TEDxRiodelaPlata
Eduardo Sáenz de Cabezón: Math is forever
Eduardo Sáenz de Cabezón: Matematika je zauvijek
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Uz zarazni humor, matematičar Eduardo Sáenz de Cabezón daje nam odgovor na pitanje koje je izluđivalo učenjake iz cijelog svijeta: čemu služi matematika? Pokazuje nam ljepotu matematike, koja nije ništa drugo nego okosnica znanosti. Teoremi, a ne dijamanti, su zauvijek.
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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Zamisli da se nalaziš u kafiću ili klubu,
kreneš razgovarati
i nakon nekog vremena
i nakon nekog vremena
00:19
and you start talking, and after a while,
the question comes up,
the question comes up,
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pojavi se pitanje:
„A čime se ti baviš?“
„A čime se ti baviš?“
00:22
"So, what do you do for work?"
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00:24
And since you think
your job is interesting,
your job is interesting,
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Budući da misliš da ti je posao zanimljiv
kažeš: „Ja sam matematičar.“
kažeš: „Ja sam matematičar.“
00:26
you say, "I'm a mathematician."
(Laughter)
(Laughter)
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(Smijeh)
Tijekom razgovora, u jednom trenutku
00:31
And inevitably, during that conversation
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00:34
one of these two phrases come up:
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neizbježno se javi
jedna od ovih dviju rečenica:
jedna od ovih dviju rečenica:
A) „Užasno mi je išla matematika,
ali ne mojom krivnjom.
ali ne mojom krivnjom.
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 je profesor
bio užasan." (Smijeh)
bio užasan." (Smijeh)
00:41
It's because the teacher
was awful." (Laughter)
was awful." (Laughter)
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I B) „Ali čemu uopće služi
matematika?“ (Smijeh)
matematika?“ (Smijeh)
00:44
Or B) "But what is math really for?"
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00:47
(Laughter)
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Pozabavit ću se slučajem B.
(Smijeh)
(Smijeh)
00:48
I'll now address Case B.
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00:50
(Laughter)
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Kada te netko 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 te za primjenu znanstvene matematike.
00:57
about applications
of mathematical science.
of mathematical science.
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Pita te: „Zašto sam morao učiti to sranje
01:00
They're asking you,
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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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koje nikad više u životu
nisam upotrijebio?“ (Smijeh)
nisam upotrijebio?“ (Smijeh)
To je ono što te zaista pita.
01:05
That's what they're actually asking.
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01:07
So when mathematicians are asked
what math is for,
what math is for,
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Stoga kada matematičare pitaju
čemu služi matematika, mi, matematičari,
podijelimo se u dvije grupe.
podijelimo se u dvije 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% matematičara
zauzima obrambeni stav.
zauzima obrambeni 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 neobičnih 0,8%,
unutar kojih sam i ja.
unutar kojih sam i ja.
01:25
There's a strange 0.8 percent,
among which I include myself.
among which I include myself.
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Tko su oni koji napadaju?
01:29
Who are the ones that attack?
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Oni koji napadaju su
matematičari koji bi ti rekli
matematičari koji bi ti rekli
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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da ovo pitanje nema smisla
jer matematika ima značenje sama po sebi.
jer matematika ima značenje sama po sebi.
01:35
because mathematics
have a meaning all their own --
have a meaning all their own --
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To je prekrasno zdanje
sa svojom vlastitom logikom
sa svojom vlastitom logikom
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 smisla stalno tražiti
sve moguće primjene.
sve moguće primjene.
01:43
in constantly searching
for all possible applications.
for all possible applications.
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Čemu služi poezija?
Čemu služi ljubav?
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? (Smijeh)
Kakvo je to pitanje? (Smijeh)
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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Hardy je, primjerice,
eksponent takvog napada.
eksponent 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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Oni koji stoje
u obrani ti kažu:
u obrani ti kažu:
„Čak i ako to ne shvaćaš, prijatelju,
matematika se nalazi u osnovi svega.“ (Smijeh)
matematika se nalazi u osnovi svega.“ (Smijeh)
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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Takvi uvijek spominju
mostove i računala.
mostove i računala.
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 znaš matematiku,
srušit će ti se most.“ (Smijeh)
srušit će ti se most.“ (Smijeh)
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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Realno, računala se svode na matematiku.
02:14
It's true, computers are all about math.
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I sada su oni također
počeli govoriti
počeli govoriti
02:17
And now these guys
have also started saying
have also started saying
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02:20
that behind information security
and credit cards are prime numbers.
and credit cards are prime numbers.
