Rotman zero semiotics.odt

8/11/2019 Rotman zero semiotics.odt

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Rotman zero semiotics

But Lear makes this domestic relation into a fnancial transaction, orce ullyinserting it into a system o mercantile exchange.

Seeking to commodi y love, or raise, he destroys it.

!he anti"ty e o #ordelia here is $dmund

%nfnity

R. & '. (il)ourn

'd %nfnitum* !he +host in !uring s -achine !aking +od out o -athematicsand /utting the Body Back in* 'n $ssay in #or oreal Semiotics0. By BrianRotman. Stan ord* Stan ord 1niversity /ress. 2334. 564 . %SB7 6"869:"5258"3.

!here is a conce t ;hich corru ts and u sets all others. % re er not to $vil,;hose limited realm is that o ethics< % re er to the infnite.

" Borges, ='vatars o the !ortoise=

7ote* !hroughout this revie; article, the term =elli sis= is re resented )y =...= instead o a character resem)ling a rounded u side"do;n caret sym)ol,due to the restrictions im osed )y internet rogramming.

%nfnity lies at one extremity o >estern and, some ;ould say, $astern0thought, one end o a meta horical line ;hich, in con ormity ;ith the non"$uclidean geometry o consciousness, )ends )ack u on itsel , its endsa earing to converge in a meeting o radical negativity and limitlessmagnitude, )eyond s ace and time.

%n the midst o his demystifcation o modernity as secularized eschatology,?ans Blumen)erg ackno;ledges that the )est evidence or it is +iordano

Bruno s a lication o the attri)ute o infnity to the ;orld Blumen)erg238@* :30. !his is not to say that the ;orld or the universe had never )een


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conceived in these terms )e ore< /lato, or one, ascri)es a conditionalinfnitude to the universe in the !imaeus section 480. 1nder the #hristianityo the Renaissance, infnity ;as the last attri)ute le t to +od, )esides )eing.% infnity migrated rom +od to the ;orld ;hen the ormer ;ithdre; romthe latter or ;hen +od ;as denied )eing as ;ell0, then no; that ;e nolonger hold the universe to )e infnite, ;here does this attri)ute resideA %nother ;ords, in ;hat disci lines or discourses does infnity still have a laceor er orm some unctionA -athematics, or one. %n his frst )ook " Signi ying7othing* !he Semiotics o ero 238:0, ;hich le t oC ;here his ne; one)egins " Brian Rotman recounted the crucial signifcance o zero in thehistory o calculation. ero, o course, has t;o distinct unctions innumerical terms* it is, on the one hand, oint o origin and telos, and on theother, a lace"holder that also aCects the value o adDacent numerals,des ite the act that it has no numerical value in itsel Rotman 238:* 250.

!he resence o infnity in classically conceived mathematics is tied to that

o zero, ;hich had a eared in the >est )y the t;el th century in the ormo the ?indu"'ra)ic sign, ;hich is also the root o ci her. Rotmanmaintained that =the mathematical infnite ;as the ruit o the mathematicalnothing* it is only )y virtue o zero that infnity comes to )e signifa)le inmathematics Rotman 238:* :20. But ;here theology and, more recently,meta hysics, ;ere dis laced as authoritative discursive systems in the ost"medieval eriod, mathematics has retained an authoritative status, not least)ecause, in addition to ;hat $instein some;hat acetiously called its

a)solute truth and indis uta)ility giving to =the exact sciences a measureo confdence ;hich they could not other;ise attain= ERosen eld 2388* 429F0,

mathematics in its instrumental unction undergirds the technological andcommercial ;orld that most eo le inha)it Rotman 2334* 2920. +enerallys eaking, rom a late"t;entieth century vantage oint, infnity is in nodanger o vanishing rom the contem orary feld o theoretical inGuiry " asituation ;hose a arent irony is su)verted )y a dee er logic.

Brian Rotman s more recent )ook, the exhaustively titled 'd %nfnitum* !he+host in !uring s -achine !aking +od out o -athematics and /utting theBody )ack in* 'n $ssay in cor oreal semiotics0 engages ;ith the ro)lem othe infnite in mathematics and semiotics. Rotman s )ook, as an essay ;itha relatively narro; set o concerns including infnity0 is a generallycoherent, o ten demanding ;ork. %n general, Rotman s systematicex loration o a ossi)le alternative to a meta hysically )ased, $uclideanmathematics raises a host o other Guestions revolving around thevenera)le ro)lem o the re resentation or signifcation o something ;hichevades reduction to the fnite materiality o this or that signifer. -ores ecifcally, Rotman s thesis is a thorough"going attem t to con ront ;hat;ould make most eo le very )ored )ut ;hich seems to make him verynervous* the ossi)ility o otentially or actually endless counting.


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!he o ening o Rotman s a)stract dra;s attention to the long"standingconnection )et;een infnity and the divine ix0, and as such introduces hisargument s rinci al element o contention* as he re eats throughout, ho;to think the infniteA >hat is meant )y the infnite in this semio"mathematical contextA ?aving introduced this oundational ro)lem,Rotman immediately shi ts a;ay rom the theo"meta hysical to themathematical and, secondarily, semiotic0 infnite, ;here it is ound at ;orkin )oth =the geometrical continuum o oints on a line and their integer")ased real num)er descri tions " t;o linked a)stractions ;hich ground all

ost"Renaissance mathematics. 'nd it is the ounding signifed, the crucialontological term, in contem orary mathematics descri tion o itsel as aninfnite hierarchy o infnite sets= ix0. !hat the o)Dect o thought is relegatedto this s ecifc context does little to alleviate the ro)lem o thinking infnity.

Rotman asks ho; a set o natural num)ers 2, 5, 4... 0 can exist, like thesym)olic order, not merely inde endently o , )ut rior to, the su)Dect ;houses them in counting x0. !his is a ro)lem )ecause o the elli sis ... 0 thatal;ays ends the exam le* ;hat Rotman calls the undamentalideogrammatic shorthand or infnity ix0. =?o;,= Rotman asks, =does infnityget to )e an exact, rigorously s ecifed mathematical o)Dect " an o)Decta)out ;hich mathematics delivers true and o)Dective kno;ledgeA= ix0. %nother ;ords, ho; does infnity, in itsel unthinka)le, get to )e thought, ;henonly a thing, )y defnition, is thinka)le can )e thought, thematized,com rehended, totalized0A !o totalize infnity as something )eyond its

resence as a sign is a logical contradiction, in that it reGuires a fnitizationo infnity, )ut then the idea o infnity is itsel a logical contradiction. Soho;, as Rotman asks, are ;e to think infnityA Rotman rightly oints out theeasily orgotten rece t that ;e =are never resented ;ith the ure idea oinfnity as such. ?o; could ;e )eA= x0. !he idea o infnity, like the idea o+od, is not a thing, ro erly s eaking. But or Rotman =)eing thought inmathematics al;ays comes ;oven into and inse ara)le rom )eing ;ritten.=%n other ;ords, it is recisely as a thing, a sign ;ord, ideogram0 thatRotman chooses to think infnity* i num)ers, )eing ;ritten, =can )euncreated, re;ritten, deconstructed, altered,= then infnity =)ecomesinse ara)le rom certain eCects o the signifer, a henomenon omathematical texts, grammar, syntax, notations, and discourse= 4@0.

