JAMES GRIME: Well, we're going to talk about illegal numbers.
And when I heard that there were these things, illegal
numbers, that some numbers were illegal, I was shocked
and surprised as well.
Today, in the modern world, numbers are used as keys to
encrypt secret information.
They're used to encrypt or protect DVDs as well, so that
you can't illegally copy films off a DVD.
You need to protect those keys.
So if you distribute those secret keys, those secret
numbers, this is a real problem.
And some people are claiming that it would be illegal to
distribute those numbers.
And so it's the number itself that becomes illegal.
And there are some other problems as well because you
can consider a digital photograph or a computer
program as simply as a string of binary digits.
And then a string of binary digits is a number.
So there is a number for a photograph
or a computer program.
So if you distribute the number, you could sort of work
out the original computer program or the image.
And if that's an illegal computer program that's
hacking data, then does the number become illegal itself?
To show you the problem, I thought, I don't want to write
down any illegal numbers in this video.
So I thought I'd come up with my own example.
So imagine if we decide to trademark the name
Numberphile.
So we're going to write down Numberphile first of all.
I'm going to use capital letters because I like the
number we got at the end better.
So I'm going to use capital letters for Numberphile.
I've written out the word Numberphile.
Now, each character in ASCII has a binary representation.
So let's do that.
So for the capital N, 01001110.
And now I can do it up for the U as well.
But I'd better get them right.
You know they'll notice.
The H, 0101.
Whoo.
So that's Numberphile written as a binary string.
So if we joined all that together, that's just one big
binary number.
Do you want to know what that number is?
So that number in decimal is 94--
040--
177.
So this is Numberphile written as a number,
the Numberphile number.
And if I catch any of you distributing this number about
on the internet, right, you're infringing our trademark, OK?
Don't let me catch you doing that.
There is a serious problem.
So I'm a mathematician, not a lawyer.
I can't talk about the full implications of this.
I'm hoping that I am giving you the extreme case, a
simplified extreme case.
But at the very least, this is what we're trying to avoid,
that numbers themselves become illegal.
That's what we're trying to avoid because the implications
of it are bizarre.
So you can't distribute these illegal numbers.
But then can you distribute the number minus 1?
Or if I write down a list of numbers where some of them are
illegal, am I allowed to distribute that list?
I hope that it's distributing the number and the intent to
infringe copyright.
But the extreme case is what we're trying to avoid.
It has become a problem.
In recent years, there have been a couple of cases where
people like Sony have sued people for distributing their
secret encryption keys for their PlayStation 3.
And the Motion Picture Association of America have
forced people to remove posts that were encryption keys for
their DVDs, which people were using to illegally copy DVDs.
This annoyed the internet.
Ah, the internet-- this annoyed them.
So then they started to taunt these people.
So what they started to do next is they
would take these numbers.
And to taunt, they would then turn these numbers into
hexadecimal.
And hexadecimal defines colors as well.
So then they become illegal colors.
If I do this for Numberphile--
I've worked this out already.
This number, which is 94 septillion and something, if I
write it in hexadecimal--
5D--
4, 2--
42, 4, 5--
so this is the Numberphile number written as hexadecimal.
Now, these groups here define a color.
Each of those groups define a color, and then we've got a
little bit extra.
So what you can do then is you can make something like this.
So these are the three colors defined by the Numberphile
number plus that little extra bit.
And then if you start posting this around on internet
forums, again, you'll be infringing our trademark, and
we'll be round to come round your house.
And we're going to stamp on all your favorite toys.
So I don't want to catch any of you doing that.
BRADY HARAN: So here are some of those taunting protests
that James referred to in the video.
These are colored flags based on the DVD and PlayStation
encoding numbers.
Of course, another issue we didn't touch on this video
surrounds copyrighting of numbers like pi.
And there's a lot of stories involving that, too.
Maybe we'll talk about that another time.
A quick thanks to James Clewett, who actually turned
the Mona Lisa into zeros and ones for me.
And if you'd like to read more about that, I'll put a link in
the video description.
And lastly, because we're a lot more relaxed about our
illegal numbers here at Numberphile, James Grime and I
have put that piece of paper used in the video on eBay in
case anyone wants to get their hands on it.
Again, links in the video description.
Thanks for watching.
And we'll be back with more videos soon.