[r-t] Shades of truth

[Don Morrison]

Responding to multiple messages from Richard in a single reply.

In general, I agree completely with Richard, at least as I understand
his underlying ideas. This all seems absolutely right to me. Thank you
for bringing all this up!

However, here are a few quibbles or confusions about some minor
corners. The first a general principle, and the rest just of examples.

The general issue I don't understand is ambiguity. In a purely
descriptive scheme we'd love to have a way to unambiguously describe
any performance. I think this can be difficult. And where this runs us
into trouble is in cases like

  - The CC proscribes property P

  - A performance can be described according to description D, which
    is automatically recognized by the CC

  - Owing to ambiguity in our descriptive apparatus, the very same
    performance can be described as D', which, unlike D, has property
    P, and thus is not recognized by the CC

In current practice this comes up with methods, where it appears the
solution is "if you're smart enough to find an alternate description
that is allowed, we'll use that one". There are cases where
a definition of a method has been convoluted from something
straightforward to a form no practical ringer would consider
appropriate, just to circumvent some restriction or other. I think
most of us don't really care for this kind of thing, but I fear what
we're discussing opens up even truth to such unattractive ploys.

The above also suffers from the problem of

  - at the time it is rung, no one is smart enough to figure out a way
    to make something legal

  - twenty years later, someone figures such a scheme out

Was the touch false for twenty years, but has suddenly become true?

On on about 30 Sept 2009, Richard Smith <richard at ex-parrot.com> wrote:
> I suspect the biggest issue is how you divide up the combination of
> [U] and [C]. My approach was to basically to write one rule for
> major and above (which is [U]) and another rule for triples and
> below (which is [C]).
>
> But I'd be interested to explore some alternatives so see whether
> they actually do produce noticeably different results.

Yes, [U] + [C] was exactly where I was being made a bit uncomfortable.

I've not managed to think it through properly, but I think how we
approach this does have some effects downstream. For example, I
believe that what folks think of as first principles here can affect
how much relaxation they have to put in to be happy with quarters of
triples and minor with lengths in the interval [1250, 1260).

I think, but may be mistaken, that the notion of a peal really started
as whole extents. [U] is a later relaxation. And if you start with the
most primitive notion being an extent of extents, then as soon as you
relax it to allow partial extents to get convenient lengths (as you
must do to allow 1260s of minor or doubles, for example) you have no
reason to prohibit things in the interval [1250, 1260). But if you
start where you have, you do. Indeed, I think this is the root of the
heated controversy that sometimes erupts between those with strong
opinions on this particular matter (which category I am here
apparently in danger of falling into myself!).

I think you're probably right, that where there's ambiguity it's good
to let history be our guide. In this particular case, I'm thinking
something based on whole extents is historically more primitive than
[U].

But I may be woefully confused. I don't feel as if I've got a clear
view of all this yet.

> It's simply a matter of establishing terminology on which we can build
> higher level concepts.  And, mathematically a row is the lowest-level
> concept that really needs defining. (Yes, arguably a bell is a lower-level
> concept, and we can argue about whether peals should be allowed if rung on
> anklunks, flower pots or bananas, but that's not a mathematical
> argument.

I'm not sure. While bell is physical, what about "blow"? A row does
still have a vaguely composite feel to it.

>  The null change is the change which maps a row to itself;
>  it is an ordinary change.

Complete aside, not in any way relevant to the discussion itself: why
do we always seem to refer to this as the "null" change instead of the
"identity" change? Application of changes certainly feels more like
multiplication than addition.

> And I'm tempted to do the same with rows, too, if I could come up with a
> remotely good generic wording.

I think this is very difficult. At least as difficult as "truth" if
we're not to be fairly prescriptive.

>  A row is the order in which bells sound during some
>  specified interval.

Perhaps this is my natural, knee-jerk, reactionary conservatism
popping out yet again, but this definition troubles me.  I'm not sure
what a "specified interval" is. Perhaps if I understood that better
some of these pathological cases would be ruled out. But here are some
worries.

- This may be made moot if I understood what "specified interval"
  meant, but who specifies it and how?

- What's the keep the whole peal from being considered a single row?

- What's to keep a two parts of Prichard's, rung without singles, from
  being considered 5,056 four bell rows and thus a touch of length
  5,056?

> Absolutely.  To be honest, I'd be quite happy if the definition of peal were
> lowered as far as:
>
>  A peal is a performance of at least 5000 rows during which
>  each bell sounds, on average, at least 5000 times.

What does "each bell sounds, on average, at least N times" mean? If it
means

  for each bell take the number of times it rings, add them all
  together, and divide by the number of bells

then if I'm in an eight bell tower and ring each of the front seven
5800 times, without ever pulling off the tenor, I can claim to have
rung an eight bell peal. Again, it may just be me being a reactionary
old-whatever, as usual, but this troubles me.

I'd have expected something like "at least N rows during which each
bell sounds at least N times", but I'm guessing that excludes some
things you were hoping to include. Can you help me understand what
curiosities you were trying to include.



-- 
Don Morrison <dfm at ringing.org>
"He had  outwitted every enemy but time."
              -- Will Durant, _The Renaissance_