TEDxRiodelaPlata
Eduardo Sáenz de Cabezón: Math is forever
Eduardo Sanc de Kabeson (Eduardo Saenz de Cabezon): Matematika je večna
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Uz očaravajući humor, matematičar Eduaro Sanc de Kabeson nam daje odgovor na pitanje koje izluđuje učenike širom sveta: čemu služi matematika? Pokazuje nam lepotu matematike koja predstavlja samu osnovu nauke. Teoreme, a ne dijamati, su večni.
Eduardo Sáenz de Cabezón - Math educator
Eduardo Sáenz de Cabezón links science with humor and stories. Full bio
Eduardo Sáenz de Cabezón links science with humor and stories. Full bio
Double-click the English transcript below to play the video.
00:13
Imagine you're in a bar, or a club,
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Zamislite da se nalazite
u kafiću ili diskoteci,
u kafiću ili diskoteci,
i počnete da pričate i nakon izvesnog
vremena u razgovoru dođete do:
vremena u razgovoru dođete do:
00:19
and you start talking, and after a while,
the question comes up,
the question comes up,
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00:22
"So, what do you do for work?"
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"A čime se ti baviš?"
00:24
And since you think
your job is interesting,
your job is interesting,
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I pošto mislite da je vaš posao zanimljiv,
00:26
you say, "I'm a mathematician."
(Laughter)
(Laughter)
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kažete: "Ja sam matematičar." (Smeh)
Kada se takav razgovor nastavi,
neizbežno se
neizbežno se
00:31
And inevitably, during that conversation
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00:34
one of these two phrases come up:
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u nekom trenutku javi
jedna od ove dve fraze:
jedna od ove dve fraze:
A) "Užasno mi je išla matematika,
ali ne mojom krivicom,
ali ne mojom krivicom,
00:37
A) "I was terrible at math,
but it wasn't my fault.
but it wasn't my fault.
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to je zato što mi je profesor bio grozan."
(Smeh)
(Smeh)
00:41
It's because the teacher
was awful." (Laughter)
was awful." (Laughter)
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I B) "Ali čemu služi matematika?"
00:44
Or B) "But what is math really for?"
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(Smeh)
00:47
(Laughter)
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Pozabaviću se slučajem B.
00:48
I'll now address Case B.
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(Smeh)
00:50
(Laughter)
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Kada vas neko pita čemu služi matematika,
00:52
When someone asks you what math is for,
they're not asking you
they're not asking you
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ne pita vas za primenu naučne matematike.
00:57
about applications
of mathematical science.
of mathematical science.
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Pita vas:
01:00
They're asking you,
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"Zašto sam morao da učim to sranje
koje nikada više neću koristiti?" (Smeh)
koje nikada više neću koristiti?" (Smeh)
01:01
why did I have to study that bullshit
I never used in my life again? (Laughter)
I never used in my life again? (Laughter)
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To je ono što te u stvari pita.
01:05
That's what they're actually asking.
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Najpre, kada matematičara pitaju
čemu služi matematika,
čemu služi matematika,
01:07
So when mathematicians are asked
what math is for,
what math is for,
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mi matematičari se delimo na grupe.
01:12
they tend to fall into two groups:
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54,51% matematičara
zauzima napadački stav,
zauzima napadački stav,
01:14
54.51 percent of mathematicians
will assume an attacking position,
will assume an attacking position,
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a 44,77 % zauzima odbrambeni stav.
01:20
and 44.77 percent of mathematicians
will take a defensive position.
will take a defensive position.
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Postoji i čudnih 0,8%,
među kojima se svrstavam.
među kojima se svrstavam.
01:25
There's a strange 0.8 percent,
among which I include myself.
among which I include myself.
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Ko su oni koji napadaju?
01:29
Who are the ones that attack?
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Napadači su matematičari
koji će vam reći da to pitanje
koji će vam reći da to pitanje
01:31
The attacking ones are mathematicians
who would tell you
who would tell you
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01:33
this question makes no sense,
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nema smisla, jer matematika
sama po sebi ima smisao,
sama po sebi ima smisao,
01:35
because mathematics
have a meaning all their own --
have a meaning all their own --
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to je prelepa struktura koja ima
sopstvenu logiku koja se izgrađuje
sopstvenu logiku koja se izgrađuje
01:38
a beautiful edifice with its own logic --
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01:41
and that there's no point
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i nema potrebe
stalno tražiti moguće primene.
stalno tražiti moguće primene.
