Knuth meets NTG members

12 Pages·1997·0.2 MB·English

BijlageN KnuthmeetsNTGmembers 38
Knuth meets NTG members
March 13th, 1996
Abstract
OnJanuary6th1996,KeesvanderLaaninformedtheNTGthatDonaldKnuthwouldbeinHollandinMarch.
KnuthwasinvitedbytheMathematischCentrum(MC,nowadayscalledCentrumvoorWiskundeenInfor-
matica,CWI)becauseofCWI’s50thanniversary. BothKnuthandMandelbrotwereinvitedasspeakersat
thecelebration.
TheNTGnoticedthatthiswasanexceptionaloccasiontoorganizeaspecialmeetingwithKnuthforallDutch
TEXandMETAFONTuserswhowouldliketomeettheGrandWizardhimself.
FortunatelyKnuthacceptedtheNTGinvitationandsoameetingwasorganizedin‘DeRodeHoed’inAm-
sterdamonMarch13th. About35peoplefromalloverthecountryandevenfromBelgiumjoinedtomeet
Knuth.
EverythingwasrecordedonbothvideoandaudiotapebyGerardvanNes. ChristinaThielevolunteeredto
writethistranscript.
ErikFrambach: Welcome,everyone. Thisisaveryspe- questions-and-answersto try to keep me honest, because
cialmeetingon theoccasionthatMr. DonaldKnuthisin theyalsodidthatinPrague. Soincasethesamequestion
Holland. TheNTGthoughtitwouldbeagoodideatotake comesup, you’llhaveto take the averageof the two an-
theopportunityandaskhimifhewouldbewillingtoan- swers.[laughter]
swerourquestionsaboutTEX,METAFONT,andanything
WietseDol: DidyouknowthatBarbaraBeetondoesthat?
elseconnectedtothethingswedowithTEX. Luckily,he
Shemailsyouandsays“Tapeeverything.”
hasagreed. SoweareveryhappytowelcomeMr.Donald
Knuthhere—thankyouforcoming.
Knuth: Yes,that’swhattheysaidinPraguetoo![laugh-
Tonightwehavetimetoaskhimanyquestionsthatwehave ter]Ithinkshe’sdesperateforthingstodo,ormaybeshe
longbeenwaitingtoposetohim[laughter]. I’msurethat justhasalotofquestions. ButbeforeIopenquestions,let
allofyouhavemany,manyquestionsthatyouwouldlike mesaythatoneofthemostinterestingquestionsaskedme
theGrandWizard’sopinionabout. So,wecouldstartnow in Praguewas after the session. And I wish it would get
withquestions. into[therecord].Thequestionwas: howdidImeetDuane
Bibby,whodidtheillustrationsforTheTEXbookandThe
METAFONTbook? Ialwayswantedpeopletoknowabout
thatsomehow.
Here’s the story. I had the idea that after writing math
books for many years, I wanted to have a book that had
moreweird—well,anyway,different—illustrationsinit.
HereI waswritinga bookaboutbooks—bookshaveil-
lustrations,sowhyshouldn’tIhaveillustrationstoo. So,I
wrotetoanartistcalledEdwardGorey.Doesanyoneknow
...
FransGoddijn: Yup.Amphigorey. Beautiful.
Knuth: Yes, Edward Gorey. Amphigorey. He makes
very morbid drawings but with a wonderfulsense of hu-
mor. I hadusedseveralofhisbookswith mychildren. I
DonaldE. Knuth: I getto ask questionstoo! [laughter] thoughthewouldbeanaturalperson. Iwrotehimtwolet-
LastSaturdayIwasinPragueandtheCzechoslovakTEX ters but he never responded. Then I wrote to a Japanese
usershadasessionsomethinglikethisandyou’llbeglad artistcalledAnno,MatsumasaAnno,whoisreallythelogi-
toknowthatIsawquiteafewcopiesof4TEXCD-ROMs calsuccessortoEscher. [...]AnodoeswhatEscherdidbut
atthatmeeting. incolor,soIaskedhimifhewoulddoit. Hesentmeback
aniceletter,saying“I’msorryIdon’thavetimebecauseI
It’snotmyfirsttimeinAmsterdam.IwasinAmsterdamin
havesomanyothercommitments,butherearefiveofmy
1961,soit’sonlybeen35years,andprobablylessthan35
yearstillthenexttime. Iguessthey’retaperecordingthese
BijlageN KnuthmeetsNTGmembers 39
booksfullofpicturesandifyouwanttouseanyofthose, takethetimetodoagood,carefuljobwithit, thenaswe
goahead.” Iwantedpersonalizedpictures. learnmoreabouttypesetting,itwillhappenthatsomething
elsewillcomealong.IpersonallyhopethatIwon’thaveto
ThenIwenttoapartyatStanfordwheretherewasalady
taketimetolearnanewsystem,becauseIhaveenoughfor
who worked for a publisher. She’d just met a brilliant
myownneeds. ButIcertainlyneverintendedthatmysys-
youngartistwhoshe’djustworkedwith. Iinvitedhimto
temwouldbetheonlytoolthatanybodywouldeverneed
cometo my house, and we spentsometimetogetherand
fortypesetting. ItriedtomakeitasgeneralasIcouldwith
he’sawonderfulperson. Duanelivesnowupinnorthern
areasonablysmallprogram,andwithwhatweknewand
California,about4hours’drivefrommyhouse,soIonly
understood about typesetting at the time. So these other
wentupthereoncetoseehim. Hesometimescomesdown
projects— I don’tconsiderthatthey’rea threatto meor
totheSanFranciscoareaonbusiness. Firstwediscussed
anything. I hopethattherewillbe somecompatibilityso
thebookandthenhesentmeabunchofdrawingsandall
that—Imean,I’dliketobeimmortal—sothatthebooks
kindsof sketchesthathe had. Originally,TEXwas going
I’vewrittennowcouldstillbetypeset50yearsfromnow
tobeaRoman,andhedrewthismaninatogawitholive
withouthavingtogothroughthefilesandeditstuff. Ilike
branchesinhishead—whichiswhythelionhastheolive
thearchivaland machine-independentaspects of TEX es-
branchesnow.Butallofasuddenhestarteddoingsketches
pecially,andItriedtosetamodel,aminimumstandardof
of his cat, which really seemed to click, and pretty soon
excellenceforotherpeopletofollow.
hehadadraftofall35orwhateverdrawings,usingalion.
Mostofthoseeventuallybecomethedrawingsinthebook, HansHagen: butwhenyoulookinthefuture,...youcon-
andweadjustedhalfadozenoftheothers. WhenIwentto sidertoday’sprogrammingbyalotofpeopleasanart,well
visitupathishouse,I gottomeetTEXthecat. Helooks alotofarttakeshundredofyearstoberecognizedasart. In
verymuchliketheoneyouseeinthebook. Sothat’sthe aboutahundredyearstherewillbeprettydifferentcomput-
storyaboutDuaneBibby. ers,theprogramminglanguageswillbechanged,themedia
onwhichweputallthosethingswillbechanged.Realpro-
Erik: Thank you. Who would like to start with the first
gramsandeverythingrelatedtothem,willtheyeverhave
question? Pleaseidentifyyourselfwhenyouaskone.
achancetobecomeimmortal,asyouseeit?
Piet vanOostrum: Mynameis Pietvan Oostrum. You
Knuth: Didyoustateyourname?[laughter]
havethiswonderfullionontheTEXbookandthelionness
ontheTheMETAFONTbook. Whataboutbabylions? HansHagen: I’mHansHagen.
