Theory of Knowledge - Course Companion for Students Marija Uzunova Dang Arvin Singh Uzunov Dang
st of prolms has n known sin atThisth 6th ntury bce. Nonthlss, lassiallastwith only fw xptionsmathmatiians,as Arhimds, avoidd th topi and itssuhthniqus for aout two millnnia.rlatdth prolms ould not xpliatdSinthy wr outsid th ralm ofgomtrially,mathmatis”. Th rtainty providd“proprgomtry was widly onsidrd an idalyall intlltual ndavours should strivthatPrhaps th anint mathmatiians didfor.want to ruin this rputation with paradoxsnotriddls thy ould not solv. Whil othrandprodution fforts produd disputs,knowldgdmonstration had for nturis uiltgomtrialas of smingly inontstal knowldg.awas not until th 1500s that a“Itgnration of mathmatiiansnwArhimds’s xprimntsrdisovrdinfinitsimals … Thir oldnsswithoff, as th “mthod of indivisils”paid… arly modrnrvolutionizdmaking possil alulationsmathmatis,aras, volums and slops that wrofunattainal. … th mthodprviouslyformalizd at th hands of NwtonwasLiniz, and am th rlialandthat w all th “alulus,” …algorithmmthod of indivisils, foundd onthparadoxial dotrin of th infinitlytham th foundation of allsmall,mathmatis.” (Alxandr 2014)modrnordr for this nw mathmatis to omIning, th old ordr ndd to shift, andintowas rsistan. By th mid-17th ntury,thrintlltuals, and powrful politialprominntrligious figurs from aross Europandorganizing to invalidat infinitsimalwrand liminat this topi from ththniqusdisours.intlltualII. PerspectivesII. Perspectives329
II. Perspectivesdid th st minds of th arly“Whyworld fight so firly ovrmodrninfinitly small? … Th fight wasthth fa of th modrn world. Twoovronfrontd ah othr ovr thampsOn th on sid wr rangdinfinitsimal.fors of hirarhy and ordr—Jsuits,thFrnh royal ourtirs, andHosians,Churh Anglians. Thy livdHigha unifid and fixd ordr in thinoth natural and human, andworld,firly opposd to infinitsimals.wrth othr sid wr omparativOnsuh as Galilo, Wallis,“liralizrs”th Nwtonians. Thy livd inandmor pluralisti and flxil ordr,ath disput ovr indivisilsDuringaov, mathmatis njoyd andsridprominnt pla in puli lif.unusuallythat might wlomd, th fild ofWhilwas also sujt to xtrnalmathmatisprssurs and rligious influns.politialthis is mind, onsidr th followingWithqustions.show us what happns whnInfinitsimalsdomains of knowldg, powr and lifthChaptr 2 xplors th rasons whyovrlap.domains hav n kpt sparat. Thisthsmovs on to onfront th diffiultyhaptrthis sparation, and to onsidr laimsofmathmatial knowldg is politial andthatin ultur.mdddth arly 1980s, th fild ofSinhas formd aroundthnomathmatisof th ida that mathmatisxplorationsnithr ultur-fr nor valu-nutral.isthat might aommodat a rang ofonand divrs ntrs of powr, andviwsinfinitsimals and thir us inhampiond(Alxandr 2014)mathmatis.”lav this story aout th lash ovrWHavn and Earth hr.mathmatis,who ar intrstd may wishRadrssk out Alxandr’s work to furthrtohow th “dangrous ida” ofxplorntrd mathmatis andinfinitsimalsrfltion aout what it mans topromptdand lgitimiz knowldg. Alxandrloklaims aout th ffts of this lashmakspolitial and rligious authority; laimsonshould and ar ing valuatd ythatothrhistorians.In mathmatis, and othr AOKs, is thr1.trad-off twn th powr of idasaHow dos an ovrlap in sujt2.twn mathmatis, politismattrrligion afft th prati ofandand th knowldgmathmatisof mathmatis to nompassprsptivsidas of small-sal Indignous soitisthhav n largly xludd from ththatand history of mathmatis. Forpratiin on of th arly thnomathmatisxampl,survys, Maria Ashr xplorslitraturmathmatial traditions of a wid rangthulturs and offrs xplanations of Navajoofof spa tim, Warlpiri undrstanding ofnotionsrlations, omplx pattrns in Malkulakinshiptraing and so on. W do not hav thsandto go ovr ths xampls in a way thatspathir intlltual traditions. Instad wfitsthat you will tak this as an invitationhopxplor th mathmatis of othr ulturs.tow offr idas and qustions to guidBlow11For discussionMathematics on the public stageand th autonomy of th fild?produd y it?II.3 Is mathematics universalor culture-bound?Rsarhrs in this fild hop to xpandyou in doing so.330
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st of prolms has n known sin at
This
th 6th ntury bce. Nonthlss, lassial
last
with only fw xptions
mathmatiians,
as Arhimds, avoidd th topi and its
suh
thniqus for aout two millnnia.
rlatd
th prolms ould not xpliatd
Sin
thy wr outsid th ralm of
gomtrially,
mathmatis”. Th rtainty providd
“propr
gomtry was widly onsidrd an idal
y
all intlltual ndavours should striv
that
Prhaps th anint mathmatiians did
for.
want to ruin this rputation with paradoxs
not
riddls thy ould not solv. Whil othr
and
prodution fforts produd disputs,
knowldg
dmonstration had for nturis uilt
gomtrial
as of smingly inontstal knowldg.
a
was not until th 1500s that a
“It
gnration of mathmatiians
nw
Arhimds’s xprimnts
rdisovrd
infinitsimals … Thir oldnss
with
off, as th “mthod of indivisils”
paid
… arly modrn
rvolutionizd
making possil alulations
mathmatis,
aras, volums and slops that wr
of
unattainal. … th mthod
prviously
formalizd at th hands of Nwton
was
Liniz, and am th rlial
and
that w all th “alulus,” …
algorithm
mthod of indivisils, foundd on
th
paradoxial dotrin of th infinitly
th
am th foundation of all
small,
mathmatis.” (Alxandr 2014)
modrn
ordr for this nw mathmatis to om
In
ing, th old ordr ndd to shift, and
into
was rsistan. By th mid-17th ntury,
thr
intlltuals, and powrful politial
prominnt
rligious figurs from aross Europ
and
organizing to invalidat infinitsimal
wr
and liminat this topi from th
thniqus
disours.
intlltual
II. Perspectives
II. Perspectives
329