[r-t] What's the meaning of a method having aparticularfalsecourse head

[Don Morrison]

On Apr 23, 2005, at 9:13 AM, Graham John wrote:

> 1. A Handbook of Composition by John Leary (CC pub 1993)
>
> Appendix 1 pg 51.
>
> "Group A is not shown. It contains the remaining in-course FCH, which 
> is
> 23456, and represents the trivial case of the plain course being false
> against itself."

This seems ambiguous. It could mean "the case of the plain course being 
false within itself", which is  the interpretation I believe you 
prefer, and what I had always assumed. But it could at least as easily 
mean "the case of ringing the plain course twice producing falseness", 
which is the interpretation I believe Richard would favor. The presence 
of the word "trivial" would seem to favour Richard's interpretation 
since a method being false in the plain course is a relatively obscure 
and serious matter, while ringing the same course twice producing 
falseness is indeed a trivial source of falseness.

> 2. Any sources listing falseness groups of methods never mention Group 
> A
> (because the methods in collections are true in the plain course) e.g.
>
> - Wratten
> - Collections of Rung Surprise (CC pub)
> - Collection of Universal Compositions
> - Methodmaster FCH derivation
> - Also the method names CRU, Roald Dahl, Deng, Bendigo etc would not 
> have
> been so named if it was a convention to include A.

I think this is rather a large leap. Whichever interpretation we choose 
to put on A falseness it is an obscure thing to worry about, and 
something we would naturally elide from most discussion of false course 
head groups. Indeed, Philip Earis, who favors the "A as the kind of 
falseness every method has" interpretation omitted it when describing 
True Surprise, even though by his convention it is also A false. And in 
CRU and True I believe the out of course only FCHs were also elided.

It really does appear to me that up until a few days ago we were all 
likely making an assumption about what A falseness means, and had not 
all been making the same one. I wonder how much of each of our 
interpretations is based on some objective benefit to the underlying 
definition we assume, and how much is simply habit based on what we 
first assumed, possibly decades ago.

Perhaps it's simply a reflection of my own bias, but I'm still puzzled 
about why those preferring the "A falseness means the trivial case all 
methods have of the same course being rung twice being false against 
itself" interpretation do prefer it. It was at some point in this 
discussion described as an "identity" but that can't really be the case 
here, can it? The false course head "groups" do not form a mathematical 
group, and I'm unaware of anyone ever having defined an operation on 
them for which there would be an identity. I suppose something could be 
defined just out of perversity, but is there any utility in having an 
identity for the elements of the partitioning of FCHs?

A further point possibly in favour of using the "A means the plain 
course is internally false" interpretation is sort of the flip side of 
the argument "A is pretty much meaningless if every method has it": if 
we choose Graham's interpretation we have a pleasantly succinct way of 
saying the plain course of a method is false in itself. But if we 
choose Richard's interpretation we have no way to represent a method 
false within its plain course in a listing of FCH groups.

I'm intrigued, too, that no one has yet really offered a definition of 
what it means for a method to have a particular FCH. We continue to 
talk about attributes of it and in particular try to describe what we 
mean by A falseness, but I don't think I've ever actually seen a 
definition of it!

I would have thought it would be something like

i) A method is said to have FCH x if and only if two rows, a and b, 
occurring at different points in its plain course are related such that 
x permuted by a = b or x permuted by b = a.

Richard's interpretation would, I think, be

ii) A method is said to have FCH x if and only if two rows, a and b, 
possibly different ones or possibly the same row, are related such that 
x permuted by a = b or x permuted by b = a.

Definition (ii) seems to me less natural. Perhaps that's just taste, or 
even more likely my wording is a reflection of my own biases. Might 
someone with the opposite biases propose how they'd define FCH so we 
can compare. If one interpretation really does have a more natural 
definition perhaps that will help explain why some of seem to cling 
strongly to one interpretation and others strongly to the other.

Anyway, can anyone in the "Richard's interpretation" camp perhaps 
explain a little more *why* you favour the interpretation you do?

Thanks!


-- 
Don Morrison <dfm at mv.com>
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