Knuth: Oh, I see ... [laughter]. Duane still does illus- Knuth: You’resayingthatit’sprettyarrogantofustoas-
trationsforspecialoccasions. He’smadeillustrationsfor sumethatwhatwedonowwilllastat all. Technologyis
theJapanesetranslationofboththeTEXbookandtheThe changingsofastthatwehaveabsolutelynoideawhatpeo-
METAFONTbook. HehasTEXandMETAbothdressedup ple are going to think of next. One hundred years ago,
inJapanesecostumes. Sonow,iftherehappenstobesome physicists were saying there was nothing more to do in
kind of an offspring that would come out of some other physics, except to get another decimal — a fifth decimal
user, then, I imagine he would glad to help do it. But it placeforthefundamentalconstants—andthenthatwould
wouldprobablybealittlebitofanillegitimatechild,from wrapupphysics. So,thereisnowaytoknowaboutthese
my point of view [laughter]. I mean, I wouldn’ttake re- things. ButIdobelievethatoncewehavethingsinelec-
sponsibilityforanythingthosecharactersdo[laughter]. tronicformandwehavemirrorsitesofthem,thereisafair
degreeofimmortality—whereaspaperburns.
Do you know anything about this project called ‘The
Clock’, being developed by Stewart Brand and his col-
leagues?He’stheonewhopublishedtheWholeEarthCat-
alogue.Theyhaveabunchofpeoplethatareconsideringif
theycouldbuildsomethingthatwouldlastforathousand
years... Idon’twanttogoontoomuchmoreaboutthat.
IdohopethatthestabilityofTEXwillmakeitpossibleto
reproducethethingswe’redoingnow,later. Andsinceit’s
fairlyeasytodothat,Ithinkitwillhappen—unlessthere’s
a nuclear holocaust. Some mathematicians have this de-
bateaboutthePlatonicview... doeseverythingin math-
ematicsexistandwe’rejustdiscoveringit,orareweactu-
allycreatingmathematics? Insomesense,oncesomething
Piet: So what are your ideas aboutthe offspringof TEX
andMETAFONT? gets put into bits, it’s mathematics and thereforeit exists
forever,evenifthehumanracediesout—it’sthere,butso
Knuth: Well,Ithinkthatnomatterwhatsystemyouhave, what?
there will be a way to improveit. If somebodywants to
Erik: Who’snext?
BijlageN KnuthmeetsNTGmembers 40
MarcvanLeeuwen: IfIcouldextendabitontheprevi- now,togettheArabicnames,IhavetouseArabTEX,toget
ousquestions. ThestabilityofTEXitself,Icouldimagine, theHebrewnames...IhadaterribletimetryingtogetHe-
mightbeastumblingblockfordevelopmentofnewthings brewfontsonCTANtwoweeksago—Icantellyouthat
exactlybecauseit’ssostableandeverybody’salreadyus- wholestoryifyouwanttoknow... Ikeptclickingonthe
ingit. Soifsomethingcomesalongthatisjustabitbetter, differentthingsandtheywouldrefertofilesthatdidn’tex-
thenpeoplewillnottendtousethatbecauseit’snotavail- istandREADMEfilesthatwerefouryearsoutofdateand
ableeverywhere,andthereareallkindsofreasonstokeep inconsistent,soIcouldn’tfindanyHebrewfonts. Maybe
onusingtheoldthing. youhaveitonyourCD...
Knuth: IguessIsaidinFloridathatpeoplearestilltrying Johannes: I could certainly point you to someone who
tousetheoldfontsthatI’mstilltryingtostampoutfrom couldhelpyouwiththeHebrewfont—Iknowsomeone
theworld.FouryearsagoIredesignedtheGreeklowercase inIsraelwho’stryingtodoHebrewsupportwithintheBa-
delta and I made the arrowheadsdarker. I didn’t change belsystem. AndtheydodotypesettinginIsraelwithTEX.
anythinginthewayTEXoperates—allthedimensionsand
Knuth: MyowntypesettingfriendinIsraelisDanBerry,
the characters’ heights and widths stay exactly the same.
who unfortunatelyis fairly committed to troff [laughter].
ButIdidtuneupalotofthecharacters. StillIseelotsof
I’m sure that I can get good Hebrew throughYannis and
math journalsarestill using theold onesfromfouryears
ago,andIgetlettersandpreprintsfrompeoplewiththeold- Omega. I sure hope UNICODE is going to arrive sooner
ratherthanlater; it’smuchbetterthanthealternativesfor
styledelta. IchangeditbecauseIjustcouldn’tstandtheold
muchthereasonsthatMarc [vanLeeuwen]mentioned. I
versions[laughter]. NowI’vegothomepages—ifIever
have some errata to TEX or something I put them there: haven’tfounda great enthusiasm in Japan for UNICODE,
becausetheyhaveasystemthatseemstoworkprettywell
http://www-cs-faculty.stanford.edu/˜knuth.
forthem,so whychange. EverytimeIask aJapanesefor
This gets to my home page, and there’s a reference say-
ing,‘ImportantnoticeforallusersofTEX’,andthatpage hisnameinUNICODE,he’llsay,‘what’sUNICODE? Here’s
says‘Lookatthelowercasedeltaandifyouhavethewrong myJISname’. ButtheJIScharactersdon’tincludetheChi-
nesecodes,andinfact,myownname—IhaveaChinese
one,youdie!’[laughter]
name— and my namein JIS isn’tquitethe same. There
Iunderstandthatpeoplehaveareluctancetochangefrom aretwodifferentUNICODEcharacters,onefortheJapanese
somethingthatthey’vebecomeaccustomedto. Iknowof versionandonefortheChinese.
two main successors to TEX: one is "-TEX and the other
isNTS."-TEXisgoingtobeapparently100%compatible Intheback? Kees?
with TEX, so if somebody doesn’t switch over to incom-
KeesvanderLaan: I havealotofquestionsofcourse.
patible features, then they have a system that still works
ButIwouldliketostartwithsomequestionsaboutMETA-
witholdthings.Thatwillallowagradualchange-over.It’ll
FONT. The first oneis: how comemacrowriting in TEX
takemorespaceonacomputer,ofcourse,butthat’snota
andMETAFONTissodifferent?
big deal these days. The people who work on "-TEX al-
wayssentmeveryreliablecommentsaboutTEXwhenthey Knuth: WhyaremacrosinTEXandMETAFONTsodif-
caughterrorsinmystuff,soIimaginethey’regoingtobe ferent? I didn’t dare make TEX as extreme as META-
doinga carefuljob. So it’ll beoneof thesethingswhere FONT.Theselanguagesareofcompletelydifferentdesign.
youwalk into a randominstallation of UNIX or whatever METAFONT is insome waysanincredibleprogramming
andyou’llfind"-TeXthereasthedefault,andyou’llstill language—it’sobject-orientedmacros. Youhavemacros
haveTEX. Then youalso havecertain otherfeaturesthat inthemiddleofrecordstructures.
mightbereallyimportanttoyouforyourspecialapplica-
ThewayIdesignedtheselanguagesisfairlysimpletode-
tions.
