Eduardo Sáenz de Cabezón: Math is forever (with English subtitles) | TED

Translator: Tomás Guarna Reviewer: Sebastian Betti

Prevodilac: Ivana Krivokuća Lektor: Mile Živković

Imagine you're in a bar, or a club,

Zamislite da se nalazite u kafiću ili diskoteci,

i počnete da pričate i nakon izvesnog vremena u razgovoru dođete do:

and you start talking, and after a while, the question comes up,

"So, what do you do for work?"

"A čime se ti baviš?"

And since you think your job is interesting,

you say, "I'm a mathematician." (Laughter)

I pošto mislite da je vaš posao zanimljiv,

kažete: "Ja sam matematičar." (Smeh)

And inevitably, during that conversation

Kada se takav razgovor nastavi, neizbežno se

one of these two phrases come up:

u nekom trenutku javi jedna od ove dve fraze:

A) "I was terrible at math, but it wasn't my fault.

A) "Užasno mi je išla matematika, ali ne mojom krivicom,

It's because the teacher was awful." (Laughter)

to je zato što mi je profesor bio grozan." (Smeh)

Or B) "But what is math really for?"

I B) "Ali čemu služi matematika?"

(Smeh)

(Laughter)

I'll now address Case B.

Pozabaviću se slučajem B.

(Smeh)

(Laughter)

When someone asks you what math is for, they're not asking you

Kada vas neko pita čemu služi matematika,

ne pita vas za primenu naučne matematike.

about applications of mathematical science.

Pita vas:

They're asking you,

"Zašto sam morao da učim to sranje koje nikada više neću koristiti?" (Smeh)

why did I have to study that bullshit I never used in my life again? (Laughter)

That's what they're actually asking.

To je ono što te u stvari pita.

So when mathematicians are asked what math is for,

Najpre, kada matematičara pitaju čemu služi matematika,

mi matematičari se delimo na grupe.

they tend to fall into two groups:

54,51% matematičara zauzima napadački stav,

54.51 percent of mathematicians will assume an attacking position,

and 44.77 percent of mathematicians will take a defensive position.

a 44,77 % zauzima odbrambeni stav.

There's a strange 0.8 percent, among which I include myself.

Postoji i čudnih 0,8%, među kojima se svrstavam.

Ko su oni koji napadaju?

Who are the ones that attack?

Napadači su matematičari koji će vam reći da to pitanje

The attacking ones are mathematicians who would tell you

this question makes no sense,

nema smisla, jer matematika sama po sebi ima smisao,

because mathematics have a meaning all their own --

a beautiful edifice with its own logic --

to je prelepa struktura koja ima sopstvenu logiku koja se izgrađuje

and that there's no point

i nema potrebe stalno tražiti moguće primene.

in constantly searching for all possible applications.

What's the use of poetry? What's the use of love?

Čemu služi poezija? Čemu služi ljubav?

What's the use of life itself? What kind of question is that?

Čemu služi sam život? Kakvo je to pitanje? (Smeh)

(Laughter)

Hardy, for instance, was a model of this type of attack.

Hardi je, na primer, predstavnik takvog napada.

And those who stand in defense tell you,

A oni koji se brane kažu

da iako ne primećujete, matematika se nalazi u osnovi svega. (Smeh)

"Even if you don't realize it, friend, math is behind everything."

(Laughter)

Those guys,

Oni uvek navode, uvek, navode mostove i kompjutere.

they always bring up bridges and computers.

"If you don't know math, your bridge will collapse."

Ako ne znate matematiku, srušiće vam se most. (Smeh)

(Laughter)

It's true, computers are all about math.

Kompjuteri se zaista svode na matematiku.

And now these guys have also started saying

Sad su počeli da govore

da se iza bezbednosti informacija

that behind information security and credit cards are prime numbers.

i kreditnih kartica nalaze primarni brojevi.

To su odgovori koje će vam dati vaš profesor matematike ako ga pitate.

These are the answers your math teacher would give you if you asked him.