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da se iza informacijske sigurnosti i
kreditnih kartica nalaze primarni brojevi.
kreditnih kartica nalaze primarni brojevi.
To su odgovori koje bi ti dao
tvoj profesor matematike kad bi ga pitao.
tvoj profesor matematike kad bi ga pitao.
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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On je jedan od onih obrambenih.
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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Ok, ali tko je onda u pravu?
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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Oni koji kažu da matematika
ne treba imati svrhu
ne treba imati svrhu
ili oni koji kažu da je
iza svega što radimo?
iza svega što radimo?
02:35
or those who say that math
is behind everything we do?
is behind everything we do?
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Zapravo, obje strane su u pravu.
02:38
Actually, both are right.
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No rekao sam vam da sam ja u onih 0,8%
koji tvrde nešto drugo, zar ne?
koji tvrde nešto drugo, zar ne?
02:40
But remember I told you
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02:42
I belong to that strange 0.8 percent
claiming something else?
claiming something else?
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Dakle, samo naprijed,
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: „Čemu služi matematika?“
02:48
Audience: What is math for?
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Ok, 6,34% vas postavilo je pitanje,
23,41% nije reklo ništa,
23,41% nije reklo ništa,
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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a onih 0,8% – nisam siguran što oni 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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Pa, dragih mojih 76,31%, istina je
da matematika ne treba služiti svrsi,
da matematika ne treba služiti svrsi,
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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istina je da se radi o lijepoj strukturi,
03:11
it's true that it's
a beautiful structure, a logical one,
a beautiful structure, a logical one,
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logičnoj, i vjerojatno
jednom od najvećih zajedničkih napora
jednom od najvećih zajedničkih napora
03:14
probably one
of the greatest collective efforts
of the greatest collective efforts
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ikad ostvarenih u ljudskoj podsvijesti.
03:17
ever achieved in human history.
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Ali isto tako istina je da tamo gdje
znanstvenici i tehničari
znanstvenici 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
koje im omogućuju napredak,
koje im omogućuju napredak,
03:26
that allow them to advance,
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oni su unutar matematičke strukture
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 otići
nešto dublje
nešto dublje
03:32
It's true that we have to go
somewhat deeper,
somewhat deeper,
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da vidimo što je
iza znanosti.
iza znanosti.
03:35
to see what's behind science.
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Znanost funkcionira pomoću intuicije,
pomoću kreativnosti, a matematika
pomoću kreativnosti, a matematika
03:37
Science operates on intuition, creativity.
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kontrolira intuiciju
i ukroćuje kreativnost.
i ukroćuje kreativnost.
03:41
Math controls intuition
and tames creativity.
and tames creativity.
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Gotovo svi koji ovo nisu čuli ranije
su iznenađeni kada čuju
su iznenađeni kada čuju
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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da kada bi uzeli papir debljine 0,1 mm,
kakav obično koristimo,
kakav obično 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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i, kada bi bio dovoljno velik,
presavinuli ga 50 puta,
presavinuli ga 50 puta,
03:55
and, if it were big enough,
fold it 50 times,
fold it 50 times,
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njegova bi debljina bila jednaka
udaljenosti Zemlje do Sunca.
udaljenosti Zemlje do 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 ti kaže: „To je nemoguće.“
Izračunaj i vidjet ćeš da je istina.
Izračunaj i vidjet ćeš da je istina.
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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To je ono čemu služi matematika.
04:09
That's what math is for.
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Istina je da znanost i sve vrste znanosti
imaju smisla samo zato što nam omogućuju
imaju smisla samo zato što nam omogućuju
04:12
It's true that science, all types
of science, only makes sense
of science, only makes sense
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da bolje razumijemo
ovaj lijepi svijet u kojem živimo.
ovaj lijepi svijet u kojem 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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Čineći to, znanost nam
pomaže izbjeći zamke
pomaže izbjeći 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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ovog bolnog svijeta
u kojem živimo.
u kojem živimo.
Ima znanosti koje nam u tom smislu
pomažu prilično izravno.
pomažu prilično izravno.
04:24
There are sciences that help us
in this way quite directly.
in this way quite directly.
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Onkološka znanost, na primjer.
04:27
Oncological science, for example.
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Postoje i druge koje gledamo izdaleka,
ponekad sa zavišću, ali i znajući
ponekad sa zavišću, ali i znajući
04:29
And there are others we look at from afar,
with envy sometimes,
with envy sometimes,
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da smo mi ono što ih podupire.
04:32
but knowing that we are
what supports them.
what supports them.
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Podupiru ih sve osnovne znanosti,
04:35
All the basic sciences
support them,
support them,
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među njima i matematiku.