scribe. Let’s take TEX. I wrote down one night what I
JohannesBraams: Youmentioned"-TEXandNTS.But thoughtwouldbea goodsourcefileforTheArtofCom-
areyoualsoawareoftheOmegaproject? puterProgramming.ItookalookatVol.2,whichIhadto
typeset. I started outon the first page, andwhen I gotto
Knuth: Oh, theOmegaproject? Yes, I’mhopingto use any copythat lookedvery muchlike somethingI had al-
thatmyselffortheauthors’namesinmyTheArtofCom- ready done I skipped that. Finally I had examples of all
puterProgramming.I’vebeencollectingthenamesofChi- thedifferentkindsoftypesettingconventionsthatoccurin
nese, Japanese, Indian, Hebrew, Greek, Russian, Arabic Vol.2. Ittotalled5printedpages—andyoucanevensee
authorsandIwanttotypesettheirnamesproperly[laugh- thesepages—exactlywhatmyoriginaltestprogramwas
ter], not just in transliteration. I have some rudimentary —inapaperbyDavidFuchsandmyself,wherewetalked
softwarethatwilldothisforproofingpurposes,forgetting aboutoptimumfontcaching.1 Inthere,wegaveanexam-
mydatabasegoingandforwritingtopeopleandsaying,‘Is pleandweshowthese5pages,whichwouldillustratewhat
thisyourname?’ WiththeOmegasystem,I’mhopingthat IwantedTEXtobeabletodo. IwroteoutwhatIthought
it’llbeaccompaniedbygoodfontsthatwillmakeitpossi- Iwouldliketotype—howmyelectronicfileshouldlook.
bleformetodothiswithoutawholepileofwork. Right Andthen,Isaid,OK,that’smyinput,andhere’smyoutput
1ACMTransactionsonProgrammingLanguagesandSystems7(1985),74.
BijlageN KnuthmeetsNTGmembers 41
—howdoIgetfrominputtooutput? Andforthis,well,it system that goes beyondthebasics. I always wanted the
lookslikeIneedmacros[laughter]. systems that I would make widely available would be be
abletohandle99%ofallapplicationsthatIknew. ButIal-
SamethingforMETAFONT.Iwentthroughmyfirstdraft
waysfeltthereweregoingtobespecialapplicationswhere
of all the fonts that later became Computer Modern. I
theeasiestthingwouldbetochangetheprogram,andnot
wrote actually in SAIL, an Algol-like compiler language,
writeamacro.
butSAIL hadamacroability,soIdevelopedafewprimi-
tivemacrosinwhichIcouldsay,‘pickupthepen’,‘draw Itriedtomaketheprogramssothattheywouldhavelog-
frompoint1topoint2’,andthingslikethat. Thesemacros ical structure and it would be easy to throw in new fea-
were compiled by the SAIL compiler into machine lan- tures. This hasn’t happened anywhere near as often as I
guage, whichwouldthen drawthe letters. I wentthough thought because people were more interested, I think, in
theentirealphabet,andbytheendoftheyear,Ihadsome inter-changeability of what they do; once you have your
300littleprograms,eachonedrawingaletter. ThenIre- own program, then other people don’t have it. Still, if I
alizedwhatkindofalanguageIwouldwanttowritein,to werealargepublisher,andIweretogetspecialprojects—
describetheletters. Sooneday,onafamilycampingtrip someencyclopaedia,someneweditionoftheBible,things
— I was in the Grand Canyonwith my wife and kids — likethat— I wouldcertainly thinkthatthe rightthing to
Itookanhouroff,satunderatreeandwroteoutthepro- dowouldbeto hireagoodprogrammerand makeaspe-
gramfortheletterA,inalanguagethatIthoughtwouldbe cial computer system just for this project. At least, that
agoodalgebraiclanguage,reflectingatahighlevelwhatI wasmy ideaaboutthe way peoplewould doit. It seems
hadbeendoingwithprettyprimitivelow-levelinstructions thathasn’thappenedverymuch,althoughinBrnoImeta
inmySAILprograms.IdidtheletterB,too. CapitalAand studentwhoiswellalongonproducingAcrobatformatdi-
B,andthenwentbacktothecampingtrip. Thesesheetsof rectlyinTEX,bychangingthecode. AndtheOmegasys-
paperwhereIhavemyoriginalprogramsarenowinStan- temthatyoumentioned,that’s150,000linesofchangefiles
ford’sarchive—theprogramfortheletterBwaspublished [laughter]. IbuiltinhookssothateverytimeTEXoutputs
in a Stanford library publication calledImprintlast year. apage,itcouldcometoawhatsitnodeandawhatsitnode
Thewomanwho’sinchargeofrarebooksandmanuscript couldbesomethingthatwascompletelydifferentin each
collectionsatStanfordisquiteinterestedinMETAFONTso versionofTEX. So,whentheprogramseesawhatsitnode,
shewrotealittlearticleaboutwhattheyhave. itcallsaspecialroutinesaying,‘howdoItypesetthiswhat-
sitnode?’ It’lllookatthesub-typeandthesub-typemight
ThatprogramagainimpliedthatIwantedsomemacrosto
beanothersub-typeputinasademooritmightbeabrand-
go with it. But these neededto be muchmorestructured
newsub-type.
than themacrosof TEX. It hadto bethat whenI said, ‘z
1prime’,thiswouldactuallybeequivalentto‘(x1prime, Similarhooksarein theMETAFONT program. Ifpeople
y 1 prime)’ and I wanted to be able to write, ‘z 1 prime’ haveextratimewhenthey’renotbrowsingtheWeb[laugh-
withoutanydelimiters. Itturnedoutthatinordertohave ter],Irecommendasagreatrecreationtoreadtheprogram
a high-levellanguagethat would feel naturalto me writ- for METAFONT. Some parts of it are pretty rough going
ingtheprogram,it hadto lookcompletelydifferentfrom andIhopethatnobodyeverfindsabugtherebecauseI’d
TEX. SoTEXandMETAFONTshareacommonformatfor hatetohaveto lookatthem[laughter]. Butthosearethe
errormessagesandcertainotherdatastructuresinside,but rasterizationroutines,thethingsthatactuallyfillinthepix-
otherwise,they’requitedifferentsystemsbecause,inorder els. Therearemanyotherthingsinthatprogram—thelin-
to have a good high-levellanguage, I don’twant to have earequationsolverthatithasandthedatastructureabilities
towastetimewritingparentheses,brackets,commas,and ...lotsofbeautifulalgorithmsareinthere—totakesquare
otherdelimiters. rootsinfixedpoint,andtheintersectionoftwocurves,and
soon. METAFONTisfulloflittleprogramsthatweregreat
Kees: It’s a nice introduction to my second question
fun to write and that I think are useful and interesting in
[laughter]:ForthefutureofMetaPost,whichallowsmark-
theirownright. IthinkwhenJohnHobbywroteMetaPost,
upofpictures,with.epsastheresult,whatisyouratti-
heenjoyedit,becausehecouldaddhisownnicelittlepro-
tudeto2.5dforMetaPostandMETAFONT?Forexample,
gramstotheonesthatarealreadythere.
addingatripleasananalogyofthepaireddatastructure?
