An unexpected tool for understanding inequality: abstract math | Eugenia Cheng

Prevodilac: Ivana Krivokuća Lektor: Tijana Mihajlović

The world is awash with divisive arguments,

Svet je prepun razdornih rasprava,

conflict,

konflikata,

fake news,

lažnih vesti,

victimhood,

žrtava,

exploitation, prejudice, bigotry, blame, shouting

iskorišćavanja, predrasuda, netrpeljivosti, okrivljavanja, vikanja

and minuscule attention spans.

i suženog opsega pažnje.

It can sometimes seem that we are doomed to take sides,

Ponekad se čini da smo osuđeni da zauzimamo stranu,

be stuck in echo chambers

da budemo zaglavljeni u eho-komorama

and never agree again.

i da se nikada više ne složimo.

It can sometimes seem like a race to the bottom,

Ponekad se može činiti kao trka do dna,

where everyone is calling out somebody else's privilege

gde svi prozivaju nekog zbog privilegija

and vying to show that they are the most hard-done-by person

i nadmeću se da pokažu da su prošli najgori tretman

in the conversation.

od svih uključenih u razgovor.

How can we make sense

Kako da nađemo smisao

in a world that doesn't?

u svetu koji nema smisla?

I have a tool for understanding this confusing world of ours,

Imam sredstvo za razumevanje ovog našeg zbunjujućeg sveta,

a tool that you might not expect:

sredstvo koje možda niste očekivali:

abstract mathematics.

apstraktnu matematiku.

I am a pure mathematician.

Ja sam čisti matematičar.

Traditionally, pure maths is like the theory of maths,

Tradicionalno, čista matematika je kao teorija matematike,

where applied maths is applied to real problems like building bridges

gde se primenjena matematika upotrebljava za stvarne probleme

poput izgradnje mostova, letova aviona

and flying planes

and controlling traffic flow.

i kontrole protoka saobraćaja.

But I'm going to talk about a way that pure maths applies directly

Ali ja ću govoriti o načinu na koji se čista matematika

direktno primenjuje u našem svakodnevnom životu

to our daily lives

as a way of thinking.

kao način razmišljanja.

I don't solve quadratic equations to help me with my daily life,

Ne rešavam kvadratne jednačine da mi pomognu u svakodnevnom životu,

but I do use mathematical thinking to help me understand arguments

ali koristim matematičko razmišljanje da bi mi pomoglo da razumem argumente

and to empathize with other people.

i da saosećam sa drugima.

And so pure maths helps me with the entire human world.

Tako mi čista matematika pomaže sa čitavim svetom ljudi.

But before I talk about the entire human world,

Ali, pre nego što počnem da govorim o čitavom svetu ljudi,

I need to talk about something that you might think of

moram da govorim o nečemu što možda smatrate

as irrelevant schools maths:

nevažnom školskom matematikom:

factors of numbers.

o činiocima brojeva.

We're going to start by thinking about the factors of 30.

Počećemo razmatranjem činilaca broja 30.

Now, if this makes you shudder with bad memories of school maths lessons,

Ako vas ovo tera da se naježite

zbog loših sećanja na časove matematike u školi,

I sympathize, because I found school maths lessons boring, too.

saosećam sa vama, jer sam i ja mislila da su časovi matematike dosadni.

But I'm pretty sure we are going to take this in a direction

Ali prilično sam sigurna da ćemo sa ovim otići u pravcu

that is very different from what happened at school.

koji se vrlo razlikuje od onog što se odvijalo u školi.

So what are the factors of 30?

Dakle, koji su činioci broja 30?

Well, they're the numbers that go into 30.

Pa, to su brojevi kojima je broj 30 deljiv.

Maybe you can remember them. We'll work them out.

Možda možete da se setite. Navešćemo ih.

To su jedan, dva, tri,

It's one, two, three,

five, six,

pet, šest,

10, 15 and 30.

10, 15 i 30.

It's not very interesting.

To baš i nije zanimljivo.

It's a bunch of numbers in a straight line.

To je gomila brojeva na pravoj liniji.

We can make it more interesting

Možemo da ovo učinimo zanimjivijim

by thinking about which of these numbers are also factors of each other

ako razmislimo koji od ovih brojeva su takođe činioci jedni drugima

and drawing a picture, a bit like a family tree,

i tako što ćemo nacrtati sliku, nalik porodičnom stablu,

to show those relationships.

da bismo prikazali te odnose.

