[r-t] Lead-based methods [was: Poll on consecutive blows in the same position]
Alexander Holroyd
holroyd at math.ubc.ca
Mon Dec 29 23:49:38 UTC 2014
This seems like a good first try, but the still undefined "process for
generating" is an unnecessary distraction.
Why not simply say:
A method is a finite sequence of changes.
On Mon, 29 Dec 2014, Don Morrison wrote:
> 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
>
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