I’mabigfanofMetaPostfortechnicalillustrations.Idon’t
Knuth: MetaPost alreadyhas a datastructurefortriples knowanythingthat’snearasgood,soI’mdoingalltheil-
becauseofcolor. SoRGBareactuallytriplesofnumbers. lustrationsofTheArtofComputerProgramminginMeta-
Post. Also, the technicalpapersI’vewrittenaregoingto
Kees: Yes,butthetripleasadatapointinspace?
be published in a series of eight volumes by Cambridge
Knuth: Ah,Isee. IdidwriteMETAFONTinawaythat UniversityPress, andalltheillustrations, exceptthepho-
tographs,aregoingtobeMetaPosted. Thefirstvolumeof
hashooksinitsothatitcanbeeasilyextended;[forexam-
theseeightwasthebook,LiterateProgramming;thesec-
ple], ifyouwantto draw3-dimensionalpictures,forper-
ondvolumeis going to come outthis summer and is go-
spectiveandprojectivegeometryinsteadofaffinegeome-
try. TheprogramitselfforMETAFONTwaswrittensothat ingto becalledSelectedPapersinComputerScience. It
reprintsadozenor15papersthatIwroteforgeneralaudi-
itcouldeasilybechangedbypeoplewhowantedtohavea
BijlageN KnuthmeetsNTGmembers 42
ences, notforspecialists in computerscience, butinSci- ingthecomputerinterpolate. Themultiplemasterfontsin
entificAmericanorSciencemagazineandthingslikethat. PostScript allow up to four parameters, and almost all of
Thethirdvolumewillbeaboutdigitaltypography,andit’ll themhaveonlyoneortwoparameters. ThemostIknow
reprintallmy articlesinTUGboatand thingsaboutTEX. of is two; probablyothers have goneall the way to four.
Whatdoyouthink,bytheway—shouldIpublishinthat Butthentheyhavetoprovidedrawingsforalltheextreme
thirdvolumethememothatIwrotetomyselfthefirstnight, pointsoftheseparameters.
whenIdesignedTEX? Iputitinacomputerfileandit’sin
In spite of this limited use of parameters, what’s avail-
thearchives,butI’venevershownittoanyone. [roundof
ablecommerciallyis quite beautiful, as far as readability
“ofcourse!” and“sure”andlaughterfromtheaudience].
isconcerned,althoughitdoesn’treallyprovidethequality
Maybeit’dsellmorebooks[morelaughter].
thatyou guyshad in the Netherlandsin the 17thcentury.
FransGoddijn: Youneedtoputitonyourhomepageand What’stheman’sname,thegreatpunchcutteratEnschede´
wecanthendecide— — he made 4.5, 5pt up to 16pt, and each letter was de-
signedforitssize,andfontshadaniceuniformappearance.
Knuth: No, no. That way we’d never sell the books Thiswouldn’thavehappenedatallwith theType1fonts.
[laughter]. Not that I’m a mercenary type of person, of There were two guys who did most of the punch cutting
course. It’sinafilecalledTEX—well‘teks’, actually. I forEnschede´andothersinthe18thcentury: Oneofthem,
havetoadmitIpronouncedit‘teks’foramonthortwo— Fleischman, was a genius for really beautiful letters; the
Iwasthinkingof‘technicaltexts’,though.tex.onewas other,Rosart,wasjustgoodatmakinglotsandlotsoflet-
thenameofthefileanditwouldmakeinterestingreading ters[laughter].2 [...] Theywerefun. Rosartwouldmake
probably,someday. allkindsofhighlydecoratedalphabetsandthingslikethat.
I have a big coffee-tablebook that gives examples of all
Andyournameis?
thefontsfromEnschede´,whichwastranslatedintoEnglish
JanKardan: InthiscompanyIwillprobablyaskavery byMatthewCarter’sfather. Anyways,inthisbook,Type-
hereticquestion, but a little heresy makesa lot of fun — foundriesintheNetherlands, you can look atthese type-
talkingaboutMETAFONT.Thereareprobablymanytype facesandweep.3
foundries now [that] crank out lots of good-qualityfonts
Still,onalaserprinter,wegetprettygoodfontsnow,and
andkerningtables.It’snotclearwhetherPostScriptorTrue
therefore it looks like there won’t be that many profes-
Typewillsurvive. DoyouthinkthatMETAFONTwillsur- sional type designers using METAFONT. Pandora was a
vivetextfonts? Nottalkingaboutthemathfonts. gooddesignbyagenuinegraphicartist. METAFONThas
Knuth: Idon’tthinktheextracapabilitiesofMETAFONT turned out to be wonderful for making ordered designs
andspecial-purposethingsforgeometry.There’snowthis
haveprovedtobenecessaryforgood-qualitytypefonts,al-
really neat system in Poland where they have TEX and
though I think that you can still make better-quality type
METAFONT in a closed loop — TEX outputs something
fontswithit. Designersfinditdifficulttothinkasacom-
andthenMETAFONT drawsacharacterandif thatdoes-
puter person does, in the sense that when people in the
n’tfit,TEXsays,‘gobackandtryitagain’. Jackowskiand
computerbusinessautomatesomething,tryingtomakethe
Ryc´kounderstandTEXandMETAFONT,andtheprograms
computerdosomething,it’snaturalforustohaveparam-
arewelldocumentedandcandothesethings. SoMetafont
eters and say that we’re going to try to solve more than
isn’tgoingtodisappearforthatreason;butit’snevergoing
oneproblem. Wetrytosolveawholevarietyofproblems
tobetaughtinhighschool.
basedontheparametersthatpeopleset. Butit’smucheas-
ier if people gave us only a single problem with a single
parameter, then we could have the computers do exactly
theprescribedthing. Computerscientistshavebecomeac-
customedtothinkingofhowwewouldchangebehavioras
conditionschange, butdesignersaren’tat all accustomed
tothis. Theyaremuchhappierifthebosssaysonemonth,
“Givemearomanfont,”andthenextmonth,“Givemea
boldfont.”It’smuchmoredifficulttosay,“Showmehow
youwoulddrawsomethingnomatterhowheavyIwantthe
letters to be.” METAFONT provides a way to solve that
problemandtodrawcharacterswithparameters,butit’sa
raredesignerwho’scomfortablewiththatnotion.Theycan
domultiplemasterfontsbymakingmultipledrawingsand
then matching up points between the drawings and hav-
2JohannMichaelFleischman,1701–1768;Jacques-Fran¸coisRosart,1714–1777.
3TypefoundriesintheNetherlandsfromtheFifteenthtotheNineteenthCenturies,byCharlesEnschede´,translatedbyHarryCarter
(Haarlem: StichtingMuseumEnschede´, 1978), 477pp. Thismagnificentbookwascomposedbyhandandprintedbyletterpressto
commemoratethe275thanniversaryofJoh.Enschede´enZonen.
BijlageN KnuthmeetsNTGmembers 43
FransGoddijn: MynameisFransGoddijnandIhaveone makeitmoregeneralandsoon. ButIdidwantatoolfor
questionwithsomesub-questions[laughter];I’dliketoask myselfby whichI couldproducebooksthatwouldmake
the sub-questions first. What I’m wondering — and this mefeelgoodafterspendingalmostallmylifewritingthose
mayhavebeenaskedoftenbefore—iswhetheryouwould books.
consider,inretrospect,whatyouhavecreated[tobe]anart
IstartedwritingTheArtofComputerProgrammingwhen
oratool? AndthereasonIaskis—whenIhearyouspeak
Iwas24yearsoldandIstillhave20yearsofworktodoon
withsomuchpassionfortypefontsandthebeautifulalgo-
it. That’salotoftime. Idon’twanttowritethosebooksif
rithmsthatyouputintoMETAFONTthatyouwouldliketo
they’regoingtocomeoutlookingawful. Iwantedaway
pointpeopletoandtherecognitionthatyougetfrompeo-
tomakeitpossible[toproducegood-lookingbooks].Orig-
plewhounderstandthat—but,thereisavastmajorityof
inally, whencomputersstarted out, they knewonlynum-
users who just got TEX from some server, never realized
bers,digits. The19th-centurycomputerscouldprinttables.