Rotman rames his discussion o infnity rom the very )eginning in terms omathematics, rather than ;hat he dismisses in the o ening aragra h as=its hiloso hico"theological o)scurities and contradictions= ix0. !his ;ill

rove to )e decisive in his su)seGuent conce tualization o a non"infnitistmathematics according to a restrictive )inary logic* either infnity is allo;ed

or in all its intolera)le unendingness, or it is excluded, and the system re"cali)rated in terms o the com ortingly ositive ground o the counting


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su)Dect s )odily limited, mortal, fnite0 resence. Hor Rotman, =the Guestiono reinstating the )ody EisF all" ervasive and crucially im ortant= 2:3 n. :0.

Rotman s ocus as he resolutely maintains0, is on the mathematical conce t" even the infnite itsel " as ;ritten * =!hinking in mathematics is al;aysthrough, )y means o , in relation to the mani ulation o inscri tions.-athematics is at the same time a lay o imagination and a discourse o;ritten sym)ols= x0. ?e then osits that =the Guestion o the mathematicalinfnite= )e osed =as a Guestion o language, as art o an overall study othe nature and ractice o mathematical signs " as art, that is, o asemiotics o mathematics= x0.

%n develo ing this semiotics Rotman renounces a = hiloso hical critiGue othe meta hysical system, the ram ant /latonism, that threads its ;aythrough the contem orary inter retation o mathematics= xi0. Rather, heengages in a critiGue o ;hat seems to him =an altogether more su)tlemeta hysical rinci le that ermeates the entire su)Dect=* =the rinci le oad infnitum continuationI inse ara)le rom the mathematical community s;holesale acce tance o the vie; that the num)ers are natural, and its

ailure to ask the Guestion o ;here these num)ers could ossi)ly havecome rom= xi0. !he Guestion o the mathematical infnite is thus rom thestart tied to the Guestion o counting and there ore to the Guestion ;ho

countsA < that is, the Guestion o a mathematical su)Dect. Rotman sinvestigation o infnity is inextrica)ly )ound u ;ith a concern or thecounting su)Dect, the one ;ho is aced ;ith the ros ect o otentiallyendless counting so succinctly ex ressed in that ideogram I . But Rotman sGuestion a)out thinking the infnite does not disa ear so easily, sinceeven the ans;er o thinking via the ;ritten still im lies someone orsomething doing the thinking. Rotman s reiterated concern ;ith reinstatingthe )ody in mathematics cannot dis el the insistence o consciousness inany discussion o infnity. %t emerges that this rhetoric o the )ody is ameans o roviding conce tual or even cognitive limits to an other;iselimitless discussion< i.e. everything cor oreal is fnite and there ore limitedand kno;a)le tem orality, im lying change and mortality, are or themoment unmentioned0. %n other ;ords, to em hasize the centrality oconsciousness " o the counting su)Dect as mind rather than )ody " ;ould )eto contaminate the investigation o one instance o radical unkno;a)ility

the mathematical infnite0 ;ith another, assuming the resence inconsciousness o a constitutive and irreduci)le negative dimension ;hetherfgured as the unconscious or other;ise0. 7evertheless, the Guestion o themathematical su)Dect s relative sel "consciousness ;ill rove to )eunavoida)le.


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!he three elements in the title o the a)stract, =+od, 7um)er, !he Body,=are resented in ascending order o im ortance to Rotman s thesis. ?ereturns, to )egin ;ith, to the to ic )rieJy )roached at the outset* theinsistence that is to say, the unavoida)ility0 o +od in any discussion oinfnity " a to ic that a ears to cause Rotman anxiety i only )ecause he

eels it distracts rom the real and rational matter at hand* a )ody")asedmathematics. =E%sF there not in the very idea o their endlessness , theircontinuation ad infnitum , something strange and other a)out the ;holenum)ers, the im rint or trace o some disem)odied transcendent maker,

erha sA= 40. Rotman rovides a )rie overvie; o the history omathematical thought 40, highlighting moments o crisis, ;hen =theGuestion o the infniteI ushed itsel to the oreground.= ?ere heem hasizes the 'ristotelian distinction =)et;een a sa e and legitimate

otential infnite, and endless coming into )eing, and a dangerous, aradox"in ested com leted or actual infnite= 90. !his distinction ;ill rove to )e o

more than historical signifcance to the su)seGuent develo ment oRotman s argument. Rotman considers the otential infnite to )e the onlyconce tion o infnity that can )e =cognized as meaning ul andmathematically inter reta)le= 990.

's in the history o hiloso hy, mathematical thought emerges out o thet;o maDor systems o 'ristotle and /lato, and modern mathematics is stillthoroughly im)ued ;ith elements o )oth, rimarily the latter. =Hor mostmathematicians, mathematics is a /latonic science, the study o timelessentities, ure orms that are someho; or other sim ly out there,

reexistent o)Dects inde endent o human volition or o any conceiva)lehuman activity= @0. %n classical terms, then, mathematics is thus conceived,inconceiva)ly, as an infnite set o infnite sets. Kveragainst this exists a

constructivist alternative, ;hich insists =that any mathematical roo o theexistence o an o)Dect had to )e in the orm o Ia fnitely s ecifa)le

rocedure that could in rinci le )e executed in the mind= @0. %n this vie;,the rogression o integers is =a otential and not an actual infnity,= ;herethe act o counting is =to )e er ormed dee inside our " (antian " intuitiono time= @0. Rotman attem ts to osition himsel as neither a /latonist nor aconstructivist constructivism )eing immersed in =an unexaminedly idealmentalism= E F0.

!his leads directly into the ro)lem o natural num)ers natural =)ecausethey are given at the outset, taken or granted as a ounding, unanalyza)leintuition outside any critiGue that might demand an account o ho; theycome or came " otentially or actually " to )e = E@F0 and the even more )asicGuestion o num)er s ultimate rovenance* =>here do num)ers come romA% not rom (ant s transcendental intuition orI+od, then ;hereA= 0. 'gainRotman has recourse to ;riting, inscri tion, signifcation, via the inesca a)le

rocess o counting, since counting =is an activity involving signs= ;hich


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=;orks throughIsignifcant re etition= 0. Hrom ;hich ollo;s a Guestion;hich eCectively re rames his initial Guestion regarding infnity in termsmore mathematical )ut no less e istemological* =?o; are ;e to imagine a)usiness o re eating the sel "same signi ying act ;ithout end, o iterating

or ever A Kr, ;hich ;ill come to the same, ;hat ;ould it mean to deny theossi)ility o endlessly re eating a signi ying actA= 0.

-athematics is erha s uniGue as a language in the num)er o signifers ithar)ours ;hich =seem to reGuire an infnity as their signifeds= 0. HorRotman this is evidence that =our contact ;ith infnity is al;ays and onlythrough ;riting= 0. !he strange thing a)out mathematical ideograms, asRotman oints out, is that they rovide )oth something to count and themeans )y ;hich to count :0. ')ove and )eyond the integers themselves,ho;ever, Rotman distinguishes a language o ormal mathematics * ;hat hecalls the #ode, com rised o terse im eratives devoid o indexicalex ressions such as su)DectMo)Dect ronouns, adver)s, inJected ver)s, etc. ";ords ;hich =tie the meaning o messages to the hysical context o theirutterance :0.= +iven this language, or #ode, Rotman then develo s amodel that reJects ;hat it means to =do mathematics,= that situates themathematical agency im lied )y the #ode.

