[r-t] A Ringing Puzzle

[Don Morrison]

On Fri, May 30, 2014 at 4:48 AM, Graham John <graham at changeringing.co.uk> wrote:
> > What is the non-method block in the case of Don's puzzle
> > method A? One lead? The whole course? If the latter it
> > definitely has leads (repeating blocks of changes)
>
> If a non-method block was defined as the whole course then it would be false
> as calls are only allowed at the end of a non-method block.
>
> If a non-method block was defined as one lead, then calls would only be
> allowed at the leadend. Don's composition with half lead calls could not be
> used. It would be extremely difficult, if not impossible, to get a
> composition without them.
>
> If a non-method block was defined as half a lead, then Don's composition can
> be used but it would be a peal in two alternating Blocks. But hang on a
> minute, a Block based upon half a lead forms a true asymmetric principle,
> therefore it is a lead of a valid method, and cannot be defined as a Block.
>
> It therefore has to be defined as two alternating asymmetric principles
> spliced, one the inverse of the other.
>
> So, the answer is that method B is a Surprise method, but method A can't
> exist as people would learn and ring it.

Thus an even more straightforward example of a non-non-method than Dixon's.

Adding to the delightful inconsitency of all this, the method, similar
to A, described by Tony Cox on this list some years ago can be rung,
meeting the CCCBR's definition of a non-method block, as he provided a
composition using only lead end calls. And Richard Smith's plain minor
method included in a (CCCBR disavowed) peal over a decade ago used only lead
end calls in its extent.

Go figure.

Am I correct in believing that this is a new attribute of the
Decisions, that the very existance of a method-like-thing can now
depend upon whether or not someone is clever enough to come up with a
suitable peal composition, extent, or MEB for it? It has certainly
long been the case that you couldn't name a method wtihout a suitable
composition to call, but has the very existence of an unrung method
been called into question for lack of a peal composition?

And a true composition of Method A can be assembled using only lead
end calls, though it would probably be impossible for normal humans*
to ring it: the obvious one of length 161,280. Though almost certainly
a shorter MEB could also be constructed.

Oh, no, wait, that doesn't work: the Decisions only allow multi-extent
blocks of Triples and below.



* There are some hand bell ringers, whom I admire, that may not fit
  this description.



-- 
Don Morrison <dfm at ringing.org>
"The problem with being consistent is that there are lots of ways to
be consistent, and they're all inconsistent with each other."
  -- Larry Wall, the Perl 6 mailing list