Shades of Truth

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I've been thinking back to the long discussion here last summer [2008] when we tried (and utterly failed) to come up with a new set of decision that we could all agree on. One of the bigger stumbling blocks was the meaning of truth, in the context of a piece of ringing.

The more I think about it, the more I'm convinced that the key realisation is that there is no single unambiguously-correct definition of what constitutes a true piece of ringing. Instead, what I think we have is a variety of different definitions that are used in different circumstances.

For example, we might start by saying that a true round block is one which:

[U] includes every row at most once; and
[R] starts and ends with the same row.

(The initials are for 'uniqueness' and 'round block' respectively.)

At a single stage on eight or more bells, that's sufficient. While touches that have intentionally satisfied only one (or neither) of these are sometimes rung (e.g. a short service touch of spliced that the conductor knows to be false), I imagine few people would want to describe them as in any way 'true'.

But the idea of a complete extent is clearly also relevant, as, on lower numbers, it's fundamental to all long touches. For reasons that will hopefully become clear shortly, I'm going to define an extent as a touch that in addition to satisfying [U] and [R], also:

[C] includes every possible row an equal non-zero number of times.

(C is short for 'complete extents'.)

If we drop down to triples, the vast majority of peals satisfy all of [U], [R] and [C]. But there are interesting cases of peals (or things claimed as peals) that satisfy any two of these.

  • Long lengths clearly cannot satisfy [U], but they are required to (and do) satisfy [R] and [C].
  • The College Youths recognise a 5014 of Grandsire rung in 1862; likewise apparently the St Martin's Guild recongise a 5026 (or 5025?) of Grandsire rung at a similar time. Clearly they did not satisfy [C]. I don't know whether the compositions have been recorded, but I strongly suspect they would have satisfied [U] and [R] much as a peal of major does.
  • And wasn't there a bobs-only peal of Grandsire rung in the Birmingham area in which all 5040 rows were rung (if the opening rounds are counted), but that did not return to rounds at the end? If so, that satisfies [C] and [U], but not [R]. Even if such a composition hasn't been rung, something similar is an interesting enough idea and definitely would be noteworthy.

Today, for a single stage peal to be true it must satisfy [R], and either (on major or above) [U] or (on triples and below) [C]. But historically this hasn't been sufficient. Multi-extent blocks are a recent innovation -- originally a peal with several extents had to be comprised of single extent blocks. Specifically it

[S] is completely divisible into one or more non-overlapping
    blocks consecutive rows such that each block individually
    satisfies [U], [R] and [C].

The impetus for relaxing this restriction came with Bankes James' 2160 of treble dodging minor. This 2160 can be divided into three 720s each of which contains every row exactly once, but does not produce rounds at the end of each 720. I don't know precisely how the CC decisions were changed to permit this, but the notes at the end of the 1961 minor collection suggest that [S] was not initially dropped entirely: rather it was weakened to only require the touch

[B] is completely divisible into one or more non-overlapping
    blocks consecutive rows such that each block individually
    satisfies [U] and [C].

(S and B stand for 'single extent blocks' and 'Bankes James blocks' respectively.) Even now that neither [S] or [B] are required, it's not unusual to choose to ring compositions that satisfy them. For example, the standard 41 minor cannot be rung in an ordinary length while satisfying one of these, but a peal in all 41 that additionally satisfies [S] is somehow more elegant than one that 'merely' satisfies [C].

Similarly, when multi-extent touches which are only [U], [R] and [C] are rung, it's not uncommon to want some other, additional structure. For example, it is sometimes claimed that there are only three true 240s of Grandsire Doubles. But what's actually meant is that there are only three true 240s containing each row once at each stroke. Likewise there is a tricky 10,080 of Stedman Triples by Rod Pipe with this property. I'd argue that this is just another, stricter form of truth. As the archetypal composition with this is Morris' 240, lets call this [M] are require that the touch

[M] includes every possible row an equal non-zero number
    of times at each stroke.

And I can imagine someone might go further and, say, look for a 30,240 of Erin Triples where each row appears once in each position in a six, or a bobs-only 30,240 of Stedman Triples where each row appears once in each position of the appropriate parity.

If there are lots of ways of achieving a particular effect it seems natural to add an additional restriction so that that is not the case. That's not just true when it comes to truth, but also methods (we allow arbitrary blows in one place in minimus, as many as four in doubles, but rarely desire more than two at higher stages) and compostions (c.f. the desire for bobs-only extents of various triples methods).

But equally, if it's impossible to do what we want within the constraints, we tend to relax them until it becomes possible. For example, the desire of quarter peal ringers to be able to ring convenient lengths leads to a weakened version of [C] in quarter peals:

[Q] there exists an integer n such that every possible
    row either occurs n times or (n+1) times.

Another example is Little Bob which I'm sure is sometimes rung in quarter peals without either splicing it with an alliace method or using variable treble. But equally, I would guess an attempt to ring a 'true' quarter is still made -- effectively by adopting a get-out clause:

[L] in a little method, rows with the principle hunt bell
    outside of the positions visited in its path are not
    deemed 'possible rows' for the purpose of [C] or [Q].

When this topic was discussed last year in the context of replacement decisions for peals, I think we made a fundamental mistake -- instead of trying to describe existing practice we tried to produce a single prescriptive definition. When previously discussing methods and compositions, I think we have largely been in agreement that such an approach was wrong. Shouldn't the same be the case with truth? Far better to simply categorise existing practice and try to provide a flexible vocabulary that allows us to talk about the truth of corner cases.

Inevitably there will be dissention as to what constitutes and acceptable degree of truth for peal, and I think it's likely that if the CC ever recognises quarter peals, the standard of truth there will be different. Personally, I can't imagine ever wanting to play the [L] get-out-of-jail card in a peal, but can imagine ringing a quarter that was only true with [L]. But equally I don't think it's any of my business (or the CC's business) to tell others that they mustn't ring [L] peals.

At present, if I ring a peal that doesn't conform to the decisions, in theory, at least, the CC includes it in their analysis but identified as non-compliant. (In practice, it doesn't always work like that because the RW sometimes refuses to publish them as peals and the CC is not required to then include them in the analysis, but that's a separate issue.)

We've rehearsed many times the reasons why this stifles innovation -- and one major problem is the tarring of everything different with perjorative term 'non-compliant'. If instead the CC simply recorded against every peal in what way it was true, this could be different. This would be especially the case if 'normal' peals, at any given stage, fell into several different truth categories. And in this respect, retaining something similar to [S] and [B] would be helpful. A significant minority of peals are not currently [S] or [B], including most complex peals of minor. Once it becomes accepted that, at a given stage, there are different classes of truth that are all accepted by ringers in general, perhaps it will become more accepted to ring more different things.

I haven't made any effort to draft these into a form that could be slotted into last years' attempt at a revised set of decisions on peals. But I think that this is the right way to head. Clearly the case of peals on multiple extents needs thought too. But by adopting multiple definitions, and treating them as descriptive rather than prescriptive, we can hopefully avoid last year's problem that we couldn't agree where to draw the line between true and false.

RAS September 2009