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

Translator: Tomás Guarna Reviewer: Sebastian Betti

Prevoditelj: Jelena Končar Recezent: Ivan Stamenković

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

Zamisli da se nalaziš u kafiću ili klubu,

kreneš razgovarati i nakon nekog vremena

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

pojavi se pitanje: „A čime se ti baviš?“

"So, what do you do for work?"

And since you think your job is interesting,

Budući da misliš da ti je posao zanimljiv kažeš: „Ja sam matematičar.“

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

(Smijeh)

And inevitably, during that conversation

Tijekom razgovora, u jednom trenutku

one of these two phrases come up:

neizbježno se javi jedna od ovih dviju rečenica:

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

A) „Užasno mi je išla matematika, ali ne mojom krivnjom.

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

To je zato što je profesor bio užasan." (Smijeh)

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

I B) „Ali čemu uopće služi matematika?“ (Smijeh)

(Laughter)

I'll now address Case B.

Pozabavit ću se slučajem B. (Smijeh)

(Laughter)

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

Kada te netko pita čemu služi matematika,

ne pita te za primjenu znanstvene matematike.

about applications of mathematical science.

Pita te: „Zašto sam morao učiti to sranje

They're asking you,

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

koje nikad više u životu nisam upotrijebio?“ (Smijeh)

That's what they're actually asking.

To je ono što te zaista pita.

So when mathematicians are asked what math is for,

Stoga kada matematičare pitaju

čemu služi matematika, mi, matematičari, podijelimo se u dvije 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% matematičara zauzima obrambeni stav.

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

Postoji i neobičnih 0,8%, unutar kojih sam i ja.

Tko su oni koji napadaju?

Who are the ones that attack?

Oni koji napadaju su matematičari koji bi ti rekli

The attacking ones are mathematicians who would tell you

this question makes no sense,

da ovo pitanje nema smisla jer matematika ima značenje sama po sebi.

because mathematics have a meaning all their own --

a beautiful edifice with its own logic --

To je prekrasno zdanje sa svojom vlastitom logikom

and that there's no point

i nema smisla stalno tražiti sve moguće primjene.

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? (Smijeh)

(Laughter)

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

Hardy je, primjerice, eksponent takvog napada.

And those who stand in defense tell you,

Oni koji stoje u obrani ti kažu:

„Čak i ako to ne shvaćaš, prijatelju, matematika se nalazi u osnovi svega.“ (Smijeh)

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

(Laughter)

Those guys,

Takvi uvijek spominju mostove i računala.

they always bring up bridges and computers.

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

„Ako ne znaš matematiku, srušit će ti se most.“ (Smijeh)

(Laughter)

It's true, computers are all about math.

Realno, računala se svode na matematiku.

And now these guys have also started saying

I sada su oni također počeli govoriti

that behind information security and credit cards are prime numbers.

da se iza informacijske sigurnosti i kreditnih kartica nalaze primarni brojevi.

To su odgovori koje bi ti dao tvoj profesor matematike kad bi ga pitao.

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

He's one of the defensive ones.

On je jedan od onih obrambenih.

Okay, but who's right then?

Ok, ali tko je onda u pravu?

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

Oni koji kažu da matematika ne treba imati svrhu

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

ili oni koji kažu da je iza svega što radimo?

Zapravo, obje strane su u pravu.

Actually, both are right.

But remember I told you

No rekao sam vam da sam ja u onih 0,8% koji tvrde nešto drugo, zar ne?

I belong to that strange 0.8 percent claiming something else?

Dakle, samo naprijed, pitajte me čemu služi matematika.

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

Audience: What is math for?

Publika: „Čemu služi matematika?“

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

Ok, 6,34% vas postavilo je pitanje, 23,41% nije reklo ništa,

23.41 percent didn't say anything,

and the 0.8 percent --

a onih 0,8% – nisam siguran što oni rade.

I'm not sure what those guys are doing.

Well, to my dear 76.31 percent --

Pa, dragih mojih 76,31%, istina je da matematika ne treba služiti svrsi,

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

istina je da se radi o lijepoj strukturi,

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

logičnoj, i vjerojatno jednom od najvećih zajedničkih napora

probably one of the greatest collective efforts

ikad ostvarenih u ljudskoj podsvijesti.

ever achieved in human history.

