Poetry Final Essay

8/13/2019 Poetry Final Essay

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Hallgren

Max HallgrenJonathan MonroeAMST 38205 December 2012

vAmbiguous orms! "oetr# an$ Mathematics

%ecause o& the $iversit# o& &orms in 'hich the# mani&est themselves( there is no

commonl# acce)te$ $e&inition o& mathematics or )oetr#* Thus( the onl# reasonable

$e&initions o& )oetr# an$ mathematics are ambiguous( an$ are unrestricte$ in the i$eas

the# can ex)ress an$ ho' these i$eas are inter)rete$* +#nn Arthur Steen o&&ers one)ossible ambiguous $e&inition o& mathematics! ,the science o& signi&icant &orm-.Ste'art

23/* n a similar vein( 'e coul$ sa# that )oetr# is ,the language o& signi&icant &orm-(

'here ,signi&icant- an$ ,&orm- are un$e&ine$ in both $e&initions* %# anal#ing the 'a#s

in 'hich the ,signi&icant &orm- is able to intro$uce i$eas( mathematics can be sho'n to

mo$el an$ )rovi$e insight into the language o& )oetr#* Although mathematics an$ )oetr#

a))ear su)er&iciall# $issimilar in &orm( the# are line$ in their use o& ambiguit# to

connect i$eas*

illiam 4m)son con$ucte$ a rigorous stu$# o& the use o& ambiguit# in )oetr# in

Seven Types of Ambiguity( 'here he $e&ines ambiguit# to be ,an# verbal nuance(

ho'ever slight( 'hich gives room &or alternate reactions to the same )iece o& language-*

This $e&inition( though( is not broa$ enough to accommo$ate a multi$isci)linar# stu$# o&

ambiguit#* or this )ur)ose( consi$er the $e&inition )ro)ose$ b# illiam %#ers in his

stu$#How Mathematicians Think( 'here he states! ,Ambiguit# involves a single

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situation or i$ea that is )erceive$ in t'o sel&consistent but mutuall# incom)atible &rames

o& re&erence-.28/* This 'ill be the $e&inition consi$ere$ throughout this )a)er*

n mathematics( a binar# relation on a set Sis $e&ine$ as a set o& or$ere$ )airs inS* n )articular( an e6uivalence relation is a s)ecial t#)e o& relation that is re&lexive(s#mmetric( an$ transitive* or exam)le( to be relate$ b# bloo$ is an e6uivalence relation!

one must be relate$ to onesel& .s#mmetr#/7 i& )erson A is relate$ to )erson %( )erson %

must be relate$ to )erson A .re&lexivit#/7 & )erson A is relate$ to )erson %( 'ho is in turn

relate$ to )erson ( )erson A must be relate$ to )erson .transitivit#/* hen one uses a

meta)hor( he is $e&ining an e6uivalence relation on t'o $istinct sub9ects* :et( one $oesnot generall# ex)lain 'hat the relation is( but instea$ allo's the rea$er to 9u$ge 'hat the

relation is b# context* & one 'ere to 'rite ,mathematics is )oetr#-( one 'oul$ loo &or

6ualities o& mathematics that are o&ten associate$ 'ith )oetr#( such as elegance an$

$ensit#* The im)lie$ meaning o& this statement seems to $i&&er &rom the statement

,)oetr# is mathematics-( 'hich 'oul$ suggest the )oetr# )ossesses 6ualities lie

rationalit# an$ motivation $es)ite the &act the statements are semanticall# e6uivalent*

;ne can see that the $egree o& elegance( brevit#( rationalit#( an$ motivation all $e&ine

e6uivalence relations* n &act( it is $ue to the existence o& multi)le e6uivalences that the

meanings o& the t'o statements are ambiguous* 4m)son $eclares this use o& ,is- to be

the &irst t#)e o& ambiguit#! ,;ne thing is sai$ to be lie another( an$ the# have several

$i&&erent )ro)erties o& virtue in 'hich the# are alie-.4m)son 2/* +ie'ise( it is o&ten

use&ul in mathematics to stu$# the general )ro)erties o& e6uivalence relations* ;ne o&ten

'rites a


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on an# set* The ambiguit# o& 'hat e6uivalence is can a$$ $e)th to )oetic )assages b#

maing the rea$er consi$er a multi)licit# o& relations bet'een i$eas rather than observing

a single relation* This is embo$ie$ b# =icanor "arra>s text in ,atch out &or the ?os)el

o& the Times- in his collectionAntipoems: How to Look Better & Fee !reat!

