Is math discovered or invented? - Jeff Dekofsky

Da li je matematika otkrivena ili izmišljena? - Džef Dekofski (Jeff Dekofsky)

Prevodilac: Milana Stojadinov Lektor: Mile Živković

Would mathematics exist if people didn't?

Da li bi bilo matematike da nema ljudi?

Since ancient times, mankind has hotly debated

Od davnina, čovečanstvo je raspravljalo

whether mathematics was discovered or invented.

o tome da li je matematika otkrivena ili izmišljena.

Did we create mathematical concepts to help us understand the universe around us,

Da li smo stvorili matematičke koncepte kako bismo razumeli univerzum oko nas,

or is math the native language of the universe itself,

ili je matematika prirodni jezik samog univerzuma,

existing whether we find its truths or not?

koji postoji spoznali mi istinu ili ne?

Are numbers, polygons and equations truly real,

Da li su brojevi, poligoni i jednačine istinski stvarne,

or merely ethereal representations of some theoretical ideal?

ili su samo uzvišena reprezentacija nekog teorijskog ideala?

The independent reality of math has some ancient advocates.

Postoje drevni zastupnici nezavisnog postojanja matematike.

The Pythagoreans of 5th Century Greece believed numbers were both

Pitagorejci Grčke iz 5-tog veka su verovali da su brojevi istovremeno

living entities and universal principles.

živi entiteti i univerzalni principi.

They called the number one, "the monad," the generator of all other numbers

Broj jedan su zvali "monada", generator svih ostalih brojeva

and source of all creation.

i izvor celog stvaranja.

Numbers were active agents in nature.

Brojevi su bili aktivni agensi u prirodi.

Plato argued mathematical concepts were concrete

Platon je tvrdio da su matematičke ideje konkretne

and as real as the universe itself, regardless of our knowledge of them.

i stvarne koliko i sam univerzum, bez obzira na naše znanje o njima.

Euclid, the father of geometry, believed nature itself

Euklid, otac geometrije, je verovao da je priroda sama po sebi

was the physical manifestation of mathematical laws.

fizička manifestacija matematičkih zakona.

Others argue that while numbers may or may not exist physically,

Drugi zagovaraju da dok brojevi mogu ili ne postojati fizički,

mathematical statements definitely don't.

matematičke izjave definitivno ne postoje.

Their truth values are based on rules that humans created.

Njihove istinitosne vrednosti su osnovane na pravilima koje su ljudi stvorili.

Mathematics is thus an invented logic exercise,

Matematika je dakle, stvorena logička vežba,

with no existence outside mankind's conscious thought,

koja ne postoji izvan ljudske svesti.

a language of abstract relationships based on patterns discerned by brains,

Jezik apstraktnih odnosa zasnovan na osnovu šablona koje nazire mozak,

built to use those patterns to invent useful but artificial order from chaos.

napravljen da pomoću tih šablona stvori koristan ali veštački red od haosa.

One proponent of this sort of idea was Leopold Kronecker,

Jedan pobornik ove ideje bio je Leopold Kroneker,

a professor of mathematics in 19th century Germany.

profesor matematike u 19. veku u Nemačkoj.

His belief is summed up in his famous statement:

Njegovo verovanje je sadržano u njegovoj slavnoj izjavi:

"God created the natural numbers, all else is the work of man."

"Bog je stvorio prirodne brojeve, sve ostalo je delo čoveka."

During mathematician David Hilbert's lifetime,

Tokom života matematičara Dejvida Hilberta,

there was a push to establish mathematics as a logical construct.

postojao je pritisak da se utemelje logičke osnove matematike.

Hilbert attempted to axiomatize all of mathematics,

Hilbert je pokušao da aksiomatizuje celu matematiku,

as Euclid had done with geometry.

kao što je Euklid uradio sa geometrijom.

He and others who attempted this saw mathematics as a deeply philosophical game

Zajedno sa ostalima uvideo je da je matematika duboka filozofska igra,

but a game nonetheless.

ali iznad svega, ipak igra.

Henri Poincaré, one of the father's of non-Euclidean geometry,

Henri Poenkare, jedan od osnivača neeuklidske geometrije,

believed that the existence of non-Euclidean geometry,

verovao je da postojanje neeuklidske geometrije,

dealing with the non-flat surfaces of hyperbolic and elliptical curvatures,

koja se bavi krivim površima sa hiperboličkim i eliptičkim krivinama,

proved that Euclidean geometry, the long standing geometry of flat surfaces,

dokazuje da euklidska geometrija, stara geometrija ravnih površi,

was not a universal truth,

nije univerzalna istina,

but rather one outcome of using one particular set of game rules.

već posledica korišćenja tačno određenih pravila igre.

