[r-t] Proof of twin-stage peals [was Anything Goes vs Peals Mean Something]

[Mark Davies]

Iain asks,

> What do you mean by "contain an extent"?  Would it have to be a continuous
> block of 5040 true rows somewhere in the peal, or can we pick and choose
> the 5040 rows from anywhere?

No, as I've been discussing with RAS, and he's agreed I think (although
doesn't want to legislate against it), picking and choosing any old rows is
not good enough.

As to what is good enough, I'm not yet sure. I thought individual leads
would be OK, but possibly this is a bit weak, too. Is there a precise way of
saying the extent must be embedded in the whole as a touch in its own right?

Here's some thoughts I have on what is wrong and what is right:

1. Within a stage, it's perfectly reasonable to combine extents (and even
one partial extent). Truth can be evaluated just by looking at what changes
the touch contains. In other word, your definition, Don's definition, and my
definition of truth all look the same here. Every change must be rung N or
N+1 times.

2. With two stages A and B, we must have an unambiguous way of separating
the changes into two sets A and B before applying rule (1) to both. The
trouble is, there is no concept of "stage" at the level of the individual
change. So I believe you need some coarser-grained unit against which the 
stage split is made.

The two-stage issue is important. If you don't attempt to solve this, then
you are accepting pretty much anything is true. For instance, you could give
me a blatantly false peal of Triples, with loads of repeated changes, and I
could say "Well this is actually a true peal of Triples and Minor. This set
of changes is unique, and they are the Triples changes; and these changes
you thought were duplicates, well actually they're Minor changes, and true
against each other. So this is a true peal."

That really is bollocks isn't it!

So I think that, although interleaving Minor and Triples changes throughout
a peal should be perfectly acceptable, it needs to be done in such a way we
can tell what the Minor changes are and what the Triples changes are. Since
peals are (currently) comprised of methods, checking this at the level of
the lead seems the finest-grained approach we would want to take.

If you don't like the idea of having to rely on leads, can you suggest
something else? The only other solution I can think of is not to allow
interleaving of changes at different stages at all, or only at extent
boundaries. This seems a bit draconian, although I suspect many people would
think it perfectly reasonable (it's what we have now isn't it?).

> We'd love the definition of "true" to be, well, true or false, but it is
> proving very difficult to get a consensus on what exactly truth is.

There's no real argument for single stages, is there? I think we are in
agreement there. The interesting question is what we do about multiple
stages. And this is important, because if we allow multiple stages, I really
don't think we want people to ring false single-stage peals and be able to
say they are true multiple-stage.

MBD