!his model is imagined as a thought ex eriment in /eircian terms, = layed

out through ;ritten signs= 80 and =organized in terms o three fgures= orsemiotic agencies o erating =simultaneously at diCerent levels odiscourse=* =the mathematical Su)Dect = " the readerM;riter o ormalmathematical texts, =;ho uses the #ode )ut has no access to anydescri tion o itsel = 80< the =/erson ,= immersed in history =and in thecultural su)Dectivity coded )y the % o natural language that ermeates themeta#ode= o in ormal mathematical language. %n other ;ords, the

Su)Dect is not a su)Dect ro erly s eaking, ;hereas the /erson is. 's i theSu)Dect ;eren t a)stract enough, it has an ='gent,= an =idealizedsimulacrum o itsel as its surrogate,= an =automaton ;ithout the a)ility toengage ;ith any meanings,= o erating =only ;ith signifers at a su)"#odedlevel.= 'll three o these agents although the 'gent is not an agent

ro erly s eaking0 are necessary to =enact a single thought ex erimentnarrative. >hat Rotman has articulated ;ith this tri le agency is the inside"out meta hysics he erceives as constitutive o mathematics, ;hich, likemany alternative universes and ossi)le ;orlds osited in fction, decreasesin verisimilitude the dee er the thought"ex erimenter the /erson A0delves. %n act, the aint echo o a ra))it hole or dim reJection o a lookingglass ;orld )ecome more insistent ;hen one notices Rotman s re eated useo the tro e o the ;aking dream or )oth the ractice o mathematics andthe theoretical0 thought ex eriment a)out it* =% read mathematical signs interms o a certain ;ritten ractice, a )usiness o mani ulatinginscri tionsthat characterizes mathematical thought as a kind o ;aking dream= xii0


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or* =EtheF thought"ex erimental model allo;s us to read mathematics as a)usiness o making certain kinds o rigorous antasies or ;aking dreams=

30. !he imagined structure o the thought ex eriment verges on theBorgesian* =!he imagining Su)Dect corres onds to the dreamer dreaming thedream, the skeleton 'gent to the imago, the fgure )eing dreamed, and the/erson to the dreamer a;ake in the conscious su)Dectivity o languagetelling the dream= 30. !he otential or this model to turn into an infnitelyregressing mise"en"a"dream is th;arted )y that third term* the conscious,su)Dective, em)odied, ;ide"a;ake /erson, recounting his or her dream, notin the mathematical meta"#ode )ut in ;hat is resuma)ly the non"mathematical language o narrative, the telling o a tale ;hich shares itsetymology ;ith tallying )oth tale and tally are tracea)le )ack to the %ndo"$uro ean Ndel, to =aim at, calculate, lie in ;ait=0, or otentially endlesscounting, )ut has or a variety o reasons succeeded in hy ostatizing a ormo ar)itrary closure ;ithin its s ecifc logic narratology0. !his is )y no

means to stray )eyond the )ounds o Rotman s text* i it is ossi)le toconceive o a discursively"constituted su)Dect that narrates itsel into )eing,it might )e ossi)le to conceive o a mathematical su)Dect that countsnum)ers into )eing. 'ssuming the unitary nature o such a su)Dect, there isno need that a limit )e im osed rom outside on the otential endlessnesso counting< the su)Dect s hysical death assuming it exists ;ithin time0 ;illguarantee its cessation.

's Rotman remarks in a later cha ter* =EcountingF resents itsel asrototy ical o the very )usiness o sign creation itsel . >e count )y

re eatedly enacting the elemental rocess o creating identity )y nulli yingdiCerence, re eatedly aOxing the same sign 2 to individual things "o)Dects, entities " that are mani estly not the same Gua individuals in the;orld")e ore"counting rom ;hich they have )een taken= @20. Rotmaninter rets counting =as a mathematical ur "cognition, as the ure anddistilled mode o the roduction o identity and sameness= @20.

Hor Rotman the cul rit is ;hat he names =the ad infnitum rinci le " therinci le o al;ays one more time @50,= ;hose mathematical version is the

axiom that = or any num)er x there exists a num)er y such that y P x Q 2,=;ithout ;hich it is im ossi)le to conceive o the endlessness o num)ers. %nconsidering the im lications o reDecting this endlessness, Rotman s ocus isonce again the counting su)Dect* rather than osit the fnitude o the

hysical universe a fnite Guantity o articles to )e counted0, Rotmansuggests the limitation o =the time"s an o an individual li e @40,= and Dustas Guickly reDects this =move o constraint= as =unacce ta)ly ar)itrary.=


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%n the triadic su)Dect o classical mathematics, it is the relation )et;eenSu)Dect and 'gent, s ecifcally their resem)lance, ;hich is crucial, and inthis res ect =the decisive characteristic is that o hysicality= 30. 'ccordingto Rotman, i it is going to count endlessly or us, as it ;ere in our lace, the'gent"imago cannot have a )ody, it =has to )e something transcendental, ithas to )e a ghost= 3"260. %t cannot even )e a u et or machine, orexam le, since any =scra o hysical )eing ho;ever rarifed and idealized=;ill necessarily sa)otage its =eCorts to count endlessly,= as it ;ill then )esu)Dect to s atio"tem oral contingencies, energy loss, entro y, and so orth.Rotman ocuses on this element o hysicality* =E;Fhy should an em)odiedmathematical Su)Dect, ;hose identity and a)ility to inter ret signs areinse ara)le rom its hysical )eing and contingent resence in the ;orld,create a totally disem)odied 'gent as its roxyA= 260. !he danger o theclassical schema is that the =disem)odied 'gent,= =a s irit, a ghost or angelreGuired )y classical mathematics to give meaning to endless counting,=

comes to resem)le the +od o meta hysics 260. !hus the ghost moves rom !uring s machine to =/lato s !rue 1nchanging ?eaven.= Rotman contendsthat it is there ore necessary to dis)elieve in this disem)odied 'gent< to=reDect not only /latonic orthodoxy, )ut, more undamentally, the very ideao disem)odiment itsel , to re use altogether the imago o endlessness=

260.

Rotman roceeds to grant this classical mathematical 'gent itsel aarticularly su)tle meta hysical rinci le E54F0 a =suita)ly idealized )ut

never a)sent= )ody 260. =!he resulting cor orealized mathematics o ensout into a ne; conce tion o iteration, o counting and there ore o ;hat ;emight and could mean )y num)er. >hat emerges is a non"$uclideanarithmetic= 26"220. 't this oint it is im ortant to read care ully, or ;hatRotman is instituting is not a denial o infnity er se the idea o infnity0 )uto ;hat ?egel called the fnite or )ad infnite s ecifcally* the endless=iteration o the same= 22< c . ?egel 24:"48 Esection 34"3@F0. Something)ecomes another< this other is itsel something< there ore it like;ise)ecomes an other, and so on ad infnitum.= ?egel 24: E34F< translationslightly modifed0. Rotman does not deny a =transcendentally mysteriousinfnitude= so much as set it oC a)solutely rom =our actual ex erience oiteration= 22< see 286 n. 250. !his interrogation o natural num)er sendlessness corres onding to a givenness 0 is re laced )y a hysicallylimited coming into )eing, determined )y the em)odied 'gent.

