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

[Mark Davies]

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.

Dale Winter writes,

> Though for what it’s worth, my reading of this thread to date was that
 > we were talking about very general methods, not just
 > lead-based methods. if others were afflicted by the same
 > confusion then our polls may mean rather less than we’d hoped.

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!

Let's not get confused. RBMs really are different to LBMs. It makes 
sense to focus on LBMs first because (a) they make up the vast majority 
of change-ringing as currently practised, and (b) they are much simpler 
- RBMs have more in common with compositions than methods. Let's worry 
about them later.

MBD