2@2 $oesn>t mae !

once it ma$e but

to$a# nothing is no'n in this regar$ .121/

%ecause o& the )olitical commentar# that imme$iatel# )rece$es this )assage( one is le$ to

believe that this is a com)arison o& the "inochet regime to the o)ressive government o&?eorge ;r'ell>s "#$%* The )oem>s title suggests( ho'ever( that "arra &eels alienate$ b#

changes in i$eas at the &oun$ation o& his no'le$ge* ;ne more im)ortant $etail is &oun$

in the original S)anish version( 'hich $i&&ers slightl# but in an im)ortant 'a#!

2@2 no son !

&ueron

ho# no se sabe na$a al res)ecto

"arra>s use o& the 'or$ ,ser- instea$ o& ,hacer- im)lies a meta)horic relationshi)

bet'een 2@2 an$ * n &act( the s#mbol ,B- can s#mbolie man# $i&&erent e6uivalence

relations in mathematics( an$ hence al'a#s )ossesses a meta)horic 6ualit#* Hence( 'e

can inter)ret ,2@2 no son - as ,there is some 'a# in 'hich 2@2 an$ are $i&&erent-*

Ma#be "arra is lamenting the $ivision o& +atin Americans $ue to )olitical unrestCt'o

an$ t'o are re&using to come togetherCthe 'hole is not the sum o& its )arts* "arra coul$

be ex)ressing nostalgia &or 'hen the 'orl$ seeme$ sim)le an$ straight&or'ar$( or he

coul$ be encouraging the rea$er to tae a broa$er vie' o& the 'orl$ an$ its com)lexities*

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As a mathematician( "arra no's that the ex)ression 2@2B is not at all a trivial resultC

in &act( it taes 25( 33 ste)s to )rove &rom a))l#ing logic to the base axioms

.Metamath/*

n an elementar# algebraic e6uation .e*g* x 2 B /( one is &ree to inter)ret x as a

)lacehol$er &or an# number belonging to a certain set .o&ten the real numbers/( or as the

)articular 'hose substitution &or x maes the ex)ression into an i$entit#* t turns out that

ambiguities o& this &orm are common in language( 'here x is a sub9ect instea$ o& a

number* "arra maes this relationshi) ex)licit in his )oem ,A$vocate &or His ;'n

ause-( 'here an unname$ man ,arrives at a grave mare$ Ex>-* The lac o&s)eci&ication o& ,x- maes the rea$er 'on$er 'hether the author inten$s the statement to

be s#mbolic o& an# o& a set o& )eo)le( or a single )erson the rea$er is inten$e$ to $iscover

through the variable>s relations to other elements o& the text* %#ers is able to ex)lain the

use&ulness o& this &orm! ,A variable is s)eci&ic an$ general at the same time FG %# not

resolving the ambiguit# until the en$ o& the )iece o& mathematics one is able to use that

ambiguit# constructivel#-.3/* n algebraic e6uations( this amounts to solving &or x* n

"arra>s )assage( one is le$ to thin ,x- is "arra>s mother because o& the unname$ man>s

)ossession o& re$ carnations an$ the )assage in ,Something +ie That- that states that ,A

D4I4"T ol$ man thro's re$ carnations at his belove$ mother>s co&&in-.KKK/* ;&

course( the solution to algebraic e6uations $oes not have to be uni6ue* or exam)le( the

e6uation x21 B 0 has the solutions x B 1 an$ x B 1* Such structures o&ten arise in

)oetr#( 'hen sub9ects are uns)eci&ie$Chinte$ at( but le&t to inter)retation* ;ne

mani&estation o& this structure is the )roblem o& )ronoun inter)retation( seen in "arra>s

,Something +ie That-!