!he Russian mathematician 7ikolai Lo)achevsky u)lished his treatise on7on"$uclidean +eometry in 285 , in ;hat is no; seen as a maDor turning

oint in the history o modern mathematical thought. But non"$uclideanthinking had already ca tured the attention o non"mathematicians, ;riterslike (leist =Kn the -arionettetheatre=0 and, at the end o the century,

ostoevsky !he Brothers (aramazov 0. %t could )e said that non"$uclidean


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mathematics is in rinci le virtually as old as $uclidean mathematics,against ;hich it defnes itsel . %n other ;ords, ;hat Rotman descri)es is arelatively ro ound e istemological shi t that is not contingent so much onthe conJuence o certain historical actors as on ;hat he sees as theimmense existential ressure exerted on the su)Dect )y the re"existentorder that is the givenness o num)er, and the un athoma)le ros ect oendlessly iterated integers stretching oC into infnity. Rotman does not needto dis rove $uclid s theory o asym totic arallels, or exam le, to ostulatea non"$uclidean geometry< this otentially unlimited line o num)ers isadeGuate* rather than stretching infnitely in either direction i.e. on the

lus or minus side o zero0, this line the tem oral x"axis on a gra h0 inRotman s schema Dust eters out into non"existence =an entro icdiminuendo=0. %n this res ect, Rotman does not or chooses not to0 see the

ull im lications o a non"$uclidean system.

Rotman s =non"$uclidean arithmetic= ur orts to )e anti"/latonic, anti"meta hysical, a"theistic, non" sychologistic, and non"relativistic.Hurthermore, although Rotman admits that his account o mathematics is=undenia)lyconstructivist= 550, it also de arts rom the constructivist line insuch im ortant res ects as the Guestion o num)er s coming into )eing 540.'t the same time, Rotman ositions his thinking a)out language in general;ithin the conJict )et;een =the so"called continental outlook dominated )y7ietzsche, ?usserl, ?eidegger, >ittgenstein, and errida= and the current

'nglo"'merican =analytic mindset associated ;ith E+ottlo)F Hrege, BertrandRussell, and their em iricist ore)ears= 2 0. !hat is, the slogan =Languages eaks man into the ;orld= versus =-an s eaks language a)out the ;orld.=

!o say that Rotman leans to;ard the latter, ho;ever, is not to suggest thathis re"conceived mathematics is also a straight or;ard reinstatement o

man.

%n his second cha ter =Language=0 Rotman oses the Guestion as to;hether mathematics can )e considered a language, ;hich, rom aconventional semiotic ers ective, may )e considered rhetorical< that is tosay mathematics may not )e ;hat Rotman calls a natural language, )ut itis a signi ying ractice, a sign system see 5:C0. Rotman s insistent anti"

sychologism is redicated on his semiotics* or him mathematics isirreduci)ly ;ritten, a series o marks made )y the em)odied mathematician,ho;ever idealized Rotman s ;ord0* =mathematical language and discoursedeal in, are oriented to;ard, and are a)out mathematicians o;ninscri tional activities< so that, i one insists on using the term, mathematicsmight )e said to re er like music0 to nothing other than itsel = 590. Kn this)asis Rotman argues that mathematics, as a signi ying ractice, =;ouldra idly )ecome unintelligi)le= ;ere it not or its as it ;ere arasitic my;ord0 relation to ;hat he calls a natural, non"mathematical hostlanguage.=


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Rotman s assertion o mathematics undamental ;rittenness has itsantecedent o course in K +rammatology 23: 0, ;here errida invokestheoretical mathematics as exem lary o a non" honetic language, one

;hich does not de end and has never de ended on the actual ormeta hysical resence o a signi ying intention errida 23: * 260. %n a longnote, Rotman makes ex licit the connection )et;een his #odeMmeta#odeo osition and errida s characterization o the relation o ;riting to s eechas secondary and su lementary, =inside a logocentricized >esternthought,= to use Rotman s ormulation. ?o;ever, Rotman claims that hisanalysis )ears an inverse relation to the rece ts o grammatology* =E;hatFo erates in mathematics is not logocentrism, not the rivileging o s eechover ;riting, o rimary sel " resence over a des ised secondarity, )ut thereverse* a orm o gra hocentrism, the rivileging o the ormal ;riting o

the #ode over an elimina)le, theoretically unnecessary " e i henomenal "meta#ode= 28@ n. 580. Rotman a ears to overlook the act that errida;as talking a)out not Dust =al ha)etic ;riting= ;hen he singled outmathematics as the model o a non" hono"logocentric, language, =untainted)y the meta hysics o resence= 28@ n. 580. %n a long note, Rotmanmaintains that the thrust o his essay is ultimately against errida sconce tion o mathematics as Guintessentially ;ritten, to;ard the locatingo =a dee ly meta hysical rinci le at ;ork ;ithin mathematics currentconce tion o num)er )ut also to reinstate the )ody and the su)Dect ;iththeir talk, noise, and hysics o resence onto the mathematical scene=

28@ n. 580. ?e ;ould root out meta hysical resence in order to )etterreinstate hysical resence in mathematics. !he recise nature o thero osed su)Dect s ideal, non"meta hysical, em)odied resence is never

adeGuately ex lained.

%n discussing mathematical language or signs, Rotman ex lains that he isre erring to =ideograms in the usual sense o ;ritten characters conveying,invoking, or denoting conce tual content " signi ying " through their gra hicidentity, as visually resented marks= 5 0. Rotman singles out the

ideograms 6 and ... as occu ying a =more rimitive and originarysigni ying level= and as there ore under inning arithmetic counting 6, 2, 5,4... 0. %t is common kno;ledge ho;ever, as Rotman himsel ex lains in hisearlier )ook, Signi ying 7othing* !he Semiotics o ero, that there ;ascounting in this sense o arithmetic rogression or tallying, long )e ore theintroduction o zero, ;hich served to o en u ;hole ne; vistas ocalculation and numerical re resentation. !he oint that Rotman does notmake is that it ;as the ince tion o zero that ermitted the re resentation,and thus in a certain sense the conce tualization, o ositive infnity. !hat is,the introduction o 6 ;as a rereGuisite or the introduction o ... as a

mathematical ideogram. Rotman does not ursue this causal relation in thene; )ook.


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ia summaries o the theories o Saussure, /eirce and, to a lesser extentBenveniste, Rotman Jeshes out his earlier line a)out =language s eakingman into the ;orld= 2 0, in so ar as su)Dectivity is constituted in the

individual language"user s a ro riation o re"existent indexical ormsmost nota)ly % 0 to defne himMhersel in relation to other users you 0,;ithin a s ecifc s atio"tem oral hysical context here, no;, this 0 460.%n Rotman s reading, the semiotic su)Dect is still an a)stract ty e, andsu)Dectivity there ore something there rior to the situated hysicality othe s eaker his erson, as Benveniste says E46F0.

Rotman s third cha ter considers the infnite in relation to the fnite, movinga;ay in his usage tem orarily rom the mathematical infnite to somethingmore meta hysical 430. %n a note, ho;ever, he seeks to distance his usageo the infnite rom ?egel s insistence on a )ad infnite that is =conditioned,conce tually limited,= and )y defnition fnite 286 n. 250. Rotman s

rotestations aside, it remains unclear ho; the mathematical infnite heela)orates diCers rom ?egel s )ad infnite, articularly in light o hiso)session ;ith the ideogrammatic infnite ... 0, and ;ith its limitation or

fnitization )y the resence o the )ody o the counting su)Dect. RotmanreDects the goodM)ad distinction and its echoes in contem orarymathematics0 on the grounds that it re resents =the inevita)le return o anunackno;ledged and )uried theism= 286 n. 250. !his theism is most

o)viously )uried )eneath the corollary to the )ad infnite< the a)soluteinfnite ;hich ?egel a o hatically )ut rather mean"s iritedly descri)es as =a;retched neither"one"thing"nor"another= ?egel 248 E39F0.

