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From: king@kestrel.ARPA
Newsgroups: net.puzzle
Subject: Re: Re: Explorer paradox * SEMI-SPOILER *
Message-ID: <4524@kestrel.ARPA>
Date: Mon, 3-Feb-86 18:29:08 EST
Article-I.D.: kestrel.4524
Posted: Mon Feb  3 18:29:08 1986
Date-Received: Wed, 5-Feb-86 01:43:58 EST
Organization: Kestrel Institute, Palo Alto, CA
Lines: 54


   From: dobro@ulowell.UUCP (Chet Dobro)
   Newsgroups: net.puzzle
   Date: 21 Jan 86 08:31:52 GMT

   > In article <1011@ecsvax.UUCP> hes@ecsvax.UUCP (Henry Schaffer) writes:
   > >> 
   > >> > From: colonel@sunybcs.UUCP (Col. G. L. Sicherman)
   > >> > Message-ID: <2667@sunybcs.UUCP>

   > >> > Here's a new one: a practical joker tampered with the Great
   > >> > Explorer's gyrocompass, so it points 45 degrees off.  The Great
   > >> > Explorer thinks he's going due north on his way to the North Pole,
   > >> > but he's really going due northwest!
   > >> > 
   > >> > Will he reach the North Pole anyway?  (Geographers keep out of this
   > >> > one!) 
   > >> 
   > 
   > My own thoughts about this are as follows.  If this explorer is following
   > the compass at all, he should eventually arrive at the north pole after a
   > number of spirals toward it.  My thinking goes like this; if this compass
   > points anything less that 90 degress away from north, he will eventually
   > find north by its vector quality.  That is to say, if you subtract the e-w
   > direction component away from the vector, you are left with the north
   > component of the vector.  This northern component may be small, but it
   > exists; so the explorer shall eventually get there.  The greater the e-w
   > component as compare to the norther component of the vector (ie. closer to
   > 90 degrees from north) the longer the distance (number of spirals) before
   > the explorer gets to the North Pole.  It can be easily visualized if you
   > think as the world as flat and repeating, and the north pole is a straight
   > line on the top.  This way the problem can be solved using simple
   > geometry.
   > 
   > 
   > 	Anyone care to comment....It seemed logical to me; but I may be
   > 	missing something fundamental - unlikely though :-).
   > 
   > 				Martin the Magician.

   This is correct given that the compas poins to the north pole and not
   magnetic-north.

						   Gryphon
Seems to me that with a GYROcompass this wouldn't work.  Let us say that a
gyrocompass points north when it is aimed at the north star (although a gimbal
arrangement may let us find a northward direction).  We get to the point under
that star.  If the compass is twisted, it points to a different star and the
explorer ends up somewhere else.  

He may smell a rat when the compass moves during the night, which it wouldn't
do if it was pointed at a pole.


-dick