He's one of the defensive ones.

Oni su odbrambeni.

Okay, but who's right then?

U redu, ali ko je u pravu?

Those who say that math doesn't need to have a purpose,

Oni koji kažu da matematika ne mora da služi ničemu,

or those who say that math is behind everything we do?

ili oni koji kažu da je ona u stvari u osnovi svega?

Actually, both are right.

Zapravo su u pravu i jedni i drugi.

But remember I told you

Ali rekao sam vam da ja spadam

u onih čudnih 0,8% koji tvrde drugačije, zar ne?

I belong to that strange 0.8 percent claiming something else?

Dakle, hajde, pitajte me čemu služi matematika.

So, go ahead, ask me what math is for.

Audience: What is math for?

(Publika postavlja pitanje)

Eduardo Sáenz de Cabezón: Okay, 76.34 percent of you asked the question,

U redu! 76,34% ljudi je postavilo pitanje,

23.41 percent didn't say anything,

23,41% je ćutalo, i za 0,8% ljudi ne znam šta rade.

and the 0.8 percent --

I'm not sure what those guys are doing.

Well, to my dear 76.31 percent --

Dobro, dragi moji 76,31%, istina je da matematika

it's true that math doesn't need to serve a purpose,

ne mora ničemu da služi, istina je da je ona dragocena logička struktura,

it's true that it's a beautiful structure, a logical one,

probably one of the greatest collective efforts

verovatno jedno od najvećih kolektivnih nastojanja

koje je čovek ikada učinio u svojoj istoriji.

ever achieved in human history.

But it's also true that there,

Ali je takođe istinito da mesto na kome naučnici i tehničari

where scientists and technicians are looking for mathematical theories

traže matematičke teorije, modele koji im omogućavaju da napreduju,

that allow them to advance,

they're within the structure of math, which permeates everything.

je tu, u matematičkoj strukturi, koja prožima sve.

Istina je da moramo da idemo dublje,

It's true that we have to go somewhat deeper,

to see what's behind science.

ka tome šta se nalazi u osnovi nauke.

Science operates on intuition, creativity.

Nauka funkcioniše kroz intuiciju, kreativnost, a matematika

Math controls intuition and tames creativity.

obuzdava intuiciju i kreativnost.

Skoro svi na svetu koji nisu čuli za to ranije, iznenade se da, kada uzmete

Almost everyone who hasn't heard this before

is surprised when they hear that if you take

list papira debljine 0,1 mm, onaj koji normalno koristimo,

a 0.1 millimeter thick sheet of paper, the size we normally use,

ako je dovoljno veliki, tako da ga možete presaviti 50 puta,

and, if it were big enough, fold it 50 times,

its thickness would extend almost the distance from the Earth to the sun.

njegova debljina bi bila jednaka udaljenosti Zemlje od Sunca.

Your intuition tells you it's impossible.

Intuicija vam govori: "To je nemoguće." Izračunajte i videćete da je moguće.

Do the math and you'll see it's right.

That's what math is for.

Tome služi matematika.

Istina je da nauka, celokupna nauka, ima smisla samo zbog toga

It's true that science, all types of science, only makes sense

because it makes us better understand this beautiful world we live in.

što čini da bolje razumemo ovaj prelepi svet u kome živimo.

I pošto to čini, pomaže nam da izbegnemo zamke

And in doing that,

it helps us avoid the pitfalls of this painful world we live in.

ovako bolnog sveta u kome se nalazimo.

Postoje nauke koje ovo direktno primenjuju.

There are sciences that help us in this way quite directly.

Oncological science, for example.

Onkologija, na primer.

And there are others we look at from afar, with envy sometimes,

Ima i drugih koje posmatramo izdaleka, ponekad i sa zavišću,

but knowing that we are what supports them.

ali znajući da smo njihova podrška.

All the basic sciences support them,

Sve osnovne nauke su njihova podrška,

uključujući matematiku.

including math.

All that makes science, science is the rigor of math.