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the# )ass the #ears )ass

the #ears

at least the# seem to be )assing

h#)othesis non &ingo

ever#thing goes on as i& the# 'ere )assing .8/

The )ronoun ,the#- in this )assage ma# be inter)rete$ as re&erring to ,the #ears- or to

some unmentione$ other sub9ects* & one inter)rets ,the#- as the #ears( one is le$ to theim)ression that the narrative voice &eels unable to hol$ onto the timeCthat the #ears

continuall# sli) through his &ingers* The other inter)retation lea$s the rea$er to believe

that the uni$enti&ie$ sub9ects &eel unable to en9o# li&e( an$ are )assive in the )rocee$ing

o& time* Moreover( the 'or$ ,)assing- can be un$erstoo$ as the )assing o& time or

)eo)le* This ambiguit# itsel& re)resents the i$ea ex)ressing the a)ath# o& time in the &ace

o& our $esires* The algebraic e6uation is re)lace$ 'ith relations on the sub9ect an$ the

solution is an inter)retation o& the i$entit# o& the sub9ect belonging to a certain set o&

s#ntacticall# viable sub9ects* ;ne coul$ there&ore argue that( lie man# )ol#nomial

e6uations( this sentence has multi)le ,solutions-* This seems to be 'hat "arra ha$ in

min$ given his re&erence to saac =e'ton>s &amous )hrase ,h#)othesis non &ingo-( use$

b# =e'ton in ,?eneral Scholium-( an essa# he attache$ to hisrincipia Mathematica*

n his essa#( =e'ton uses this )hrase to ex)ress his re&usal to )ostulate ho' gravit# is

able to act on ob9ects* "arra>s use o& the )hrase suggests he $oes not 'ant to tell us ho'

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he 'oul$ inter)ret his o'n )assages* n &act( the title o& the )oem is )erha)s intentionall#

ambiguous to account &or the $iscontinuous an$ largel# unrelate$ narratives*

The mathematical i$ea corres)on$ing to choice o& language in )oetr# is the choice

o& s#mbolic re)resentation* n mathematics( the s#mbols in an ex)ression ma# be

inter)rete$ as $i&&erent ob9ects 'ith $i&&erent relations 'ithout altering the meaning o& the

overall ex)ression* or exam)le( &or a &unction f$e&ine$ on some subset o& the real

numbers( the in$e&inite integral is generall# 'ritten in the notation

Lf

.x/$x *Man# )eo)le &amiliar 'ith calculus 'oul$ be sur)rise$ to learn that this combination o&

s#mbols is intrinsicall# ambiguous* n elementar# calculus( one inter)rets the ex)ression

so that ,L- an$ ,$x- are )urel# &ormal s#mbols acting ma))ing the &unction fto another

&unction( calle$ its anti$erivative* :et( mathematicians $evelo)e$ a rigorous 9usti&ication

&or vie'ing ,$x- as a mathematical ob9ect in its o'n right( calle$ a $i&&erential &orm

.Samelson 52252/* This inter)retation suggests the generaliation o& the integral b#

combining $i&&erential &orms( 'hich lie artan accom)lishe$ in the earl# 20thcentur#(

centuries a&ter the original &ormulation o& the integral* The linguistic counter)art o& this

ambiguit# is mor)hological ambiguit#* This t#)e o& ambiguit# is largel# unuse$ in

tra$itional )oetr#( but can be &oun$ in ecilia NicuOa>s ,el )oema cogna$othe )oem-!

res)on$

e

sibila

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PcuQl es

nuestra

ver $a$R

P)or 6u

est amos

a 6uR .3U/

NicuOa taes ambiguit# one ste) &urther( limiting our abilit# to $istinguish bet'een thebeginning an$ en$ o& each 'or$* +ie $ivi$ing the integral ex)ression into its constituent

s#mbols( the $ivisions o& each &ragment o& NicuOa>s 'or allo's the rea$er to ex)lore

each meaning o& the resultant a$$ition o& &ragments* or exam)le( in the &irst stana( one

can construct ,cuQl es nuestra ver$a$-( or ,'hich is our truth-* ;ne can construct

,cuQles nuestra ver$a$-( almost ,'hich o& our truths-* ;ne can construct ,cuQl es nuestra

ver $a$-( or ,'hich is ours to see $a$-* n the secon$ stana( one can construct ,)or6u

estamos a6u-( or ,'h# are 'e here-* ;ne can also construct ,)or6u est Amos a6u-(

'hich is almost ,'h# is Amos here- .re&erring to the Hebre' )ro)het Amos/( or ,'h# is

it necessar# &or ?o$ to sen$ his )ro)hets to us-* This 'oul$ be consistent 'ith )resence

o& sibila( or oracle( in the &irst stana* ;ne can construct ,)or6u est amos a 6u-( almost

,'h# is love to 'ho-( thro'ing +atin in the mix* This seemingl# rhetorical 6uestion is

central to NicuOa>s messageClove shoul$ not be selective* The &act that these 6uestions

all occur simultaneousl# in these &ragments maes the rea$er consi$er their connection!

