[r-t] Some Thoughts on Extensions

[Ben]

Just a few thoughts on extending methods...

In Section D of the CC Decisions on Methods, it is robustly declared that
names of methods should include the stage: "The title of a hunter shall
consist of Name, Class <...> and Stage.". Examples of this are "Plain Bob
Doubles", "Cambridge Surprise Major". Principles do not need the Class to
be included, as in "Stedman Triples", "Titanic Cinques" and so on. In my
opinion this makes extensions difficult.

It is my contention that, included in the full definition of a method
should be the way of extending that method to different stages, if
extension is possible or desired. I see no reason why, once a method
together with any wished-for extension is defined, the originator of the
method should not have naming rights over all stages of that method,
whether someone has actually rung the method at a particular stage or not.
In many cases, the way that a method extends is obvious but this is not
always the case. A case in point is Cambridge. If someone were to ring what
we know as Cambridge Surprise on (say) 26 handbells, and decide to name it
Grantchester Meadows Surprise 26, no one would be surprised if that naming
were to be turned down in favour of Cambridge Surprise 26, and quite
rightly too in my opinion.  Cambridge and many other methods will continue
to be recognisably what they are no matter on how many bells they are rung.
This holds good for Plain Bob etc., as well as many other methods. No one
could or should get away with renaming Plain Bob to something else merely
because they had rung it for the first time at a new stage. To that end, I
developed Place Notation Description Language (or PNDL) that allows a
method and its way of extending to higher stages to be defined on any
arbitrary number of bells. The main reason for PNDL was to generate Place
Notation for methods on huge numbers of bells, maybe 100 or even more in
order to be able to "ring" methods on a computer screen using colours,
without real bells at all, but I soon realised that this possibility
clashed with the conventional naming of methods as it is done at present.

For an illustration of this, consider the PNDL for Double Oxford and Double
Bob respectively. An explanation of PNDL is given elsewhere (
http://bennewsam.co.uk/Braiding Rainbows/PNDL Documentation.html).

@("Double Oxford Bob",6,~,2)
\(
   'x'
   !(4,n,2,'[i-3][i]x')
)
'[n-1][n]'
/
'12';


@("Double Bob",4,~,2)
\(
   'x'
   !(4,n,2,'1[n]x')
)
'[n-1][n]'
/
'12';

Both of the above will generate Place Notation for both methods up to any
arbitrary number of bells. For instance, the Place Notation for Double
Oxford on 8 bells is:

x 14 x 36 x 58 x 78 x 58 x 36 x 14 x 12

and for Double Bob on the same number of bells it is:

x 18 x 18 x 18 x 78 x 18 x 18 x 18 x 12

If a small change is made to the PNDL for Double Oxford (changing the 6 in
the first line to a 4), it allows Place Notation for Double Oxford Minimus
to be generated. This turns out to be:

x 14 x 34 x 14 x 12

which is exactly same as Double Bob Minimus, and therefore prohibited under
the rules as they stand at present. I see no reason why both cannot
coexist. Using PNDL as above, each method is defined differently together
with the way that each method extends, the fact that at any particular
stage the same place notation is generated should be seen as fortuitous but
does no harm.


Extending a Method
===============

In extending a method to a higher stage, there a limited number of
possibilities. Bear in mind that in this discussion, when I say "work" I
mean "places made" or a small block containing places made, and that any
hunting or dodging of  higher numbered bells that occurs as a result of
that "work" is incidental.

When a method is extended, any particular piece of work may:

(a) Stay where it is
(b) Move with the increasing stage
(c) Expand by duplication

A simple example of (a) is the place making in Kent Treble Bob, where the
notation 34 x 34 is common to all stages. An example of (b) would be a lead
end change of 56 in Minor becoming 78 in Major and so on, and an excellent
example of (c) is Kent Treble Bob again, in which the notation 1 x 12 x is
repeated one more time for each even stage . So for instance the first half
lead of  Kent Treble Bob Minor is 34 x 34.1 x 12 x 1 x 12 x 1 and for Major
it is 34 x 34.1 x 12 x 1 x 12 x 1 x 12 x 1 and so on for higher stages.
This has the effect of expanding the "slow" work from one lead end to the
next at every stage.