01:43
in constantly searching
for all possible applications.
for all possible applications.
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Čemu služi poezija? Čemu služi ljubav?
01:45
What's the use of poetry?
What's the use of love?
What's the use of love?
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Čemu služi sam život?
Kakvo je to pitanje? (Smeh)
Kakvo je to pitanje? (Smeh)
01:47
What's the use of life itself?
What kind of question is that?
What kind of question is that?
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01:50
(Laughter)
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Hardi je, na primer,
predstavnik takvog napada.
predstavnik takvog napada.
01:52
Hardy, for instance, was a model
of this type of attack.
of this type of attack.
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01:56
And those who stand in defense tell you,
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A oni koji se brane kažu
da iako ne primećujete, matematika
se nalazi u osnovi svega. (Smeh)
se nalazi u osnovi svega. (Smeh)
01:58
"Even if you don't realize it, friend,
math is behind everything."
math is behind everything."
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02:03
(Laughter)
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Oni uvek navode, uvek,
navode mostove i kompjutere.
navode mostove i kompjutere.
02:04
Those guys,
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02:06
they always bring up
bridges and computers.
bridges and computers.
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Ako ne znate matematiku,
srušiće vam se most. (Smeh)
srušiće vam se most. (Smeh)
02:10
"If you don't know math,
your bridge will collapse."
your bridge will collapse."
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02:12
(Laughter)
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Kompjuteri se zaista svode na matematiku.
02:14
It's true, computers are all about math.
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Sad su počeli da govore
02:17
And now these guys
have also started saying
have also started saying
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da se iza bezbednosti informacija
02:20
that behind information security
and credit cards are prime numbers.
and credit cards are prime numbers.
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i kreditnih kartica
nalaze primarni brojevi.
nalaze primarni brojevi.
To su odgovori koje će vam dati
vaš profesor matematike ako ga pitate.
vaš profesor matematike ako ga pitate.
02:25
These are the answers your math teacher
would give you if you asked him.
would give you if you asked him.
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Oni su odbrambeni.
02:29
He's one of the defensive ones.
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02:31
Okay, but who's right then?
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U redu, ali ko je u pravu?
Oni koji kažu da matematika
ne mora da služi ničemu,
ne mora da služi ničemu,
02:33
Those who say that math
doesn't need to have a purpose,
doesn't need to have a purpose,
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ili oni koji kažu
da je ona u stvari u osnovi svega?
da je ona u stvari u osnovi svega?
02:35
or those who say that math
is behind everything we do?
is behind everything we do?
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Zapravo su u pravu i jedni i drugi.
02:38
Actually, both are right.
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Ali rekao sam vam da ja spadam
02:40
But remember I told you
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u onih čudnih 0,8%
koji tvrde drugačije, zar ne?
koji tvrde drugačije, zar ne?
02:42
I belong to that strange 0.8 percent
claiming something else?
claiming something else?
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Dakle, hajde,
pitajte me čemu služi matematika.
pitajte me čemu služi matematika.
02:45
So, go ahead, ask me what math is for.
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(Publika postavlja pitanje)
02:48
Audience: What is math for?
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U redu! 76,34% ljudi je postavilo pitanje,
02:51
Eduardo Sáenz de Cabezón: Okay,
76.34 percent of you asked the question,
76.34 percent of you asked the question,
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02:56
23.41 percent didn't say anything,
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23,41% je ćutalo, i za 0,8% ljudi
ne znam šta rade.
ne znam šta rade.
02:59
and the 0.8 percent --
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03:00
I'm not sure what those guys are doing.
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Dobro, dragi moji 76,31%,
istina je da matematika
istina je da matematika
03:03
Well, to my dear 76.31 percent --
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03:07
it's true that math doesn't need
to serve a purpose,
to serve a purpose,
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ne mora ničemu da služi, istina je
da je ona dragocena logička struktura,
da je ona dragocena logička struktura,
03:11
it's true that it's
a beautiful structure, a logical one,
a beautiful structure, a logical one,
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verovatno jedno od najvećih
kolektivnih nastojanja
kolektivnih nastojanja
03:14
probably one
of the greatest collective efforts
of the greatest collective efforts
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koje je čovek ikada učinio
u svojoj istoriji.
u svojoj istoriji.
