## 666 - Numberphile

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PETE WATTS: Well, the number 666 is pretty famous, or I

suppose you could say infamous.

666 is called the number of the beast.

And the reason that the number 666 has become infamous is not

just because it's some kind of nice number.

It has got a lot of interesting mathematical

properties.

JAMES GRIME: Perhaps disappointingly,

mathematically 666--

not that special.

PETE WATTS: But it's famous because of its use in the

Bible, where it is the number of the beast.

Let me read the relevant passage.

JAMES GRIME: The one thing that I do know where it turns

up is in the game of roulette.

So roulette--

here's a roulette table.

This is the Monte Carlo roulette table.

PETE WATTS: "Let him who has understanding reckon the

number of the beast, for it is a human number.

Its number is 666."

JAMES GRIME: There's an American roulette table as

well, which is slightly different.

The American table has a 0 and a 00, whereas the Monte Carlo

roulette table just has the one 0.

PETE WATTS: The New Testament-- the Bible wasn't

written in English.

This is just a translation.

So in the original Greek manuscripts, the number is

actually written as three letters.

The Greeks didn't have symbols for writing numbers.

It's the same as if in English, we had to use the

letter A for one, the letter B for two, and so on.

Greek is like this.

It uses letters to represent numbers.

Hebrew is like this.

Letters are used to represent numbers.

And those are the two main languages of the Bible.

JAMES GRIME: So all roulette tables, though, use the

numbers 1 to 36.

So here, the Monte Carlo roulette table has 37 slots--

0, 1, 2, 3, up to 36.

PETE WATTS: So alpha, the first letter of the Greek

alphabet represents the number one.

Beta, the second letter, represents number two.

Gamma, the third letter, represents number three.

Now, if we carried on like this, we wouldn't be able to

form big numbers very easily.

So then, as we go on, the letter iota comes

to represent 10.

Kappa is 20.

And then we've got to now go to our 100's.

So rho, which is the equivalent of our letter R,

represents 100.

Sigma, the next letter--

just like we go R, S, rho, sigma in Greek--

200.

Now what this means is that every word also has a

numerical value.

JAMES GRIME: The Monte Carlo table was by a man called

Francois Blanc.

In fact, the first version of roulette was invented by a

mathematician called Blaise Pascal, a really early version

of the idea.

He's a brilliant French mathematician--

really interesting life.

But the version I want to talk about is the Monte Carlo

roulette table.

So Francois Blanc invented this.

And they say that he made a deal with the devil for the

secrets of roulette, because the numbers of a roulette

PETE WATTS: So for example, my name is Pete.

Pi--

famous mathematical symbol which is the first letter of

my name, which would be 80, so pi, P for Pete, 80.

Epsilon and E, that would be 5.

Tau, a T, that would be 300.

And finally, another E, 5.

So the number of my name is 390.

JAMES GRIME: It is just a coincidence.

It's a nice little funny story told by gamblers who have

perhaps suffered at the hands of the roulette table.

666 then, if it is the sum of consecutive numbers, 1 to 36,

that means it's also known as a triangle number.

That's what a triangle number is.

Let's have a look at those.

PETE WATTS: OK.

So in the Bible, the famous number 666 comes in

Revelation, chapter 13.

"This calls for wisdom.

Let him who has understanding reckon the number of the

beast, for it is a human number.

Its number is 666."

Now, in English, this word "reckon" actually comes from a

Greek word which means calculate.

So it's almost like the text is saying, I'm going to give

you a riddle.

You need to calculate the number of the beast.

This number, 666, actually relates to a name.

Now, in Greek, this is called isopsephy, the idea that a

name can be a number as well, or a number can be a name.

And in Hebrew thought, the same idea is called gematria,

which actually relates to our English word "geometry." It

has the same Greek origin.

Many people have seen the Book of Revelation as directed

against the Roman Empire.

So when it comes to calculating the number of the

beast, this evil figure within the book, many of them presume

that this figure must be something to do with the

Empire, and in particular, its particularly evil leader Nero.

So the way that this is calculated from the number 666

is to take the letters of Nero Caesar.