Sve što čini nauka da bi bila nauka jeste strogost matematike.

I ta strogost se javlja jer su njeni rezultati večni.

And that rigor factors in because its results are eternal.

Sigurno ste rekli ili vam je neko nekada rekao

You probably said or were told at some point

that diamonds are forever, right?

da su dijamanti večni, zar ne?

Zavisi šta podrazumevate pod večnošću!

That depends on your definition of forever!

Teorema, to stvarno traje večno! (Smeh)

A theorem -- that really is forever.

(Laughter)

Pitagorina teorema je istinita

The Pythagorean theorem is still true

even though Pythagoras is dead, I assure you it's true. (Laughter)

iako je Pitagora umro, kad vam ja kažem. (Smeh)

Even if the world collapsed

I kada bi se svet srušio, Pitagorina teorema bi bila istinita.

the Pythagorean theorem would still be true.

Gde god da se dodiruje par kateta sa jednom dobrom hipotenuzom, (Smeh)

Wherever any two triangle sides and a good hypotenuse get together

(Laughter)

the Pythagorean theorem goes all out. It works like crazy.

Pitagorina teorema funkcioniše na najvišem nivou. (Aplauz)

(Applause)

Well, we mathematicians devote ourselves to come up with theorems.

Dakle, mi matematičari smo posvećeni stvaranju teorema.

Eternal truths.

Večnih istina. Ali nije uvek tako lako znati

But it isn't always easy to know the difference between

šta je večna istina, teorema, a šta je samo pretpostavka.

an eternal truth, or theorem, and a mere conjecture.

You need proof.

Potrebna je demonstracija.

For example,

Na primer, zamislite da ovde imam veliko, ogromno, beskonačno polje.

let's say I have a big, enormous, infinite field.

Želim da ga prekrijem jednakim delovima, ne ostavljajući razmak.

I want to cover it with equal pieces, without leaving any gaps.

Mogao bih da koristim kvadrate, zar ne?

I could use squares, right?

Mogao bih da koristim trouglove. Krugove ne, ostavljaju praznine.

I could use triangles. Not circles, those leave little gaps.

Which is the best shape to use?

Koji je najbolji oblik koji bih mogao da koristim?

One that covers the same surface, but has a smaller border.

Onaj koji pokriva istu površinu ima najmanje stranice.

In the year 300, Pappus of Alexandria said the best is to use hexagons,

Papos Aleksandrijski je 300. godine rekao da je najbolje koristiti šestouglove,

just like bees do.

kao što to čine pčele. Ali to nije dokazao.

But he didn't prove it.

The guy said, "Hexagons, great! Let's go with hexagons!"

Tip je rekao: "Šestouglovi, o sjajno, hajde, šestouglovi!"

He didn't prove it, it remained a conjecture.

Nije to dokazao, ostala je pretpostavka, rekao je: "Šestouglovi!"

"Hexagons!"

Svet se, kao što znate, podelio na papiste i antipapiste,

And the world, as you know, split into Pappists and anti-Pappists,

until 1700 years later

do 1700 godina kasnije,

when in 1999, Thomas Hales proved

kada je Tomas Hejls 1999. godine dokazao da su Papus

that Pappus and the bees were right -- the best shape to use was the hexagon.

i pčele u pravu, najbolje je koristiti šestouglove.

And that became a theorem, the honeycomb theorem,

I to je postalo teorema, teorema košnice,

koja će ostati istina zauvek, uvek i zanavek,

that will be true forever and ever,

for longer than any diamond you may have. (Laughter)

duže od bilo kog dijamanta koji imate. (Smeh)

But what happens if we go to three dimensions?

Ali šta ako hoćemo 3 dimenzije?

Ako želim da ispunim prostor jednakim delovima,

If I want to fill the space with equal pieces,

ne ostavljajući praznine,

without leaving any gaps,

I can use cubes, right?

mogu da koristim kocke, zar ne?

