[r-t] Method extension

[Mark Davies]

Hmm. I think we need to step back and try and clear the fog!

First of all, I think method extension is a really nice thing to have. 
It's great that LB Minor extends to LB 20, Grandsire Doubles extends to 
Caters, and Bristol Major extends to Maximus (and of course all the 
others in between and beyond). It is also very pleasant that, if there 
are two methods called Foobar Surprise Major and Foobar Surprise Royal, 
that we can expect there to be a close, rational relationship between 
them. It's all really good stuff, and method ringing is better off for it.

However, method extension is also a somewhat slippery concept. I think 
this is because, on the one hand whilst there are clear demonstrable 
mathematical relationships between methods that do extend each other, on 
the other hand most methods don't extend at all, and worse, when we are 
looking for extensions there is not necessarily any hard and fast way of 
choosing one specific extension system.

There are several ways to look at this fuzziness. One way is to pick 
your favourite extension system and argue that it is right and all 
others are wrong. Another is, like Philip, to throw in the towel and say 
there should not be any consistent centralised support for method extension.

I take a third view - that this underlying fuzziness is part of the 
beauty and ageless appeal of bell ringing. And that we can live with it 
perfectly well.

So let's take Little Bob Minor. The normal extension to the Major seems 
good, but it's not the only way to do it. There doesn't seem to be much 
wrong with hunting the treble to 6th's instead (of course this is 
currently named Gainsborough). There doesn't seem to be much wrong with 
adding a hunt bell and making a Little Bob Triples method 
(3.1.7.147.1.147.7.1 - currently unrung!). The "antients" as Robin terms 
them were happy to create extensions by adding hunts, and did indeed 
think Plain Bob and Grandsire were the same method. So here we have 
three good, clear but totally different relationships, and you could 
develop a sensible algorithm to follow any of them. However I think, 
aesthetically, the current LB extension is the best of the bunch. So 
we're happy.

Similarly with Cambridge Minor. It could be argued (reasonably) that 
there are several other potential extensions, certainly based on the 
place notation. You could look (as Andrew Johnson has done) at the 
current extension and say "Why if there are only single pairs of places 
in the Minor, is there a 1258 in the Major"? However the current 
extension does have a clear structural rationale (the 1258 arises 
because, in this style of extension, the front and back works are 
extended separately, and so places at the lower stage which never 
co-exist, such as 12 and 36, can happily do so at the higher, giving 
1258); and of course the blue line of the accepted extension also has a 
very clear similarity. So we've got the best result here, too.

I think finding the "best result" for extension is worthwhile. But it is 
difficult, and sometimes subjective. If we look at Bristol Major, it 
seems clear that the Royal and Maximus *are* really good extensions, but 
their structure and worth is perhaps not immediately apparent. If you 
were looking to extend Bristol Major you might spend a lot of time 
trying to find a suitable mx Royal method, and be disappointed. (In fact 
in its current extension Bristol *does* have the same LH group at all 
stages: but it is -8, not the first answer you might have thought of. -8 
mod 7 working bells is +6 = mx, -8 mod 9 working bells is +1 = g, -8 mod 
11 working bells is +4 = j, and so on; the -8 arises from the speed with 
which the bells course to the half-lead.)

The current Central Council Decisions do however give the standard 
extension for Bristol straight off, as well as telling us that London 
Major doesn't really have any proper extensions to Royal or Maximus. I 
suspect that PABS's conceptually purer system (which I really like the 
sound of) will do exactly the same thing. And that is useful.

Putting all of the above together, I would argue that:

1. We should stick with the concept of method extension, warts and all.

2. But finding good extensions is difficult, so algorithmic support for 
conductors needs to be provided. Up to now that algorithm has been Tony 
Smith's brain. It has done a pretty good job to be fair, but is in need 
of urgent replacement.

3. Despite (2), it is highly unlikely that there will ever be one 
perfect algorithm that can tell you the "right" extension in all 
circumstances. So we need flexibility. The algorithms can suggest good 
extension(s) to conductors, but if they disagree, or find a better way, 
then human intuition and ingenuity should be accommodated.

4. Finally, we shouldn't forget the obverse problem: to keep consistency 
the algorithms should also flag up cases where a band unknowingly rings 
a good extension/contraction of an existing method.

Given the protocols above, we just need a website which can host 
different extension algorithms. Doesn't matter how they work, who has 
authored them, or how many or few of them there are, as long as they all 
produce some kind of justifiable result. The algorithms are there to 
suggest good extensions, and to spot cases where good extensions have 
been missed. The rest - the actual naming and selection of the right 
extension - can be left to the discretion of the band, perhaps with some 
level of oversight from whatever the Methods Committee becomes.

Job done? Now we just need to crack on with the coding!

MBD