h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

Not mine, but posted elsewhere on the BBC. A work of some merit!

posted by Rumbaba (U13744896)

Hilberts Hotel
Quoted from this message





Professor David Hilbert used the example of a hotel with an infinite number of guests and an infinite number of rooms to explain to his students how the concept of infinity is used in mathematics .

I wrote this poem a few years ago. The maths is correct but the grammar is woeful and I haven't had time or inclination to correct it. I posted this on the science board a few weeks ago, when the subject of Hilbert's hotel came up.


Hilbert's Hotel (infinity and beyond)

Professor David Hilbert was infinitely clever
the list of guests at his hotel went on and on forever
he claimed it didn't matter I'd arrived when it was full
He'd simply find a room for me by following this rule

the basis of the method, on which my hotel's run
is that everybody in room X should move to X + 1
and by this clever strategy your check-in isn't thwarted
room 1 becomes available and everybody's sorted

I wasn't very good at maths; in fact I failed the Higher*
And I didn't think the Nobel Laureate could be a liar
But I was extremely sceptical and didn't think it right
I feared I'd have to find another place in which to spend the night

I waited at reception while they sorted out the keys
The other guests, I have to say, were somewhat less than pleased
But it seemed to work, for me at least, I unpacked all my gear
And opened up the minibar to get myself a beer

'Another guest has just arrived, a close friend of my brothers'
I'm sorry but you'll have to move, and so will all the others'
I packed up my belongings and I quickly used the loo
Before strolling down the corridor to enter No 2

A plate of cod & chips arrived; I said 'it's not for me'
It must be for the gentleman residing now at 3
And the 'pretty lady' from the bar that's knocking on his door
Is looking for the bloke who's now ensconced at No 4

Then four and twenty virgins, who'd come from Inverness
ideally wanted 12 rooms but could cope with slightly less
agreed to sleep 3 to a room, as it was getting late
So everybody in room X moved on to X + 8

An infinity of guests appeared, a veritable crowd
He'd relaxed the usual policy NO COACH PARTIES ALLOWED
'This isn't going to work', I said, 'your theory's shot to Hell
It depends on finite numbers showing up at your hotel

There is a variation to the theory I've been saving
You'll see, when I've explained it, that is works on this occasion
If everybody in room X moves to the room that's double
Then, oddly, by this simple trick, it gets me out of trouble

Around this time my high regard for Hilbert was revised
And his theory of infinity I utterly despised
I though it was ridiculous that I should have to pay
For a room I had, in theory, where I never got to stay

Eventually, as tempers frayed and fisticuffs ensued
And David Hilbert's strategy began to come unglued
A committee was established to see what could be done
But all they could agree on was that Hilbert should be hung

We need a real solution that is scrupulously fair
One guest suggested bingo and another knelt in prayer
'Oh why don't we play cards for it?' I sneeringly replied
'And just to make it interesting, we'll have a shilling on the side'

'The answer’s very simple, let's forget about the rule
And stick a notice on the door that says 'The hotel's full'
And when another guest arrives, there can't be any doubt
He isn't going to be checked in till someone first checks out'

The moral of this story is, in case you haven't guessed,
There's always room at Hilbert's, but it's really not the best
Professor Hilbert knows his mathematics very well
But knows absolutely **** all about running a hotel