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

[Mark Davies]

Matthew asks,

> What exactly do you mean by "embedded in the whole as a touch in it's own
> right"?

I didn't say that! I said "embedded in the whole as a touch in its own
right". Makes much more sense. ;-)

I think the touch idea may be a bit too restrictive, in fact. You have an
extent of Minor, you want to embed it in a peal of Triples. Does it have to
be extractable in some fashion as an extent touch in its own right? Well you 
could argue that, but it is a restriction. It would be nice to be  able to 
ring extents of Minor which form into two or more blocks that can't 
ordinarily be linked, by embedding the blocks into the Triples. No?

> Yes, that isn't what we want, although it would have to be very carefully
> constructed to be able to lift out whole extents of minor.

No, not if we allow one partial extent in a peal. You don't want to exclude
that, do you?

> Can i also just note my (continued) disagreement to limiting this to 2
> stages (but that's another issue).

Not limiting methods to just two stages, remember - only the process of
proof. If you allow multiple stages for proof, you have the Triples and
Singles problem, and open up the field to obviously false peals again. So
the 2 stage rule is not stopping you ringing what you want to ring, it's
just ensuring that whatever you do ring has a reasonable standard of truth
applied to it.

> I know it's not paticularly nice, but could you embed the stage in the
> definition of a method? Then all the rows of that method are at that stage
> or higher

Yes, that's what I originally meant I think. So that, if you ring Grandsire
Doubles, Plain Bob Doubles and Plain Bob Minor, all the rows in the
Grandsire Doubles and PB Doubles are treated at the lower stage.

This is quite neat, but it would prevent certain things: you couldn't ring a
Doubles extent of Grandsire Doubles, and also use variable-cover Grandsire
Doubles as part of an extent of Minor. Are we bothered? Yes, probably - this
seems a valid thing to want to do.

The best I can do at the moment is to reduce it to individual leads. Any
given lead has to be considered at either one stage or another. That's
pretty reasonable - although as RAS has pointed out you could ring lots of
single-change methods.

MBD