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.
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)
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.
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.
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.
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.
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.
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.
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.
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.
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.
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)
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.
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)
And I think there are some questions
that math just cannot answer.
Thank you.
(Applause)