$o 'e share some universal truth( an$ is this the e# to &in$ing our common originCour

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$a$R s the reason )ro)hets are sent to us because 'e $o not love each other

uncon$itionall#R Are 'e here to $iscover the truth 'e shareR

The &act that NicuOa is able to success&ull# 'rite )oetr# in such an

unconventional 'a# suggests a reexamination o& 'hat is an$ isn>t )oetr#* +ooing at

"arra>s 'or( &or exam)le( one can see the $isa))earance o& elements o& tra$itional

)oetr# lie regularit# o& &orm* This is re&lecte$ in the language in "arra>s )oetr#Che

o&ten uses 'or$s that re&lect em)tiness an$ $eath( seen in )oems lie ,He>s $ea$- an$

,A)ro)os o& =othing-* "arra maes ex)licit that he is sen$ing a message 'ith 'hat his

)oetr# lacs in his ,inal "oem-( 'here he 'rites .an$ $oesn>t/!GGGGGGGGGGGGGG

GGGGGGGGGGGGGG

GGGGGGGGGGGGGG

GGGGGGGGGGG

GGGGGGGGGGGGGGGG

GGGGGGGGGGG

>m not sure >m maing m#sel& clear!

hat reall# mean to sa# is the &ollo'ing! .1/*

"arra>s em)t# s)aces in both his choice o& choice o& &orm an$ his message blur the line

bet'een &igure an$ groun$* His use o& )unctuation &rustrates inter)retationCthe colon in

the secon$ to last line coul$ im)l# that his message is the last line o& the )oem( or that the

elaborations are ,neste$-* "erha)s "arra is tr#ing to mae a statement about ho'

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language is constructe$ through an analog# to set theor#* n set theor#( the em)t# set V

is the set containing no other sets( an$ the set W V X is the set containing the em)t# set* &

one lets the sets be a meta)hor &or statements( the set W V X corres)on$s to "arra>s

)assage* This is signi&icant because o& its relation to Non=eumann>s construction o& the

or$inal numbers( 'here V B 0 an$ W V X B 1* The set W V X contains the mathematical

re)resentation o& nothing( #et it is re)resentative o& existence* The construction o& the

remain$er o& the natural numbers is an in$uctive extension o& this )rinci)le! WW V X( V X

B 2( WWW V X( V X( W V X( V X B 3( etc* "ossibl#( "arra is bringing to our attention &act that

it is im)ossible to construct )oetr# 'ithout maing a statement 'ith 'hat is missing*Joan Ietallac is also a'are o& the ambiguit# o& &igure an$ &orm( an$ maes use o& this

i$ea several times inroce'ura (egies) *estern +iv +ont,'! n )art 18 o& the

collection>s e)on#mous )oem( Ietallac leaves a hole in her other'ise homogenous

)aragra)h an$ inserts the ca)tion ,?*18- on the bottom line o& the hole* ;ne is &ree( o&

course( to inter)ret the ca)tion as re&erring 'riting or the ga)* Ietallac also uses this in

her )oem ADSA""4IA=4-( an eleg# &or Ste&an itterman 'here she removes the

letters ,a-( ,i-( ,$-( an$ ,s- &rom an original )oem( &ollo'e$ b# the letters in the al)habet

a$9acent to these( until each line is blan* The &irst co)# o& the )oem is )rimaril#

Ietallac>s original &igure( 'hile the &inal co)# is the groun$ reveale$ b# the

$isa))earance o& the letters* %ut 'hat can one sa# about the )enultimate co)#R t is the

