Exploring other dimensions - Alex Rosenthal and George Zaidan

Istraživanje drugih dimenzija - Aleks Rozental i Džordž Zejdan (Alex Rosenthal and George Zaidan)

Prevodilac: Tijana Mihajlović Lektor: Ivana Korom

We live in a three-dimensional world

Živimo u trodimenzionalnom svetu

where everything has length,

u kom sve ima dužinu,

width,

širinu

and height.

i visinu,

But what if our world were two-dimensional?

ali šta bi bilo ako bi naš svet bio dvodimenzionalan?

We would be squashed down

Bili bismo sabijeni

to occupy a single plane of existence,

da zauzmemo jedinu osnovu postojanja,

geometrically speaking, of course.

u geometrijskom smislu, naravno.

And what would that world look and feel like?

Kako bi onda svet izgledao i kako bismo ga osećali?

This is the premise

Ovo je premisa

of Edwin Abbott's 1884 novella, Flatland.

iz novele Edvina Ebota iz 1884. godine, „Ravnozemlje”.

Flatland is a fun, mathematical thought experiment

Ravnozemlje je zabavan, matematički misaoni eksperiment

that follows the trials and tribulations of a square

koji prati dogodovštine i nevolje jednog kvadrata

exposed to the third dimension.

izloženog trećoj dimenziji.

But what is a dimension, anyway?

Šta je dimenzija, inače?

For our purposes, a dimension is a direction,

Za naše potrebe, dimenzija je pravac,

which we can picture as a line.

koji možemo zamisliti kao liniju.

For our direction to be a dimension,

Da bi naš pravac bio dimenzija,

it has to be at right angles to all other dimensions.

mora da bude pod pravim uglom u odnosu na sve ostale dimenzije.

So, a one-dimensional space is just a line.

Dakle, jednodimenzionalan prostor samo je linija.

A two-dimensional space is defined

Dvodimenzionalan prostor se definiše

by two perpendicular lines,

dvema linijama pod pravim uglom,

which describe a flat plane

koje opisuju ravnu osnovu

like a piece of paper.

kao što je list papira,

And a three-dimensional space

a trodimenzionalni prostor

adds a third perpendicular line,

dodaje treću liniju pod pravim uglom,

which gives us height

što daje visinu

and the world we're familiar with.

i svet sa kojim smo najbolje upoznati.

So, what about four dimensions?

Pa, šta je sa četvrtom dimenzijom?

And five?

I petom?

And eleven?

Jedanaestom?

Where do we put these new perpendicular lines?

Gde stavljamo sve ove nove linije pod pravim uglom?

This is where Flatland can help us.

Ovo je mesto kod koga nam Ravnozemlje može pomoći.

Let's look at our square protagonist's world.

Pogledajmo u svet našeg četvrtastog glavnog lika.

Flatland is populated by geometric shapes,

Ravnozemlje je naseljeno geometrijskim oblicima,

ranging from isosceles trianges

koji se kreću od jednokrakih trouglova

to equilateral triangles

preko istostraničnih trouglova,

to squares,

pentagons,

kvadrata, pentagona, heksagona,

hexagons,

all the way up to circles.

sve do krugova.

These shapes are all scurrying around a flat world,

Svi ovi oblici jurcaju kroz ravni svet,

living their flat lives.

živeći svoje ravne živote.

They have a single eye on the front of their faces,

Imaju jedno oko na prednjem delu svojih lica

and let's see what the world looks like

i pogledajmo kako svet izgleda

from their perspective.

iz njihove perspektive.

What they see is essentially one dimension,

Ono što oni vide je u suštini jedna dimenzija,

a line.

linija,

But in Abbott's Flatland,

ali u Ebotovom Ravnozemlju

closer objects are brighter,

bliži predmeti su svetliji

and that's how they see depth.

i na taj način vide dubinu.

So a triangle looks different from a square,

Dakle, trougao izgleda drugačije od kvadrata,

looks different a circle,

drugačije od kruga,

and so on.

i tako dalje.

Their brains cannot comprehend the third dimension.

Njihovi umovi ne mogu da shvate treću dimenziju.

In fact, they vehemently deny its existence

Zapravo, oni žestoko poriču njeno postojanje

because it's simply not part of their world

jer ona jednostavno nije deo njihovog sveta ili iskustva.

or experience.

But all they need,

Međutim, samo im treba, kako se ispostavlja,

as it turns out,

is a little boost.

malo podsticaja.

One day a sphere shows up in Flatland

Jednoga dana se sfera pojavljuje u Ravnozemlju

to visit our square hero.

da bi posetila našeg četvrtastog junaka.

Here's what it looks like

Evo kako izgleda

when the sphere passes through Flatland

kada sfera prođe kroz Ravnozemlje

from the square's perspective,

iz perspektive kvadrata,

and this blows his little square mind.

a ovo je potpuno šokiralo kvadrat.

