Theory of Knowledge - Course Companion for Students Marija Uzunova Dang Arvin Singh Uzunov Dang
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Theory of Knowledge - Course Companion for Students Marija Uzunova Dang Arvin Singh Uzunov Dang

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argue that, while there’s a biological grounding,I’dand cultural traits are necessary for thelanguageanimals hav a quantitativ sns, forManying al to distinguish whih undlxamplwith newborns and infants show that, ifStudiesshow them eight dots repeatedly and thenyouit to 16 dots, areas in the right parietalchangeof the brain respond to a change incortexhas ld som rsarhrs to thoriz thatThisnumrial sns is innat.asuh as Rafal Núñz, argu that thOthrs,of a iologially ndowd numrargumntis asd on skthy sin: inauratsnsof iologial volution, ovr-undrstandingon WEIRD population sampls (asmphasisin Chaptr 8) and ovrintrprtationdisussdrsults from traind animals. W must alsoofth diffrn twn quantial andnotognition: quantial rlats to hownumrialappls thr ar in a askt, or how manymanyon a oard, whras numrial ognitiondotswith symols suh as 3, 4 and 5.dalsbecause a behaviour seems to derive from anJustcapacity, that doesn’t mean the behaviourinnateitself innate. ... No non-human animal has yetisfound able to distinguish 152 items from 153.beencan’t do that, no matter how hard you trainChimpsyet many children can tell you even by thethem,of ve that the two numbers dier in the sameageas do the equally abstract numbers 2 and 3:wayrsarhrs do not apt that numrialOthris a ulturally drivd aility.ognitionthat th rain is “prdisposd to aquirargusnumr systm” that ultur an furthraand rfin. But without this iologialshaphumans would nvr hav a numrapaity,Chaptr 8 w nountr th ida ofInan argumnt that naturnaturultur,ultur ar so tightly onntd inandrlationships that w ar ttr offologialsparating thm. If w apt Núñz’snotfor th momnt, that quantialargumntannot volv into numrialognitionwithout th influn of ultur, whatognitiondo w hav? Núñz suggsts thatvidnulturs around th world hav no wordsmanysymols for numrs largr than fiv or six.orwords quivalnt to “many” ar usd.Instad,the language of the Munduruku people of theInfor example, adesu indicates ‘several’Amazon,ade implies ‘really lots’. These cultureswhereaswith what to us looks like imprecision: it reallylivematter if, when the oranges are divideddoesn’tone person gets 152 and the other 153. Andup,if we aren’t so number-xated, it reallyfrankly,matter. So why bother having words todoesn’tdiffrns twn larg numrsSmallmattr for many thnologial andlarlyappliations. Howvr, on argumntsintifithat humans’ innat quantial sns isisth diffrn twn on andlogarithmi:is muh gratr than twn fiv and six,twofor most ativitis in th human ra, thisandsuffiint.wasII. PerspectivesII. Perspectivesestablishment of number itself’.(Ball 2017)aility (Nidr quotd in Ball 2017).of food is iggr, and it appars innat to humans.numerosity. This response is very similar in adults.(Ansari quoted in Ball 2017)distinguish them?(Ball 2017)Arithmetic scale1 2 3 4 56 7 8 9 10 13 16namely, by 1 … .Logarithmic scale(Núñez quoted in Ball 2017)6 7 8 9 12 161 2 3 4 5Arithmti and logarithmi salsFigure 11.3Nuroiologist Andras Nidr, for xampl,333