)revious co)# 'ithout the letters ,n- an$ ,x-( but( because it consists o& all #>s( it coul$

be inter)rete$ as a s#mbol &or the chromosomes o& the victimCthe essential in&ormation

about his genetic i$entit#* The &act that it can be inter)rete$ as &igure or groun$ b# itsel&

raises several 6uestions about human i$entit#! hen $oes a victim o& a terminal $isease


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Hallgren

cease to be a living human beingR The com)lete $isa))earance o& Ste&an>s name be&ore

this stage hints that Ietallac believes he 'as &inishe$ long be&ore he 'as $ea$*

urthermore( the a))arent s#mmetr# o& the im)ortance o& &igure an$ groun$ highlights

the ambiguit# o& the meaning o& an eleg#* s an eleg# a )assage about someone>s li&e or

their $eathR

t is clear that the )oetr# o& "arra( Ietallac( an$ NicuOa are in some 'a#s ver#

$i&&erent &rom tra$itional )oetr#* n this context( tra$itional )oetr# is meant to mean

)oetr# )rominentl# &eaturing regular &orm an$ rh#thm( elo6uent language( or a))eal to

aesthetics* The alternative )oetr# o& these "arra an$ others &ocuses more on)hiloso)hical i$eas( an$ a$vancement in language an$ &orm* The a))earance o&

)rominent alternative )oetr# in the mainstream 'ill be sho'n to be in strong

corres)on$ence 'ith the a))earance o& alternative geometries in mathematics an$ the

subse6uent ex)ansion o& the stu$# o& abstract s)ace*

Most o& the theorems taught in high school geometr# 'ere $evelo)e$ b# an

ancient ?ree mathematician name$ 4ucli$ using a set o& &ive axioms* :et( in the 1th

centur#( mathematicians began to $iscover ne' t#)es o& geometr# that are sel&consistent

but $istinct &rom 4ucli$ean geometr# .?reenberg 1UU18/* All o& these geometries

agree 'ith 4ucli$>s &irst &our axioms( but $i&&er in the &i&th axiom( o&ten calle$ the

)arallel )ostulate( 'hich can be state$ as &ollo's!

For every ine an' for every point that 'oes not ie on there e-ists a uni.ue

ine m through that is parae to /

;ne o&ten uses the terms ,)oint-( ,line-( ,lie on-( ,bet'een-( ,congruent-( an$ ,)lane-

'hen $escribing geometric ob9ects* Most )eo)le thin the# no' 'hat these buil$ing

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blocs o& geometr# mean $es)ite the &act that the terms must be un$e&ine$ &or a

consistent geometric s#stem* The# 'oul$ most liel# &in$ the )oints an$ lines o&

s)herical geometr# to be incom)atible 'ith their $e&initions* n s)herical geometr#( a

,)oint- is a )air o& $iametricall# o))ose$ )oints on a s)here( an$ a ,line- is a circle that

lies on the intersection o& the s)here 'ith a )lane that )asses through the s)here>s center*

Theorems generall# acce)te$ as true in 4ucli$ean geometr# are o&ten &alse in s)herical

geometr#( lie the "#thagorean Theorem* :et( the results o& non4ucli$ean geometries

are 9ust as vali$ as those o& tra$itional geometr#* t is the ambiguit# o& the inter)retations

o& terms lie ,line- an$ ,)oint- that allo's &or this ex)ansion to tae )lace*here non4ucli$ean geometries lac the )arallel )ostulate( "arra>s )oetr# lacs

some as)ects o& conventional )oetr#* He &re6uentl# uses collo6uial language(

unconventional &orms( an$ arguabl# subversive themes* an the )oetr# o& =icanor "arra

be calle$ non4ucli$eanR "arra>s 'ors in some 'a#s )ossess the necessar# 6ualities o&

)oetr#( in the same 'a# non4ucli$ean geometries )ossess the necessar# &eatures o&

geometr#* hat 6uali&ies this association o& seemingl# $istinct &ormsR n mathematics(

sets .inclu$ing geometric ob9ects/ are o&ten classi&ie$ accor$ing to to)ological

e6uivalence( an e6uivalence relation that loos at the &un$amental structure o& each set*

or exam)le( even though each geometr# $i&&ers in its s)eci&ic )ro)erties( it can al'a#s

be $escribe$ using coor$inatesCor$ere$ ntu)lets o& numbers that $escribe ob9ects in

an# geometrical s)ace* This abilit# to inter)ret ob9ects in a $istinct but entirel# $i&&erent