03:17
ever achieved in human history.
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Ali je takođe istinito
da mesto na kome naučnici i tehničari
da mesto na kome naučnici i tehničari
03:19
But it's also true that there,
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03:21
where scientists and technicians
are looking for mathematical theories
are looking for mathematical theories
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traže matematičke teorije,
modele koji im omogućavaju da napreduju,
modele koji im omogućavaju da napreduju,
03:26
that allow them to advance,
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je tu, u matematičkoj strukturi,
koja prožima sve.
koja prožima sve.
03:28
they're within the structure of math,
which permeates everything.
which permeates everything.
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Istina je da moramo da idemo dublje,
03:32
It's true that we have to go
somewhat deeper,
somewhat deeper,
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ka tome šta se nalazi u osnovi nauke.
03:35
to see what's behind science.
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Nauka funkcioniše kroz intuiciju,
kreativnost, a matematika
kreativnost, a matematika
03:37
Science operates on intuition, creativity.
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obuzdava intuiciju i kreativnost.
03:41
Math controls intuition
and tames creativity.
and tames creativity.
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Skoro svi na svetu koji nisu čuli
za to ranije, iznenade se da, kada uzmete
za to ranije, iznenade se da, kada uzmete
03:45
Almost everyone
who hasn't heard this before
who hasn't heard this before
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03:47
is surprised when they hear
that if you take
that if you take
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list papira debljine 0,1 mm,
onaj koji normalno koristimo,
onaj koji normalno koristimo,
03:50
a 0.1 millimeter thick sheet of paper,
the size we normally use,
the size we normally use,
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ako je dovoljno veliki,
tako da ga možete presaviti 50 puta,
tako da ga možete presaviti 50 puta,
03:55
and, if it were big enough,
fold it 50 times,
fold it 50 times,
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njegova debljina bi bila
jednaka udaljenosti Zemlje od Sunca.
jednaka udaljenosti Zemlje od Sunca.
03:58
its thickness would extend almost
the distance from the Earth to the sun.
the distance from the Earth to the sun.
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Intuicija vam govori: "To je nemoguće."
Izračunajte i videćete da je moguće.
Izračunajte i videćete da je moguće.
04:04
Your intuition tells you it's impossible.
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04:07
Do the math and you'll see it's right.
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Tome služi matematika.
04:09
That's what math is for.
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Istina je da nauka, celokupna nauka,
ima smisla samo zbog toga
ima smisla samo zbog toga
04:12
It's true that science, all types
of science, only makes sense
of science, only makes sense
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što čini da bolje razumemo
ovaj prelepi svet u kome živimo.
ovaj prelepi svet u kome živimo.
04:15
because it makes us better understand
this beautiful world we live in.
this beautiful world we live in.
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I pošto to čini,
pomaže nam da izbegnemo zamke
pomaže nam da izbegnemo zamke
04:19
And in doing that,
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04:20
it helps us avoid the pitfalls
of this painful world we live in.
of this painful world we live in.
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ovako bolnog sveta u kome se nalazimo.
Postoje nauke
koje ovo direktno primenjuju.
koje ovo direktno primenjuju.
04:24
There are sciences that help us
in this way quite directly.
in this way quite directly.
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Onkologija, na primer.
04:27
Oncological science, for example.
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Ima i drugih koje posmatramo izdaleka,
ponekad i sa zavišću,
ponekad i sa zavišću,
04:29
And there are others we look at from afar,
with envy sometimes,
with envy sometimes,
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ali znajući da smo njihova podrška.
04:32
but knowing that we are
what supports them.
what supports them.
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Sve osnovne nauke su njihova podrška,
04:35
All the basic sciences
support them,
support them,
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uključujući matematiku.
04:38
including math.
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Sve što čini nauka da bi bila nauka
jeste strogost matematike.
jeste strogost matematike.
04:40
All that makes science, science
is the rigor of math.
is the rigor of math.
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I ta strogost se javlja
jer su njeni rezultati večni.
jer su njeni rezultati večni.