So 30 is going to be at the top like a kind of great-grandparent.

Dakle, broj 30 će biti na vrhu kao neki pradeda.

Six, 10 and 15 go into 30.

Brojevi 6, 10 i 15 su delitelji broja 30.

Five goes into 10 and 15.

Broj 5 je delitelj brojeva 10 i 15.

Two goes into six and 10.

Brojem 2 su deljivi brojevi 6 i 10.

Three goes into six and 15.

Broj 3 je delitelj brojeva 6 i 15.

And one goes into two, three and five.

A brojem jedan možemo podeliti brojeve dva, tri i pet.

So now we see that 10 is not divisible by three,

Sada vidimo da broj 10 nije deljiv brojem 3,

but that this is the corners of a cube,

ali to su temena kocke,

which is, I think, a bit more interesting

što je, rekla bih, malo zanimljivije od gomile brojeva na pravoj liniji.

than a bunch of numbers in a straight line.

We can see something more here. There's a hierarchy going on.

Ovde možemo videti nešto više. Postoji hijerarhija.

At the bottom level is the number one,

Na donjem nivou je broj jedan,

then there's the numbers two, three and five,

zatim su tu brojevi dva, tri i pet,

and nothing goes into those except one and themselves.

a oni nisu deljivi nijednim brojem osim broja jedan i samim sobom.

You might remember this means they're prime.

Možda se sećate da to znači da su prosti brojevi.

At the next level up, we have six, 10 and 15,

Na sledećem nivou imamo 6, 10 i 15,

and each of those is a product of two prime factors.

a svaki od njih je proizvod dva prosta činioca.

So six is two times three,

Dakle, šest je dva puta tri,

10 is two times five,

deset je dva puta pet,

15 is three times five.

petnaest je tri puta pet.

And then at the top, we have 30,

A potom na vrhu imamo 30,

which is a product of three prime numbers --

koji je proizvod tri prosta činioca -

two times three times five.

dva puta tri puta pet.

So I could redraw this diagram using those numbers instead.

Tako mogu da ponovo nacrtam ovaj dijagram koristeći ove brojeve.

We see that we've got two, three and five at the top,

Vidimo da imamo brojeve dva, tri i pet na vrhu,

we have pairs of numbers at the next level,

imamo parove brojeva na sledećem nivou,

and we have single elements at the next level

imamo pojedinačne elemente na sledećem nivou

and then the empty set at the bottom.

i zatim prazan prostor na dnu.

And each of those arrows shows losing one of your numbers in the set.

Svaka od ovih strelica pokazuje gubitak jednog broja u skupu.

Now maybe it can be clear

Možda će biti jasno

that it doesn't really matter what those numbers are.

da nije bitno koji su to brojevi.

In fact, it doesn't matter what they are.

Zapravo, nije bitno koji su.

So we could replace them with something like A, B and C instead,

Zato ih možemo zameniti, recimo, sa A, B i C,

and we get the same picture.

i dobijamo istu sliku.

So now this has become very abstract.

Ovo je sad postalo vrlo apstraktno.

The numbers have turned into letters.

Brojevi su se pretvorili u slova.

But there is a point to this abstraction,

Ali, ova apstrakcija ima poentu,

which is that it now suddenly becomes very widely applicable,

a to je da sada odjednom ovo postaje vrlo široko primenjivo,

because A, B and C could be anything.

jer A, B i C mogu biti bilo šta.

For example, they could be three types of privilege:

Na primer, mogu biti tri vrste privilegija:

rich, white and male.

biti bogat, belac i muškarac.

So then at the next level, we have rich white people.

Onda na sledećem nivou imamo bogate belce.

Here we have rich male people.

Ovde imamo bogate muškarce.

Here we have white male people.

Ovde imamo bele muškarce.

Then we have rich, white and male.

Onda imamo bogate, belce i muškarce.

And finally, people with none of those types of privilege.

I najzad, ljude bez ijedne od tih privilegija.

And I'm going to put back in the rest of the adjectives for emphasis.

Ubaciću i ostatak prideva radi naglašavanja.

So here we have rich, white non-male people,

Dakle, ovde imamo bogate belce koji nisu muškarci,

to remind us that there are nonbinary people we need to include.

da nas podseti da postoje nebinarni ljudi koje moramo uključiti.

Here we have rich, nonwhite male people.

Ovde imamo bogate muškarce koji nisu bele rase.

