[r-t] Extension and Contraction

[John Harrison]

In article <325e3e39-1ac0-d0e1-a2cf-013545175737 at snowtiger.net>,
   Mark Davies <mark at snowtiger.net> wrote:

> Considering the N=0 case to be part of the extension sequence sounds
> logical, ...  However it seems to go against the precept that pieces of
> work cannot be invented by an extension, but instead should be
> generated from something already present on the lower stage.

As an aside I don't think we should devalue the concept of zero, whose
introduction was a fundamental advance in mathematics.

We have inherited the language of extension, which biases thought towards
unidirectional  mechanisms.  That's probably a relic of the fact that
method ringing began on small numbers and then progressed to higher
numbers, so extension was the context in which the idea of relationships
between methods at different stages emerged.  

The Decisions were an attempt to regularise prior evolution, but in doing
so they built in the concept of a directed process of 'extension' rather
than the more general concept of 'relationship' between stages. 

The Framework recognises that there are potentially many different types of
inter-stage relationship, but the language of 'extension' used to describe
such relationships, and the relationships described, were essentially
imported from the Decisions.  V2 should be aiming to 'do it properly', by
asking the sort of questions that Mark is raising. I believe part of that
is to think of processes that create relationships between stages rather
than just processes that create higher stages from lower ones.  If we adopt
that mindset I think the other questions will be easier to answer.

> Initially it seemed to me to be an unpleasant complication to the
> extension process,

The Framework should be about managing complication, not declaring parts of
the world out of bounds because they don't fit the tidy abstractions we
would like to use.

-- 
John Harrison
Website http://jaharrison.me.uk