But a slight complication is that the letters are actually

written in Hebrew and not Greek.

The reason for that is it's often in Jewish thought, in

Hebrew thought, that the idea of making letters and numbers,

or making names from numbers, had some significance.

One way to write Nero Caesar in Hebrew is like this.

Now, just like in Greek, each letter

corresponded to a number.

The same is true in Hebrew.

So the first letter of the Hebrew alphabet is alef.

So this corresponds to number one.

Bet corresponds to number two.

And then we move into our 10's as well.

So yod corresponds to number 10.

Resh corresponds to 200.

So we have a very similar system.

Both the Greeks and Hebrew language used letters to

represent numbers.

So this says Nero Caesar in Hebrew.

The nu, the N, is number 50.

The R, the resh, is 200.

Vav is 6.

Nu is 50.

Qoph is 100.

Samekh is 60.

And then resh is 200.

Now, if you add up all of these, we come to 666.

So Nero Caesar, the name Nero Caesar, has a

numerical value of 666.

Why is it spelt slightly funnily?

We've got here N, R, the equivalent of a N. So we've

got Neron Caesar.

The reason for that is that the Greek way of writing Nero

Caesar was Neron Caesar.

I think this is the most obvious explanation.

Partly because there are other examples at the time in other

Hebrew and Greek text of this kind of riddle.

The idea of a number representing a name is

convincing because this Neron Caesar, this particular

spelling, is in common use.

And also, John as an author uses very Hebraic concepts.

He draws on a lot of Hebrew ideas.

Some people argue that Greek is his second language.

He thinks in Hebrew, but he writes in Greek.

So he's imbued with Hebrew ideas.

PETE WATTS: But also, it adds to kind of the complexity of

it in terms of it being a riddle, a secret.

So no one wants to write a book under imperial

persecution saying the root of all evil is Nero Caesar.

You're not going to spell that out.

So this is kind of a way that the number system of the time

uses a code to kind of protect the author, protect the

recipients from an out and out criticism.

JAMES GRIME: A triangle number, then, can be written

like a triangle.

Here, I'm going to take some dots and write them--

squeak--

in a triangle.

And you see, each row is a different number.

So now I've got one, two, three, four.

So the first triangle number--

it's just 1, on its own.

The second triangle number is the first two rows there, so 1

plus 2, which is 3.

The third triangle number is this triangle--

one, two, three--

which is 6.

The fourth triangle number is that, and so on, and so on.

And the 36th triangle number--

so the very last row would have 36 dots on it.

It would be the 36th triangle number.

That is 666.

PETE WATTS: 666 has been used to indicate virtually

anything, where anyone who's been evil and evil, rude, or

so on, has been found to add up somehow to the number of

666, using all sorts of bizarre counting systems.

What generally happens is that people take the English

alphabet, A to Z, and use the numbers 1 to 26 to try and

come up with some code.

But you can see that that's actually nothing like the

genuine way that Hebrew and Greek use their numbers.

Because there, in Hebrew and Greek, we get units, tens, and

hundreds whereas these codes that tend to be made up these

days use just the number 1 to 26, A to Z. And then they

involve all sorts of bizarre things like adding people's

middle names and so on to come up with present-day figures.

JAMES GRIME: Of course, we know about the

associations with 666.

But mathematically speaking, it's not a particularly

interesting, exciting number for its own sake.

It's more of a cultural, important number.

that some manuscript, some other early manuscripts from

the third century and so on, actually have the number 616.

So the number of the beast in these texts is 616.

Now, what's interesting is that if you take off this

final N in Hebrew and have just Nero

Caesar, that equals 616.

So in other words, people are saying, I already know that

the answer is Nero Caesar, but I'm not sure about how you

worked it out.

I'm going to correct it, if you like.

I think the number ought to be 616.

So in a way, that confirms that they were thinking of

Nero Caesar, even from the second, third century and so

on, really early on.

So that's a nice bit of evidence that confirms that,

certainly among the early Christians, the answer to this

riddle was Nero Caesar.

[INTERPOSING VOICES]