'a# is the ambiguit# that connects the geometries* hat in$ o& structure can 'e &in$

that is &oun$ in both tra$itional an$ alternative )oetr#R The exam)les investigate$ thus

&ar( have &eature$ semantic structures 'hich allo' &or ambiguit#( as 'ell as the

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'hat it means to )ossess an i$ea or ex)erience* Ma#be an i$ea cannot be 6uanti&ie$* An

ex)erience cannot be measure$* s this a )oetic statementR A )oetic statement must be

ambiguousl# $e&ine$( or else 'e 'oul$ be able to unambiguousl# $e&ine )oetr# as

,literature &eaturing the use o& )oetic statements-* The a))earance o& these statements in

the anal#sis o& "arra>s 'riting suggest the# are corres)on$ent to ,)oint-( ,line-( an$ the

other un$e&ine$ ob9ects o& geometr#* +ie these ob9ects( )oetic statements buil$ the

meaning o& a )oem( an$ ma# a))ear even in ver# $istinct &orms( such as that &oun$ in

,Mission Accom)lishe$-*

Although mathematics $oes not o&&er much insight into the macrosco)ic$eviations &rom tra$itional &orm that is o&ten characteristic o& alternative )oetr# .NicuOa>s

$ra'ings( &or exam)le/( the &iel$ o& om)utational +inguistics o&&ers a glim)se o& ho'

structural ambiguit# can arise 'hen one attem)ts to )arse )oetr# in a s#stematic 'a# b#

using &ormal languages to anal#e natural languages .4i9c an$ Ynger 180182/* A

&ormal language is a set o& s#mbols( calle$ atomic &ormulas( an$ a set o& o)erations on

these s#mbols that create ne' &ormulas( also calle$ 'ell&orme$ strings* These s#mbols

have no s)eci&ie$ meanings o& their o'n( but one ma# use &ormal languages to mo$el the

construction o& grammaticall# correct sentences using recursive trans&ormation rules*

Similarl#( one ma# use these rules to $econstruct a sentence in a natural language into

relations bet'een the atomic &ormulas* :et( even in this strictl# mathematical

&rame'or( ambiguities &re6uentl# arise* The most interesting case &rom the vie')oint o&

om)utational Semantics is that o& the structural ambiguit#( 'hich occurs 'hen the

$econstruction o& a sentence results in t'o or more s#ntactic structures* This t#)e o&

ambiguit# has been &eature$ be&ore in the &irst )assage &rom "arra* Ho'ever( 'hereas

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most )oets use this ambiguit# to lin an$ create i$eas( language )oets lie Joan Ietallac

o&ten use this ambiguit# to &orce the rea$er to create his o'n meaning* 4m)son classi&ies

this as the sixth t#)e o& ambiguit#! ,hen a statement sa#s nothing FG so that the rea$er

is &orce$ to invent statements o& his o'n-* These )assages o&ten incor)orate )arataxis( as

in Joan Ietallac>s ,=ot a age- &romroce'ura (egies)*estern +iv +ont,'! ,aroun$

them in us 'e 'ere ver# the#-.11/* t is clear that a $irect anal#sis o& this )assage 'ill

not give an# 'ell&orme$ strings* The rea$er can insert )unctuation an$ connectives or

e$it the mor)holog# o& 'or$s so that such anal#sis is )ossible( but in such extreme cases

this re6uires ma9or changes* ;ne coul$ inter)ret this as ,'hen 'e 'ere aroun$ them( 'e&elt alienate$ &rom ourselves-( or ,'e &elt aligne$ 'ith them 'hen 'e 'ere near them-*

:et( there are no other in$ications in the )assage su))orting either claimCin &act( the