Rotman gives a;ay his osition vis"a"vis the infnite as source o=inconsistencies, contradictions, aradoxes, antinomies, and other

roductions o discourse intolera)le to mathematical reasoning= 430* itlainly makes him nervous. %n this vein, Rotman traces the im act o eno saradoxes on su)seGuent mathematical thought. Kn the one hand, there is

a distrust o motion, )ased on infnite divisi)ility and infnitesimal Guantities" in other ;ords the amiliar stadium and arro; aradoxes " and on the otherhand a distrust o the very o osite, =an infnitely straight line,= ;hich gaverise to $uclid s arallel line axiom, ;herein = arallel straight lines arestraight lines ;hich, )eing in the same lane and )eing roduced indefnitelyin )oth directions, do not meet one another in either direction= Rosen eld4@0 960.

Rotman orges ahead in his Guest to ormulate a critiGue o the endlessiteration o counting ;hich remains ;ithin =a Guite narro;ly dra;nconce tion o the rational= @90, and thus aves the ;ay or the emergence


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o non"$uclidean arithmetics ;hich allo;s or a kind o closure @ 0. 7on"$uclidean num)ers are themselves, in Rotman s vie;, a unction o theentro ic hysical universe rather than the other ;ay around0, and as suchdo not )ehave in the redicta)le and ure manner o the natural num)erso $uclidean arithmetic. Rotman allo;s or the ossi)ility ho;ever that hisesta)lishing the ossi)ility o denying the ad infnitum rinci le is )y nomeans =to )e taken as a re udiation o the classically conceived $uclideaninfnite as such= @80. ?e readily admits that, rom the contem orary,/latonist or constructivist vie; oint, the ado tion o a non"$uclideanmathematics resents no =real challenge to the idea o infnity= @80. '

$uclidean system contains ;ithin itsel the ground or the re resentation o the unre resenta)le infnity, +od, !ruth " an aesthetic o the su)lime0,;hereas a non"$uclidean system like Rotman s rovides the language, themeta horics, or the re resentation only o a fnite, ex eriential reality o aunitary, em)odied consciousness ;ithin the theoretically kno;a)le hysical

universe< in short, a henomenology o a counting Su)Dect ;ithout the idealterm o an a)solute s irit. 60.

Hollo;ing Rotman s reasoning, time is to arithmetic counting andrecounting0 ;hat s ace is to geometry and fguration 60 thus the urtheranalogy could )e made " as it in act is )y Rotman " o arithmetic to logic asgeometry to rhetoric Ee.g. 8F0. !his stark distinction )lurs, ho;ever* orcounting to un old, the s atial o eration o diCerential disru tion mustoccur< the iteration o num)ers, as in ver)al language, de ends ondiCerence, ;hich is, as errida ointed out, s atial in its unctioning errida23: 0. Rotman is there ore too dogmatic in his contention that =counting,ho;ever idealized, is a tem oral rocess.= %t ;as to esca e such strictly)inary thinking that errida coined diCTrance , ;hose eCects are neitherexclusively tem oral nor s atial, redicated on an a)sence ;hich has nocorres onding resence to negate it. !he a)sence, the eCect o the trace, indiCTrance is irreduci)le, )ut Rotman s re ashioned mathematics is

redicated on ;hat might )e called an irreduci)le resence c . 28@ n. 580.'s Rotman remarks in the next cha ter, =mathematical logic is inse ara)le

rom a s ecies o rhetoric= 80, and rhetoric, ;ith the ersuasionalem hasis Rotman gives it here, suggests a relatively traditional model os eaker and audience in a relationshi o mutual resence, ho;ever

attenuated or idealized. %n this sense, the one doing mathematics isanalogous to the s eaker, using his or her ;hole )ody in the re ertoire o

communicative acts that constitutes rhetoric " and a very strange ;ay odoing mathematics.

Rotman fnally oses the Guestion at the crux o his thesis* ;hat is thenature o the relation )et;een =the em irically constituted, cor orealmathematical su)Dect ;ho sits do;n to read, ;rite, and count mathematicalsigns,= and the fctive )eing, the =imagined simulacrum,= Rotman osits ;ho


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is the one ;ho actually er orms the endless countingA 50. !his Guestionnever receives a satis actorily clear ans;er, ;hich ham ers Rotman s o;n

ersuasiveness at key oints.

!he oregoing Guestion leads, in the next cha ter =$x erimental !hought=0,directly into Rotman s advocation o the mathematical thought ex erimentas the most via)le means o ex loring this relation )et;een su)Dect andagent 0. Rotman sees thought ex eriments as germane to the ractice o mathematics :0. !heir most signifcant unction is to eCect a shi t rom theactual to the virtual, rom ex erience to the imagining o ex erience 80,recalling the earlier analogy o the tri artite dreaming su)Dect. !he a)senceo = amiliar indexical signs= in the #ode is evidence, or Rotman, o acenturies"old, ormalist, a otro aic eCacing o any s atio"tem orallylocata)le su)Dect :40. Rotman sees this as a concerted eCort to constructan %"less, meta hysical mathematical su)Dect, in an =al;ays"already there

resent* a timeless voice rom no one and rom no;here= :90. %n eCect, the/erson s task is to re ort on and inter ret the relation )et;een Su)Dect and'gent =imaginer and its imago=0< the relative degree o similitude )et;eenthese t;o on ;hich the Su)Dect, as =idealization o the /erson,= cannotcomment, having no access to the =indexical sel "descri tion= rovided )ythe meta#ode :80. Rotman ;ould have us )elieve in a su)Dect that isalready there, already constituted and em)odied, and yet una)le to re er toitsel reJexively i it ;ere merely an a)stract mathematical su)Dect, this;ould not )e a ro)lem0. Knce again, Rotman notes the isomor hicresem)lance this model )ears to that o the dream, ;ith the single rovisothat =mathematics deals in ;aking dreams,= or the likely reason that realdreams are not the direct roduct o rational consciousness. !o use theanalogy o the dream Gua dream ;ould )e to allo; or the ossi)ility

ho;ever fgurative0 o an unconscious unction, and there ore o a groundas a)yssal as the zero"infnite diCerential is or mathematics.

