Da Vinci's Vitruvian Man of math - James Earle

Da Vinčijev Vitruvijanski čovek matematike - Džejms Erl (James Earle)

Prevodilac: Miloš Milosavljević Lektor: Ivana Korom

This image of the Vitruvian Man, taken from Leonardo's sketches,

Ova slika "Vitruvijanskog čoveka"

uzeta iz Leonardovih skica

has become one of the most recognizable symbols of the Renaissance.

postala je jedan od najprepoznatljivijih

simbola renesanse.

But why?

Ali zašto?

To je običan crtež perom i mastilom na papiru, jel' tako?

It's a simple pen and ink drawing, right?

Nije!

Wrong!

Let's start to answer this question with a math problem.

Da počnemo odgovor na ovo pitanje

matematičkim problemom.

Znam kako da izračunam površinu kruga.

I know how to calculate the area of a circle.

Uzmem vrednost broja "pi"

I take the value for pi and multiply it by the radius squared.

i pomnožim ga sa poluprečnikom na kvadrat.

I also know how to take the area of a square.

Takođe znam kako da izračunam površinu kvadrata.

I multiply the base by itself.

Pomnožim njegovu stranicu sa samom sobom.

But how can I take the area of a circle and create a square with an equal area?

Ali kako da uzmem površinu kruga

i napravim kvadrat sa istom površinom?

This is a problem often called "squaring a circle"

Ovo je problem koji se često zove "kvadratura kruga"

i koji je postavljen još u antičko doba.

that was first proposed in the ancient world.

And like many ideas of the ancient world,

I kao i mnogim idejama iz antičkog doba,

i ovoj je dat novi život tokom renesanse.

it was given new life during the Renaissance.

Kako se ispostavilo

As it turns out, this problem is impossible to solve

ovaj problem je nemoguće rešiti

zbog prirode broja "pi",

because of the nature of pi,

but that's another story.

ali to je druga priča.

Leonardo's sketch,

Leonardov crtež,

na koji su uticali spisi

which is influenced by the writings of the Roman architect, Vitruvius,

rimskog arhitekte Vitruvija,

postavlja čoveka tačno u centar

places a man firmly at the center of a circle and a square.

kruga i kvadrata.

Vitruvius claimed the navel is the center of the human body

Vitruvije je tvrdio da je pupak

centar ljudskog tela

and that if one takes a compass and places the fixed point on the navel,

i ako uzmete šestar

i stavite jedan njegov kraj na pupak,

a circle can be drawn perfectly around the body.

možete opisati savršen krug oko tela.

Additionally, Vitruvius recognized that arm span and height

Pored toga, Vitruvije je prepoznao

da se raspon ruku i visina

have a nearly perfect correspondence in the human body,

skoro savršeno poklapaju kod čoveka

thus placing the body perfectly inside a square as well.

i prema tome se telo može savršeno staviti i u kvadrat.

Leonardo used the ideas of Vitruvius

Leonardo je iskoristio Vitruvijeve ideje

to solve the problem of squaring a circle metaphorically

da reši problem kvadrature kruga metaforično

using mankind as the area for both shapes.

koristeći muškarca kao površinu za oba oblika.

Leonardo nije samo mislio o Vitruviju.

Leonardo wasn't just thinking about Vitruvius, though.

There was an intellectual movement in Italy at the time called Neoplatonism.

Bio je čitav intelektualni pokret

u Italiji u to doba

pod nazivom neoplatonizam.

This movement took an old concept from the 4th century

Ovaj pokret je uzeo stari koncept

iz 4. veka, koji su razvili Platon i Aristotel,

developed by Plato and Aristotle,

called "The Great Chain of Being."

zvani "veliki lanac života".

This belief holds that the universe has a hierarchy resembling a chain,

Ovo verovanje zastupa tvrdnju da je univerzum hijerarhija

koja podseća na lanac

and that chain starts at the top with God,

koji počinje na vrhu sa Bogom

i onda se spušta nadole preko anđela

then travels down through the angels, planets, stars, and all lifeforms

planeta,

zvezda

i svih oblika života

pre nego što se završi sa demonima i đavolima.

before ending with demons and devils.

Early in this philosophic movement,

Rano u ovom filozofskom pokretu

mislilo se da je mesto čoveka u ovom lancu

it was thought that mankind's place in this chain was exactly in the center.

tačno u centru.

Because humans have a mortal body accompanied by an immortal soul,

Zbog toga što ljudi imaju smrtno telo

koje prati besmrtna duša,

we divide the universe nicely in half.

imamo prikladno mesto koje deli univerzum na pola.

Around the time Leonardo sketched the Vitruvian Man, however,

Otprilike u vreme kad je Leonardo skicirao

"Vitruvijanskog čoveka",

a Neoplatonist named Pico Della Mirandola had a different idea.

neoplatonista Piko de la Mirandola

je imao drugačiju ideju.

He pried mankind off the chain

On je izbacio čoveka iz lanca

tvrdeći da ljudi imaju jedinstvenu sposobnost

and claimed that humans have a unique ability

da zauzmu koju god poziciju žele.

to take any position they want.

Pico claimed that God desired a being capable of comprehending

Piko je tvrdio da je Bog želeo

da bude sposoban da razume

the beautiful and complicated universe he had created.

divan i komplikovan svet koji je stvorio.

This led to the creation of mankind,

I zbog toga je stvorio čoveka

which he placed at the center of the universe

koga je stavio u centar univerzuma

with the ability to take whatever form he pleases.

sa sposobnošću da uzme koji god oblik hoće.

Mankind, according to Pico,

Čovek, po Piku,

could crawl down the chain and behave like an animal

može da otpuzi niz lanac i ponaša se kao životinja

or crawl up the chain and behave like a god,

ili da se popne uz lanac i ponaša se kao bog,

izbor je naš.

it's our choice.

Looking back at the sketch,

Ako se vratimo na crtež

we can see that by changing the position of the man,

možemo videti da menjanjem položaja

čovek može da ispuni nekompatibilne površine

he can fill the irreconcilable areas of a circle and a square.

kruga i kvadrata.

If geometry is the language the universe is written in,

Ako je geometrija jezik kojim je univerzum ispisan

then this sketch seems to say we can exist within all its elements.

onda ovaj crtež izgleda kaže

da možemo da postojimo u svim njegovim delovima.

Čovek može da ispuni koji god oblik želi

Mankind can fill whatever shape he pleases geometrically

geometrijski

and philosophically as well.

i filozofski takođe.

In this one sketch, Leonardo was able to combine

U ovom jednom crtežu

Leonardo je uspeo da iskombinuje

the mathematics, religion, philosophy, architecture,

matematiku,

religiju,

filozofiju,

arhitekturu

and artistic skill of his age.

i umetničku veštinu svog doba.

No wonder it has become such an icon for the entire time period.

Nije ni čudo da je postao ikona

za sva vremena.