[r-t] Definitions so far

[Graham John]

Don wrote:

>> Stage: a name given to the number of bells ringing changes. 
>> [makes it clearer that a cover bell is not included]

> No, it's the number of bells ringing in a row. Bells don't ring
> in changes. And, as you've not defined "change" yet, you've
> set up a circular chain of definitions.

If you look at Tim's version the circularity was there through the use of N in defining Row, as N is the Stage. In this definition, it was purely to exclude a cover bell, otherwise you need first to define cover bell which could be difficult without introducing another circularity. I am trying to think ahead here, because in this discussion we have introduced an as yet undefined Stationary Bell in Methods. By getting the definition of Stage and Row right, we can ensure that proof is against Rows of a particular Stage i.e. excludes a cover bell, but Stationary Bells being within a Row are included in the proving of truth.        

>> Change: A transposition of bells from their Places in one Row into the 
>> next Row. [doesn t need Stage as Row above uses Stage in its 
>> definition]

> If you depend upon the Row's stage to define this, you need to be explicit that both Rows are of the same stage. 

Do they have to be of the same stage? What happens when you change method from Stedman Cinques to Bristol Maximus. Can't you cast an 11 bell Row into a 12 Bell one.

>> Simple Change: A transposition where one or more adjacent pairs
>> of bells swap Place.  [shorter and excludes Null Change so that the 
>> subtypes don t overlap]

> Erk. "Adjacent pairs of bells swap Place"? Something more explicit
> would be far better. We know what it means, but I doubt that my
> late mother, may she rest in peace, a non-ringer, would necessarily
> have known, and depending upon preconcieved notions is a large
> part of what got us into the temperature of water in which we
> currently swim.

More explicit can be more confusing. What did you have in mind?

>>  Null Change: A transposition where no bell moves Place.
>> [simpler definition]
>> Jump Change: A transposition where one or more bells
>> moves to a non-adjacent Place. [defined by what it is,
>> rather than what it isn t]

> You've radically recast what Tim was defining.
> You've partitioned changes into three, disjoint classes,
> where he had only two. I think this is a mistake.
> Doubly so in light of the recent vote that said more folks
> don't have a problem with null changes. It's not at all clear
> to me we even need a definition of "null change" -- where
> are we going to use that term? But if we do, as a particular
> kind of Simple Change makes a lot more sense.

I think you are trying to slide null changes under the carpet, Don. Null changes and Jump changes have been very deliberately excluded from the existing decisions and virtually all the 300 years of practice. Just because the majority of small group of mostly mathematicians on ringing theory think allowing the null change is a good idea, does not make it acceptable to all, and the same goes for Jump changes. By having clear subtypes, Simple defines changes that are accepted by the current decisions and Null and Jump covers the rest. We have broadened the definition of Change to include all three, and that satisfies our objective of describing what is rung. There may be some who will only want to ring Methods and Compositions containing Simple Changes, others may be happy with Null Changes but not Jump changes, some might want to ring a peal only containing Jump changes. Having non-overlapping subtypes in these definitions gives terminology to describe a composition or a method accordingly, and for the sum of the subtypes to equal the number of changes rung.

> If I am overruled on this, though, there would then be two further fixes that would be needed:
> 1) the order would need to go null->simple->jump or jump->simple->null.

This as an unordered list, what is the need for order?

2) the name "simple change" would need to change, since a null change is simpler than a simple change!

I'm happy for an alternative word to be used.

Graham