!he irony o his triadic model, ;hich Rotman seems to a reciate, is thatthe Su)Dect s cor oreal resence ;ithin the circuit is entirely meta horical,even ideal, only in terms o a diCerent ideal order than its idealized roxy,the 'gent 8 0. !he 'gent is more ideal, the /erson less so* the circuit in itsentirety is an a)straction, a fction 320. !his raises a num)er o interestingGuestions, such as ;hat is the nature o idealized cor orealityA the Su)Decthas =an idealized )ut not nonexistent )ody E266F=0 >hy should the su)Dect)e mortalA Rotman asks 350. !he 'gent, =i it is to er orm the o erationsimagined or it )y the Su)Dect, ;ill not merely exhi)it some idealized versiono the Su)Dect s cor oreality, )ut ;ill ossess no hysical resence;hatsoever. %t ;ill )e a ghost= 340. %t seems that the only reason thisSu)Dect needs to )e em)odied at all is to set it oC rom the 'gent it dreamsu to er orm tasks the Su)Dect is revented rom er orming )ecause it isem)odied and there ore mortal. !his, at least, might )e the o)vious


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conclusion. Rotman, though, is determined to use the Su)Dect s cor orealityto limit the 'gent s ideally attenuated i.e. meta horical0 cor oreality 390,such that the 'gent =cannot )e allo;ed to er orm any action that is notca a)le " otentially " o )eing realized, o )eing materially instantiated andmade actual ;ithin the hysical universe inha)ited )y the su)Dect= 390. !hisis )ecause =asking an 'gent to er orm inherently nonrealiza)le actions, isto invoke a )eing ;ho moves in a universe other than the one ;e " and allconceiva)le mathematical Su)Dects " occu y= 390* a )eing a)le to actaccording to $uclidean hysical la;s. ?ence the attention aid to the degreeo similarity in the relation )et;een Su)Dect and 'gent. !his is a crucialmoment in Rotman sargument* =the envelo e o the Su)Dect s attenuatedcor oreality is sim ly every imagined action or ;hich it is not im ossi)lethat it )e instantiated and )ecome actual= 3@0. %n other ;ords, any rocesso otentially infnite duration, such as endless counting, ;ould )e ruled out.

Rotman s reinter retation o iteration demands that =the ideogram oindefnite continuation " the ... " = )e re;ritten to signal the ne; limitassociated ;ith it* ... U . !he latter is the sign or the limit o mechanicaldissi ation 2630, ;hich a lies to the automaton"'gent< Rotman also

rovides another sign ... V, or the Su)Dect s =cognitive ade"out intounintelligi)ility= 2630. Rotman s Dustifcation or im osing this seeminglyar)itrary limit is that, unlike the 'gent not a true agent at all0 =;hat theSu)Dect does must )e intelligi)le, intersu)Dectively inter reta)le in terms osigns= 26@0. Rotman s model makes no rovision or the unintelligi)le,irrational, unthinka)le, im ossi)le, or unkno;a)le. !hus he im oses this

limit o intelligi)ility, =the rinci le o this"universe realiza)ility= 26 0, theU , ;hich, he maintains, is very amiliar in =nonmathematical situations=26@0. ?ere, Rotman has recourse to = erce tual sychology,= in a slight

de arture rom his other;ise un;avering ocus on the )ody.

Hor Rotman, then, mathematics and infnity )ecome incom ati)le )ecausehenomenology and infnity are already in a sense mutually exclusive< that

is to say, the ros ect o indefnite iteration on the meta" model stories";ithin"stories< lays";ithin" lays< ex onents";ithin"ex onents, adding u tohy erex onents< in short, any manner o code0 soon )reaks do;n intounintelligi)ility, uncogniza)ility 2680. Rotman sums u the inherentlyrhetorical nature o this sort o s eculation* =one can no more exhi)it ormake mani est such a limit than think the unthinka)le or utter the ineCa)le=

2680. He; sentences in the )ook )etter ex ress Rotman s staunchlyrationalist attitude vis"a"vis the negative, ;hich might have )een some;hatdisa ointing, had his real interest actually )een infnity. 's he states at theend o this cha ter* =EtheF ;hole account here s rings rom a semiotically)ased re usal to acce t the currently availa)le ex lanations " in act, lack oex lanations " as to ho; the natural num)ers come into the ;orld to )ehumanly o)served and mani ulated= 2240.


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!his is )y no means to suggest that Rotman is ;rong in ;hat he says a)outcognition s resistance to meta"iteration ast a certain level 2630. Rotmaninsists that he is not in these exam les rehearsing the neo"heraldic mise"en"

a)ime , ;hich he ;ants to restrict to the domain o visual re resentation< amove ;hich is not only re"em ted )y the ;ides read a lication o thisterm throughout literary studies or exam le0, )ut it remains unclear ;hythe exam les he rovides rom other codes s eech, ;riting, arithmeticE26:F0 are su)stantively diCerent rom that o a ainting";ithin"a" ainting,and so on. $ven more than this, mise"en"a)ime s vertiginous structureim lies a otentially endless iterating continuation in either direction* aclassic instance o )0ad infnitum in ractice 2630.

Rotman is also adamant that his cognitive limit"designation V 0 not )etaken or a reinstatement o the (antian transcendental limit. !he rationale)ehind this denial oCers insight into the ostensi)ly anti"meta hysical Gualityo Rotman s model* = or the #ode o mathematics the cogniza)le is neithermore nor less than the sym)oliza)le, since the inse ara)ility o ideas romtheir inscri tion, o signifeds rom signifers, inherent in mathematicalactivity, orces one to cou le ;hat is imagina)le ;ith the intersu)Dective

roduction and exchange o ;ritten signs= 2260. 'n em)racing o the mostliteral sense o errida s =il n y a as d hors"texte .= $ven the imagination issu)Dect to a limit determined )y ;hat is imagina)le or the Su)Dect as the

idealization o the /erson 226"220.

%n ex loring the ossi)ility o a non"$uclidean arithmetic, Rotman uses theo)vious analogy o non"$uclidean geometry, ;hose rovenance is discusseda)ove. ?e ;onders =;hether one can treat geometry s relation to its o)Dectas a aradigm or arithmetic s relation to its o)Dect= 2280. !his is highly

ro)lematic* frst o all, Rotman Jatly states that geometry s o)Dect is=extension in s ace,= ;hereas arithmetic s is = assage through time.= % thefrst ;ere acce ta)le under certain circumstances, the second is sim lyunacce ta)le. /erha s Rotman intends something else )y o)Dect < other;iseit ;ould seem that = assage through time= has to do rather ;ith thesu)Dect s ex erience o using arithmetic, ;here counting, say, trans iresover time, in a manner directly analogous to reading. !he latter, in so ar asit de ends on a materially resent text, has its o;n )uilt"in limit unction*reading sto s either artifcially, ;hen the age or )ook or articular storycomes to an end, or ;hen the reader gets tired or has to do something else.

!his ;ould corres ond to Rotman s realiza)ility limit. Kn the macro" level,the act that there is a fnite num)er o legi)le texts in the ;orld relative tothe li e"s an o a single reader0 determines the eGuivalent o the cognitivelimit unction. But erha s reading is not the )est analogy or counting, atleast not rom Rotman s oint"o "vie;* erha s ;riting is )etter< )ut even


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;riting as narrating, re"counting0, as suggested a)ove, has its internally"instituted, conventionalized means o coming to an end, ho;ever ar)itrary.'nd o course it is only air to recall that Rotman s counting su)Dect iss ecifc to mathematics, and could not )e ex ected to have anything to sayto a ;riting or reading su)Dect at a arty " let alone )ehave like one "

articularly not in the a)sence o indexical ex ressions, like %.

