[r-t] Ben Constant's Yorkshire Royal

[Mark Davies]

Philip writes,

> Eg is Chandler's 23-spliced a simple re-arrangement of Smith's 23 spliced?
> Are they identical even? Would you refer to either as Arr. from trad?

There are several levels of "composition identity", the first couple of
which are surely unarguable:

1. If, no matter how the composition is written down, the same rows in the
same order are rung, then the compositions are identical. This is clearly
not the case with your example.

2. The next level is invariance by symmetry. If the calling of a composition
is the rotation or reversal of another, then it is a variation. This is not
the case with your example, either (the methods are different, and the
methods are part of the calling).

3. Now we get to a level where there is some subjectivity. If the calling of
a composition is identical (up to symmetry) to the calling of another, with
the exception of the insertion, deletion or replacement of some small
idempotent blocks (e.g. 3H), then it is a variation.

Now level 3 is subjective because, how many blocks do we allow, and how
small need they be? For some compositions, I can proceed to delete blocks
like 3W, 3H etc until I have nothing left. WHWH is an obvious idempotent
block, but so is 2W2H2W2H.

So some degree of judgement is needed, which, yes, means discussion and
arguments over the boundary cases. But your example still doesn't fall into
this category.

4. Level 4 is fairly similar to level 3, but here we allow differences other
than insertion or deletion of idempotent blocks. For instance, MB gives the
same transformation as 2W. A composition whose calling is identical to
another's, with the exception of MB versus 2W, would be a variation under
this rule.

Whether this level is truly separate from level 3 I wouldn't like to argue
too strongly: of course the reason MB=2W is because the blocks MBW and WWW
are both idempotent.

Nevertheless, in practice it seems that "two different callings to give the
same permutation" feels slightly different to "removing or adding an
identity calling". Your example finally comes in here, Philip. Chandlers is
related to Smith's by the replacement (between bobs) of blocks of methods
which generate the same transformation.

Now, would I say that Chandlers is a variation of Smith's, under the "level
4" rule? No, I don't think I would. *Every* block in the peal has been
replaced with a different calling. We could look more closely at the methods
involved: if every block had changed but the methods were TVs of each other
with the same falseness, I might change my mind. Or, if there were very much
fewer methods, or fewer methods had been changed, right down to the trivial
case of a single-method peal being rung to a different method - again I
would change my mind.

In summary, I think there are some inarguable rules about composition
identity. And then I think there is a less-well-defined area where
compositions can be shown to be related, and if the relationship is very
close, then we should recognise it.

Well, I do recognise it - this is exactly how the G&B composition collection 
is constructed.

MBD