Then the sphere lifts the square

Zatim je sfera podigla kvadrat

into the third dimension,

u treću dimenziju,

the height direction where no Flatlander has gone before

u pravcu visine gde nikada pre toga niko iz Ravnozemlja nije otišao

and shows him his world.

i pokazala mu njegov svet.

From up here, the square can see everything:

Odavde, kvadrat može sve da vidi:

the shapes of buildings,

oblike zgrada,

all the precious gems hidden in the Earth,

sve dragocene dragulje skrivene u Zemlji,

and even the insides of his friends,

čak i unutrašnjost svojih prijatelja,

which is probably pretty awkward.

što je verovatno prilično čudno.

Once the hapless square

Nekada bespomoćni kvadrat

comes to terms with the third dimension,

shvata treću dimenziju,

he begs his host to help him

moli svog domaćina da mu pomogne

visit the fourth and higher dimensions,

da poseti četvrtu i više dimezije,

but the sphere bristles at the mere suggestion

ali sfera se nakostreši na samu pomisao

of dimensions higher than three

o dimenzijama višim od treće

and exiles the square back to Flatland.

i baci u izgnanstvo kvadrat nazad u Ravnozemlje.

Now, the sphere's indignation is understandable.

E, sad, sferino ogorčenje je razumljivo.

A fourth dimension is very difficult

Četvrtu dimenziju je veoma teško uklopiti

to reconcile with our experience of the world.

sa našim doživljajem sveta.

Short of being lifted into the fourth dimension

Pošto nas posetilac hiperkocka

by visiting hypercube,

ne može podići u četvrtu dimenziju,

we can't experience it,

ne možemo je doživeti,

but we can get close.

ali možemo joj se približiti.

You'll recall that when the sphere

Sećate se da,

first visited the second dimension,

kada je sfera prvi put posetila drugu dimenziju,

he looked like a series of circles

izgledala je kao niz krugova

that started as a point

koji su započeli kod tačke

when he touched Flatland,

na kojoj je dodirnula Ravnozemlje,

grew bigger until he was halfway through,

rasli do polovine puta,

and then shrank smaller again.

a zatim se ponovo smanjili.

We can think of this visit

Možemo da razmišljamo o ovoj poseti

as a series of 2D cross-sections of a 3D object.

kao o nizu 2D preseka 3D predmeta.

Well, we can do the same thing

Pa, možemo uraditi istu stvar

in the third dimension with a four-dimensional object.

u trećoj dimenziji sa četvorodimenzionalnim predmetom.

Let's say that a hypersphere

Recimo da je hipersfera

is the 4D equivalent of a 3D sphere.

4D ekvivalent 3D sfere.

When the 4D object passes through the third dimension,

Kada 4D predmet prođe kroz treću dimenziju,

it'll look something like this.

izgledaće slično ovome.

Let's look at one more way

Pogledajmo još jedan način

of representing a four-dimensional object.

predstavljanja 4D predmeta.

Let's say we have a point,

Recimo, imamo tačku,

a zero-dimensional shape.

nulti dimenzionalni oblik.

Now we extend it out one inch

Sada je proširimo za 2,5 santimetra

and we have a one-dimensional line segment.

i imamo jednodimenzionalni linijski segment.

Extend the whole line segment by an inch,

Proširimo ceo segment za 2,5 santimetra

and we get a 2D square.

i dobijamo 2D kvadrat.

Take the whole square and extend it out one inch,

Uzmimo ceo kvadrat i proširimo ga za 2,5 santimentra

and we get a 3D cube.

i dobijamo 3D kocku.

You can see where we're going with this.

Možete da vidite kuda ovo vodi.

Take the whole cube

Uzmimo celu kocku

and extend it out one inch,

i proširimo je za 2,5 santimetra,

this time perpendicular to all three existing directions,

ovoga puta pod pravim uglom u odnosu na tri postojeća pravca

and we get a 4D hypercube,

i dobijamo 4D hipekocku,

also called a tesseract.

koja se još naziva i teserakt.

For all we know,

there could be four-dimensional lifeforms

Koliko znamo,

mogli bi postojati četvorodimenzionalni oblici života

somewhere out there,

negde tamo,

occasionally poking their heads

provirujući s vremena na vreme

into our bustling 3D world

u naš užurbani 3D svet

and wondering what all the fuss is about.

i pitajući se oko čega je sva ova frka.

In fact, there could be whole

Zapravo, mogli bi postojati

other four-dimensional worlds

čitavi drugi četvorodimenzionalni svetovi

beyond our detection,

van našeg vidika,

hidden from us forever

skriveni zauvek od nas

by the nature of our perception.

zbog prirode naše percepcije.

Doesn't that blow your little spherical mind?

Zar to ne šokira vaš mali sferičan um?