But it's also true that there,

Ali isto tako istina je da tamo gdje znanstvenici i tehničari

where scientists and technicians are looking for mathematical theories

traže matematičke teorije koje im omogućuju napredak,

that allow them to advance,

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

oni su unutar matematičke strukture koja prožima sve.

Istina je da moramo otići nešto dublje

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

to see what's behind science.

da vidimo što je iza znanosti.

Science operates on intuition, creativity.

Znanost funkcionira pomoću intuicije, pomoću kreativnosti, a matematika

Math controls intuition and tames creativity.

kontrolira intuiciju i ukroćuje kreativnost.

Gotovo svi koji ovo nisu čuli ranije su iznenađeni kada čuju

Almost everyone who hasn't heard this before

is surprised when they hear that if you take

da kada bi uzeli papir debljine 0,1 mm, kakav obično koristimo,

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

i, kada bi bio dovoljno velik, presavinuli ga 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 bi debljina bila jednaka udaljenosti Zemlje do Sunca.

Your intuition tells you it's impossible.

Intuicija ti kaže: „To je nemoguće.“ Izračunaj i vidjet ćeš da je istina.

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

That's what math is for.

To je ono čemu služi matematika.

Istina je da znanost i sve vrste znanosti imaju smisla samo zato što nam omogućuju

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

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

da bolje razumijemo ovaj lijepi svijet u kojem živimo.

Čineći to, znanost nam pomaže izbjeći zamke

And in doing that,

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

ovog bolnog svijeta u kojem živimo.

Ima znanosti koje nam u tom smislu pomažu prilično izravno.

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

Oncological science, for example.

Onkološka znanost, na primjer.

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

Postoje i druge koje gledamo izdaleka, ponekad sa zavišću, ali i znajući

but knowing that we are what supports them.

da smo mi ono što ih podupire.

All the basic sciences support them,

Podupiru ih sve osnovne znanosti,

među njima i matematiku.

including math.

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

Sve to čini znanost, znanost je strogost matematike.

I ta strogost se javlja jer su njezini rezultati vječni.

And that rigor factors in because its results are eternal.

Vjerojatno ste rekli ili vam je nekad netko rekao

You probably said or were told at some point

that diamonds are forever, right?

da su dijamanti vječni, zar ne?

Ovisi o tome što podrazumijevate pod tim pojmom.

That depends on your definition of forever!

Teorem – to zaista jest zauvijek! (Smijeh)

A theorem -- that really is forever.

(Laughter)

Pitagorin teorem, on je i dalje istinit

The Pythagorean theorem is still true

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

iako je Pitagora mrtav, uvjeravam te. (Smijeh)

Even if the world collapsed

Čak i da se svijet sruši, Pitagorin teorem bi i dalje nastavio biti istinit.

the Pythagorean theorem would still be true.

Gdjegod se dodiruju par kateta i dobra hipotenuza (Smijeh)

Wherever any two triangle sides and a good hypotenuse get together

(Laughter)

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

Pitagorin teorem funkcionira izvrsno.

(Applause)

(Pljesak)

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

Mi, matematičari, posvećeni smo pronalasku teorema.

Eternal truths.

Vječnih istina. Ali nije uvijek tako lako razabrati

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

vječnu istinu, ili teorem, od obične pretpostavke.

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

You need proof.

Treba vam dokaz.

For example,

Primjerice, recimo da ovdje imam veliko, golemo, beskonačno polje.

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

Želim ga prekriti jednakim dijelovima, ne ostavljajući nikakvih praznina.

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

Mogao bih upotrijebiti kvadrate, zar ne?

I could use squares, right?

Mogao bih upotrijebiti trokute. Ne krugove, oni ostavljaju praznine.

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

Which is the best shape to use?

Koji je najbolji oblik koji mogu upotrijebiti?

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

Onaj koji pokriva jednaku površinu, ali ima manje stranice.

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

Pap Aleksandrijski je 300. godine rekao da je najbolje upotrijebiti heksagone,

just like bees do.

kao što to čine pčele. Ali nije to i dokazao!

But he didn't prove it.