whocreatedit,anduseittotypesetnotalwaysverypretty
Thenwehadcomputersthatcoulddonumbersandletters,
documents[laughter].Theydothatinaverycrudewayand
butonlyonateletypemachine;soyouhadsomecapitallet-
don’tcareless. YoufrozeTEXatacertainpoint,allowing
tersanda32-characterset. Butthen,afterIgraduatedfrom
otherpeopletobuildaroundit. Iwaswonderinghowsuch
college,wegot... letmesee,Iwasprobablytenyearsout
athingwouldfeeltoafather—areyoufatherofapiece
ofcollegebeforewecoulddolowercaselettersonacom-
ofartthatotherpeopleuseasatool,orisitachildthatyou
puter. Youknow,thePASCALlanguage,whenitcameout,
havefrozeninitsdevelopment,thatwillnevergrowup...
it used all uppercase letters — there was never any con-
therearesomanyquestions...ifyoujustgobacktotheart
siderationthat therewouldbemorethan 64charactersin
vs.toolidea,andyourfeelingsaboutthat.
acomputer’srepertoire. Finally,wewerebeginningtosee
Knuth: Obviously, if I write somethingthat hasa lot of inthemiddle70sthatcomputerscouldactuallydolower-
powertodomanydifferentthings,it’llbepossibletomake caseletters,andproducesomethingthatlookedalittlebit
it do awful things. I just came from the Rijksmuseum, readable,alittlebitlikebooks. Wow![laughter].
wheretheyhaveanexhibitcalled“TheAgeofUgliness”. Thentherewasthisdevelopmentoftypographicsoftware
It was a wholebunchof fancy silver bowls fromthe late starting at MIT in 1960 and going through 4 or 5 gener-
19thcentury.... Whenyousayanart, I’mnotsureIun- ations, leading to troff and EQN, where there was even
derstandexactlywhatyoumean. Tome,artisusedintwo mathematics being typeset. In 1977 I therefore knew an
quitedifferentsenses,mostoftennowadaysinthesenseof existence theorem: It was possible to typeset something
fineart,whileart,originally,Kunst,wasanythingthatwas thatlookedalmostlikegoodmathematics. EQNwasbeing
not natural — so we have the word artificial, something usedinphysicsjournalsandexperienceshowedthatsecre-
that is made by people instead of by nature. The Greek tariescouldlearnhowtodoit. SoIthought,“Whynotgo
wordis techne[laughter]. Butthen youreferto atoolas all the way to the end, to convergence?” What I wanted
somethingthatismaybejustadevicethatisthefastestway todowithTEXwasnottobealittlerefinementovertroff
togetfromheretotherebutmaybeyoudon’tcareaboutel- and the other things, but I was saying now, “Let me try
egance... ButwhatIthinkyoumeanwhenyoutalkabout togotothebesttypographythat’severbeenachievedby
artistheaesthetics—somethingaboutbeautyandsome- mankind”Exceptfortheilluminatedgoldleaftypeoflet-
thingwithalittlebitofloveinit. WithTEX,myideawas tering, I wanted to at least — when it came to black and
tomakeitpossibletoproduceworksthatyouareproudof; whiteprinting—I wantedto matchthe bestconventions
Iassumedthatpeoplecanenjoyactuallyspendingalittle that had been achieved. Computer typesetting had gone
extratimemakingtheresultsbetter. Ididn’texpectthatthe throughthislengthydevelopment,gettingalittlebetterand
wholeworldwouldbedoingthis[laughter]. alittlebetter. Itwastimetosay,“Well,let’sjumptotheend
Incidentally, I can’t understandthe mentality of a person now.” Of course, I didn’tthink this would be an activity
who writes graffiti on a beautifulbuildingalthoughI can thateverybodywouldwanttodo. Buttherewereenough
see why drawing is fun. Why would you want to scrawl peoplethat would care abouttrying to get as much qual-
something — some kind of animal instinct of territory ityaspossible,thattheycouldbe—well,that’swhyIfi-
mightaccountfor it, I suppose, but it’s really impossible nallymadeTEXmoreavailable. TheAmericanMathSo-
formetoconceiveofsuchactions. cietywerethefirstpeople,nearlythefirstpeoplewhocon-
vinced me that I should make the system do more than I
When it comes to matters of aesthetics, you can’t dictate
originallyintended.
taste. You can’t say that your idea of beauty is going to
matchanyoneelse’sideaofbeauty. ButIdidwanttohave AndriesLenstra: Whydidn’tyoustartfromtroff? Itwas
a tool where we could reach the highest levels of beauty completelyinappropriate?
accordingtoourowntastes. Ididn’tallowpeopletohave
Knuth: Yes,yes. Yousee,troff waspatchedontopof...
letterspacingveryeasily,butItriedtomakeeverythingelse
Imean,therewasawholesystem,itwasafifthgeneration,
easy[laughter]. .... Ofcourse,IoriginallydesignedTEX
eachofwhichwasapatchonanotherone. Soitwastime
justformyself, forTheArtofComputerProgramming;I
to scrap it and start all over again: “Here’s what the lan-
thoughtmysecretaryandIweregoingtobetheonlyusers.
guageshouldbe,solet’sdesignsomegooddatastructures
Anditwasn’tuntillaterthatIwasconvincedthatIshould
BijlageN KnuthmeetsNTGmembers 44
forit.” Not“Let’strytobecompatible.” Ihadtheadvan- wholefieldofartificialintelligencehasbeenoneofthear-
tagethatIwasnotatBellLabs,whereIwouldn’tbehurt- easthathashadgreatestspin-offstocomputersciencebe-
inganybody’sfeelingsbysaying,“Let’sthrowitallaway” causethey’vetriedtosolveveryhardproblems.Especially
[laughter].ItwasimpossibleforthepeopleatBellLabsto in theearly days, they came up with methodsthat turned
dosuchathing—itwouldn’tbenice. Butitoccurredto outtobeusefulinmanyotherpartsofcomputerscience.
methatnowthatwehadproofthatthisgoalwaspossible,I So,it’smyfeelingthatwhenpeopleareworkingonmore
shouldstartover,andrethinkhowIcouldgetfrominputto ambitiousgoals,theydeveloppowerfultechniquesthatof-
output,sotheprogramcouldbemuchmoreunified,much ten have very relevant spin-offs. Even so, after they’ve
smaller, and would also work. I mean, troff was collaps- solved that problem, they’regoing to think of something
ingallthetime. AlotoftheearliestusersofTEXhadbeen elsewhichwillbeanotherrefinementandsoon—they’ll
frustratedbytroff breakingoverandoveragain,soithad neverhaveasituationwherethey’regoingtoautomatically
gottenunwieldy.Butithadalsoprovedthattherewaslight createthemostbeautifuldocument. There’sgoingtobea
attheendofthetunnel. timewhenyoucanlookattheoutputandseethatyoucan
stillimproveit. Designersofthemostautomaticsystems
IalsohadtoscrapTEX,youknow,andstartoveragain;af-
would be well advised to at least still leave a chance for
terfiveyears,Idecidedthatitwouldbebesttogobackand
somebodyto movesomething up and down and fake out
re-do the program. But it would have been very hard to
theirautomaticalgorithm.
