So, I have a feature on my website where every week people submit hypothetical questions for me to answer, and I try to answer them using math, science and comics.
Imam dodatak na svom vebsajtu gde svake nedelje ljudi postavljaju hipotetička pitanja na koja treba da odgovorim. Pokušavam da odgovorim na njih koristeći matematiku, nauku i stripove.
So for example, one person asked, what would happen if you tried to hit a baseball pitched at 90 percent of the speed of light? So I did some calculations. Now, normally, when an object flies through the air, the air will flow around the object, but in this case, the ball would be going so fast that the air molecules wouldn't have time to move out of the way. The ball would smash right into and through them, and the collisions with these air molecules would knock away the nitrogen, carbon and hydrogen from the ball, fragmenting it off into tiny particles, and also triggering waves of thermonuclear fusion in the air around it. This would result in a flood of x-rays that would spread out in a bubble along with exotic particles, plasma inside, centered on the pitcher's mound, and that would move away from the pitcher's mound slightly faster than the ball. Now at this point, about 30 nanoseconds in, the home plate is far enough away that light hasn't had time to reach it, which means the batter still sees the pitcher about to throw and has no idea that anything is wrong. (Laughter) Now, after 70 nanoseconds, the ball will reach home plate, or at least the cloud of expanding plasma that used to be the ball, and it will engulf the bat and the batter and the plate and the catcher and the umpire and start disintegrating them all as it also starts to carry them backward through the backstop, which also starts to disintegrate. So if you were watching this whole thing from a hill, ideally, far away, what you'd see is a bright flash of light that would fade over a few seconds, followed by a blast wave spreading out, shredding trees and houses as it moves away from the stadium, and then eventually a mushroom cloud rising up over the ruined city. (Laughter)
Na primer, jedna osoba je pitala: šta bi se desilo kada biste pokušali da udarite bejzbol lopticu bačenu jačinom 90% od brzine svetlosti? Napravio sam neke proračune. Uglavnom kada objekat leti kroz vazduh, vazduh će strujati oko njega, ali u ovom slučaju, lopta će ići toliko brzo da molekuli vazduha neće imati vremena da se sklone sa puta. Loptica bi udarala u, ali i kroz njih, i sudar sa tim molekulima vazduha bi istisli azot, ugljenik i vodonik iz loptice, deleći ga na sitne čestice i takođe kidajući talase termonuklearne fuzije u vazduh oko njega. Ovo bi rezultiralo poplavom rendgenskih zraka koji bi se širili u balon zajedno sa egzotičnim česticama, unutrašnje plazme, centrirane na brdašcu i to bi pomerilo sa brdašca malo brže nego loptica. U tom trenutku, oko 30 nanosekundi domašni plato je dovoljno udaljen da svetlo nije imalo vremena da ga dostigne što znači da udarač i dalje vidi bacača kako baca i nema pojma da je nešto pogrešno. (Smeh) Nakon 70 nanosekundi lopta će dostići domašni plato ili u najmanju ruku oblak rastuće plazme koja je bila lopta i progutaće palicu i udarača, i plato i hvatača i sudiju i početi da ih sve razdvaja kako počinje da ih vraća kroz zaštitnu mrežu, koja takođe počinje da se razdvaja. Ako gledate sve ovo sa brda daleko videli biste jak svetlosni bljesak koji bi izbledeo nakon nekoliko sekundi, praćen eksplozivnim talasom koji se širi sekući drveće i kuće dok se pomera od stadiona, a na kraju bi se atomska pečurka izdigla iznad uništenog grada. (Smeh)
So the Major League Baseball rules are a little bit hazy, but — (Laughter) — under rule 6.02 and 5.09, I think that in this situation, the batter would be considered hit by pitch and would be eligible to take first base, if it still existed.
Pravila Glavne bejzbol lige su pomalo nejasna ali - (Smeh) - pod pravilom 6.02 i 5.09 mislim da bi u toj situaciji smatrali da je udarač pogođen dobacivanjem i mogao bi da zauzme prvu bazu ako bi i dalje postojala.
