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

[Alexander Holroyd]

On Mon, 29 Dec 2014, Mark Davies wrote:

> Ander writes,
>
>> Can someone explain to me what a lead-based method is, and how it differs
>> from a non-lead-based method?
>
> LBMs are defined by a finite sequence of changes (place notation). RBMs can 
> be based on finite sequences of changes, but in addition apply rules 
> *dependent on the position of individual bells*. This means that they cannot 
> be defined by a sequence of changes, since those changes vary depending on 
> where the bells are.
>
> Here is a simple example using a 5-bell RBM. Ring St Simons Doubles, except 
> that if the 2 and 4 come together on the front, make places instead of 
> dodging. If this method is started from rounds, the first lead looks like St 
> Martins, the rest St Simons. However if started from e.g. 12534, there is no 
> St Martins. This is a trivial example, but shows how RBMs differ from LBMs.

To me this distinction is spurious.  Both of these examples comprise a 
finite sequence of place notations.  In both cases this sequence can be 
described by simply listing the place notations, or by any of infinitely 
many "rules", some of them involving the rows and others not.  (And the 
same is true of every sequence).  But the sequence is the same however it 
is described.  The "dependency" that you seem to see as so fundamental is 
in the eye of the beholder, and to me does not seem worthy of a an 
entirely different genre of method.

The St Simon's St Martin's example actually illustrates this point well.

Consider:
1. The 4-lead touch MSSS.
2. The same 4-lead touch but thought of as Mark describes, with the method 
"determined" by the bells on the front.
3. A plain course of stedman doubles.

Does anyone seriously want to claim that 1 and 3 are more similar to each 
other than either is to 2?  (After all, 1 and 2 are THE SAME TOUCH, just 
thought of in a very slightly different way).  Yet according to the 
proposed scheme, 2 is not even method ringing.

> We were definitely talking about LBMs! I can't see how anyone could have been 
> confused over that - see e.g. Survey 2: "Do you think a lead should always be 
> the minimum non-divisible block?".
>
> https://www.surveymonkey.com/s/SL735FJ.
>
> The answers can't apply to RBMs - they might not even have leads!

Not so.  It is only the more restrictive (and confused) possible answers 
that run into difficulties.  If a lead can be any length one wishes then 
there is no problem.