dothatif my friendin the nextofficehaddoneit[laugh-
ter]. So, I just have this philosophythat therewill beal- ThephilosophythatIhadwhenIdidTEXwasthatIwould
wayssomepeoplewhoaremoreinterestedinqualitythan trytohaveasystemthatdid99%ofeverythingautomati-
others,andIwantedtomakeTEXgoodforthem. Idon’t cally,andthenIwouldlookatwhatremainedandIwould
seeanygoodwaytomakeitimpossibletomakeabaddoc- kludgetherest. Butkludgingitisonewaytosayit;another
ument,unlessyouhaveonlyasystemwith asmallmenu wayofsayingitis“Tidyuptherest,” or“Dotthei’sand
ofoptions;that’sgoodforalargeclassofusers,tomakea cross the t’s.” My feeling is that this non-automaticpart
systemthat’ssosimplethatyoucan’tpossibledoanything givesmealittleextrapridethatIhaveputthespitandpol-
uglyinit. ishonthefinalproduct,thatIknowIdidit. Ifitoccursa
lot,thenit’sanuisanceandI’mwastingtime. ButifIcan
Erik: Ithinkit’stimeforacoffeebreaknow—we’lltake
reallylimitthisto 1%—if I’vespent30hourswritinga
fiveortenminutes.
paperandittakesmeonlyanother15minutestocleanup,
thenI’mhappytodoanother15minutesattheend. It’sa
smalllittleextrathatgivesmeachancetocelebratethefact
Knuth: Johannes,youhadaquestionthatyouhadtoask,
thatI’vefinishedthepaper.
solet’sgetthatoverwith[laughter].
ThespacingthatTEXdoesworstrightnow,inmyexperi-
Johannes Braams: It’s abouttypesetting. What is your
ence,iswithrespecttosquarerootsignsbeingalittletoo
opinion about the skyline model of typesetting? In TEX, tight,withtheoperandeithertooclosetotheradicalsign
you talk aboutboxes: each letter is inside a box, and we
ortooclosetothebarlineorboth;IfindthatI’mmostof-
glueboxestogethertoaline,andthelineitselfisinsidea
ten fiddlingwith that. I’veadoptedin the bookConcrete
box,andeachlineisviewedasaboxandtheboxesarefit-
MathandalsoinTheArtofComputerProgrammingnow,
tedtogethertoformaparagraph.Theskylinemodeltriesto
theconventionwhereinthemathformulaIputan@-sign
goalittlebitfurtherthantherigidboxandline,andtriesto
where I want one math unit of extra space. The @-sign
takeintoaccountthatsomeofthedescendersintheupper
isthendefinedtohaveamathcodeofhexadecimal8000,
lineandthehighpartsin thelowerlinedon’toverlap,so
whichmeansthatthiswillinvokeinmathmodeandthe@-
thatyoucouldactuallyhavelinesmuchtightertogether—
sign will beregardedas a macro thatadds onemath unit
especiallyinmathtypesetting,thatcouldbeanadvantage.
ofspace. SoI’lltype‘squarerootof’‘@-sign’‘logofn’
[laughter],becauseotherwisethespacebefore‘el’isalittle
Knuth: Hmmm,Iguessyou’retalkingaboutgeneralprin-
bittootight. Nowmaybeeventhisskylinemodelwouldn’t
ciplesofcomputergraphicswhereyouhaverectanglesin-
knowthat‘el’wastootight,maybeitwould. Butit’scases
side a picture, instead of having the rectangles grouped
likethat...
onlyinsideofarectangle....Thiscertainlywouldbeama-
jorchangeinallthedatastructuresofTEX. Youcouldgoto Themostcommoncase reallyis whereI havesomething
aquadtreestructureorsomethinglikethat. Allthethings like ‘x squared over 3’, where you have a simple super-
thatpeopleusetosolvehidden-lineproblemsanddoren- scriptandthenaslash,andthenthedenominator. There’s
dering, to find out what’s in frontof something else, and almostalwaystoomuchspacebeforetheslash. Andthisis
allthealgorithmstheyusetomakemovieslikeToyStory. true,Ifind,inallthebooksthatIusedtothinkweretype-
Itwouldbemostvaluable,Iimagine,forcatchingunusual setperfectlybyhand[laughter],butnowI’msensitiveto
casesinmathformulas. this. Now I go through, typically with emacs, and look
foralloccurrencesofsomethingwithaone-characterexpo-
Ihavetwofeelingsaboutthesethings. OneisthatIliketo
nentfollowedbyaslash,andmostofthoselookbetterwith
seepeopleextendingthethingsthatcomputerscandoau-
tomatically.Peoplelearnalotwhentheytrytodothis. The
BijlageN KnuthmeetsNTGmembers 45
anegativethinspacebeforetheslash. ItwouldbenicerifI forthings,andoneofthethingswetrytoavoidinmathe-
didn’thavetodothat. Butstill,it’sasmallthingforme. maticsisdoublesubscripts. IreadoneFrenchPhDthesis
wheretheauthorhadfivelevelsofsubscripts[laughter]—
Wouldtheskylinemodelhelpmemuch? SometimesIrun
hekeptpaintinghimselfintoatrap. Hestartedoutwitha
into cases where I’ll add another word to the answer to
setx throughx ,sothenwhenhetalkedofasubset,ithad
anexerciseinordertoavoidaclashbetweenlines. Here, 1 n
tobexsub-i throughxsub-i ,andthenhewantedtotalk
the lines are actually notgetting spread apart too far, but 1 k
ofasubsetofthis,sothenhehadatheoremthatsays,leta
they’resoclosetogetherthatthe‘subscriptkless-than-or-
sub-bsub-c... andsoon[laughter]. Itrytochoosenota-
equalton’willclashwithaleftparenthesisinthenextline.
tionsthatgivemetheeconomyofthoughtatahighlevel.
AndIdon’twantthetypetobequitesoclosetogetherthere.
Now,ifIhadbeensmarter,Iwouldhavedesignedmy(cid:20)- That’s why I probably didn’t believe in a great deal of
signtohaveadiagonalstrokeunderthe<insteadofahor- mark-upintheTEXbook;Iwouldbegintypewritertypeand
izontalbar, and I wouldn’thavehad thoseclashes— too endtypewritertypeforsectionsbysaing\beginttand
lateforthatnow.[laughter] \endtt. IwouldalsodelimitthelinesandwhenI’mpre-
sentingpartsoftheplainTEXmacros,\beginlinesand
Kees?
\endlines—thosemacrosareinthefile,sinceit’svery
Kees: May I ask you a question about your attitude to importanttometoseehowthatworks. Butinothercases,
mark-upingeneral?Andletmeillustrateitbyfirsttellinga I’ve left [things] as simple as possible, for me to see vi-
story. WhenwestartedwithusingTEXetc.,wemeanactu- suallythebeginningandendofstuff. It’ssomethingalso
allywestartwithLATEX—Imean,thatistheeffectinHol- likeproblemsolving—sometimes,ifI’vesolvedaprob-
land. AndthenIlookedattheproductsofthemark-upand lemandI’mnotworriedaboutitanymore,Iforgettotell
Ididnotlikeit. AndthenIwaswondering,whatisyour anybodyelsethe solution. I wasalwaysaverybadcom-
attitudeto that? I’m sorry to say so, I paged throughthe mitteechairmanbecauseI’mnotverygoodatfinishingthat
TEXbookfiletexbook.texandIlookedatallthethings last endingline, I guess. Still, withhtml, thedocument
inthereandthenIthought,“Well,Ihavesomeideaofwhat wasshortandIdecidedthatmyhomepagesweregoingto
yourideasareofmark-up.”Andwhenyouexplainedabout beusedbymanydifferentkindsofbrowsingsoftwaresoI
METAFONT and all those thingsnot in there, which you hadbetterbeveryrigorous.