04:38
including math.
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Sve to čini znanost,
znanost je strogost matematike.
znanost je 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 njezini rezultati vječni.
jer su njezini rezultati vječni.
04:44
And that rigor factors in
because its results are eternal.
because its results are eternal.
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Vjerojatno ste rekli
ili vam je nekad netko rekao
ili vam je nekad netko rekao
04:49
You probably said or were told
at some point
at some point
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da su dijamanti vječni, zar ne?
04:51
that diamonds are forever, right?
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Ovisi o tome što podrazumijevate
pod tim pojmom.
pod tim pojmom.
04:56
That depends on
your definition of forever!
your definition of forever!
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Teorem – to zaista
jest zauvijek! (Smijeh)
jest zauvijek! (Smijeh)
04:58
A theorem -- that really is forever.
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05:00
(Laughter)
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Pitagorin teorem,
on je i dalje istinit
on je i dalje istinit
05:02
The Pythagorean theorem is still true
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iako je Pitagora mrtav,
uvjeravam te. (Smijeh)
uvjeravam te. (Smijeh)
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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Čak i da se svijet sruši, Pitagorin teorem
bi i dalje nastavio biti istinit.
bi i dalje nastavio biti istinit.
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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Gdjegod se dodiruju par kateta
i dobra hipotenuza (Smijeh)
i dobra hipotenuza (Smijeh)
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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Pitagorin teorem funkcionira izvrsno.
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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(Pljesak)
Mi, matematičari, posvećeni smo
pronalasku teorema.
pronalasku teorema.
05:27
Well, we mathematicians devote ourselves
to come up with theorems.
to come up with theorems.
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Vječnih istina. Ali nije uvijek
tako lako razabrati
tako lako razabrati
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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vječnu istinu, ili teorem,
od obične pretpostavke.
od obične pretpostavke.
05:35
an eternal truth, or theorem,
and a mere conjecture.
and a mere conjecture.
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Treba vam dokaz.
05:38
You need proof.
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05:41
For example,
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Primjerice, recimo da ovdje imam
veliko, golemo, beskonačno polje.
veliko, golemo, beskonačno polje.
05:43
let's say I have a big,
enormous, infinite field.
enormous, infinite field.
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Želim ga prekriti jednakim dijelovima,
ne ostavljajući nikakvih praznina.
ne ostavljajući nikakvih praznina.
05:48
I want to cover it with equal pieces,
without leaving any gaps.
without leaving any gaps.
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Mogao bih upotrijebiti kvadrate, zar ne?
05:52
I could use squares, right?
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Mogao bih upotrijebiti trokute.
Ne krugove, oni ostavljaju praznine.
Ne krugove, oni 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 mogu upotrijebiti?
koji mogu upotrijebiti?
05:58
Which is the best shape to use?
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Onaj koji pokriva jednaku površinu,
ali ima manje stranice.
ali ima manje stranice.
06:01
One that covers the same surface,
but has a smaller border.
but has a smaller border.
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Pap Aleksandrijski je 300. godine rekao
da je najbolje upotrijebiti heksagone,
da je najbolje upotrijebiti heksagone,
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 nije to i dokazao!
Ali nije to i 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: „Heksagoni, odlično!
Daj mi heksagone!“
Daj mi heksagone!“
06:13
The guy said, "Hexagons, great!
Let's go with hexagons!"
Let's go with hexagons!"
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On to nije dokazao,
ostalo je na pretpostavci.
ostalo je na pretpostavci.
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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„Heksagoni!“ I svijet se, kao što znate,
podijelio na papiste i antipapiste,
podijelio 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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sve do 1700 kasnije
06:24
until 1700 years later
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kada je 1999. Thomas Hales dokazao
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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da su Pap i pčele bili u pravu,
da je najbolje upotrijebiti heksagone.
da je najbolje upotrijebiti heksagone.
I to je postalo teorem,
teorem o pčelinjem saću,
teorem o pčelinjem saću,
06:40
And that became a theorem,
the honeycomb theorem,
the honeycomb theorem,
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koji će biti istinit
uvijek i zauvijek,
uvijek i zauvijek,
06:43
that will be true forever and ever,
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dulje od bilo kojeg dijamanta.
06:45
for longer than any diamond
you may have. (Laughter)
you may have. (Laughter)
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(Smijeh)
Ali što se dogodi ako
pređemo na tri dimenzije?
pređemo na tri dimenzije?
06:48
But what happens if we go
to three dimensions?
to three dimensions?
