From: Emlyn O'regan (oregan.emlyn@healthsolve.com.au)
Date: Tue Feb 25 2003 - 15:45:51 MST
The first time I came across it was on an old Doctor Who episode, but I'm
sure they lifted it from elsewhere. I don't know where, though.
btw, you can also ask either guardian "If I had come to see you yesterday,
and asked you the way to St Ives, what would you have told me?". Whatever
answer the guardian gives will be the correct way.
Emlyn
> -----Original Message-----
> From: Brett Paatsch [mailto:paatschb@ocean.com.au]
> Sent: Tuesday, 25 February 2003 20:32
> To: extropians@extropy.org
> Subject: Anyone know the source of this old teaser? (was Skepticism
> about Game Theory (was IRAQ sort of...)
>
>
> It goes like this.....
>
> ------------------------------------------------------
>
> A traveller "X" wants to get to St Ives and arrives at a T
> intersection
> (see Fig A. below) at which stand two "custodians of the pass"
> "O" and "O".
>
>
>
> (path 1) <-----------------------------> (path 2)
> O | O
> (custodian C1) | (custodian C2)
> |
> |
> X (the traveller)
>
>
> (Fig. A.)
> [How things *look* to traveller X approaching the T intersection
> with two "custodians" and two possible paths. ]
>
>
> Traveller X has been reliable informed that the correct path
> to St Ives can be taken by either turning left or turning right
> but he has not been told which.
>
> Traveller X knows that one of the custodians of the pass
> will always respond to questions with a lie and the other
> will always respond with the truth. Both of these custodians
> know each other well and both know the actual way to
> St. Ives. T does not know which custodian is the liar and
> which is the truth teller.
>
> He is permitted only one question to one of them to determine
> the way to St Ives. But one question is enough.
>
>
> What is the question?.
>
> (answer at bottom of the post just in case anyone doesn't
> know and wants to try and work it out themselves)
>
>
>
>
>
>
>
>
>
> Fig B. Shows the truth that Traveller X can't "see".
>
>
> (path 1 is ....
> ( path 2 is....
> the way to St. Ives) <---------- ---------> NOT the way)
> O | O
> (C1 always tells the truth) | (C2 always lies)
> |
> X
>
>
> Figure B.
> -----------------
>
>
>
> [The answer:]
>
> Traveller X can ask either custodian "which way would
> he (the other custodian) have told me to go if I had
> asked him the way to St Ives.
>
> Then Traveller X knows the way is the opposite.
>
> Traveller X still does not know if he spoke to the liar
> or the truth teller and he doesn't care as he is already
> on his way to St Ives.
>
> -----------
>
> Lee is quite reasonably sceptical about the use of the
> term "game theory" in relation to the Iraqi crisis.
>
> I applaud that scepticism, and if I can explain my "reasoning",
> without losing too much time I'd like to give it a shot. In
> some ways its easier to just give "the answers" and not "the
> method". The answers should be testable, and challengeable
> themselves even if the method is not. (The first "answer" was
> that Bush should approach Chirac and ask him to come
> up with a standard of proof to be applied generally by the
> Security Council in order to decide whether a particular
> go-to-war decision was warranted. This answer has the
> appeal of preserving the UN and affixing accountability for
> failure and of making poor faith or poor judgement
> apparent - I think).
>
> I don't know if the above problem is really about "game
> theory" per se. But the phenomenon that is that problem and
> Axelrods "discovery" that the principles of tit for tat are
> teachable and once learnt constitute a strategy that cannot be
> beaten in iterative prisoners games even by those who know
> they are playing against it has certainly influenced my sense
> that the current Iraq crisis and the "standoff" within the UN
> is rationally resolvable despite human passions.
>
> I don't know that what I am actually doing is game theory with
> capital letters. I think what I am doing is trying to come up with
> a set of rules or a procedure which is guaranteed to give the best
> possible outcome given certain facts and given that those facts
> can be presented to free agents who have choice but who are
> bounded to act in the social world in only finite and limited ways.
>
> Perhaps rather than game theory I am doing a sort of transaction
> analysis.
>
> Maybe I'm just being a w**ker. But if so I am not being so
> knowingly.
>
> Regards,
> Brett
>
>
>
>
>
>
>
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