Monday, 31 January 2011

Labyrinth - The Riddle of the Two Doors

Lately, I have introduced the classic eighties film Labyrinth to Emilia. Even at four months old she is eminently capable of realising that, despite it's original Box Office failure, it remains one of the best movies of its type and a testament to the late great Jim Henson. Of course, that is not just my opinion, but verifiable fact so there...

Now, those of you who have seen the film will recall that halfway through, Sarah is faced with "the riddle of the two doors" - something that I believe took its inspiration from the work of Raymond Smulluan's "Knights and Knaves" logic puzzles - in order to avoid certain death.

The challenge is presented by these talking doors thus: "One of us leads to the castle, one of us leads to certain death. One of us always tells the truth; the other always lies."

Now, Sarah successfully guesses correctly (she actually ends up falling down a hole through a chasm of bizarre talking hands, before descending into an oubliette, but this is down to the goblin king punishing her for claiming it is "a piece of cake", rather than her own poor choice) - but I have always found it a very optimistic viewpoint that she could solve this for the first time under the pressure of having to save her baby brother in the space of thirteen hours...

Yes, I know it's a fantasy film - I promise I'm not taking it that seriously. It's just that the only way to answer the riddle correctly is to ask a certain question in a manner structured in mathematical logic, rather than intuition or cunning. The solution is not to find out which door is lying and which one is telling the truth, but to find a way of them both giving you the same answer. So - if you ask either door, as Sarah does: "If I asked the other door would he lead to the castle?" then whatever answer they give you is the opposite of the truth as follows:

1. You are either asking a truthful door what a lying door would say, OR
2. You are asking a lying door what a truthful door would say

Door one happens to be the correct door, so given that she asked door two the question, in scenario one from above, if he says YES, then door one IS the correct door (as he is truthful). In scenario two, if he says NO then door one IS STILL the right door (as he is a liar)

The point here is that the roles are such that the scenario remains the same when switched around - the two variables don't remain consistent, so therefore, providing you ask the correct question, you will determine the outcome by definition.

Now, it took me several views to even understand what the hell Sarah was on about - the reason being that to solve this by pure logic would require either a working understanding of this problem, or a pen and paper to map out the process. She had neither and was considerably up against it (what with only a few hours to get to the center armed with nothing other than a temperamental dwarf and a big hairy orange creature whose only friends are rocks. Also - with the choice as being life or death, I fine it hard to imagine that you would be content to rush through to a decision on the spot...

I'm taking it too seriously again, I know, I know... and I'm really just jealous because a fictional character played by a fifteen-year-old Jennifer Connolly is able to do what I cannot. Having said all that, if you want to have matters re-balanced by reality, there is always Karl Pilkington's approach to consider. Here's how he approached a similar puzzle when quizzed by Ricky Gervais...

Monday, 24 January 2011

Super XV and Mr Cipriani

The wonderful Super XV rugby union competition is due to kick off shortly (now having had an extra team to make up the numbers in Melbourne Rebels). I always regard this as great Saturday morning television, but with the added bonus of Danny Cipriani being added to the ranks at the new club.

Perhaps there is something fitting in the fact that he is joining a team known as “the Rebels” as that is what he has effectively become within the RFU – be it his fault or otherwise. I cannot recall the last time I saw something with such talent, nor am I able to quite forgive the powers that be in the way they have handled him – that is to say, abysmally.

It is true that he sometimes struggle to control a game at fly half and also that he does not offer the physicality in defence of a Wilkinson or Goode. However, it was not his fault that he suffered such a horrific ankle break, nor his fault that he was rushed back so early for the Autumn Internationals that followed. Perhaps a fresh start in the warmer climate of the southern hemisphere is exactly what he needs and if he can reproduce this kind of form, then surely he will start to feature on Martin Johnson’s radar once more…