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Ako želim ispuniti prostor jednakim
dijelovima, ne ostavljajući praznine,
dijelovima, ne ostavljajući praznine,
06:51
If I want to fill the space
with equal pieces,
with equal pieces,
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06:55
without leaving any gaps,
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mogu upotrijebiti kocke, zar ne?
06:56
I can use cubes, right?
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Ne kugle, one ostavljaju
male praznine. (Smijeh)
male praznine. (Smijeh)
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 mogu upotrijebiti?
koji mogu upotrijebiti?
Lord Kelvin, onaj po kojemu su nazvani
čuveni Kelvinovi stupnjevi, rekao je
čuveni Kelvinovi stupnjevi, rekao je
07:04
Lord Kelvin, of the famous
Kelvin degrees and all,
Kelvin degrees and all,
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da je najbolje upotrijebiti
skraćeni oktaedar (Smijeh)
skraćeni oktaedar (Smijeh)
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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koji je, kao što svi znate,
(Smijeh) ovo ovdje! (Pljesak)
(Smijeh) ovo ovdje! (Pljesak)
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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Tko još nema skraćeni oktaedar
kod kuće? (Smijeh)
kod kuće? (Smijeh)
07:30
Who doesn't have a truncated
octahedron at home? (Laughter)
octahedron at home? (Laughter)
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Makar i plastični. „Dušo, uzmi
skraćeni oktaedar, imamo goste.“
skraćeni oktaedar, imamo goste.“
07:32
Even a plastic one.
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07:34
"Honey, get the truncated octahedron,
we're having guests."
we're having guests."
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Svi imaju jednog! (Smijeh)
Ali Kelvin to nije dokazao.
Ali Kelvin to nije dokazao.
07:36
Everybody has one!
(Laughter)
(Laughter)
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07:38
But Kelvin didn't prove it.
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Ostalo je na pretpostavci,
Kelvinovoj pretpostavci.
Kelvinovoj pretpostavci.
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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Svijet se, kao što znate, tada podijelio
na kelviniste i antikelviniste
na kelviniste i antikelviniste
(Smijeh)
07:50
(Laughter)
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sve dok netko stotinjak godina kasnije
07:51
until a hundred or so years later,
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nije pronašao bolju strukturu.
07:58
someone found a better structure.
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Weaire i Phelan pronašli su
ovu stvarčicu ovdje
ovu stvarčicu ovdje
08:02
Weaire and Phelan
found this little thing over here --
found this little thing over here --
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(Smijeh) ovu strukturu
kojoj su nadjenuli vrlo dovitljivo ime
kojoj su nadjenuli vrlo dovitljivo 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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„Weaire-Phelanova struktura“. (Smijeh)
08:15
(Laughter)
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Izgleda kao čudna stvar,
ali nije tako čudna,
ali nije tako čudna,
08:17
It looks like a strange object,
but it isn't so strange,
but it isn't so strange,
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postoji i u prirodi.
08:20
it also exists in nature.
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Vrlo je zanimljivo 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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bila korištena 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 Michael Phelps osvojio
osam zlatnih medalja i postao
osam 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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najbolji plivač svih vremena.
Dobro, sve dok se ne pojavi
netko bolji, zar ne?
netko bolji, zar ne?
08:38
Well, until someone better
comes along, right?
comes along, right?
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Kao što se može dogoditi
i Weaire-Phelanovoj strukturi.
i Weaire-Phelanovoj strukturi.
08:42
As may happen
with the Weaire-Phelan structure.
with the Weaire-Phelan structure.
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Najbolja je sve dok
se ne pojavi nešto bolje.
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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No pazite jer ova zaista ima šanse
08:47
But be careful, because this one
really stands a chance
really stands a chance
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da za stotinjak godina, ili čak njih 1700,
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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netko dokaže da je ovo
najbolji mogući oblik.
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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Tada će postati teorem,
istina, uvijek i zauijek.
istina, uvijek i zauijek.
09:02
It will then become a theorem,
a truth, forever and ever.
a truth, forever and ever.
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Dulje od bilo kojeg dijamanta.
09:07
For longer than any diamond.
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Dakle, ako želiš nekome reći
da ćeš ga voljeti zauvijek,
da ćeš ga voljeti zauvijek,
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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(Smijeh)
možeš mu pokloniti dijamant,
ali ako mu želiš reći
ali ako mu želiš reći
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 ćeš ga voljeti uvijek i zauvijek,
daj mu teorem!
daj mu teorem!
09:24
give them a theorem!
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(Smijeh)
09:26
(Laughter)
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Ali samo malo! Morat ćeš to dokazati
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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(Pljesak)
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