[r-t] Lead-based methods [was: Poll on consecutive blows in the same position]

[Don Morrison]

On Mon, Dec 29, 2014 at 2:49 PM, Tim Barnes <tjbarnes23 at gmail.com> wrote:
> Can Don ... provide a more generic definition of a rules-based
> method? I'm interested to find out if Don is as good at proposing
> solutions as he is at pointing out flaws ;)

Considering confirmation bias, I wonder if anyone can be as good at
proposing solutions as at pointing out flaws, assuming they really
apply themselves to the latter?

Giving it a try, anyway....

At first I was skeptical that it's even possible. As I wrote earlier
today, in light of Ander's observation I'm not convinced that there is
a real distinction in the absence of calls. There's a fuzzy
I'll-know-it-when-I-see-it feel about how LBMs and RBMs differ, but
when you get down to trying to define them precisely it tends to all
go up in a puff of interestingly colored, scented smoke. Cf., also,
Iain's observation about how they meld in practice.

However, I wonder if something like the following (actual definition
between the horizontal rules at the end of this message) might allow
us to finesse the problem of calls?

Caveats:

* This is at most just a starting place. If it seems a valuable
way forward, it will need a lot of tidying up.

* There are a lot of terms or ideas assumed to be already defined, including

** Row. Probably not too controversial.

** Change. Still a little controversial, at least because of jump-changes
and the null change, but I don't think those two issues impact this in
any meaningful way; that is, I think it works whether or not you allow
jump-changes and whether or not you allow the null change.

** What it means for two rows to be the same. Probably not controversial.

** What it means for two changes, or sequences of changes, to be the same.
Probably not controversial.

** Stage. This is potentially a can of worms, as evidenced by some
of the discussion of weird link methods (e.g. the ones used in
my quarter callings). I suspect that if we pursue this further,
a definition of "stage" needs to preceed a definition of "method".

* "A process for generating a sequence of" may be troublingly vague,
though at root, that's it's job! If there's value in going forward I'm
sure someone will come up with a better way of phrasing this.

* I've insisted that a method be a round block (in the Graham John
sense, not the Variation and Transposition sense). I don't know that
this is essential. But given that any non-round-block can just be
repeated as many times as needed to get back to where you started it
seems possibly worthwhile, and does not reduce what can be rung. I
don't know if this is a good idea or not. I will not be surprised
if it needs to be jettisoned.

* I've deliberately avoided using meaningful names for the kinds of
methods defined, instead substituting Greek letters. If this is
thought worth pursuing, then these abstract labels should be replaced
with something more descriptive. I didn't want to use descriptive
names to start, though, as they can rather prejudice things
prematurely. But in case it's not immediately clear, what I'm trying
to model is

** What folks mean by a lead based method (albeit possibly just a
single lead per course) I'm hoping is captured by β-method.

** What folks mean by rule based method, if you intend RBM and LBM
to be disjoint classes, is captured, I hope, by "all methods that
are not β-methods".

** α-methods are intended to weed out the really bizarre cases,
such as a method generated by some random process. I don't think
anyone has ever rung a non-α-method, at least not deliberately.

----------------------------------------------------------------------

A method at stage N is a process for generating a sequence of changes
at that stage, such that when applied successively to permute a row at
that stage, when the final change of the sequence is applied the the
resulting row is the same as the initial row. (That is, if we start
with row r0, and the result of applying the first change of the
sequence to r0 is r1, we then apply the second change of the sequence
to r1, producing r2, etc., until after the last of the n changes we
arrive at rn, and rn = r0.)

An α-method is a method that when applied two or more times starting
with the same row always produces the same sequence of changes.

A β-method is an α-method that when applied to any of the N! possible
starting rows always results in the same sequence of changes.

----------------------------------------------------------------------

So, does something like this help in any way?



-- 
Don Morrison <dfm at ringing.org>
"Like all well-conceived classifications, this one is useful
and clear; like all classifications it is false."
  -- Fernando Pessoa, "Toward Explaining Heteronymy",
     tr Jonathan Griffin