Not spheres, those leave little gaps. (Laughter)

Lopte ne, jer ostavljaju praznine. (Smeh)

What is the best shape to use?

Koji je najbolji oblik koji bih mogao da koristim?

Lord Kelvin, of the famous Kelvin degrees and all,

Lord Kelvin, onaj po kome su nazvani Kelvinovi stepeni i tako to, rekao je

said that the best was to use a truncated octahedron

da je najbolje koristiti skraćeni oktaedar, (Smeh)

which, as you all know --

a to je, kao što svi znate, (Smeh) ovo ovde! (Aplauz)

(Laughter) --

is this thing here!

(Applause)

Come on.

Hajde! Ko još nema skraćeni oktaedar kod kuće? (Smeh)

Who doesn't have a truncated octahedron at home? (Laughter)

Even a plastic one.

Makar i plastični.

Dušo, donesi skraćeni oktaedar, dolaze nam gosti.

"Honey, get the truncated octahedron, we're having guests."

Everybody has one! (Laughter)

Svi ga imaju! (Smeh) Ali Kelvin nije ovo dokazao.

But Kelvin didn't prove it.

It remained a conjecture -- Kelvin's conjecture.

Ostala je pretpostavka, Kelvinova pretpostavka.

The world, as you know, then split into Kelvinists and anti-Kelvinists

Svet se, kao što znate, podelio na kalviniste i antikalviniste, (Smeh)

(Laughter)

until a hundred or so years later,

sve dok stotinak godina kasnije

neko nije pronašao bolju strukturu.

someone found a better structure.

Weaire and Phelan found this little thing over here --

Veire i Felan su pronašli ovu stvarčicu,

(Smeh) ovu strukturu kojoj su nadenuli veoma maštovito ime

(Laughter) --

this structure to which they gave the very clever name

"the Weaire-€“Phelan structure."

struktura Veire i Felan. (Smeh)

(Laughter)

It looks like a strange object, but it isn't so strange,

Deluje kao čudan predmet ali nije tako čudan,

it also exists in nature.

javlja se i u prirodi.

Vrlo je zanimljivo to da je ova struktura, zbog svojih geometrijskih svojstava,

It's very interesting that this structure,

because of its geometric properties,

korišćena u izgradnji Centra za vodene sportove

was used to build the Aquatics Center for the Beijing Olympic Games.

za Olimpijske igre u Pekingu.

There, Michael Phelps won eight gold medals,

Tamo je Majkl Felps osvojio 8 zlatnih medalja i postao

and became the best swimmer of all time.

najveći plivač svih vremena.

Well, until someone better comes along, right?

Dobro, svih vremena dok ne dođe neko bolji, zar ne?

As may happen with the Weaire-€“Phelan structure.

Kao što je slučaj sa strukturom Veire i Felan,

najbolja je dok se ne pojavi nešto bolje.

It's the best until something better shows up.

But be careful, because this one really stands a chance

Ali pazite, jer ona ima šanse

da, iako prođe stotinak godina, makar bilo i za 1700 godina,

that in a hundred or so years, or even if it's in 1700 years,

neko dokaže da je ovo najbolji mogući oblik.

that someone proves it's the best possible shape for the job.

It will then become a theorem, a truth, forever and ever.

I tada će postati teorema, istina zauvek, uvek i zanavek.

Duže od bilo kog dijamanta.

For longer than any diamond.

So, if you want to tell someone

Dakle, ako želite da kažete nekome da ćete ga voleti zauvek, (Smeh)

that you will love them forever

you can give them a diamond.

možete mu pokloniti dijamant, ali ako želite da kažete

But if you want to tell them that you'll love them forever and ever,

da ćete ga voleti uvek i zanavek, poklonite mu teoremu! (Smeh)

give them a theorem!

(Laughter)

To ćete ipak morati da dokažete,

But hang on a minute!

You'll have to prove it,

so your love doesn't remain

da vaša ljubav ne bi ostala pretpostavka.

a conjecture.

(Aplauz)

(Applause)