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

Tip je rekao: „Heksagoni, odlično! Daj mi heksagone!“

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

On to nije dokazao, ostalo je na pretpostavci.

"Hexagons!"

„Heksagoni!“ I svijet se, kao što znate, podijelio na papiste i antipapiste,

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

until 1700 years later

sve do 1700 kasnije

when in 1999, Thomas Hales proved

kada je 1999. Thomas Hales dokazao

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

da su Pap i pčele bili u pravu, da je najbolje upotrijebiti heksagone.

And that became a theorem, the honeycomb theorem,

I to je postalo teorem, teorem o pčelinjem saću,

koji će biti istinit uvijek i zauvijek,

that will be true forever and ever,

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

dulje od bilo kojeg dijamanta.

(Smijeh)

But what happens if we go to three dimensions?

Ali što se dogodi ako pređemo na tri dimenzije?

Ako želim ispuniti prostor jednakim dijelovima, ne ostavljajući praznine,

If I want to fill the space with equal pieces,

without leaving any gaps,

I can use cubes, right?

mogu upotrijebiti kocke, zar ne?

Not spheres, those leave little gaps. (Laughter)

Ne kugle, one ostavljaju male praznine. (Smijeh)

What is the best shape to use?

Koji je najbolji oblik koji mogu upotrijebiti?

Lord Kelvin, of the famous Kelvin degrees and all,

Lord Kelvin, onaj po kojemu su nazvani čuveni Kelvinovi stupnjevi, rekao je

said that the best was to use a truncated octahedron

da je najbolje upotrijebiti skraćeni oktaedar (Smijeh)

which, as you all know --

koji je, kao što svi znate, (Smijeh) ovo ovdje! (Pljesak)

(Laughter) --

is this thing here!

(Applause)

Come on.

Tko još nema skraćeni oktaedar kod kuće? (Smijeh)

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

Even a plastic one.

Makar i plastični. „Dušo, uzmi skraćeni oktaedar, imamo goste.“

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

Svi imaju jednog! (Smijeh) Ali Kelvin to nije dokazao.

Everybody has one! (Laughter)

But Kelvin didn't prove it.

It remained a conjecture -- Kelvin's conjecture.

Ostalo je na pretpostavci, Kelvinovoj pretpostavci.

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

Svijet se, kao što znate, tada podijelio na kelviniste i antikelviniste

(Smijeh)

(Laughter)

until a hundred or so years later,

sve dok netko stotinjak godina kasnije

nije pronašao bolju strukturu.

someone found a better structure.

Weaire and Phelan found this little thing over here --

Weaire i Phelan pronašli su ovu stvarčicu ovdje

(Smijeh) ovu strukturu kojoj su nadjenuli vrlo dovitljivo ime

(Laughter) --

this structure to which they gave the very clever name

"the Weaire-€“Phelan structure."

„Weaire-Phelanova struktura“. (Smijeh)

(Laughter)

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

Izgleda kao čudna stvar, ali nije tako čudna,

it also exists in nature.

postoji i u prirodi.

It's very interesting that this structure,

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

because of its geometric properties,

bila korištena 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 Michael Phelps osvojio osam zlatnih medalja i postao

and became the best swimmer of all time.

najbolji plivač svih vremena.

Well, until someone better comes along, right?

Dobro, sve dok se ne pojavi netko bolji, zar ne?

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

Kao što se može dogoditi i Weaire-Phelanovoj strukturi.

Najbolja je sve 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

No pazite jer ova zaista ima šanse

da za stotinjak godina, ili čak njih 1700,

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

netko 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.

Tada će postati teorem, istina, uvijek i zauijek.

Dulje od bilo kojeg dijamanta.

For longer than any diamond.

So, if you want to tell someone

Dakle, ako želiš nekome reći da ćeš ga voljeti zauvijek,

that you will love them forever

(Smijeh)

you can give them a diamond.

možeš mu pokloniti dijamant, ali ako mu želiš reći

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

da ćeš ga voljeti uvijek i zauvijek, daj mu teorem!

give them a theorem!

(Smijeh)

(Laughter)

Ali samo malo! Morat ćeš to dokazati

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.

(Pljesak)

(Applause)