Re: [Phys-L] Inference Lab Design

[brian whatcott <betwys1@sbcglobal.net>]

On 8/19/2012 12:41 PM, Jeff Bigler wrote:
> On 8/19/2012 2:29 AM, D.V.N. Sarma wrote:
> > Talking about inference, here is a story I have read somewhere
> > which some of you may be knowing already.
> >   
> > There is a society of logicians. Anybody who wants join the society
> > will be given a test and only those who pass the test
> > are admitted.
> >   
> > Once three new candidates applied for membership.  The society
> > devised a test for them. They were told that they will be bindfolded
> > and three caps will be placed one each on their heads. The caps will
> > be either black or white. Then their blindfolds will be removed.
> > The candidate cannot see the color of the cap on his own head but
> > only of those on the heads of the other two. A candidates who sees
> > one or more white caps should rise his hand. From the hands raised
> > one has to guess the color of the cap on his own head.
> >   
> > The candidates were blindfolded and three white caps were placed on
> > their heads. The blindfolds were removed. All the three raised hands.
> > Presently one of them said that his cap is white. How did he guess that?
> I must be missing something.  Suppose the candidate who spoke up was
> candidate #3 (C3).  The following situations are both possible:
>
> 	C1	C2	C3
> cap	white	white	white
> hand	raised	raised	raised
>
> 	C1	C2	C3
> cap	white	white	black
> hand	raised	raised	raised
That is the primary conclusion of course. But then, one candidate 
ponders on the situation
and proceeds in this way:    If my cap were black, then each of the 
other candidates could
 infer immediately that their hat was white; but there was a pregnant 
pause, because the
question was not answerable by their initial  cogitation, so it follows 
that my cap is indeed
white, so though I hesitated, I now know.

[I have not heard this particular puzzle before, but the puzzle concept 
of 'the hound that
 does not bark' or pregnant pause  is shared with several puzzles of 
this kind]

Brian W
p.s. "There is a story which some of you may be knowing already" is a 
use of the present
 continuous tense which is unusual in  English or American usage - 
though it is strictly
 more correct  than the more usual "some of you may know" - -  from 
those of us who treat
'know' as a perfect or instantaneous form in the usual way.
 This is heard sometimes in Anglo-Indian speakers - though given the 
surname Sarma,
this is not exactly Holmes level inference. Notice though, that Jeff is 
comfortable writing
"I must be missing something" where  I am missing" is a present 
continuous form.
Notice here that Bigler is slightly unusual in English surnames, where 
you might expect Biggler,
so  again without any great leaps of intellect one concludes that Jeff's 
folks immigrated
 a hundred years or more ago.