[r-t] applicability and timing (was The null change)

[Tim Barnes]

Sorry in advance for a lengthy post - catching up and responding to several
posts in one email:

On Tue, Dec 30, 2014 at 8:19 AM, Don Morrison <dfm at ringing.org> wrote:

> On Tue, Dec 30, 2014 at 10:27 AM, Tim Barnes <tjbarnes23 at gmail.com> wrote:
> > Hopefully it's clear enough that the 5
> > restrictions we've voted on to date (falseness in plain course, lead
> > divisibility, single lead courses, rotation, number of consecutive blows)
> > referred to restrictions on β-methods.
>
> You'd be disappointed if I ever agreed that something is "clear
> enough", right?
>

I should have been more precise - I meant that in polls to date we have
only been gauging people's options as they relate to β-methods, not whether
these restrictions apply beyond β-methods.

I'd be careful about extrapolating too much from one data point. It is
> not uncommon for folks to be away for a few days, so 48 hours sounds
> awfully tight. Waiting a bit longer is only a problem if the next
> issue depends upon the outcome of the previous one, right? Often they
> are sufficiently independent progress can be made while waiting, I think.
> As, indeed, you seem to be doing, thank you!
>

That's fair - we can start the next poll before finishing the previous one
if they are sufficiently independent - a better way to move things along
faster.


On Tue, Dec 30, 2014 at 9:36 AM, Don Morrison <dfm at ringing.org> wrote:

> While you've framed the [null change] question fairly tightly, it really
> is part of
> a whole hierarchy of questions, where the answer to a question higher
> up the hierachy can disallow a possible answer further down it.
>
> 1) Is the null change even a part of change ringing? Put another way,
> when we define a "change" does that definition include the identity?
> 2a) If the answer to (1) is "yes", can we use the null change in calls?
> 2b) If the answer to (1) is "yes", can we use the null change in methods?
> 3) If the answer to (2b) is "yes", can we use the null change in α-methods?
> 4) If the answer to (3) is "yes", can we use the null change in β-methods?
>

I agree we could look at it that way, but for the sake of easing progress,
I think it's still valid just to consider the null change question in
relation to β-methods for now, and come back to its broader applicability
later on.  I know this approach means we could change our minds on a
decision down the road once we've considered its broader applicability, but
I think that's ok for getting some opinions determined sooner.


On Tue, Dec 30, 2014 at 5:59 PM, Matthew Frye <matthew at frye.org.uk> wrote:

> I'm not convinced that ringing things in whole pulls is the same as
> allowing use of the null change.


Allowing the null change clearly would allow 'Whole-Pull Cambridge' to be
named as a method (when using the results of our other polls to date).  But
when we get on to debating compositions, there may be a case for allowing
whole pull ringing to be allowed as a form of composition, i.e. a different
way of using the underlying method without having to create a new method.
Not dissimilar to the question of whether horizontal splicing of London
Minor and Cambridge Minor to produce true maximus rows is a valid form of
composition.  I would think we would still want truth to be assessed at the
row level (not pairs of rows), so whole-pull ringing would mostly apply to
compositions such as a 1440 of minor that is an extent rung in whole pulls.


On Wed, Dec 31, 2014 at 10:41 AM, Philip Earis <pje24 at cantab.net> wrote:

> For me, the axiom is that what we are describing is permutations / rows
> where each bell rings once and once only.
>

Agree this is a helpful line in the sand to draw.  I had been wondering
whether Don's inclusion in his top level method definition of the words "to
permute a row" intended that cylindrical ringing is not method ringing.
Regardless, for the time being in this debate, let's draw the line at
permutations / rows where each bell rings once and once only.


On Wed, Dec 31, 2014 at 12:48 PM, Graham John <graham at changeringing.co.uk>
 wrote:

> Given the de facto use of the null change, and its practical purpose in
> completing some MEBs, we should determine how its use should be recorded
> (description, not prescription). However, as we count changes, not rows, I
> feel that many might argue that when no bells change position, you have not
> rung a change.
>

If we accept the null change, we should probably have a separate vote on
how to count these changes / rows, given the disagreement.  Two points I'd
make on this are: (1) 'change' can be thought of as a colloquialism for
transposition (in this case the subset of all possible transpositions that
do not move any bell further than its adjacent position).  When thought of
as a transposition, the identity transposition seems as valid as any other
transposition, and doesn't need to be counted differently.  But when we use
the term 'change', it can lead us to think that something needs to change;
(2) counting rows and changes separately (if the null change shouldn't be
counted) seems to me not to meet the 'keep it simple' test.


On Mon, Dec 29, 2014 at 1:58 PM, Don Morrison <dfm at ringing.org> wrote:

> 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.


A couple of comments on these definitions (which I think are very helpful
in moving us forward):

- Is the top level definition of method so broad that it could include call
changes?  A key feature of methods seems to be that they involve
memorization by ringers (call changes don't).  Could this be added to the
definition to exclude call changes?

- By defining a method as a round block, I think the output of your
definition for Original Minor would be x16x16x16x16x16x16.  However I would
say the correct output is x16.  In my mind, a plain course is a composition
- albeit a very simple composition - of a method (ring the method
repeatedly with no calls until it comes round).  Methods, calls and
stationary bells are the building blocks for compositions, and it's not
until you get to compositions that you're talking about rows (which a plain
course has).  At the method level, you're just taking about changes.  For
this reason, I wouldn't include the round block constraint in your
definition.

Following on from this, it's a shame that the definition of method needs to
refer to a row at all, but this is needed if you want to distinguish
between α and β.  For this reason, I'm wondering whether a 3-level
hierarchy is needed.  Would an alternative definition be:

A method at stage N is a process for generating a sequence of changes at
that stage, which are memorized by ringers for the purpose of generating
permutations of N bells where each bell rings once and only once.

A β-method is a method that is a static sequence of finite changes.

TJB
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