Theorem?

[Don Morrison]

When distinguishing surprise/delight/treble bob methods the current decisions say "an internal place" at a cross section, while version 7 of the Descriptive Framework and Requirements developed by Tim and this group say "a working bell makes an internal place" at a cross section. I presume there is no deliberate intention that what the current decisions consider surprise/deight/treble bob be changed for sufficiently bizarre methods. If so, that would seem to imply that there should be a theorem stating that whenever one or more internal places are made at a cross section, at least one of them is made by a working bell (subject to the further stipulation, made explicit in the v7DFR, that non-treble-dodging hunt bells are considered "working" for this purpose). While this is clearly true for the simple cases, it is not at all clear, at least to me, that it is true for multiple hunt bells in a single lead with possibly different numbers of dodging positions, different numbers of dodges, and different phases, possibly some dodging at hand and others at back.

Has anyone a proof or counter-example?

-- 

Don Morrison <d...@ringing.org>

"Much can be said about cabbages.... In the mass, however, they lack

a certain something; despite their claim to immense nutritional and

moral superiority over, say, daffodils, they have never been a sight

to inspire the poet's muse."           -- Terry Pratchett, _Mort_

[Tim Barnes]

Don -- yes, there wasn't an intention to change the definitions of TB / Surprise / Delight, even for 'bizarre' methods.  Any additional hunt bells that are 'beyond' Treble Dodging (i.e. Treble Place, Alliance or Hybrid) are deemed to be working bells for the determination of TB / Surprise / Delight, which was intended to give the same results as the 'an internal place' language of the current Decisions.  

However you may have uncovered a difference.  If a method has two non-overlapping little treble dodging hunt bells that are out of phase in a certain way, I think it's possible one of them could make an internal place while the other is moving through a cross section.  That internal place wouldn't be taken into consideration in the subgroup doc, whereas I think it would be in the current Decisions.  I need to think this through more fully, but is this the sort of thing you had in mind?

Revisiting the method classification rules after a several-month gap reminded me of how complex they can be in edge cases.  I hope we can eventually get to a simpler approach, along the lines of RAS's proposals last year.

[Don Morrison]

On Thu, Mar 9, 2017 at 2:15 PM, Tim Barnes <tjbar...@gmail.com> wrote:

> However you may have uncovered a difference. If a method has two

> non-overlapping little treble dodging hunt bells that are out of

> phase in a certain way, I think it's possible one of them could make

> an internal place while the other is moving through a cross section.

> That internal place wouldn't be taken into consideration in the

> subgroup doc, whereas I think it would be in the current Decisions.

> I need to think this through more fully, but is this the sort of

> thing you had in mind?

Exactly.

-- 

Don Morrison <d...@ringing.org>

"Life in this world...is, as it were, a sojourn in a cave. What can we

know of reality? For all we see of the true nature of existence is,

shall we say, no more than bewildering and amusing shadows cast upon

the inner wall of the cave by the unseen blinding light of absolute

truth, from which we may or may not deduce some glimmer of veracity,

and we as troglodyte seekers of wisdom can only lift our voices to the

unseen and say, humbly, 'Go on, do Deformed Rabbit...it's my

favourite.'"                      -- Terry Pratchett, _Small Gods_