How does math guide our ships at sea? - George Christoph

Transcriber: tom carter Reviewer: Bedirhan Cinar

Prevoditelj: Ivan Stamenković Recezent: Sanda L

As you can imagine, 400 years ago,

Kao što možete zamisliti, prije 400 godina,

navigating the open ocean was difficult.

navigacija na oceanu bila je teška.

The winds and currents pushed and pulled ships off course,

Vjetar i struje gurali su brodove s kursa,

and so sailors based their directions on the port they left,

tako da su se mornari ravnali prema luci iz koje su otišli,

attempting to maintain an accurate record of the ship's direction and the distance sailed.

pokušavajući točno pratiti smjer i udaljenost broda.

This process was known as dead reckoning,

Ovaj proces poznat je kao mrtvi račun,

because being just half a degree off could result in sailing right past the island that lay several miles just over the horizon.

jer ako promašite samo pola stupnja, otplovit ćete pored otoka preko horizonta.

This was an easy mistake to make.

Lako je bilo napraviti ovakvu grešku.

Thankfully, three inventions made modern navigation possible:

Srećom, tri izuma su omogućila modernu navigaciju:

sextants, clocks and the mathematics necessary to perform the required calculations quickly and easily.

sekstanti, satovi i matematika, potrebni da se izračuni rade brzo i lako.

All are important. Without the right tools, many sailors would be reluctant to sail too far from the sight of land.

Svi su važni, jer bez pravih alata teško bi bilo tako daleko ploviti.

John Bird, an instrument maker in London,

John Bird, izrađivač instrumenata u Londonu,

made the first device that could measure the angle between the sun and the horizon during the day,

napravio je prvi uređaj koji je mjerio kut između sunca i horizonta tijekom dana,

called a sextant.

nazvan sekstant.

Poznavanje tog kuta je važno, jer se mogao usporediti s kutom iz Engleske u isto doba.

Knowing this angle was important, because it could be compared to the angle back in England at the exact same time.

Comparing these two angles was necessary to determine the longitude of the ship.

Usporedba ova dva kuta bila je potrebna da bi se odredila dužina broda.

Clocks came next.

Sljedeći su bili satovi.

In 1761, John Harrison, an English clockmaker and carpenter,

1761. godine, John Harrison, stolar i urar iz Engleske,

built a clock that could keep accurate time at sea.

izradio je sat koji može pratiti vrijeme na moru.

The timepiece that could maintain accurate time while on a pitching, yawing deck in harsh conditions

Sat koji je mogao pratiti vrijeme u teškim uvjetima,

was necessary in order to know the time back in England.

bio je potreban kako bi se znalo vrijeme u Engleskoj.

There was one catch though:

Postojala je jedna kvaka:

since such a timepiece was handmade, it was very expensive.

kako je sat bio ručni rad, bio je jako skup.

So an alternate method using lunar measurements and intense calculations was often used to cut costs.

Alternativa je bila korištenje lunarnih mjera i računanja da se smanje troškovi.

The calculations to determine a ship's location for each measurement could take hours.

Kalkulacije kojima bi se odredio položaj broda dugo su trajale.

But sextants and clocks weren't useful unless sailors could use these tools to determine their position.

Ali sekstanti i satovi su bili beskorisni ako ih mornari nisu mogli koristiti.

Fortunately, in the 1600s, an amateur mathematician had invented the missing piece.

Srećom, oko 1600. matematičar amater izumio je dio koji nedostaje.

John Napier toiled for more than 20 years in his castle in Scotland to develop logarithms, a calculation device.

John Napier radio je 20 godina u Škotskoj da bi razvio logaritme, sustav računanja.

Napier's ideas on logarithms involved the form of one over E and the constant 10 to the seventh power.

Napierove ideje o logaritmima uključuju jedan kroz E i konstantu od 10 na sedmu.

Algebra in the early 1600s was not fully developed,

Matematika 1600. nije bila skroz razvijena

and Napier's logarithm of one did not equal zero.

i Napierov logaritam jedan nije bio jednak nuli.

This made the calculations much less convenient than logarithms with a base of 10.

Zbog toga kalkulacije nisu bile toliko prikladne kao logaritmi s bazom 10.

Henry Briggs, a famous mathematician at Gresham College in London,

Henry Briggs, poznati matematičar s Gresham Collegea u Londonu,

read Napier's work in 1614, and the following year made the long journey to Edinburgh to meet Napier.

pročitao je Napierov rad 1614., a zatim otputovao u Edinburgh upoznati Napiera.

Briggs showed up unannounced at Napier's castle door

Pojavio se nenajavljen pred vratima

and suggested that John switch the base and form of his logarithms into something much simpler.

i predložio da John zamijeni bazu i oblik svog logaritma u nešto jednostavnije.

They both agreed that a base of 10 with the log of one equal to zero

Složili su se da bi baza 10 s logom jedan koji je jednak nuli

would greatly simplify everyday calculations.

pojednostavila računanje.

Today we remember these as Briggs Common Logarithms.

Danas pamtimo to kao Briggsove obične logaritme.

Until the development of electric calculating machines in the 20th century,

Dok nisu izumljeni električni kalkulatori u 20. stoljeću,

any calculations involving multiplication, division, powers, and extraction of roots with large and small numbers

bilo kakva računanja dijeljenjem, množenjem, potencijama, korijenima,

were done using logarithms.

rađena su uz pomoć logaritama.

The history of logarithms isn't just a lesson in math.

Povijest logaritama nije samo lekcija iz matematike.

There were many players responsible for successful navigation.

Puno je činitelja koji su odgovorni za uspjeh navigacije.

Instrument makers, astronomers, mathematicians,

Izrađivači instrumenata, astronomi, matematičari,

and of course sailors.

i naravno, mornari.

Creativity isn't only about going deep into one's field of work,

Kreativnost nije samo istraživanje svog polja rada,

it's about cross-pollination between disciplines too.

već i križanje između disciplina.