But in 1960, Nobel Physics laureate Eugene Wigner

1960. dobitnik Nobelove nagrade za fiziku Eugen Vigner

coined the phrase, "the unreasonable effectiveness of mathematics,"

skovao je frazu: "nerazumna efikasnost matematike",

pushing strongly for the idea that mathematics is real

snažno podržavajući ideju da je matematika stvarna

and discovered by people.

i da su je ljudi otkrili.

Wigner pointed out that many purely mathematical theories

Vigner je istakao da mnoge teorije čiste matematike

developed in a vacuum, often with no view towards describing any physical phenomena,

koje su nastale ni iz čega, često ne opisujući fizičke pojave,

have proven decades or even centuries later,

dokazane decenijama i vekovima kasnije,

to be the framework necessary to explain

zapravo su neophodan okvir za objašnjenje

how the universe has been working all along.

kako univerzum funkcioniše sve vreme.

For instance, the number theory of British mathematician Gottfried Hardy,

Npr, teorija brojeva britanskog matematičara Gotfrida Hardija,

who had boasted that none of his work would ever be found useful

koji se hvalio da nijedan njegov rad neće biti koristan

in describing any phenomena in the real world,

za opisivanje bilo koje pojave u stvarnom svetu,

helped establish cryptography.

pomogao je da se osnuje kriptografija.

Another piece of his purely theoretical work

Još jedan njegov čisto teorijski rad

became known as the Hardy-Weinberg law in genetics,

postao je poznat kao Hardi-Vajnbergov zakon u genetici,

and won a Nobel prize.

i dobio je Nobelovu nagradu.

And Fibonacci stumbled upon his famous sequence

I Fibonači je nabasao na svoj čuveni niz

while looking at the growth of an idealized rabbit population.

dok je posmatrao rast idealizovane populacije zečeva.

Mankind later found the sequence everywhere in nature,

Zatim je čovečanstvo opažalo ovaj niz svuda u prirodi,

from sunflower seeds and flower petal arrangements,

od rasporeda zrna suncokreta i krunica cveća,

to the structure of a pineapple,

do strukture ananasa,

even the branching of bronchi in the lungs.

čak i do grananja bronhija u plućima.

Or there's the non-Euclidean work of Bernhard Riemann in the 1850s,

Takođe, tu je i neeuklidski rad Bernarda Rimana iz 1850-tih,

which Einstein used in the model for general relativity a century later.

koji je Ajnštajn koristio pri modeliranju teorije relativnosti vek kasnije.

Here's an even bigger jump:

Evo još većeg skoka:

mathematical knot theory, first developed around 1771

matematička teorija čvorova, zasnovana oko 1771.

to describe the geometry of position,

kako bi se opisala geometrija položaja,

was used in the late 20th century to explain how DNA unravels itself

primenjena je krajem 20-tog veka pri objašnjavanju kako se raspliće DNK

during the replication process.

tokom procesa replikacije.

It may even provide key explanations for string theory.

Možda pruži i ključno objašnjenje za teoriju struna.

Some of the most influential mathematicians and scientists

Neki od najuticajnijih matematičara i naučnika

of all of human history have chimed in on the issue as well,

svih vremena takođe su dotakli problem,

often in surprising ways.

često na iznenađujuće načine.

So, is mathematics an invention or a discovery?

Dakle, da li je matematika izum ili otkriće?

Artificial construct or universal truth?

Veštačka konstrukcija ili univerzalna istina?

Human product or natural, possibly divine, creation?

Ljudska proizvod ili prirodna, verovatno božanska, kreacija?

These questions are so deep the debate often becomes spiritual in nature.

Ova pitanja su toliko duboka da debate često po prirodi postaju spiritualne.

The answer might depend on the specific concept being looked at,

Odgovor može da zavisi od određenog koncepta koji se posmatra,

but it can all feel like a distorted zen koan.

ali isto tako može da izgleda kao uvrnuta zen koana.

If there's a number of trees in a forest, but no one's there to count them,

Ako je u šumi određen broj drveća, i nema nikoga da ih prebroji,

does that number exist?

da li taj broj postoji?