Here we have non-rich, white male people,

Ovde imamo bele muškarce koji nisu bogati,

rich, nonwhite, non-male,

one koji su bogati a nisu belci ni muškarci,

non-rich, white, non-male

one koji nisu bogati, belci su i nisu muškarci

and non-rich, nonwhite, male.

i one koji nisu bogati ni belci, a muškog su pola.

And at the bottom, with the least privilege,

I na kraju, sa najmanje privilegija,

non-rich, nonwhite, non-male people.

su ljudi koji nisu bogati, nisu belci i nisu muškarci.

We have gone from a diagram of factors of 30

Prešli smo sa dijagrama činilaca broja 30

to a diagram of interaction of different types of privilege.

na dijagram interakcija različitih vrsta privilegija.

And there are many things we can learn from this diagram, I think.

Postoji mnogo stvari koje možemo naučiti sa ovog dijagrama, rekla bih.

The first is that each arrow represents a direct loss of one type of privilege.

Prva je da svaka strelica predstavlja direktan gubitak jedne vrste privilegija.

Sometimes people mistakenly think that white privilege means

Ponekad ljudi pogrešno misle da privilegije belaca podrazumevaju

all white people are better off than all nonwhite people.

da svi belci bolje prolaze od svih koji nisu belci.

Some people point at superrich black sports stars and say,

Neki ljudi ukazuju na sportske zvezde koji su veoma bogati crnci i kažu:

"See? They're really rich. White privilege doesn't exist."

„Vidite? Oni su baš bogati. Belačke privilegije ne postoje.“

But that's not what the theory of white privilege says.

Ali to nije ono o čemu govori teorija o privilegijama belaca.

It says that if that superrich sports star had all the same characteristics

Ona kaže da, kada bi ta prebogata sportska zvezda imala iste osobine,

but they were also white,

ali takođe bila i bele rase,

we would expect them to be better off in society.

očekivali bismo da će imati bolji položaj u društvu.

There is something else we can understand from this diagram

Postoji još nešto što možemo uvideti sa ovog dijagrama

if we look along a row.

ako pogledamo duž jednog reda.

If we look along the second-to-top row, where people have two types of privilege,

Ako pogledamo drugi red odozgo, gde ljudi imaju dve vrste privilegija,

we might be able to see that they're not all particularly equal.

možda ćemo moći da vidimo da nisu svi naročito jednaki.

For example, rich white women are probably much better off in society

Na primer, bogate žene bele rase verovatno mnogo bolje prolaze u društvu

than poor white men,

nego siromašni beli muškarci,

and rich black men are probably somewhere in between.

a bogati muškarci crne rase su verovatno negde između,

So it's really more skewed like this,

tako da je u stvari više nakrivljen ovako,

and the same on the bottom level.

a isto je i na donjem nivou.

But we can actually take it further

Ali zapravo možemo ići i dalje

and look at the interactions between those two middle levels.

i pogledati interakcije između ta dva srednja nivoa.

Because rich, nonwhite non-men might well be better off in society

Jer bogatim ljudima koji nisu belci i nisu muškarci možda bolje ide u društvu

than poor white men.

nego siromašnim belim muškarcima.

Think about some extreme examples, like Michelle Obama,

Pomislite na ekstremne primere kao što su Mišel Obama

Oprah Winfrey.

i Opra Vinfri.

They're definitely better off than poor, white, unemployed homeless men.

Definitivno su u boljoj situaciji

nego siromašni, beli, nezaposleni muškarci beskućnici,

So actually, the diagram is more skewed like this.

tako da je u stvari dijagram više iskrivljen ovako.

And that tension exists

A ta napetost postoji

between the layers of privilege in the diagram

između slojeva privilegija na dijagramu

and the absolute privilege that people experience in society.

i apsolutnih privilegija koje ljudi doživljavaju u društvu.

And this has helped me to understand why some poor white men

Ovo mi je pomoglo da razumem zašto su neki siromašni beli muškarci

are so angry in society at the moment.

trenutno toliko ljuti u društvu.

Because they are considered to be high up in this cuboid of privilege,

Zato što se smatra da se nalaze visoko u ovom kvadru privilegija,

but in terms of absolute privilege, they don't actually feel the effect of it.

ali u smislu apsolutnih privilegija zapravo ne osećaju efekat toga.

And I believe that understanding the root of that anger

Smatram da je razumevanje izvora tog besa mnogo produktivnije

is much more productive than just being angry at them in return.

nego prosto zauzvrat se ljutiti na njih.