Take as an example the method Chalfont Slow Course Minor, which has the
place notation  & x 14 x 1236 x 1236 +12. or in full notation:

x 14 x 1236 x 1236 x 1236 x 14 x 12

http://www.bennewsam.co.uk/Method%20Images/Chalfont%
20Slow%20Course%20Minor.jpg

This method has two hunt bells, one (the treble) that is a normal plain
hunt, and the other one (the second bell)  alternates  between leading and
second's place. Other than that, it is worth noting that in any one lead
only one other bell gets to lead, and also that a place is made just above
the treble (in fourth's place). Because the lead end change is "12", all
other bells dodge at the lead end. This method has not (so far) been
officially extended, but if it were to be we would have to identify which
features should be preserved and which ones expanded. The place notation
for a plain hunt is x 1 (repeated), so this will be needed to underlie any
other places made. In order to preserve its nature as being a "Slow course"
method with the "slow" secondary hunt bell, the place notation structure x
12 x 1 must be extended over the whole lead at every stage, and in
addition, if we wish to have another "slow bell" for each lead in a similar
manner to Kent Treble Bob, then that structure needs to be x 12 x 12. Any
other places made need to be merged in with this underlying structure:

x 1 x 12 x 12 x 12 x 12 x 12 x 1 x 12

http://www.bennewsam.co.uk/Method%20Images/First%20Changes.jpg

Having created the "slow" work in this way, further places have to be added
to ensure there are always an odd number of places made before the treble.
This preserves the path of the treble as a plain hunt. Here is the result,
omitting the "external" place at the back. The result is an already
existing method, Maplin Slow Course Major, that looks a lot like Plain Bob
on the back six, with a "Little" hunt bell and "slow" work added at the
front:

x 1 x 123 x 123 x 123 x 123 x 123 x 1 x 12

http://www.bennewsam.co.uk/Method%20Images/Second%20Changes.jpg

So far, the way of extending Chalfont Slow Course Minor has been obvious:
clearly we had to preserve the features of the plain hunt and "little" hunt
bells, and it would probably be a good idea to extend the other "slow work"
as well. The biggest problem remains though, what to do about the fourth's
place made (above the treble), as in the 14 near the beginning and end of
the lead. Should it be left as 14 (case (a)) or should the place made stay
as "n-2" (case (b)) or should the work expand so that a place is always
made immediately above the treble (case (c))?

(a) x 14 x 123 x 123 x 123 x 123 x 123 x 14 x 12

(b) x 16 x 123 x 123 x 123 x 123 x 123 x 16 x 12

(c) x 14 x 1236 x 123 x 123 x 123 x 1236 x 14 x 12


(a)
http://www.bennewsam.co.uk/Method%20Images/Chalfont%20No%201.jpg

(b)
http://www.bennewsam.co.uk/Method%20Images/Chalfont%20No%202.jpg

(c)
http://www.bennewsam.co.uk/Method%20Images/Chalfont%20No%203.jpg

Any of these would be acceptable, the decision should be made based on
which method produces the best or most interesting result. None of these
three methods have yet been rung or named at the time of writing. These
possibilities are not exhaustive, and different extensions are indeed
possible. I have not covered, for instance, the possibility of work
expanding in two directions at once.

The point is that the way a method extends, if any, should be defined along
with the method. In the case above we have three different methods that
happen to be identical at stage 6. There is nothing wrong with this in
principle. The PNDL (Place Notation Description Language,
https://www.google.co.uk/webhp?sourceid=chrome-instant&
rlz=1C1ASUM_enGB530GB530&ion=1&espv=2&ie=UTF-8 -
q=%22Place+Notation+Description+Language%22)
for these three methods (that all extend indefinitely) follows, each one
subtly different. I have given each a new name, despite the fact that at
stage 6 they are all identical with Chalfont Slow Course Minor:

(a)
@("Chalfont Slow Course No.1", 6, ~, 2)
\(
  'x14x'
  !(6,n,2,'123[n]x')
)
'123[n]' { Half lead }
/
'12' { Lead end }
;

(b)
@("Chalfont Slow Course No.2", 6, ~, 2)
\(
  'x1[n-2]x'
  !(6,n,2,'123[n]x')
)
'123[n]' { Half lead }
/
'12' { Lead end }
;

(c)
@("Chalfont Slow Course No.3", 6, ~, 2)
\(
  'x14x'
  !(6,n,2,'123[i]x')
)
'123[n]' { Half lead }
/
'12' { Lead end }
;
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