Re: Question: arrival-time puzzle

[John Denker <jsd@MONMOUTH.COM>]

Jim Green asked:
> >>Is this true???

David Bowman answered:
> >Yes.

At 06:38 AM 7/11/00 -0500, brian whatcott wrote:
> Actually, no.
>
> Jim, there you go again, noticing that the Emperor has no clothes.

1) The arrival-time puzzle does not claim imperial majesty.

2) The arrival-time puzzle is quite well clothed.  It may have a few specks
of dust on its clothes, but the specks are much smaller than Brian imagines.

> The misdirection here is supposing that a succession of real world buses
> can be independent and identically distributed in time.

Suppose busses adhere to the usual safety rule of 3 seconds in-trail
separation.  IF (big if) we assume a one-lane road, that's a fraction 0.005
of the specified average interval.  So, the anti-bunching phenomenon means
my claimed times might be limited to two significant digits.  But I only
claimed them to one significant digit.  So the nit-pick, in addition to
being irrelevant, is just plain wrong.

Furthermore, Brian has no basis for assuming a one-lane road.  If busses
can pass each other, my claimed times are good to at least 4 significant
digits.  Since only one sig dig was sufficient to make the point of the
puzzle, this is getting pretty silly.

In general, it seems unprofessional to walk up to a puzzle, dream up some
nits to add to it, and then point them out as if they were an intrinsic
part of the puzzle.

> ... if one recalls the universal real world bus-scheduling
> constraint: out of the depot, the order of the buses is known.

Hogwash.

======================

All too often, students go into what I call _lawyer mode_.  They argue "I
was unable to solve this puzzle.  But look, there is something wrong with
the puzzle.  It's not my fault!"  They think they can get off on a
technicality.

Usually, this tactic is dishonest.  It suggests that if the puzzle had been
perfect, the student would have solved it.  (Usually, I doubt it very much.)

Secondly, although this tactic works in TV courtrooms, it rarely works in
real courtrooms.  And real-world research jobs or engineering jobs are
verrry unlike courtrooms.  Your collaborators won't let you off on a
technicality.  If you have a bad attitude toward technicalities, folks will
just stop collaborating with you.

Again:  the rule is:
  If find nits in the question, rephrase the question.
  Answer the question that _should_ have been asked.

=========================

Specific anecdote:  Once I was the teaching assistant for a
physics-for-nonmajors course.  On a quiz, the professor drew a wave and
marked off certain distances, and asked what those distances
represented.  The intended answers were things like amplitude, phase,
wavelength, et cetera.  But there was a nit:  The professor had drawn the
wavelength line so that it went from one node to the _third_ succeeding
node, not the second.

It was fascinating to see how the students responded.
 *) About a third of them said "wavelength".  I gave full credit for
this;  if the professor didn't notice, I wasn't going to carp if the
students didn't notice.
 *) About a third of them said "1.5 wavelengths".  I gave extra credit for
this.
 *) About a third of them left it blank.  A goodly number of these left
the amplitude etc. questions blank also, so it was easy to assume they
hadn't learned any of the names.  But even for the ones who got the other
parts of the question right, I gave _no_ credit for the non-answer.

I used the occasion to expound upon the rule:
  If find nits in the question, rephrase the question.
  Answer the question that _should_ have been asked.