04:44
And that rigor factors in
because its results are eternal.
because its results are eternal.
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Sigurno ste rekli
ili vam je neko nekada rekao
ili vam je neko nekada rekao
04:49
You probably said or were told
at some point
at some point
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da su dijamanti večni, zar ne?
04:51
that diamonds are forever, right?
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Zavisi šta podrazumevate pod večnošću!
04:56
That depends on
your definition of forever!
your definition of forever!
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Teorema, to stvarno traje večno! (Smeh)
04:58
A theorem -- that really is forever.
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05:00
(Laughter)
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Pitagorina teorema je istinita
05:02
The Pythagorean theorem is still true
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iako je Pitagora umro, kad vam ja kažem.
(Smeh)
(Smeh)
05:05
even though Pythagoras is dead,
I assure you it's true. (Laughter)
I assure you it's true. (Laughter)
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I kada bi se svet srušio,
Pitagorina teorema bi bila istinita.
Pitagorina teorema bi bila istinita.
05:08
Even if the world collapsed
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05:09
the Pythagorean theorem
would still be true.
would still be true.
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Gde god da se dodiruje par kateta
sa jednom dobrom hipotenuzom, (Smeh)
sa jednom dobrom hipotenuzom, (Smeh)
05:12
Wherever any two triangle sides
and a good hypotenuse get together
and a good hypotenuse get together
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05:16
(Laughter)
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Pitagorina teorema funkcioniše
na najvišem nivou. (Aplauz)
na najvišem nivou. (Aplauz)
05:17
the Pythagorean theorem goes all out.
It works like crazy.
It works like crazy.
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05:20
(Applause)
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05:27
Well, we mathematicians devote ourselves
to come up with theorems.
to come up with theorems.
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Dakle, mi matematičari smo posvećeni
stvaranju teorema.
stvaranju teorema.
Večnih istina.
Ali nije uvek tako lako znati
Ali nije uvek tako lako znati
05:31
Eternal truths.
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05:33
But it isn't always easy to know
the difference between
the difference between
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šta je večna istina, teorema,
a šta je samo pretpostavka.
a šta je samo pretpostavka.
05:35
an eternal truth, or theorem,
and a mere conjecture.
and a mere conjecture.
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Potrebna je demonstracija.
05:38
You need proof.
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05:41
For example,
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Na primer, zamislite da ovde imam
veliko, ogromno, beskonačno polje.
veliko, ogromno, beskonačno polje.
05:43
let's say I have a big,
enormous, infinite field.
enormous, infinite field.
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Želim da ga prekrijem jednakim delovima,
ne ostavljajući razmak.
ne ostavljajući razmak.
05:48
I want to cover it with equal pieces,
without leaving any gaps.
without leaving any gaps.
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Mogao bih da koristim kvadrate, zar ne?
05:52
I could use squares, right?
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Mogao bih da koristim trouglove.
Krugove ne, ostavljaju praznine.
Krugove ne, ostavljaju praznine.
05:54
I could use triangles.
Not circles, those leave little gaps.
Not circles, those leave little gaps.
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Koji je najbolji oblik
koji bih mogao da koristim?
koji bih mogao da koristim?
05:58
Which is the best shape to use?
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Onaj koji pokriva istu površinu
ima najmanje stranice.
ima najmanje stranice.
06:01
One that covers the same surface,
but has a smaller border.
but has a smaller border.
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Papos Aleksandrijski je 300. godine rekao
da je najbolje koristiti šestouglove,
da je najbolje koristiti šestouglove,
06:05
In the year 300, Pappus of Alexandria
said the best is to use hexagons,
said the best is to use hexagons,
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kao što to čine pčele.
Ali to nije dokazao.
Ali to nije dokazao.
06:10
just like bees do.
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06:12
But he didn't prove it.
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Tip je rekao: "Šestouglovi, o sjajno,
hajde, šestouglovi!"
hajde, šestouglovi!"
06:13
The guy said, "Hexagons, great!
Let's go with hexagons!"
Let's go with hexagons!"
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Nije to dokazao, ostala je
pretpostavka, rekao je: "Šestouglovi!"
pretpostavka, rekao je: "Šestouglovi!"