So this is the kind of question I answer, and I get people writing in with a lot of other strange questions. I've had someone write and say, scientifically speaking, what is the best and fastest way to hide a body? Can you do this one soon? And I had someone write in, I've had people write in about, can you prove whether or not you can find love again after your heart's broken? And I've had people send in what are clearly homework questions they're trying to get me to do for them.
Ovo je vrsta pitanja na koja odgovaram i ljudi mi pišu dosta drugih čudnih pitanja. Neko mi je pisao govoreći: "Naučno govoreći, koji je najbolji i najbrži način sakrivanja tela? Možete li da to učinite uskoro?" Neko je pisao, ljudi su pitali: možete li dokazati da li je moguće pronaći novu ljubav nakon slomljenog srca? Neki ljudi su slali pitanja tipična za domaće zadatke koje su hteli da uradim za njih.
But one week, a couple months ago, I got a question that was actually about Google. If all digital data in the world were stored on punch cards, how big would Google's data warehouse be? Now, Google's pretty secretive about their operations, so no one really knows how much data Google has, and in fact, no one really knows how many data centers Google has, except people at Google itself. And I've tried, I've met them a few times, tried asking them, and they aren't revealing anything.
Ali jedne nedelje, pre par meseci dobio sam pitanje vezano za Gugl. Ako su svi digitalni podaci smešteni na bušenoj kartici koliki bi bio Guglov magacin? Gugl je prilično tajanstven o svojim operacijama, pa gotovo niko i ne zna koliko Gugl podataka ima. Zapravo, niko i ne zna koliko centara podataka ima Gugl, osim ljudi u Guglu. Sreo sam ih nekoliko puta, pokušao da ih pitam, ali oni ništa ne otkrivaju.
So I decided to try to figure this out myself. There are a few things that I looked at here. I started with money. Google has to reveal how much they spend, in general, and that lets you put some caps on how many data centers could they be building, because a big data center costs a certain amount of money. And you can also then put a cap on how much of the world hard drive market are they taking up, which turns out, it's pretty sizable. I read a calculation at one point, I think Google has a drive failure about every minute or two, and they just throw out the hard drive and swap in a new one. So they go through a huge number of them. And so by looking at money, you can get an idea of how many of these centers they have. You can also look at power. You can look at how much electricity they need, because you need a certain amount of electricity to run the servers, and Google is more efficient than most, but they still have some basic requirements, and that lets you put a limit on the number of servers that they have. You can also look at square footage and see of the data centers that you know, how big are they? How much room is that? How many server racks could you fit in there? And for some data centers, you might get two of these pieces of information. You know how much they spent, and they also, say, because they had to contract with the local government to get the power provided, you might know what they made a deal to buy, so you know how much power it takes. Then you can look at the ratios of those numbers, and figure out for a data center where you don't have that information, you can figure out, but maybe you only have one of those, you know the square footage, then you could figure out well, maybe the power is proportional. And you can do this same thing with a lot of different quantities, you know, with guesses about the total amount of storage, the number of servers, the number of drives per server, and in each case using what you know to come up with a model that narrows down your guesses for the things that you don't know. It's sort of circling around the number you're trying to get. And this is a lot of fun. The math is not all that advanced, and really it's like nothing more than solving a sudoku puzzle.
