)f(gro)n(ws)e(up)j(with)h (genomics,)f(thinking)300 1308 y(digitally)i(ab)r(out)h(the)g(ev)n (olution)e(of)i(life)g(on)f(earth,)i(our)e(metho)r(ds)h(of)f(computer)g (programming)300 1424 y(will)26 b(c)n(hange.)36 b(\(Some)26 b(ideas)g(in)g(this)h(direction)e(are)h(already)e(with)j(us.\))53 b(T)-7 b(raditionally)g(,)25 b(computer)300 1540 y(programs)35 b(are)h(written)h(in)g(a)g(di\013eren)n(t)g(w)n(a)n(y)f(from)h (biological)e(ones.)65 b(There's)36 b(a)h(programmer)300 1656 y(in)30 b(the)g(lo)r(op,)g(an)g(in)n(telligence,)g(whic)n(h)f(giv) n(es)g(computer)g(programs)f(a)h(logical)g(structure)g(that)h(bi-)300 1773 y(ological)j(programs)g(lac)n(k)g(\(not)j(to)e(men)n(tion)h (commen)n(ts!\).)59 b(Y)-7 b(et)35 b(it)g(is)g(notable)f(that)i(no)n(w) n(ada)n(ys,)300 1889 y(large-scale)23 b(soft)n(w)n(are)g(systems)i(are) f(to)r(o)h(big)g(to)h(b)r(e)f(understo)r(o)r(d)g(in)h(detail)f(b)n(y)g (an)n(y)g(individual,)h(let)300 2005 y(alone)33 b(mec)n(hanically)f (analysed)g(or)h(v)n(eri\014ed,)h(and)g(indeed,)h(the)f(pro)r(cess)e (of)i(industrial)f(soft)n(w)n(are)300 2121 y(design)25 b(already)g(seems)g(as)g(close)h(to)f(ev)n(olution)g(b)n(y)h(natural)f (selection)g(as)h(to)f(mathematical)h(logic.)300 2238 y(Soft)n(w)n(are)34 b(at)g(a)h(place)g(lik)n(e)f(Microsoft)g(is)h (generated)f(b)n(y)h(an)f(unending)h(pro)r(cess)f(of)h(exp)r(erimen)n (t)300 2354 y(and)30 b(test,)g(co)r(de)g(and)g(correct,)f(a)g(pro)r (cess)g(in)h(whic)n(h)g(individual)g(h)n(uman)g(in)n(telligences)f (seem)h(less)300 2470 y(imp)r(ortan)n(t)e(than)g(they)g(used)g(to.)38 b(Soft)n(w)n(are)27 b(systems)g(ev)n(olv)n(e)g(from)g(one)h(generation) f(to)g(the)i(next,)300 2586 y(and)f(they)g(are)f(nev)n(er)g(p)r (erfect,)i(but)g(they)f(w)n(ork.)37 b(The)28 b(pro)r(cess)f(is)h (repugnan)n(t)f(to)h(some)f(computer)300 2703 y(scien)n(tists,)g(but)h (it)h(is)e(scalable)f(and)i(unstoppable.)466 2819 y(Finally)-7 b(,)28 b(a)f(prediction)g(that)h(is)g(not)f(really)g(a)g(prediction,)g (just)h(a)g(pious)f(wish.)300 3025 y Fh(12.)40 b(If)30 b(we)g(start)f(thinking)h(now,)h(mayb)l(e)f(we)g(c)l(an)g(c)l(o)l(ok)h (up)e(a)h(go)l(o)l(d)h(name)f(for)h(our)e(\014eld!)1745 3266 y Fg(*)82 b(*)h(*)466 3502 y(T)-7 b(able)31 b(1)f(lists)h(some)g (highligh)n(ts)f(from)g(the)i(history)e(of)h(scien)n(ti\014c)g (computing.)46 b(Its)31 b(attempt)300 3618 y(to)h(extrap)r(olate)f(to)h (the)g(future)g(summarises)f(some)h(of)g(the)g(though)n(ts)g(I)g(ha)n (v)n(e)f(expressed)f(in)j(this)300 3734 y(essa)n(y)-7 b(.)466 3851 y(When)31 b(I)g(lo)r(ok)n(ed)f(at)h(this)g(collection)f (of)h(predictions,)h(I)e(w)n(as)g(startled)h(to)f(see)h(that)g(a)g (theme)300 3967 y(emerges)19 b(from)i(them.)35 b(Some)21 b(are)e(what)i(one)f(migh)n(t)h(call)f(purely)h(tec)n(hnical.)34 b(The)21 b(others,)g(ho)n(w)n(ev)n(er,)300 4083 y(those)27 b(mark)n(ed)g(b)n(y)g(asterisks,)f(suggest)h(a)g(trend:)1077 4298 y Fh(Human)i(b)l(eings)h(wil)t(l)h(b)l(e)f(r)l(emove)l(d)h(fr)l (om)f(the)g(lo)l(op.)673 b Fg(\()p Fa(\003)p Fg(\))466 4490 y(I)25 b(\014nd)h(I)g(ha)n(v)n(e)e(en)n(visioned)g(an)i (unsettling)f(future,)h(a)f(future)h(in)g(whic)n(h)f(h)n(umans,)h (though)f(still)300 4606 y(the)k(taskmasters)e(of)i(computers,)g(are)e (no)i(longer)f(m)n(uc)n(h)g(in)n(v)n(olv)n(ed)g(in)h(the)g(details)f (of)h(getting)g(the)300 4722 y(tasks)i(done.)47 b(Fift)n(y)32 b(y)n(ears)e(from)h(no)n(w,)h(it)g(is)f(hard)f(to)i(imagine)f(that)g (our)g(mac)n(hines)f(will)i(still)g(b)r(e)300 4839 y(dim)25 b(enough)f(to)h(b)r(ene\014t)h(m)n(uc)n(h)e(from)h(our)e(assistance.)35 b(Sk)n(etc)n(h)24 b(y)n(our)g(needs)h(to)f(the)h(mac)n(hine,)g(and)300 4955 y(then|w)n(ell,)j(y)n(ou)f(migh)n(t)g(as)g(w)n(ell)h(go)e(ha)n(v)n (e)h(a)g(cup)h(of)f(co\013ee.)466 5071 y(That's)g(m)n(y)h(rep)r(ort)f (from)g(2000,)f(do)n(wn)h(here)g(on)g(the)h(exp)r(onen)n(tial.)1869 5419 y(7)p eop %%Page: 8 8 8 7 bop 300 266 3181 4 v 300 365 a Fg(T)-7 b(able)23 b(1.)35 b(Some)23 b(past)g(and)g(future)g(dev)n(elopmen)n(ts)f(in)i (scien)n(ti\014c)f(computing.)35 b(The)23 b(asterisks)f(mark)300 482 y(items)28 b(summarised)f(b)n(y)g(\()p Fa(\003)p Fg(\).)466 679 y Fh(Befor)l(e)k(1940)466 795 y Fg(Newton's)d(metho)r(d) 466 911 y(Gaussian)f(elimination)466 1027 y(Gauss)g(quadrature)466 1143 y(least-squares)e(\014tting)466 1260 y(Adams)j(and)f(Runge{Kutta)g (form)n(ulas)466 1376 y(Ric)n(hardson)f(extrap)r(olation)466 1552 y Fh(1940{1970)466 1668 y Fg(\015oating)h(p)r(oin)n(t)h (arithmetic)466 1785 y(F)-7 b(ortran)466 1901 y(\014nite)28 b(di\013erences)466 2017 y(\014nite)g(elemen)n(ts)466 2133 y(simplex)g(algorithm)466 2250 y(Mon)n(te)f(Carlo)466 2366 y(orthogonal)e(linear)i(algebra)466 2482 y(splines)466 2598 y(FFT)466 2775 y Fh(1970{2000)466 2891 y Fg(quasi-Newton)g (iterations)466 3007 y(adaptivit)n(y)466 3123 y(sti\013)h(ODE)f(solv)n (ers)466 3239 y(soft)n(w)n(are)f(libraries)466 3356 y(Matlab)466 3472 y(m)n(ultigrid)466 3588 y(sparse)g(and)i(iterativ)n(e)e(linear)h (algebra)466 3704 y(sp)r(ectral)g(metho)r(ds)466 3821 y(in)n(terior)f(p)r(oin)n(t)i(metho)r(ds)466 3937 y(w)n(a)n(v)n(elets) 466 4113 y Fh(2000{2048)466 4229 y Fg(linear)f(algebra)f(in)i Ff(O)r Fg(\()p Ff(N)1258 4199 y Fe(2+)p Fd(\017)1382 4229 y Fg(\))g(\015ops)466 4346 y(m)n(ultip)r(ole)g(metho)r(ds)466 4462 y(breakthroughs)e(in)h(preconditioners,)g(sp)r(ectral)g(metho)r (ds,)g(time)i(stepping)e(for)g(PDE)400 4578 y(*)d(sp)r(eec)n(h)j(and)h (graphics)e(ev)n(erywhere)400 4694 y(*)e(fully)k(in)n(telligen)n(t,)g (adaptiv)n(e)e(n)n(umerics)400 4810 y(*)e(loss)j(of)g(determinism)400 4927 y(*)d(seamless)j(in)n(terop)r(erabilit)n(y)400 5043 y(*)d(massiv)n(ely)i(parallel)h(computing)g(made)h(p)r(ossible)f(b)n(y) g(ideas)g(related)g(to)h(the)g(h)n(uman)f(brain)400 5159 y(*)d(new)k(programming)d(metho)r(ds)j(made)f(p)r(ossible)h(b)n(y)f (ideas)g(related)g(to)g(natural)g(selection)p 300 5220 V 1869 5419 a(8)p eop %%Trailer end userdict /end-hook known{end-hook}if %%EOF