%n discussing $uclid s unease a)out his o;n axiom o arallels, Rotmanchooses to ignore the trou)lesome =idea o a straight line )eing rolongedinfnitely ar= 2230. ?e re uses to ackno;ledge that this unease may have)een the result o the ossi)ility, contrary to reason and logic, o the t;oasym totic lines eventually meeting, at a oint that cannot )e ormulated inthe terms o either $uclidean geometry or the (antian categories, or;hatever< a oint that is neither s atial nor tem oral< that is not a oint,

ro erly s eaking< that is im ossi)le, inconceiva)le, and so orth. Rotmancontends that the arithmetical cognate to the arallel axiom is the adinfnitum rinci le itsel 2560. !here is no reason to disagree ;ith thisconclusion, although in his ex lanation Rotman does not clari y the mosto)vious )asis or the com arison* unending counting, like an endlessstraight line, is unthinka)le< )oth are in eCect meta hors or a meta hysical

reality inaccessi)le to thought. 'nd, like the line, the iterating series onum)ers ;ill end u curving )ack u on itsel , in defance o $uclidean

rece ts as much as the hysical la;s that govern the universe* ;hatRotman is arguing or here is, a ter all, a henomenology as it is a model oro)Dective reality.

>hat Rotman ails to mention is that 'ristotle and ?egel are not the onlyhiloso hers to have theorized diCering orders o infnity< an excusa)le

omission,given the roclaimed mathematico"semiotic ocus o hisdiscussion. %n the eriod o e istemological u heaval that resulted in ;hatBlumen)erg has termed the modern age, there ;as a trend o thought thathad numerous oints o contact escartes, /ascal0 ;ith the hiloso hical

mainstream )ut remained or a variety o reasons on the margins.Blumen)erg himsel singles out t;o thinkers, +iordano Bruno and 7icholas#usanus, as )eing o signal im ortance in the transition rom the remodernto the modern. #usanus, the more medieval o the t;o, ;as a )isho ,)ureaucrat, theologian, and mathematician, ;ith a scientifc cast o mindthat makes him one o the frst modern thinkers, at once seminal andliminal. But it is #usanus s lace in the history o mathematics that Dustifeshis mention here. >hat kee s him in the eyes o some rom ully crossingthe threshold into modernity is, among other things, his use o mathematics" s ecifcally geometry " to render an a roximation o ;hat is other;isea)solutely unre resenta)le* +od s infnite )eing.


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'rgua)ly, and erha s aradoxically, one o the most com elling as ects o#usanus s thought is his sym athy ;ith negative theology, and the mannerin ;hich he com)ines its language and logic ;ith a geometricalmeta horics. 1nlike the advocates o conventional, aOrmative theology,#usanus s use o geometry is redicated on a relation o a)solute non"resem)lance )et;een the orm and ;hat it re resents. !here is anun)ridgea)le distance )et;een, say, a straight line and the er ect,infnitely straight line that is +od. Hor #usanus, every fnite line artakes ocurvature, since i it ;ere really, maximally straight it ;ould )e the=maximum, infnite line= there can )e only one0, a change ;hich, on therhetorical level as o osed to the conce tual0 amounts to a lea rom theas it ;ere concretely sym)olic into ure meta hor octa %gnorantia 40.

!he straight line in geometry, or that matter, is never actually straight, as itis inesca a)ly determined )y ;hat might )e called the non"$uclideanuniverse o allen creation. %n the created ;orld, all lines are crooked. !he

same holds or more com lex geometrical fgures* one that is in act used inthe octa %gnorantia is the olygon inscri)ed ;ithin a circle octa%gnorantia 2. 4< 4. 2< 4. 90. Hor #usanus, this com ound fgure re resents theincommensura)le diCerence )et;een the intellect and truth< as the num)ero the olygon s sides increases, it gro;s increasingly similar to the circle,;ithout ever achieving identity ;ith it " ;ithout, in short, ever )ecominga)solutely circular. 'nd this irreduci)le diCerence, as that ;hich se aratesthe intellect and truth, remains infnite, no matter ho; small the incrementsse arating the t;o a ear to )ecome see octa %gnorantia 2. 40.

Like /lato and many others, #usanus is =care ul to distinguish the infnity othe cosmos rom that o +od= ?arries 0, )ut unlike /lato and like +regoryo 7yssa< see )elo;0, #usanus recognizes a radical discontinuity )et;eenthe t;o* the cosmos is rivatively infnite< that is, =it lacks limits in ;hich itcan )e enclosed, ;hile the infnity o +od recludes all indeterminacy=

i)id.0. !his is )y no means to suggest that #usanus articulated a vision o auniverse cut oC irremedia)ly rom +od " this is a much more recentdevelo ment. !he infnity o the universe, in #usanus s ;ords, =contrasts;ith the infnity o +od )ecause it is due to a lack, ;hereas Ethe infnityF o+od is due to an a)undance !hus, the infnity o matter is rivative, E)ut theinfnityF o +od is negative= octa %gnorantia 5. 80. 7ote 20

Rotman s crucial mistake is in not recognizing or at least notackno;ledging0 that geometry, es ecially certain orms o antici atory non"$uclidean geometry, em loyed geometrical orms or a ur ose com letelyother than the re resentation o ;hat Rotman )lithely calls =the structure oactual externally resented s ace= 2560. 'nd this is not to have recourse toa variation on classical infnitist mathematics< rather, it is to dra; attentionto an a o hatic trend o thinking, grounded in the unthinka)ility o therelation )et;een )eing and non")eing, created and uncreated sel and


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otherA0 " the roto"diCTrance that +regory o 7yssa in the ourth centurynamed diastema * 7ote 50 the irreduci)le ga or interval )et;een thereach o human cognition ;hat can )e kno;n0 and +od s a)soluteunkno;a)ility as ;hat Levinas has called =Being )eyond )eing= Levinas23820. !he diastema s determination is radically negative< it descri)esneither one term or the other )ut the diCerential relation )et;een them,grounded in unkno;a)ility. 7ote 40 's a name or =the ga that se aratescreation and #reator= +regorios :0, ;hich is )oth ontological ande istemological, diastema is unam)iguously theological, )ut this does not

revent its logic rom )eing a ro riated and a lied in other contexts in;hich is aced the ro)lem o thinking something unthinka)le ;herethinking, in Rotman s terms, is re resenting0. %n other ;ords, ;here there isno longer any Guestion o denying ontological continuity, thee istemological discontinuity remains. !hus in terms o diCerent orders oinfnity, there is no )asis o resem)lance as there is or, say, /lato s universe

o conditioned infnitude, created in imitation o the eternal attern.

>hat ;e receive rom this ersistent strain o a o hatic thought, then, is ameans o thinking a)out not merely t;o diCerent orders o infnity, )uta)out t;o diCerent orders o things " mutually contradictory,incommensura)le " at the same time< that is, o thinking a)out their relation,the irreduci)le s ace )et;een the fnite and the infnite or fnitely infniteand negatively infnite0, since consciousness, )eing fnite, remainsnecessarily on one side. !he great insight o this a o hatically"inJectedstrain o thought is that, i the a)solute cannot )e thought in itsel i.e. i it isno longer an o tion or thought0, then the relation can, in the ositive ormo a fgure or an irreduci)le ga , ;hich, no matter ho; close the mindseems to come to an a rehension o the a)solute, remains uncrossa)le)ecause it is fnite and )ounded on one side, and un)ounded and infnite onthe other. %n other ;ords, as an alternative to Rotman s alternative, it is notnecessary to ;orry a)out the infnite at all.

