So I've previously mentioned that there's a lot of maths in Futurama and I'm gonna show you two more bits of maths from Futurama.
There's an episode called The Duh-Vinci Code where the, the Planet Express crew are
investigating a mystery around the Last Supper,
they think there may be a robot sat around a table as one of the Apostles. And so they go to
Future-Roma, as they call it, and
they're in a crypt and they find
this tomb with this mysterious Roman
number on it. Well it's not a number, and it's not a date either really it looks more like a Roman
mathematical equation. - "Look at these Roman numerals." - So to understand what this is all about we need to look at Mersenne numbers.
And I'm sure Mersenne numbers have cropped up previously on Numberphile, but just to remind you: a Mersenne number, Father Mersenne was a, I think a
Parisian monk who would correspond with lots of other mathematicians.
And he came up with this number which is of the form 2 to the power p minus 1, where p is prime. And
so let's put in some prime numbers. 2 to the power 2 minus 1, is 4 minus 1 is 3.
Let's put in another prime number, 2 to the power 3 minus 1, is 8 minus 1, is 7.
2 to the power 4 we're not interested in because that's not a prime. But 5 minus 1 is
8, 16, 32, that would be 31 if we take away the 1. 2 to power 6 we're not interested in. Seven is a prime;
32, 64, 128 so that's a 127.
Next prime is 2 to the 11. Now one thing you'll notice about these,
2 to the power 11 minus 1. So that is 2, 4, 8, 16, 32, 64, 128, 256,
512,
1024,
2048 minus 1 is
2047. So these are called Mersenne numbers, ok. And
we put in a prime here and bang, at the other end
we get a prime, a prime, a prime, and a prime.
Now this one, okay,
this is a bit tricky actually. This one it's hard to tell whether or not it's a prime,
but at first sight this seems to be a pretty good way of generating primes and actually is a very good way of generating primes.
But it's not foolproof. And in fact the first number, the first Mersenne number that's not a prime is this one here, 2047.
Because
2047 equals,
let me have a look, I'm doing it from memory. It's 23 times
89 okay.
So this Mersenne number is not a Mersenne prime. And this
equation is kind of embedded up here, because if we translate from these Roman numerals, what we've got is 2
to the power 11
minus, in brackets, 10 23,
multiplied by 50, 60, 70, 80, 90,
minus 1 is 89, ok? And 2 to the power 11, we know is
2048, we know that this is
2047 so this minus this equals a 1. So what we've got is is the kind of a Mersenne number here
which is not a Mersenne prime, which is why it's kind of a little bit interesting
encoded on this tom- in this tomb in Future-Roma in Futurama in Roman numerals.
So that's one of the things that, if you're watching the episode, you kinda think it's a funny story,
it's an interesting story - typical Futurama. But hidden within it is this weird mathematical reference
which you'd only get if you pause it, freeze frame it, unpack the maths and then you figure out what's happening.
"Aha! The marking indicate how many places we need to take!"
"A 1, okay we're there."
They love maths and and they're not mathematicians anymore,
and, and that this is just their way of expressing that love of maths.
(Brady: I'm not super familiar with how animation shows are made)
(but I've seen bits and pieces, and I know these guys are obviously sitting and writing scripts in a writers' room,)
(other people actually do the drawings and the animations.) - Yeah. - (This is not germane to the story in any way)
(so did they just put like a note in there saying 'if there's a gravestone,)
(make sure you put this number on the side' or how do they communicate?)
Yeah no, no they do, they they write it in detail that you know, this is, this is,
every aspect of what they want in the scene. I remember the very - one of the very - very, very first episode of The Simpsons,
first kind of real episode of The Simpsons. There was a joke about calculus and
they get it wrong. On the blackboard the maths is actually not correct.
And I think that was an example where they scribbled out some maths, they sent it off to be animated and
whoever was doing the animation didn't really appreciate how important the mathematical detail was and there's an error.
But I think ever since then they've been very careful with what their mathematical instructions are and they're very, very careful to check them afterwards
as well no doubt. So yeah. In an episode called The Honking
where the Futurama crew go off to a spooky castle for the reading of a will and
it's all a bit scary and they're walking through this castle and then suddenly blood appears on the wall.
"Zero, one, zero, one, one, zero, zero, one, zero, one." - Okay, so it's this binary sequence in blood,
it's on the wall. All a bit scary. So let's find out what this binary sequence is in decimal, we've got a
1, 2, 4, 8, 16, 32,
64, 128, 256. Ok, so if we add these up we've got 5,37, 101,
357. Okay, that equals
357. Now 357 is not a particularly interesting number, as far as I know.
It doesn't scream out as being a perfect number or a Mersenne Prime or any of those interesting numbers
we come across sometimes. But then Bender, the robot,
turns around and he sees the number reflected in a mirror. And so the binary digits are switched around.
So let's have a look at this binary sequence now, if we reverse the digits. We now have a 1 0
1 0 0 1
1 0 1 0. Ok, so we can now translate that binary sequence back into decimal.
We've got a 2, no 4s, we've got 8,
16, 32, 64, we've got a 128,
no 256s and a 512.
2 and 8 is 10, 10, 16 is 26, 26 and 128 is 154,
154 and 512 is 666.
The number of the devil, the number of the beast. And so Bender, he's just completely terrified and he runs away screaming.
"1010011010. AHHH!"
But what I so much love about this, is that it's never explained why Bender is so terrified.
The only way that you the viewer will ever understand what's happening is if you the viewer, while you're watching it, can do the binary
to decimal translation in your head on the fly in half a second. Otherwise, it doesn't make any sense. So
that's the level of
mathematical, kind of,
of trivia that's kind of embedded in this program.
If you enjoyed this video and would like to hear even more from Simon,
well you're in luck because he's the special guest in the most recently released episode of the Numberphile podcast.
You can find it on your podcast player of choice,
you can also go to the Numberphile website or you can listen via YouTube on the Numberphile2 channel.
There'll be links on the screen and down in the video description