[r-t] Asymmetric Doubles

[Martin Bright]

On Fri, 2010-08-06 at 09:51 +0100, Graham John wrote:
> Defining a bob and single using nature in the way I suggested broadens their
> definition, allowing any type of call to be classed simply as either a bob
> or a single.

I think there's still an issue.  You have to decide whether you mean (i)
swapping two/three bells *from what they would have been doing*
(changing the nature of the rows from what they would have been), or
(ii) swapping two/three bells *in the coursing order* (changing the
nature of the coursing order).  These are different, and neither works
in all cases.

Consider first Bristol Major.  Here a bob on the face of it affects 5
bells, but we get around that by saying that really it only affects
three, but sends you to a different lead of the course as well.  So
we're looking at what the call does *up to the action of the group of
lead heads*, in other words, what it does to the coursing order.  A bob
takes you to another course of the same nature, and a single to a course
of the opposite nature.  Definition (ii) seems to be the one we need.

But now consider Bob Doubles.  The problem is that the lead head is out
of course, being a 4-cycle.  So there's no notion of the nature of a
course - each course has two in-course lead heads and two out-of-course
ones.  You can see this in the coursing order too - the call taking 5324
to 5342=2534 can be viewed either as swapping the pair (24) or as
cycling the triple (235).  So here definition (ii) isn't well defined,
so we might try to use definition (i) instead.

Martin