haveimplicit—amIwrongifIsummarizethis,thatyou
WhileI was developingTEX, I attendedoneof themeet-
adheretosomethinglikeminimalmark-up?
ingsofthecommitteethatdesignedSGMLandhadavery
gooddiscussionwithCharlieGoldfarbandtheotherpeo-
Knuth: Yes. Forexample,whenIamreadingEdsgerDi-
pleonthecommittee—weonlyhadthatonemeetingnear
jkstra’sbooks, everytime I getto a section whereit says
Stanford. CertainlyIappreciatethefactthatthisstructure
‘Endof Comment’, it strikes me as redundant. And I al-
makesitpossibletobuildotherkindsofprogramsaround
waysthink,“Oh,yes,thisisEdsger’sstyle.” WhenIwrote
what you have. The more structure you have in a docu-
apaperforhis60thbirthday,Isaidattheend,“Acknowl-
ment,theeasieritistomakeadatabasethatincludesthings
edgment,IwanttothankEdsgerforsuch-and-such,”and
aboutit,andknowswhat’sgoingon. Ineverobjectedtoit;
‘EndofAcknowledgment’[laughter].4 Butthat’stheonly
Ijustalwaysfeltthatinordertomaximizemyefficiency,I
timeinmylifeI’lleverdothat. MaybeI’manillogicalper-
didn’twanttomessaroundwithfullmark-upunlessIhad
son,butapparentlyhalfthepeopleusinghtmlnowtype
to.
only thep at the beginningof a paragraph,and theother
half type only a /p at the end of a paragraph [laughter].
X: SGML allows minimizations; that’s why the end-
Hardlyanybodyusesboth,accordingtowhatmyspiestell
paragraph is not necessary. So that’s one of the reasons
me. AndIdon’tknowwhattheheckthesesystemsactu-
whyit’ssodifficultsometimes. Youhaveaformalization
allydowiththeunbracketedmaterial. WhenIwritehtml,
tominimize.
I’mscrupulouswithmymark-up. Ifyoulookatmyhome
pages — I’ll pay you $2.56 if you find any case where I Knuth: ButLATEXdoesn’tallowit.
started somethinganddidn’tcloseit with therighttag. I
Johannes: Butwedohavesomebooks,however,permit-
tried to be very careful in that, and to indent everything
verywell,andsoon. ButIfounditaterriblenuisance,be- tingomittedend-tagsinLATEX3,butthat’snotfarenough
along.
causeit’snotthewayIthink.
I think a high-level language, to me, is something that Knuth: Well,talktohim[laughter].Idon’tneedaspecial
shouldreflectitsstructureinsomevisualwaybutnotnec- editorforhtml—peoplearehypingfancythingswhere
essarily explicitly; so that, whenI knowtheconventions, youcanclickonatoolandit’llputinthestartandendtag
we can suppress some things. Parentheses are one such together—butwhenIwrotemyfiles,Ididmakeupasim-
conventionandmathematicsgota lotbetter whenpeople pleemacsmacrothatwouldtakewhatevertagIjusttyped
inventedothernotationslikeoperatorprecedencethatwe andcreatetheend-tag. Allithadtodowassearchbacktill
canseestructurewithoutspellingitoutintoomuchdetail. itfoundaless-thansignandthencopythatstringtwiceand
A mathematicianspends a lot of time choosing notations
4BeautyisOurBusiness(Springer,1990),242.
BijlageN KnuthmeetsNTGmembers 46
putaslashinfrontofit,soIusedthatallthetime—itwas theolddays,IwouldhavechangedtheplainTEXmacros
easy. sothatitwouldnotusetheheightoftheminussigninthe
\rightarrowfilloperator[...]6 Anyways,I’venow
Johannes: Quite different type of question now, from
toldyouthereasonwhyit’stherefortheotherones.
someonewho’dliketoaskhere: literally,hewrites,“Why
is theheightof theminussign in the cm symbolfontthe Johannes: Anotherquestion,whichisaboutmultiplelan-
sameastheheightofthecmrplussign?” guages. There’saproblemwhenyouhaveoneparagraph
whereyouhavedifferentlanguages.
Knuth: Ah. Alotofpeoplearewonderingaboutthatone.
Where youhave‘a minusc’ or yousay ‘x sub minus’or Knuth: Yes,the\lccodechanges. Thisisthe...
something,whyis itthatthe heightanddeptharegreater
Johannes: And I’vebeen told thatinside oneparagraph
than the actualshape of the minussign?. In fact, it’s not
just the plus and minus, it’s also the C, −, (cid:6), (cid:7), (cid:8), (cid:9), youcanonlyuseonehyphenationtable,whichistheone
⊗,(cid:11),(cid:2)and(cid:4)—ifyoulookatthecodeforthese,there whichisactiveattheendoftheparagraph. So,switching
hyphenationtablesinsideparagraphs. Suppose,forexam-
isabeginarithcharmacrothatbeginsallofthearithmetic
ple,youhaveaparagraphwithEnglishtext,withaGerman
charactersinthefont,guaranteeingthattheywillhavethe
quoteinsideit,theGermanquotebeingseverallineslong.
samesize.
Johannes: Butitdoesn’tsaywhy. Knuth: IknowthatTEXwillproperlykeeptrackofwhich
hyphenation table to use. The glitch, the mistake, that
Knuth: That’sright—itdoesn’tsaywhy.Andthereason I didn’t anticipate is if the two languages have different
\lccode mappings — so that each has a differentidea
isthatearlyon,Iwantedcertainthingstolineupthesame.
ofwhichcharactersarelowercase. Whenyouhyphenate,
Forexample,ifyouhad
youneedtohyphenateanuppercasewordthesameasan
p p
x C y C x − y; lowercaseword,soTEXusesthe\lccodeofacharacter
toconverteveryletterintothelowercasecodeofthatlet-
ter. Ididn’tanticipatethatpeoplemight,fordifferentlan-
Iwantedthesquarerootsignstobeplaceinthesameway.
guages,havea differentmappingfromuppercasetolow-
Otherwise,youwouldget
ercase. Andsoit’sthatmappingthat,attheendofapara-
p p
x C y C x − y: graph, applies to all the languagesin the paragraph. But
otherwise, TEX is careful to keep track of what language
[slightlyexageratedheretoshowthepoint]Andsothere youhave.
are many other cases where you have formulas where Andbytheway,there’safilecalledtex82.bug. Goto
there’saplussigninonepartofaformulaandaminussign the CTAN archives, and find subdirectory /knuth, and
intheotherpart,andforconsistencyofspacing,itoughtto underthat/errata,andthat’swherethisis. Attheendof
looksymmetrical. Thereareothercases, I readilyadmit, tex82.bugthisparticularerrorabout\lccodeismen-
whereyouhaveonlyaminussign—youneverhaveasim- tionedasbeingsomethingthat’sanoversightthat’stoolate
ilarthingwithaplussign,andyouwonderwhythere’sex- tofix.
traspaceleftthere. SoIsay\smash minus[laughter]
inthosecases. MarcvanLeeuwen: Why is it too lateto fix? It would
conflictwithotherthings?
Johannes: The particular application, why this question
wasasked—MichaelDownesfromtheAMS— Knuth: Yes. Sothatpeoplearealreadyusingthesethings
inlotsofdocuments,andit’sveryhardtochange.Infact,I
Knuth: Yes, Michael Downes, he has more experience don’tseeanywaytofixit[laughter].Iwouldsaythatwhen
thananyofusinthisroom;he’sthechieftypesetterofmost youarefacedwithasituationwhereyou’redoingmultiple
ofthemathematicsintheworld. languageswithmultiple\lccodes,thisisagoodreason
towriteyourownversionofTEX.