Seeing these abstract structures can also help us switch contexts

Sagledavanje ovih apstraktnih struktura nam može pomoći i da promenimo kontekst

and see that different people are at the top in different contexts.

i vidimo da su različiti ljudi na vrhu u različitim kontekstima.

In our original diagram,

Na našem prvobitnom dijagramu,

rich white men were at the top,

bogati beli muškarci su bili na vrhu,

but if we restricted our attention to non-men,

ali ako bismo ograničili pažnju na one koji nisu muškarci,

we would see that they are here,

videli bismo da su ovde,

and now the rich, white non-men are at the top.

i sada su na vrhu bogati ljudi koji su beli i nisu muškarci.

So we could move to a whole context of women,

Možemo preći na čitav kontekst žena,

and our three types of privilege could now be rich, white and cisgendered.

i naše tri vrste privilegija sada mogu biti bogati, beli i cisrodni.

Remember that "cisgendered" means that your gender identity does match

Upamtite da „cisrodni“ znači da se vaš rodni identitet poklapa

the gender you were assigned at birth.

sa rodom koji vam je dodeljen pri rođenju.

So now we see that rich, white cis women occupy the analogous situation

Sada vidimo da bogate i bele cis žene zauzimaju sličnu situaciju

that rich white men did in broader society.

kao i bogati beli muškarci u širem društvu.

And this has helped me understand why there is so much anger

Ovo mi je pomoglo da razumem zašto je toliko besa usmereno

towards rich white women,

prema bogatim ženama bele rase,

especially in some parts of the feminist movement at the moment,

naročito u nekim delovima feminističkog pokreta trenutno,

because perhaps they're prone to seeing themselves as underprivileged

jer su možda sklone da sebe vide kao manje privilegovane

relative to white men,

u odnosu na bele muškarce

and they forget how overprivileged they are relative to nonwhite women.

i zaborave koliko su više privilegovane u odnosu na žene koje nisu bele rase.

We can all use these abstract structures to help us pivot between situations

Svi mi možemo koristiti ove apstraktne strukture

da nam pomognu da razlikujemo situacije

in which we are more privileged and less privileged.

u kojima smo više ili manje privilegovani.

We are all more privileged than somebody

Svi mi smo više privilegovani od nekoga

and less privileged than somebody else.

i manje privilegovani od nekog drugog.

For example, I know and I feel that as an Asian person,

Na primer, znam i osećam da sam, kao osoba azijskog porekla,

I am less privileged than white people

manje privilegovana od ljudi bele rase

because of white privilege.

zbog privilegija belaca.

But I also understand

Ali takođe shvatam

that I am probably among the most privileged of nonwhite people,

da sam verovatno među najprivilegovanijima u grupi ljudi koji nisu belci,

and this helps me pivot between those two contexts.

a to mi pomaže da se orijentišem između ta dva konteksta.

And in terms of wealth,

A u pogledu bogatstva,

I don't think I'm super rich.

mislim da nisam mnogo bogata.

I'm not as rich as the kind of people who don't have to work.

Nisam bogata kao ljudi koji ne moraju da rade.

But I am doing fine,

Ali mi dobro ide,

and that's a much better situation to be in

i to je mnogo bolja situacija

than people who are really struggling,

u odnosu na ljude koji se baš muče,

maybe are unemployed or working at minimum wage.

koji su možda nezaposleni ili rade za minimalnu platu.

I perform these pivots in my head

Vršim te preokrete u svojoj glavi

to help me understand experiences from other people's points of view,

da bi mi pomogli da razumem iskustva sa stanovišta drugih ljudi,

which brings me to this possibly surprising conclusion:

što me dovodi do možda iznenađujućeg zaključka,

that abstract mathematics is highly relevant to our daily lives

da je apstraktna matematika izuzetno značajna za naš svakodnevni život

and can even help us to understand and empathize with other people.

i da nam čak može pomoći da razumemo druge i saosećamo sa njima.

My wish is that everybody would try to understand other people more

Moja želja je da svi pokušaju da bolje razumeju druge ljude

and work with them together,

i sarađuju sa njma

rather than competing with them

umesto da se nadmeću

and trying to show that they're wrong.

i pokušavaju da pokažu da nisu u pravu.

And I believe that abstract mathematical thinking

Verujem da nam apstraktno matematičko razmišljanje

can help us achieve that.

može pomoći da to postignemo.

Thank you.

Hvala.

(Applause)

(Aplauz)