06:16
He didn't prove it,
it remained a conjecture.
it remained a conjecture.
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06:19
"Hexagons!"
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Svet se, kao što znate, podelio
na papiste i antipapiste,
na papiste i antipapiste,
06:21
And the world, as you know,
split into Pappists and anti-Pappists,
split into Pappists and anti-Pappists,
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do 1700 godina kasnije,
06:24
until 1700 years later
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kada je Tomas Hejls 1999. godine
dokazao da su Papus
dokazao da su Papus
06:30
when in 1999, Thomas Hales proved
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06:35
that Pappus and the bees were right --
the best shape to use was the hexagon.
the best shape to use was the hexagon.
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i pčele u pravu,
najbolje je koristiti šestouglove.
najbolje je koristiti šestouglove.
I to je postalo teorema, teorema košnice,
06:40
And that became a theorem,
the honeycomb theorem,
the honeycomb theorem,
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koja će ostati istina zauvek,
uvek i zanavek,
uvek i zanavek,
06:43
that will be true forever and ever,
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duže od bilo kog dijamanta koji imate.
(Smeh)
(Smeh)
06:45
for longer than any diamond
you may have. (Laughter)
you may have. (Laughter)
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06:48
But what happens if we go
to three dimensions?
to three dimensions?
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Ali šta ako hoćemo 3 dimenzije?
Ako želim da ispunim prostor
jednakim delovima,
jednakim delovima,
06:51
If I want to fill the space
with equal pieces,
with equal pieces,
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ne ostavljajući praznine,
06:55
without leaving any gaps,
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mogu da koristim kocke, zar ne?
06:56
I can use cubes, right?
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Lopte ne, jer ostavljaju praznine. (Smeh)
06:58
Not spheres, those leave little gaps.
(Laughter)
(Laughter)
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07:01
What is the best shape to use?
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Koji je najbolji oblik
koji bih mogao da koristim?
koji bih mogao da koristim?
Lord Kelvin, onaj po kome su nazvani
Kelvinovi stepeni i tako to, rekao je
Kelvinovi stepeni i tako to, rekao je
07:04
Lord Kelvin, of the famous
Kelvin degrees and all,
Kelvin degrees and all,
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da je najbolje koristiti
skraćeni oktaedar, (Smeh)
skraćeni oktaedar, (Smeh)
07:09
said that the best was to use
a truncated octahedron
a truncated octahedron
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07:16
which, as you all know --
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a to je, kao što svi znate, (Smeh)
ovo ovde! (Aplauz)
ovo ovde! (Aplauz)
07:19
(Laughter) --
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07:21
is this thing here!
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07:22
(Applause)
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07:27
Come on.
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Hajde! Ko još nema
skraćeni oktaedar kod kuće? (Smeh)
skraćeni oktaedar kod kuće? (Smeh)
07:30
Who doesn't have a truncated
octahedron at home? (Laughter)
octahedron at home? (Laughter)
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Makar i plastični.
07:32
Even a plastic one.
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Dušo, donesi skraćeni oktaedar,
dolaze nam gosti.
dolaze nam gosti.
07:34
"Honey, get the truncated octahedron,
we're having guests."
we're having guests."
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Svi ga imaju! (Smeh)
Ali Kelvin nije ovo dokazao.
Ali Kelvin nije ovo dokazao.
07:36
Everybody has one!
(Laughter)
(Laughter)
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07:38
But Kelvin didn't prove it.
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Ostala je pretpostavka,
Kelvinova pretpostavka.
Kelvinova pretpostavka.
07:40
It remained a conjecture --
Kelvin's conjecture.
Kelvin's conjecture.
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07:44
The world, as you know, then split into
Kelvinists and anti-Kelvinists
Kelvinists and anti-Kelvinists
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Svet se, kao što znate, podelio
na kalviniste i antikalviniste, (Smeh)
na kalviniste i antikalviniste, (Smeh)
07:50
(Laughter)
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sve dok stotinak godina kasnije
07:51
until a hundred or so years later,
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neko nije pronašao bolju strukturu.
07:58
someone found a better structure.
