The Coin Problem
A Blue Coin is sitting on top of a red coin. Both coins have milled edges. We show the coins orientation by arrows.
The blue coin is rolled to the right -- without slipping -- around the rim of the red coin until it is immediately below the red coin. Like so ?
or is the blue coin now like so ?
So after rolling, is the orientation of the blue coin the same as originally, or is it now inverted?
Solving the Coin Problem
This page is part of a web-site devoted to the study of qualitative thinking,
with an emphasis on those problems,
quite formidable and challenging,
called Dragons
which can be solved
without having to write anything down or perform a calculation.
See Dragons for
an introduction to Dragons with a physics emphasis,
Mostly dragons have answers like yes/no, more/the same/less,
left/right, top/bottom, up/down.
But also there is a category of such problems called by the philosopher
of mathematics Lakatos, Monsters, wherein the problem is to debug
what looks like a counter-example to a known solution to a problem.
But if you learn that YOUR solution to a Dragon is false --
the canonical wrong answer -- and become convinced that this is indeed so --
then to you this first solution IS a Monster,
that has to be debugged.
Enough said. Get out two coins, both the same size, and hold one still on the table,
Set both coins to the same orientation, heads up say, and
roll the other half-way around the other without slipping.
What happened? Was it what you predicted?
If yes, you may be interested to read of other approaches.
If no, you have a Monster in hand. Do it again until
you are totally convinced as to what actually happens.
Take a look at the following solutions.
In these two very different approaches to Andy diSessa's Coin Problem,
one is motivated by the Process heuristic,
the other by the Reciprocity heuristic.
The term heuristic means a problem-solving idea --
and this term is so used on these web pagess.
But we use a heuristic -- in bold to denote a structured bundle
of problem-solving ideas clustered about one core heuristic.
This concept of heuristics was first provided in the downloadable paper,
Harvey A. Cohen, The Art of Snaring Dragons,
M.I.T. Artificial Intelligence Laboratory Memo 338,
May 1975
Terms such a schemas and p_prims have been used by later writers with
similar meanings.
The original account of the Coin Problem is on pages 26-29 of the paper,
Andrea di Sessa, "Phenomenology and the Evolution of Intuition". in Deidre Gentner and Albert L. Stevens,
(Editors), Mental Models Lawrence Erlbaum Assoc., Hillsdale N.J., pp 15-33 (1983).
In this paper the term p_prim is used.