Stoga sam odlučio da samostalno otkrijem. Postoji nekoliko stvari koje sam ovde posmatrao. Počeo sam sa novcem. Gugl mora da otkrije koliko su novca potrošili, uopšteno tako možemo da ograničimo koliko centara podataka bi mogli da izgrade jer veliki centri podataka koštaju određenu količinu novca. Možete ograničiti količinu tržišta hard diskova koje oni uzimaju, što ispada prilično srazmerno. Pročitao sam jednom proračune. Mislim da Gugl ima propust sa diskom svakih par minuta i samo odbacuju hard disk i dodaju novi. Troše veliki broj njih. Posmatrajući kroz novac možete dobiti ideju koliko mnogo ovih centara imaju. Možete posmatrati struju. Pogledajte samo koliko im treba struje, jer vam treba određena količina da biste pokrenuli servere, a Gugl je efikasniji nego većina ali im treba još osnovnih uslova i to vam omogućava da ograničite broj servera koje imaju. Možete pogledati kvadraturu i videti, za neke centre koje znate, koliko su veliki. Koliko je to prostora? Koliko servernih čvorova može tamo stati? Za neke centre podataka, možete dobiti dve informacije. Znate koliko troše, i takođe, jer moraju da ugovore sa lokalnom upravom kako bi dobili struju, mogli biste da znate šta su ugovorili da kupe, pa znate koliko struje to iziskuje. Možete videti razmere tih brojeva i shvatiti da za centre podataka gde nemate informacije, možete otkriti, ali možda imate jednu od ovih, znate kvadraturu i možete otkriti da je možda struja proporcionalna. Možete isto uraditi sa različitim količinama, sa pretpostavkama o maksimalnoj količini smeštanja, broju servera, broju hard diskova po serveru, i u svakom sučaju koristeći ono što znate da biste osmislili model koji sužava vaše pretpostavke za stvari koje ne znate. To je donekle kruženje oko broja koji želite da postignete. I veoma je zabavno. To nije toliko napredna matematika, i nije ništa više od rešavanja sudokua.
So what I did, I went through all of this information, spent a day or two researching. And there are some things I didn't look at. You could always look at the Google recruitment messages that they post. That gives you an idea of where they have people. Sometimes, when people visit a data center, they'll take a cell-cam photo and post it, and they aren't supposed to, but you can learn things about their hardware that way. And in fact, you can just look at pizza delivery drivers. Turns out, they know where all the Google data centers are, at least the ones that have people in them.
Prošao sam kroz sve te informacije, potrošio dan ili dva istražujući. Neke stvari nisam promatrao. Možete uvek da gledate Guglove oglase za zapošljavanje koje postavljaju. To vam daje uvid u to gde imaju ljude. Ponekad, kada ljudi posete centar podataka slikaće telefonom i postaviće na internet, a ne bi trebalo, ali možete da naučite nešto o njihovom hardveru na taj način. U suštini, možete videti raznosače pica. Ispada da znaju gde su svi Guglovi centri podataka, barem oni koji imaju ljude tamo.
But I came up with my estimate, which I felt pretty good about, that was about 10 exabytes of data across all of Google's operations, and then another maybe five exabytes or so of offline storage in tape drives, which it turns out Google is about the world's largest consumer of.
Istupio sam sa svojom procenom, koju sam smatrao veoma dobrom, da ima oko 10 eksabajta podataka širom svih Guglovih operacija, a potom ostalih otprilike 5 eksabajta svih oflajn skladišta na strimerima, čiji je Gugl najveći svetski korisnik. Došao sam do ove procene
So I came up with this estimate, and this is a staggering amount of data. It's quite a bit more than any other organization in the world has, as far as we know. There's a couple of other contenders, especially everyone always thinks of the NSA. But using some of these same methods, we can look at the NSA's data centers, and figure out, you know, we don't know what's going on there, but it's pretty clear that their operation is not the size of Google's.
i ovo je zapanjujuća količina podataka. To je dosta više od bilo koje druge organizacije u svetu, koliko mi poznajemo. Postoji par drugih kandidata, posebno što svako uvek pomisli na Nacionalnu sigurnosnu agenciju. Koristeći neke od istih metoda, možemo posmatrati centre podataka NSA i otkriti da ne znamo šta se tamo događa. ali je prilično jasno da njihove operacije nisu veličine Guglovih.
Adding all of this up, I came up with the other thing that we can answer, which is, how many punch cards would this take? And so a punch card can hold about 80 characters, and you can fit about 2,000 or so cards into a box, and you put them in, say, my home region of New England, it would cover the entire region up to a depth of a little less than five kilometers, which is about three times deeper than the glaciers during the last ice age about 20,000 years ago.
