42 and Douglas Adams - Numberphile

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.