[r-t] Shades of truth

[Richard Smith]

Graham John wrote:

> You have not mentioned Changes.

No.  That's not because I don't think the definition of a 
change is important, but because I think it's orthogonal to 
the definition of truth.  Similarly I made no mention of how 
long a peal should be, though I personally think that is the 
most important part of what a peal is.

> Therefore a peal of Minor with 5040 rows but only 720 
> changes would be [U,R,C].

I assume you mean a peal where each row is rung seven times 
before changing to the next one?  I would argue that such a 
performance is 'true' in any usual sense of the word.  (In 
my terms, it's just [R,C] -- no touch of longer than 720 of 
minor can be [U].)

> [M] would also be true if you rang each row 8 times before 
> changing.

Correct.

> Is this still change-ringing?

Quite possibly not, and I'm not necessarily arguing to the 
contrary.  But I do think they can be 'true' (in whatever 
sense).

Matthew Frye wrote (quoting DFM quoting me):

>>> Why do we include truth in that list?
>
> Why do we include changes or rows in that list? Why do we 
> have a list at all?

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 think a problem with the current decisions is that they 
use basic definitions to proscribe certain types of ringing. 
For example, in the current decisions, jump changes or the 
null change (where no bells move) are proscribed by defining 
a change in such a way that neither of these fit it.  I 
think that's fundamentally wrong.  In the case of a change, 
I think the correct way forward is to define it in a very 
general way:

   A change is the mapping of one row to the next row.

(I'm not actually happy with 'mapping' for a number of 
reasons, but it's better than anything else I've thought 
of.  And I'd also like to make it clearer that the change 
that maps 123456 to 214365 is the same as the change that 
maps 654321 to 563412.)

Then we define various types of change:

   An ordinary change is any change that just involves the
   transposition of zero or more pairs of adjacent bells.

   An jump change is any permutation that is not an ordinary
   change.

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

And if it is felt necessary to proscribe null and jump 
changes, we should do so in a later section on recognition. 
(Personally I'd rather allow any these too; but it that's a 
bridge too far, then I'd rather we explictly disallowed them 
in a separate section.)

   The Central Council does not recognise performances which:

     - include changes other the ordinary changes;
     - [...]


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

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

   An ordinary row is a row in which each bell sounds
   precisely once.

And we would presumably add 'rows other than ordinary 
rows' to the list of things that the Central Council doesn't 
recognise.


In this way, we've excluded precisely the same things as the 
current decisions, but we've done it explicitly in a 
separate list of prohibited things, rather than implicitly 
through the definitions.

Why is this approach good?  Well, from time to time people 
will ring things that include jump changes, null changes, 
cylindrical rows and changes, and so on.  We may or may not 
like this, and some of us may wish the Central Council not 
to recognise such performances.  However this does not mean 
we shouldn't have a standard, well-defined vocabulary with 
which to describe them.

Take cylindrical methods, for example.  I'm not necessarily 
suggesting the CC should recognise such things, or that 
anything like the following should be included in the 
decisions, but it would be very easy to see how they /could/
be added:

   A cylindrical row is a row in which all but two bells
   sound precisely once, one bell does not sound, and the
   bell to sound first also sounds last.

   An ordinary cylindrical change is a mapping between (i) an
   ordinary row and a cylindrical row, or (iii) vice versa.
   In case (i) it is effected by removing the last bell from
   the ordinary, or in case (ii) by removing the first bell
   in the row.  The other bells may change as in an ordinary
   change.  A type (i) change must always be followed by a
   type (ii) change, and a type (ii) change must always be
   preceded by a type (i) change.

   In a piece of ringing involving cylindrical rows and
   changes, the set of possible rows is the set of all
   ordinary and cylindrical rows, and the definitions of
   truth (etc) are interpreted accordingly.

... And with just three short additional decisions, and no 
other modifications, we have added a full description of 
cylindrical to the rules.  We don't need to touch any 
definitions associated with methods or truth because these 
are orthogonal to it, and are already defined using the 
general terms, row and change.

> [...] I think that the main issue would (should?) be to 
> set this minimum standard (at whatever level) then the 
> categorisations could be drawn within that, hopefully 
> without much controversy.

I agree, so long as the minimum standard is suitably low. 
And that almost certainly means lower than most of us would 
choose to consider an acceptable definition of 'true'.  It 
should probably be what your average quarter-peal ringer 
would consider to be true.  In terms of my earlier email, 
that's probably [Q,L].  In other words, it should be 
possible to ring a fixed-treble 1280 of Little Bob Minor 
without splicing it with anything, and call it true.  I 
strongly suggest the majority of us, myself included, don't 
really think this is good enough -- that's what the higher 
classes of truth are for.

> As I remeber, much of the discussion last time was about 
> how to deal with multiple stages and/or "cover" 
> bells/variable cover/similar, none of which has been 
> touched on this time (and which I am not going into now).

Indeed.  But I think the root cause was the same -- that we 
were trying to apply a single type of truth to everything.

Don Morrison wrote (of Graham John's example):

> Though I, and I suspect Richard, would even there prefer 
> to approach it as being the sort of change ringing that 
> includes such constructions versus the sort that doesn't: 
> just because I don't think I'd enjoy ringing such a thing 
> doesn't mean I'd want to prevent those that do from 
> indulging their interests.

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.

We can still use other terms to tighten things down.  For 
example, we might define 'change ringing' as a sequence of 
(non-null?) ordinary changes, and then we'd be free to talk 
abut change ringing peals, as opposed to, say, call change 
peals, jump change peals, or cylindrical peals.

And, of course, none of this stops the the CC from casting 
discredit on the composers of 'palpably false compositions' 
or 'worthless methods' (a decision adopted in 1903 and 
unchanged since), refusing to recognise ringers who allow a 
'shift or error in ringing' to go uncorrected, or
deprecating gramophones as unworthy of the Church of God.

RAS