!o;ards the end o the )ook Rotman seems to come almost ull"circle, in anackno;ledgement o the inesca a)ility o $uclidean conce ts on thegrounds o an admittedly du)ious intuitive o)viousness 25:0* =evidently,realiza)le arithmetic is radically non "$uclidean. But against this diCerencethere is also an identity* any acce ta)le understanding o num)er has to )elocally $uclidean= 25:0. Rotman suggests that there ore there are t;oorders o num)er, one ideal the classical ordinals 0 and one realiza)le,)ut then ;onders ho; one ;ould )e a)le to tell the diCerence )et;eenthem* =does it not seem that counting to ten on our fngers is counting toten " ;hether the counting is rolonged )eyond 26U or 26 )y a realiza)le'gent or )y a classical ad infnitum agent a)le to count oreverA= 2580Rotman identifes a diCerence or divergence here, )et;een =classicalandrealiza)le= arithmetical la;s 2580.


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!he ideogram V denotes the limit o ;hat makes sense on a universallevel< U denotes the corres onding limit on a su)Dective level. #an the limitsym)olized )y V )e thought o as cognate ;ith the #usan notion o a

rivative infnite A i.e. not as a limit" unction o the hysical universe )ut o ;hat is ossi)le ;ithin that universe0. ' rinci le i unstated0 goal oRotman s thesis seems to )e the elimination o contradiction and aradox,o undecida)ility in any guise eg. 246"420. %n other ;ords, Rotman s notiono a =realiza)le arithmetic= is =locally $uclidean,= and =radically non"$uclidean= only on a glo)al scale 252"460. Rotman s mathematical model,as undamentally ;ritten, con orms ;ith neither the hono"logocentric northe grammatological ;here each iteration o an utterance, ;ritten ors oken, is a ne; signi ying event conditioned )y its context andinde endent o a resent signi ying intention as roo o origin0< rather,

Rotman argues or a mathematics in ;hich ;riting and thinking areinterde endent to the extent that the Su)Dect s active resence " notmerely the intention )ut the )ody itsel " is reGuired or any mathematicalact to take lace 2940. !hat is, or Rotman, each im lementation omathematical signs is a uniGue and originary event, regardless o theiterative, conventional nature o these signs, ;hich Rotman in actackno;ledges 296"920. Kn the other hand, Rotman does not allo; or the

rimacy o either the ;orld or mathematics as a)solute origin< the ;orld,al;ays already mathematized, rovides mathematics ;ith its s atio"tem oral model 295"990. Rotman identifes an oscillation =not confned to

mathematical signs, )ut having a articular orce or them=0 )et;een thesignifer s coexistence as material mark and as =general, idealized, non"materially resented ty e = 2990. 7either recedes the other, nor have theyexisted in this state o mutual de endence orever, since that ;ouldcontravene the non"$uclidean nature o the system. !his is the onlyconcession Rotman makes to any sort o irrationality or irresolva)ility,

re erring to ground his model in ;hat is eCectively the henomenology othe singular mathematical Su)Dect, =a semiotic agency made availa)le )ythe code " engaged in the dreaming o its o;n numerical )oundaries= [email protected] makes ex licit the connection )et;een this Su)Dect and

henomenological ex erience o the ;orld in terms o his discussion o time*the time that the Su)Dect inha)its, he states, is the same as that inha)ited)y =any reader o this text= 29:0.

Rotman admits to having deli)erately excluded rom his model o thedreaming0 mathematical Su)Dect any level or dimension o

unconsciousness, and that this is an attem t to re ress consciouslyA0 ;hatis otentially one o the most interesting as ects o a roDect o denyinginfnity. %n admitting this, Rotman only dra;s attention to ;hat amounts to

the unintentional0 dialectical negation o infnity* as he admits ;ithout


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;anting to, the o)Dect o re ression emerges as ;hat is most interesting234 n. @50.

7otes

20 Hor a urther ex lanation as to ;hy #usanus s universe is not reallyinfnite and a valiant attem t at a clarifcation o #usanus s com lex ando ten con using use o terms like rivatively and negatively infnite0, see?o kins 23:8* 46"45. # . escartes s letter to #hanut o &une 2 9:, in;hich he cites #usanus on the issue o the =indefnite extension= o theuniverse over against the infnity o +od escartes 5520.

Back to ;here you le t oC.

50 =>e have no $nglish ;ord )y ;hich to translate diastema. !o translate itas ga or interval could )e to miss out its meaning o extendedness=

+regorios :@0. +regorios oints out that diastema has )een translated intoHrench as es acement , suggestive at once o s acing, diCerence andmovement i)id.0.

Back to ;here you le t oC.

40 % o;e this o)servation to #harles Lock.Back to ;here you le t oC.

Re erences

Blumen)erg, ?ans 238@0 !he Legitimacy o the -odern 'ge. Ro)ert ->allace trans.0 #am)ridge, -ass. and London* -%! /ress.

Borges, &orge Luis 23 90 ='vatars o the !ortoise.= La)yrinths. onald '. Wates and &ames $. %r)y eds.0. 7e; Work* 7e; irections* 565"568.

errida, &acGues 23830 $dmund ?usserl s =Krigin o +eometry=* 'n%ntroduction. &ohn /. Leavey, &r. trans.0. Lincoln and London* 1niversity o7e)raska, 2383.


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""" 23: 0 K +rammatology. +ayatri S ivak trans.0. Baltimore and London* &ohns ?o kins.

escartes, RTne 23:60 /hiloso hical Letters. 'nthony (enny trans. anded.0. Kx ord* #larendon.

+regorios, /aulos -ar 23880 #osmic -an* !he ivine /resence " !he !heology o St. +regory o 7yssa. 7e; Work* /aragon ?ouse.

?arries, (arsten 23:@0 =!he %nfnite S here* #omments on the ?istory o a-eta hor.= &ournal o the ?istory o /hiloso hy 24. 2 &anuary0* @"2@.

?egel, +. >. H. ?egel s Logic /art % o the $ncyclo edia o 28460. >illiam>allace trans.0. Kx ord* #larendon, 23:@.

?o kins, &as er 23:80 ' #oncise %ntroduction to the /hiloso hy o 7icholaso #usa. -innea olis* 1niversity o -innesota.

""" trans.0 23360 7icholas o #usa Kn Learned %gnorance* ' !ranslation and' raisal o e octa %gnorantia. -innea olis* 'rthur &. Banning.

Levinas, $mmanuel 23820 Kther;ise than Being, or Beyond $ssence.'l honso Lingis trans0. ?ingham, -ass.* (lu;er 'cademic.

Lock, #. &. S. 23350 =!exts o the Body and the -ind* Semiotics and theHace.= E1n u)lishedF.

/lato. !imaeus and #ritias. London* /enguin, 23:2.

Rosen eld, B. '. 23880 ' ?istory o 7on"$uclidean +eometry* $volution othe #once t o a +eometric S ace. ')e Shenitzer trans.0. 7e; Work, Berlin,etc.*S ringer erlag.


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Rotman, Brian 238:0 Signi ying 7othing* !he Semiotics o ero London*-acmillan.

Russell &. '. (il)ourn is a graduate student in the #entre or #om arativeLiterature at the 1niversity o !oronto. ?is thesis deals ;ith the relationshi)et;een negative theology and the modern novel, and he also ;orks on flmand literature. Russell is currently teaching in the Literary Studies rogramat ictoria #ollege, 1. o !.

Documents

Rotman zero semiotics.odt