II. Perspectivesognitiv nurosintist StanislasThhas suggstd that whil WstrnDhanand hildrn gnrally us an vnlyadultsnumr lin, th Mundurukuspada logarithmi sal. Th rsarhrsusthat hildrn who larn to spaspulatarithmtially must first ovromnumrslogarithmi intuitions. Howvr,innatis an insapal irony in Wstrnthrattmpting to prisly quantifysintistsimpris mapping of quantitis y athgroup of Indignous Popl doingsmallTh rsarhrs hav notd that thpuzzls.in thir rsults is too grat to allowvariailityaout outoms from th rpliationThinkingto what xtnt would you gnralizrisis,aout humans having a logarithmilaimssns?quantialeasy to read this as a ‘primitive’ way of reasoning,It’santhropology has long dispelled such patronisingbut… . You develop words and concepts forprejudicetruly matters to your society. From a practicalwhatone could argue that it’s actually theperspective,homogeneous group of industrialisedsomewhatthat look odd, with their pedantic distinctioncultures1,000,002 and 1,000,003.betweenmathmatiian Morris Klin has writtnThthat “ompard with thondsndinglyof thir immdiat sussors,aomplishmntsGrks, th mathmatis of th EgyptiansthBaylonians is th srawling of hildrn justandto writ as opposd to grat litratur”larningattituds xprssd in this quot havThstrongly ritiizd and nouragd thnffort in mathmatis. Klin’sdolonizationhos th sam myths nountrdommntfurthr ompliat mattrs, thr isTothat th two systms—quantial andvidnprossd diffrntly in thnumrial—arand thrfor appar to unorrlatd.rain,hallngs th ida that th quantialThisvolvd into a numrial systm.systmdos this mattr for knowldg? ThHowinflun mathmatis duation,impliationsxampl. Rsarhrs at th Johns Hopkinsforshowd a orrlation twnUnivrsityaility to disriminat twn14-yar-olds’numrial quantitis (suh as th numrxatdots in an imag) and thir tst sors inofall th way ak to kindrgartnmathmatiset al 2008). Th orrlation has n(Halrdato dvlop duational tools to assss andusdmathmatial aility, for xampl inimprovthat ask hildrn to quikly assss howtstslanguag th origin of our numrialCouldand of mathmatis? Did w ginsns,in itself may be a necessary condition forLanguagebut it is not sucient for it … . All knownnumber,cultures have language, but by no means allhumanexact quantication in the form of number.havehistory and th human andlswhr—insins—that non-Wstrn ulturs andnaturalis a urious and hallngingMathmatisin th widr movmnt for duationalasand dolonizing duation. Enrgizdquityhav arisn in at last two aras. Ondatshow th history of mathmatis is told andisTh sond takls th prsistnt liftaught.mathmatis is nutral from th point ofthatlass and gndr. This has n th sit ofra,dat and ontrovrsy, suh as thsignifiantmovmnt in lat 2017.#IStandWithRohll11for strong onlusions.many dots ar on a pag.ounting whn w ould nam numrs?(Núñez quoted in Ball 2017)(Ball 2017)II.4 Diversity and many mathematicsintlltual traditions lag hind.(Klin 1985).334

II. Perspectives

ognitiv nurosintist Stanislas

Th

has suggstd that whil Wstrn

Dhan

and hildrn gnrally us an vnly

adults

numr lin, th Munduruku

spad

a logarithmi sal. Th rsarhrs

us

that hildrn who larn to spa

spulat

arithmtially must first ovrom

numrs

logarithmi intuitions. Howvr,

innat

is an insapal irony in Wstrn

thr

attmpting to prisly quantify

sintists

impris mapping of quantitis y a

th

group of Indignous Popl doing

small

Th rsarhrs hav notd that th

puzzls.

in thir rsults is too grat to allow

variaility

aout outoms from th rpliation

Thinking

to what xtnt would you gnraliz

risis,

aout humans having a logarithmi

laims

sns?

quantial

easy to read this as a ‘primitive’ way of reasoning,

It’s

anthropology has long dispelled such patronising

but

… . You develop words and concepts for

prejudice

truly matters to your society. From a practical

what

one could argue that it’s actually the

perspective,

homogeneous group of industrialised

somewhat

that look odd, with their pedantic distinction

cultures

1,000,002 and 1,000,003.

between

mathmatiian Morris Klin has writtn

Th

that “ompard with th

ondsndingly

of thir immdiat sussors,

aomplishmnts

Grks, th mathmatis of th Egyptians

th

Baylonians is th srawling of hildrn just

and

to writ as opposd to grat litratur”

larning

attituds xprssd in this quot hav

Th

strongly ritiizd and nouragd th

n

ffort in mathmatis. Klin’s

dolonization

hos th sam myths nountrd

ommnt

furthr ompliat mattrs, thr is

To

that th two systms—quantial and

vidn

prossd diffrntly in th

numrial—ar

and thrfor appar to unorrlatd.

rain,

hallngs th ida that th quantial

This

volvd into a numrial systm.

systm

dos this mattr for knowldg? Th

How

influn mathmatis duation,

impliations

xampl. Rsarhrs at th Johns Hopkins

for

showd a orrlation twn

Univrsity

aility to disriminat twn

14-yar-olds’

numrial quantitis (suh as th numr

xat

dots in an imag) and thir tst sors in

of

all th way ak to kindrgartn

mathmatis

et al 2008). Th orrlation has n

(Halrda

to dvlop duational tools to assss and

usd

mathmatial aility, for xampl in

improv

that ask hildrn to quikly assss how

tsts

languag th origin of our numrial

Could

and of mathmatis? Did w gin

sns,

in itself may be a necessary condition for

Language

but it is not sucient for it … . All known

number,

cultures have language, but by no means all

human

exact quantication in the form of number.

have

history and th human and

lswhr—in

sins—that non-Wstrn ulturs and

natural

is a urious and hallnging

Mathmatis

in th widr movmnt for duational

as

and dolonizing duation. Enrgizd

quity

hav arisn in at last two aras. On

dats

how th history of mathmatis is told and

is

Th sond takls th prsistnt lif

taught.

mathmatis is nutral from th point of

that

lass and gndr. This has n th sit of

ra,

dat and ontrovrsy, suh as th

signifiant

movmnt in lat 2017.

#IStandWithRohll

11

for strong onlusions.

many dots ar on a pag.

ounting whn w ould nam numrs?

(Núñez quoted in Ball 2017)

(Ball 2017)

II.4 Diversity and many mathematics

intlltual traditions lag hind.

(Klin 1985).

334

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