Sabirajući sve ovo, došao sam do druge stvari na koju možemo odgovoriti, a to je: koliko bušenih kartica bi bilo potrebno? Bušena kartica može da sadrži oko 80 karaktera, a možete da uglavite oko 2000 kartica u kutiju i stavite ih, recimo, moja regija Nove Engleske, čitava regija bi pokrila dubinu do malo manje od 5 kilometara, što je oko 3 puta dublje od glečera tokom poslednjeg ledenog doba pre oko 20 000 godina.
So this is impractical, but I think that's about the best answer I could come up with. And I posted it on my website. I wrote it up. And I didn't expect to get an answer from Google, because of course they've been so secretive, they didn't answer of my questions, and so I just put it up and said, well, I guess we'll never know.
Ovo je nepraktično, ali mislim da je to najbolji odgovor koji mogu da smislim. Postavio sam to na svoj vebsajt. Napisao sam. Nisam očekivao da dobijem odgovor od Gugla jer naravno, oni su bili veoma tajanstveni, nisu odgovorili na moja pitanja i stavio sam to i rekao: "Pretpostavljam da nikada nećemo saznati."
But then a little while later I got a message, a couple weeks later, from Google, saying, hey, someone here has an envelope for you. So I go and get it, open it up, and it's punch cards. (Laughter) Google-branded punch cards. And on these punch cards, there are a bunch of holes, and I said, thank you, thank you, okay, so what's on here? So I get some software and start reading it, and scan them, and it turns out it's a puzzle. There's a bunch of code, and I get some friends to help, and we crack the code, and then inside that is another code, and then there are some equations, and then we solve those equations, and then finally out pops a message from Google which is their official answer to my article, and it said, "No comment." (Laughter) (Applause)
Nakon nekog vremena dobio sam poruku, par nedelja kasnije od Gugla, koja kaže: "Hej, neko ovde ima kovertu za tebe." Uzeo sam je i otvorio a unutra su bile bušene kartice. (Smeh) Bušene kartice sa logom Gugla. Na tim karticama postoji gomila rupica, i zahvalio sam se. I šta imamo ovde? Uzeo sam jedan softver i počeo da ga proučavam, da skeniram, i ispada da je to zagonetka. Postoji gomila kodova. i zato zovem prijatelje da mi pomognu i zajedno krekujemo kod, a onda je unutra drugi, a zatim su tu neke jednačine, i rešavamo ih, a zatim na kraju iskoči poruka od Gugla koja je njihov zvaničan odgovor na moj članak i kaže: "Bez komentara." (Smeh) (Aplauz)
And I love calculating these kinds of things, and it's not that I love doing the math. I do a lot of math, but I don't really like math for its own sake. What I love is that it lets you take some things that you know, and just by moving symbols around on a piece of paper, find out something that you didn't know that's very surprising. And I have a lot of stupid questions, and I love that math gives the power to answer them sometimes.
Volim da računam ove stvari, nije da volim da se bavim matematikom. Ima tu dosta matematike, ali ne volim matematiku samu po sebi. Volim to što vam matematika omogućava da uzmete neke stvari koje znate i samo pomeranjem simbola na parčetu papira otkrijete nešto što niste znali što je veoma iznenađujuće. Primam dosta glupih pitanja i volim što matematika daje snagu da ih odgovorim ponekad.
And sometimes not. This is a question I got from a reader, an anonymous reader, and the subject line just said, "Urgent," and this was the entire email: "If people had wheels and could fly, how would we differentiate them from airplanes?" Urgent. (Laughter)
A ponekad ne. Ovo je pitanje koje sam dobio od čitaoca, anonimnog čitaoca, a u naslovu je pisalo: "Hitno." a ovo je bio čitav mejl: "Ako bi ljudi imali točkove i mogli leteti, kako bismo ih razlikovali od aviona?" Hitno. (Smeh)
And I think there are some questions that math just cannot answer. Thank you. (Applause)
Mislim da ima nekih pitanja na koja matematika ne može da odgovori. Hvala vam. (Aplauz)