Johannes: He hasaproblemproperlyattachingasuper-
scriptontopofthe\rightarrowfill... Andries Lenstra: Could I ask a question? Happily
enough, I’m not the first person to mention LATEX, so I
Knuth: The \rightarrowfill? OK ... The
may mentionit now. There’sa situation that often arises
\rightarrowfillis this thing that makes a rightar-
when people try to write a PhD thesis where they want
row of any desired length, and then he wants to put a
tochangeLATEXcodebecausetheythinkthey knowbet-
superscript on this. What’s the macro for building that
ter about things of beauty or typography, and unhappily
up? Ihaven’tusedthatpageinalong... [laughter]5 The
enoughtheyarenotexpertsonLATEX, so theydon’tsuc-
\rightarrowfill is made up of minus signs and so
ceedortheysucceedbadly. Ingeneral,peoplewhoknow
probablyif I hadknownMichael... knownaboutthatin
5Knuthwastryingtoremember\buildrel;seeTheTEXbook,p.437.
6Infact,the\leftarrowfilland\rightarrowfillmacrosnowomittheheightanddepthoftheminus,inplain.tex
version3.14159(March1995).
BijlageN KnuthmeetsNTGmembers 47
abouttypographycan’twritebeautifulLATEXcodeorother andifnot,wouldyouthinkofgivingitabetterprogram-
formsofcode,andviceversa—peoplewhoknowhowto minglanguage?
write these forms of code, are no experts on typography.
Knuth: InsomesenseIputinmanyoftheprogramming
Whatdoyouthinkoftheendeavorsinthepasttobringthe
featureskickingandscreaming,andI’lltrytoexplainthe
two worlds together, for instance, as Victor Eijkhout has
triedtodowithhislollipopformat,amachinetocreate background.IknowhowLesliewentaboutwritingLATEX
— first he wouldwrite the algorithmsoutin a high-level
otherformats. Iwouldhavethoughtthatitwouldhavehad
programminglanguage,withwhile’sandif-then’sandso
abigsuccessbuttheoppositeseemstobethetruth. What
on, andthen he wouldpretty muchmechanicallyconvert
doyouthinkofit?
thistoTEXmacros. IfIhadsuspectedthatsuchastylewas
Knuth: I’m notfamiliar with thedetailsoflollipop. goingtobethemostcommonuseofTEX,Iprobablywould
IsupposethatwasbasedonafamousquotationfromAlan haveworried a lot in thosedays. Now, computersare so
Perlis,whosaidthat,“Ifsomebodytellsyouthathewantsa fastthatIdon’tworrysomuchabouttherunningtime,be-
programminglanguagewhichwillonlydotherightthing, causeitstillseemstogozip!
givehimalollipop.”
Inthe70s,Ihadanegativereactiontosystemsthattriedto
Andries: Yes. beallthingstoallpeople. EverysystemIlookedathadits
ownuniversalTuringmachinebuiltintoitsomehow,and
Knuth: I’m sure that the lollipop effort was instructive everybody’s was a little different from everybody else’s.
andworthwhile,butIdon’tknowthedetailssoIcan’tan- SoIthought,“Well,I’mnotgoingtodesignaprogramming
swer in great detail on this. Probably the type designers language; I wanted to have just a typesetting language.”
didn’tfindthelanguageeasytolearn. Idothinkthatwe’re Littlebylittle,Ineededmorefeaturesandsotheprogram-
having much more communication now, as every month mingconstructsgrew. GuySteelebeganlobbyingformore
goesby,betweenthepeoplethatknowabouttypeandthe capabilitiesearly on, and I putmanysuch thingsinto the
peoplethatknowaboutmacros. It’sjustamatteroftime secondversionofTEX,TEX82,becauseofhisurging.That
as we wait for these waves to continuemoving — we’re madeitpossibletocalculateprimenumbersaswellasdo
nowherenearaconvergentstage, whereTEXhasreached complicatedthingswithpagelayoutandfigureplacements.
its natural boundaryand the type designershave reached ButthereasonIdidn’tintroduceprogrammingfeaturesat
their naturalboundary. They’restill movingtowardeach firstwasbecause,asa programmer,Iwastired ofhaving
other. Idon’tthinkit’slikeahyperbolicgeometry,where to learn ten different almost-the-same programming lan-
theyneverwillgettogether. guagesforeverysystemIlookedat;Iwasgoingtotryto
avoidthat. Later, I realised that it was sort of inevitable,
ThemaindifficultyofcourseisthatTEXisfree, andsoa
butI triedtokeepitascloseto theparadigmofTEXasa
lot of people will say, “Well, how could it be any good,
character-by-charactermacrolanguageasIcould.AsIsaid
ifyou’renotchargingmoneyforit?” Alotofthepeople
before,Iwasexpectingthatthereallyspecialapplications
in the typedesign communitywouldonly workin things
wouldbedonebychangingthingsinthemachinelanguage
wherethere’smoneybehindit;moneyprovestothemthat
code. But peopledidn’tdo that, they wanted to putlow-
it’s worth talkingto people. So it justtakes alittle while
levelthingsinatahigherlevel.
till they see some goodexamples, which will makethem
moreopenforthesediscussions. Andthat’shappeningall
Piet: Whatdoyouthink,forexample,ofsomethinglike
thetimeindifferentcountries.
buildinginaprogramminglanguagewhichis,fromasoft-
In the Czech RepublicI was quite delighted to learn that wareengineeringpointofview,easiertouse?
thenewencyclopaediainCzech,whichisthefirstonefor
Knuth: Itwouldbeniceiftherewereawell-understood
manyyears,isbeingdonewithTEX. Andnotonlythat,it’s
standardforaninterpretiveprogramminglanguageinside
beingdonewithaveryhighbudget. Theymadethisdeci-
ofanarbitraryapplication. Takeregularexpressions—I
sionbecausetheytriedalltheothersystemsandweredis-
defineUNIX as“30definitionsofregularexpressionsliv-
gustedwiththem. TheyhadgoodresultswithTEX. Many
ing under oneroof.”[laughter]Every part of UNIX has a
othercommercialpublishersareusingittoobecausethey
slightly different regular expression. Now, if there were
talktotheirfriendsatthebigpublishinghouses. Thiswill,
auniversalsimpleinterpretivelanguagethatwascommon
Ithink,besolvedwithtime. Andproductslikelollipop
toothersystems,naturallyIwouldhavelatchedontothat
areveryworthwhileinthemeanwhiletofacilitatethis. It
rightaway.
takestimetobringdifferentcommunitiestogether. Ithink
thefinancialfactorisdefinitiveforalotofpeople. Piet: The Free Software Foundation is trying to do that
andSunistryingtodoitandMicrosoftistryingto...
PietvanOostrum: Idon’tknowifyouhaveeverlooked
into theLATEX codeinside, butif youlookintothat, you Knuth: TheFreeSoftwareFoundationistryingactually
gettheimpressionthatTEXisnotthemostappropriatepro- toincludealsothesolutionsofSunandMicrosoft. Inother
gramminglanguagetodesignsuchalargesystem. Didyou words,tomakealloftheconventionsworksimultaneously
everthinkofTEXbeingusedtoprogramsuchlargesystems asmuchaspossible. Andthatconflictswithmyownstyle,
whereI’vetriedtohaveunityratherthandiversity...Idid-