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Veire i Felan su pronašli ovu stvarčicu,
08:02
Weaire and Phelan
found this little thing over here --
found this little thing over here --
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(Smeh) ovu strukturu kojoj su nadenuli
veoma maštovito ime
veoma maštovito ime
08:08
(Laughter) --
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08:09
this structure to which they gave
the very clever name
the very clever name
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08:13
"the Weaire-Phelan structure."
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struktura Veire i Felan. (Smeh)
08:15
(Laughter)
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Deluje kao čudan predmet
ali nije tako čudan,
ali nije tako čudan,
08:17
It looks like a strange object,
but it isn't so strange,
but it isn't so strange,
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javlja se i u prirodi.
08:20
it also exists in nature.
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Vrlo je zanimljivo to da je ova struktura,
zbog svojih geometrijskih svojstava,
zbog svojih geometrijskih svojstava,
08:22
It's very interesting that this structure,
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08:24
because of its geometric properties,
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korišćena u izgradnji
Centra za vodene sportove
Centra za vodene sportove
08:27
was used to build the Aquatics Center
for the Beijing Olympic Games.
for the Beijing Olympic Games.
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za Olimpijske igre u Pekingu.
Tamo je Majkl Felps osvojio
8 zlatnih medalja i postao
8 zlatnih medalja i postao
08:32
There, Michael Phelps
won eight gold medals,
won eight gold medals,
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08:35
and became the best swimmer of all time.
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najveći plivač svih vremena.
Dobro, svih vremena
dok ne dođe neko bolji, zar ne?
dok ne dođe neko bolji, zar ne?
08:38
Well, until someone better
comes along, right?
comes along, right?
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Kao što je slučaj
sa strukturom Veire i Felan,
sa strukturom Veire i Felan,
08:42
As may happen
with the Weaire-Phelan structure.
with the Weaire-Phelan structure.
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najbolja je dok se ne pojavi nešto bolje.
08:45
It's the best
until something better shows up.
until something better shows up.
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Ali pazite, jer ona ima šanse
08:47
But be careful, because this one
really stands a chance
really stands a chance
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da, iako prođe stotinak godina,
makar bilo i za 1700 godina,
makar bilo i za 1700 godina,
08:52
that in a hundred or so years,
or even if it's in 1700 years,
or even if it's in 1700 years,
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neko dokaže
da je ovo najbolji mogući oblik.
da je ovo najbolji mogući oblik.
08:57
that someone proves
it's the best possible shape for the job.
it's the best possible shape for the job.
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I tada će postati teorema,
istina zauvek, uvek i zanavek.
istina zauvek, uvek i zanavek.
09:02
It will then become a theorem,
a truth, forever and ever.
a truth, forever and ever.
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Duže od bilo kog dijamanta.
09:07
For longer than any diamond.
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Dakle, ako želite da kažete
nekome da ćete ga voleti zauvek, (Smeh)
nekome da ćete ga voleti zauvek, (Smeh)
09:10
So, if you want to tell someone
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09:15
that you will love them forever
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možete mu pokloniti dijamant,
ali ako želite da kažete
ali ako želite da kažete
09:18
you can give them a diamond.
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09:20
But if you want to tell them
that you'll love them forever and ever,
that you'll love them forever and ever,
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da ćete ga voleti uvek i zanavek,
poklonite mu teoremu! (Smeh)
poklonite mu teoremu! (Smeh)
09:24
give them a theorem!
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09:26
(Laughter)
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To ćete ipak morati da dokažete,
09:27
But hang on a minute!
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09:30
You'll have to prove it,
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da vaša ljubav ne bi ostala pretpostavka.
09:32
so your love doesn't remain
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09:34
a conjecture.
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(Aplauz)
09:36
(Applause)
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ABOUT THE SPEAKER
Eduardo Sáenz de Cabezón - Math educatorEduardo Sáenz de Cabezón links science with humor and stories.
Why you should listen
Eduardo Sáenz de Cabezón links science with humor and stories. He studied theology and has a PhD in mathematics from the University of La Rioja. He speaks on these two topics in universities and secondary schools as a storyteller for children, youth and adults. Sáenz de Cabezón has also been a professor of Computer Information Systems, Discrete Mathematics and Algebra at the University of La Rioja since 2010.
He won the FameLab contest for scientific monologues in Spain in 2013.
Eduardo Sáenz de Cabezón | Speaker | TED.com