)ronouns ,'e- an$ ,the#- $o not a))ear an#'here else in the stana* The sole metho$ o&

arriving at an# in$ o& semantic meaning in much o& Ietallac>s text is through o)erating

on the text*

:et( it is unliel# that Ietallac inten$e$ &or the entiret# o& her 'or to lac a

message* ;n 'hat level( then shoul$ 'e loo &or meaningR This )roblem is closel#

intert'ine$ 'ith the central )roblems o& To)olog#( the most recentl# $evelo)e$ o& the

ma9or branches o& mathematics* To)olog# is a 'a# o& )reserving the structure an$

essential characteristics o& a set 'ithout )a#ing attention to some o& the $etails* A

to)ological s)ace is a set together 'ith a set containing subsets o& ( calle$ a to)olog#(

that $e&ines a t#)e o& structure on .A$ams an$ ranosa 2/* The ambiguit# arises in

that the sets in an# to)olog# over are calle$ ,o)en sets-* %ecause o& the 'a#to)ologies are $e&ine$( all o)en sets o& a set have similar 6ualities( so one ma# )rove

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Hallgren

theorems about o)en sets o& a s)ace in general* This i$ea can be use$ to anal#e

Ietallac>s )oem ,=ot a age-( a 'or constructe$ &rom the beginnings an$ en$ings o&

boos* %ecause o& the heterogeneous an$ restrictive origin o& the in$ivi$ual lines( it

'oul$ be o& limite$ use to loo at the )oem line b# line* :et( its structure an$ origin

sho' the im)ortance o& ex)erimentalist )hiloso)h# to Ietallac* Also( the &act that

Ietallac create$ a )oem 'ith unconventional &orm in the )rocess o& $iscar$ing

anti6uate$ texts coul$ $emonstrate the im)ortance she )laces on a$vancing )oetr#

through ne' structural elements* A&ter this largescale un$erstan$ing has been

$evelo)e$( the ,to)olog#- o& the )oem ma# be re&ine$* The )oem begins 'ith the )hrase,scienti&ic in6uir#( seen in a ver# broa$ )ers)ective-( )robabl# re&erring to Ietallac>s

belie&s about John age>s or her o'n 'or* Ietallac>s choice to combine the sentences

,=ot a buil$ing( this earth( not a cage(Z The artist- liel# re&lect her i$eas about the

res)onsibilit# o& the artist* This $emonstration o& the )oem>s multi)le la#ers highlights

the ambiguit# o& ,on 'hat level the text is meant to be un$erstoo$-( or ,'hat are the o)en

sets o& the )oem-*

n 'hat res)ect( then( are mathematics an$ )oetr# the science an$ language o&

signi&icant &ormR ;ne ma# inter)ret the signi&icance o& a &orm to be the 6ualit# that

allo's &or multi)le inter)retations( an$ thus the creation o& i$eas through reconciliation

o& these ambiguities* The ,&orm- 'oul$ corres)on$ to the meaning behin$ a s#mbolic

ex)ression in mathematics( or the semantics o& a )oetic com)osition* Then signi&icant

&orms are the birth)lace o& i$eas( an$ that math an$ )oetr# are the languages in 'hich 'e

ex)lore these i$eas*

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Hallgren

ors ite$

4i9c( J* Nan( an$ hristina Ynger* +omputationa Semantics with Functiona

rogramming* ambri$ge! ambri$ge Y"( 2010* "rint*

?reenberg( Marvin J*(uci'ean an' 0on1(uci'ean !eometries: 2eveopment an'

History* San rancisco! *H* reeman( 180* "rint*

"arra( =icanor( an$ +i erner*Antipoems How to Look Better an' Fee !reat/=e'

:or! =e' Directions %oo( 200* "rint*Ietallac( Joan*roce'ura (egies: *estern +iv +ont3'* =e' :or! Ioo&( 2010* "rint*

Samelson( Hans* [Di&&erential orms( the 4arl# Da#s7 or the Stories o& Deahna\s Theorem

an$ o& Nolterra\s Theorem*[ The American Mathematica Monthy108*K .2001/!

n* )ag* "rint*

Ste'art( an*Letters to a 4oung Mathematician* =e' :or! %asic ( a Member o& the

"erseus ?rou)( 200K* "rint*

NicuOa( ecilia*5nstan* F%erele#( ali&*! ]else# St*( 2002* "rint*

["roo& 4x)lorer Home "age Metamath*[roof (-porer 1 Home age 1 Metamath*

=*)*( n*$* eb* 05 Dec* 2012*

A$ams( olin onra$*( an$ Iobert Davi$* ranosa*5ntro'uction to Topoogy: ure an'

Appie'* Y))er Sa$$le Iiver( =J! "earson "rentice Hall( 2008* "rint*

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