Uploaded by numberphile on 08.03.2012

Transcript:

JAMES GRIME: OK, so 42 is maybe not such a special

number in mathematics, but a very special

number in nerd culture.

PHIL MORIARTY: Good.

Good, good, good.

Did you want to do something with 42?

JAMES GRIME: Yes.

So you take a piece of paper.

It's very thin.

Let's fold this in half.

Fold it in half again.

Fold it in half again.

Imagine you can keep doing this, and in reality you can't

keep doing this.

But imagine you can keep folding it in half, and each

time you do, it will double in thickness.

And if you fold it 42 times, that's enough to reach from

the Earth to the moon.

You notice when 42 turns up, you keep noticing it.

But that's not really all that remarkable, since any two

digit number will turn up one hundredth of the time.

GERARDO ADESSO: Today we're in my office, and we are talking

about numbers.

And when I was asked about thinking about the number, I

just realized that there is a number that I see every day

when I enter my office, and this number is 42.

Because we are in this office, B42.

JAMES GRIME: 42 is maybe not such a special number in

mathematics, but a very special

number in nerd culture.

42 is the answer to life, the universe, and everything.

GERARDO ADESSO: If you'll now go on Google, the answer to

life, the universe, and everything.

So Google calculator gives you as an answer, 42.

PHIL MORIARTY: 42 is the answer to life, the universe,

and everything.

I am a huge, huge, huge Douglas Adams fan.

My favorite book is The Hitch Hiker's Guide To The Galaxy.

All my favorite books are the trilogy of five books that

makes up Douglas Adams' work in terms of a character called

Arthur Dent.

JAMES GRIME: The author Douglas Adams, a great comedy

writer, wrote first a radio series called the Hitch

Hiker's Guide To The Galaxy.

In the show they built a super computer, a giant super

computer to work out the meaning of life, the universe,

and everything.

And after millions of years, it decided that the meaning of

life, the universe, and everything was 42.

PHIL MORIARTY: At which point the people who programmed the

computer and built the computer were rather

disappointed, but the computer quite rightly said, well,

what's the question?

And they said it's the ultimate question.

The ultimate question of life, the universe, and everything.

But what's the question?

Which is, I think is a completely valid thing.

So then the idea was to build a supercomputer which would

calculate the ultimate question.

And the supercomputer was Earth, and we formed part-- or

humans formed part of that organic framework.

JAMES GRIME: You've ruined the ending!

PHIL MORIARTY: Oh, yeah, if you really haven't listened

to, or watched, or read the Hitch Hiker's Guide To The

Galaxy books, you haven't lived.

So go out and get them now.

JAMES GRIME: A perhaps slightly embarrassing

confession is that I used to be involved with the Hitch

Hiker's Guide To The Galaxy fan club.

And I use to help run it, briefly.

Just a few years ago when the film came out, I remember it

was quite an exciting time.

I don't see them anymore.

It's a shame, but I know more things about 42 than I

really ought to.

GERARDO ADESSO: This number, 42, is said

to be a pronic number.

JAMES GRIME: A what, sorry?

GERARDO ADESSO: A pronic number.

JAMES GRIME: What does that mean?

GERARDO ADESSO: I can write it for you.

So a pronic number is a number which is obtained as the

multiplication of two successive integers.

So for instance, in the case of 42, 42 is

equal to 6 times 7.

These are one after the other, and any number which is like

this is called pronic.

For instance, 2 times 3, 3 times 4, and so on.

JAMES GRIME: Douglas Adams, I think chose this number

because it kind of has a funny sound.

40, all those O's, 42, it's a funny sound.

PHIL MORIARTY: Again, if you go on the web, and if you read

some of the articles about 42, there are arguments ranging

from, well actually it's 101010 in binary, which is a

nice binary number.

And in fact, in the television program that flashes up.

When they say 42, you see the binary.

JAMES GRIME: You'll find 42 comes up a lot in comedy and

other shows, partly because of Douglas Adams and because he

used it, but partly because it's just a funny sound.

GERARDO ADESSO: Then there is another interesting property,

which is slightly more complicated about this number.

And it is the fact that it's defined to be a primary

pseudoperfect number.

JAMES GRIME: A what?

GERARDO ADESSO: A primary pseudoperfect number.

JAMES GRIME: Go on, what does that mean?

GERARDO ADESSO: OK, so first of all, you have to find out

what are the prime factors of 42.

OK, so write down 42 as 2 times 3, which is 6 times 7.

So these are its prime factors.

Primary to the perfect number is such that the sum of the

inverse of each prime factor plus the sum of the inverse of

the number itself is 1.

1 over 2 plus 1 over 3 plus 1 over 7, and these are the sum

of the inverses of each prime factor.

Then plus 1 over the number itself.

If you work out this calculation, you can put

everything under the common denominator.

The result is one.

There are not so many numbers that have this property.

The next one after 42 is, I think 1,806.

And then you immediately go to very huge numbers.

So it appears like any [INAUDIBLE]

property, but it's not.

JAMES GRIME: The story is he sat--

he wrote it in his garden, he sat in his back garden.

He thought, what number should I choose?

It should be a sort of smallish number.

It should be a sort of boring number.

42 will do, and he picked 42.

PHIL MORIARTY: There's also arguments that 6 times 9, if

you look at that problem in base 13, out

pops the number 42.

All these mad, mad things that Douglas Adams himself said

were absolutely bonkers.

He said he chose 42 because it's a funny number.

He thought it was a funny number.

GERARDO ADESSO: And then there is another, for instance

another one which 42 belongs to.

It's the sequence of harshad numbers.

Harshad is written like this.

So what is a harshad number?

It's a number that is divisible by

the sum of its digits.

So you have 42, take 4 plus 2.

This is 6.

And 42 is divisible by 6.

So any number with this property is

called harshad number.

JAMES GRIME: Do you think it's a funny number?

PHIL MORIARTY: Oh, I don't know.

If it's an interesting one.

Would I have gone for 42?

I don't know.

What number is funnier than 42?

71?

I don't know.

68?

GERARDO ADESSO: If you're very bright in mathematics, and you

participate in the International Olympiads of

Mathematics, and the total mark to achieve the perfect

score is set at 42.

JAMES GRIME: Is that a coincidence, or do you think

someone did that on purpose?

GERARDO ADESSO: Well, this I don't know.

We need to ask the people who are involved in these

committees.

But before Douglas Adams, that was already quite a lot of

attention on this number from works by Lewis Carroll.

And you know, mathematicians, they are known to have a

particular taste for recurrences and

nerdiness, so to say.

So it may be that this was chosen on purpose.

But I don't know.

JAMES GRIME: In the fan club magazine, they would have a

column all about where people have seen

the number 42 recently.

And it was a bit of fun, except for one guy.

He took it quite seriously.

He actually thought there was a mystical meaning

behind the number 42.

Genuinely thought there was.

And he used to go through the phone book and look for

multiples of 42 in peoples' phone numbers.

He used to find a multiple of 6, find a multiple of 7,

multiply them together and go oh, look.

It's a multiple of 42.

How amazing.

It really isn't that remarkable if you look for

things like that.

PHIL MORIARTY: Soon as I see it, there's an instant

resonance there when I see 42.

And in fact, one of the experiments I want to do,

we're working with taking a silicon surface.

Surface like this, where we put hydrogen atoms on it.

And then we take a tip of a scanning probe microscope and

remove the hydrogen atoms one at a time.

And one thing I really want to do is put 42 on

a surface in atoms.

JAMES GRIME: Fox Mulder's apartment in the X-Files was

apartment 42, which may be a reference to Hitch Hiker.