🚀 go-pugleaf

Hi folks,

A Missouri Manure Grinder looks something like this:

                  +--------------+ -- +--------------+
                  |              | || |              |
                  |              | |*\|              |
                  |              | ||\\              |
                  |              | -- \\             |
                  |              |    |\\            |
                  +--------------+    +-\\-----------+
                                     |===*===|
                  +--------------+    +---\\---------+
                  |              |    |    \\        |
                  |              |    |     \\       |
                  |              |    |     (*)      |
                  |              |    |              |
                  |              |    |              |
                  +--------------+    +--------------+

They are quite cute.  You grab the handle (the (*) part) and move it left
or right, and the next thing you know the two pistons are traveling back
and forth in the two tracks in curious reciprocating fashion.  Just the
right sort of thing for a transplanted Ozark Missourian such as myself
as I chaw on a piece of wheat and stroll through a Texas cow pasture!

ASSERTION:  There exists a broad constructive generalization of the
Missour Manure Grinder in two dimensions.  The generalization is such
that an arbitrarily large number of related devices can be defined
simply by using a compass and straight edge.

PROBLEM: (Primarily for physicists.) See if you can recreate the Bollinger
Generalization of the Missouri Manure Grinder, and express the problem in
as clear and abstract a form as possible.  Describe key properties of the
overall class of Bollinger Generalizations of Mo. Manure Grinders (BGMMGs).

EXTRA PROBLEM: Can the 2D BGMMG be generalized further to 3 dimensions?
To n arbitrary dimensions?

WHY I'M ASKING: While I'm no physicist and thus don't count, I've noticed
that a persistent trait of many of the more famous and innovative physicists
is the ability to mentally manipulate and generalize curious geometrical
problems.  I am curious how some of you might do on this one.

APPLICATIONS:  Here's a tough one.  If you find the generalization, can you
go on to figure out how and whether it applies, oh, say, to particle physics
or Standard Theory?  Or perhaps Hilbert spaces?  Please note that in no way
am I saying that it has any relevance whatsoever.  On the other hand, I've
also noticed that it can be very risky to say that *any* kind of mathematical
formalization is irrelevant to physics.  The linkages are often subtle, but
can be profound.  Is there one for BGMMG?  I certainly don't know.  Do you?

BACKGROUND: This is my unpublished work of my own, so I doubt you can look
it up anywhere (barring similar work by someone else, of course -- I have
not done any serious literature search on this one).  If someone wants to
act as the "holder" of my generalization to verify that I do indeed have
one and am not just setting up a little wild goose chase, I'd be glad to
do so (say with Dr. Baez or Dr. Chase, for example).

(If you disdain puzzles such as this as being irrelevant to physics, you might
read the rather interesting section in Gleick's book "Genius" origin of Martin
Gardner's Scientific American column.)

				Cheers,
				Terry Bollinger

+--------------------------------------------+-------------------------------+
| Terry Bollinger                            | Phone: 214-518-3538           |
| Advanced Switching Laboratory, NEC America |   Fax: 214-518-3499           |
| 1525 Walnut Hill Lane, Irving, Texas 75038 | Email: terry@asl.dl.nec.com   |
+--------------------------------------------+-------------------------------+