[r-t] Extension

[Robin Woolley]

Hi All,

Tim Barnes:

".. it would be very helpful if you could post your Extension document 
to this list."

I'm not sure I want to do this, given the invective I've faced for 
daring to have different opinions to some on this list. I'm not sure 
that it is 100% correct, and there are still bits missing, but I'll ask 
PN whether I might let the list have it.


"...I'm having the same challenge with PABS's algorithm ..."

We often had difficulty understanding PABS on Methcom - he's usually 
right I've found.

"...  It's curious in some ways that the Exercise has adopted a 1:1 
naming solution to a 1:many problem."

In general, we have a many:many problem. As examples:
1:1 - Brentford B6 (&34.1x1x1.56,2 at stage 8, etc.)
1:many - Cambridge S6
many:1 - Reverse B6 & College B6 both give &x1x1x5x5,1 at stage 8)
many:many - I haven't the software for trawling the lists, but I'm 
reasonably sure there are some.

There is no reason, in the 1:many situation, extensions should not be 
numbered, as in London No.1 -> No.4 at stage10 - tho' these are not 
compliant as we know - a glance at the p.n. in 9-0 shows why.

"Presumably under any algorithm some methods won't extend, so there's a 
question of whether bands should have discretion to name extensions in 
good faith in these cases."

There are some 1:0 examples. Taxal D6 is one. Is this a problem? I don't 
think it is BUT the case of Newcastle S6 is interesting. I discussed 
this in the RW as a 'Methcom Sketch'. The S8 version is an honest 
attempt because the obvious extension does not exist at stage8 - but 
does at all others.

Once again, the Decision is based on what was rung and accepted as 
'good' extensions - i.e., retaining characteristics of the parent seen 
to be as fundamental. These have been developed over the years to allow 
many more extension paths but there are bits I don't like. I have 
already mentioned indefinacy but, and I can't believe I'm saying this, I 
agree with PJE about (G)D1a - constant lead length in Little methods. I 
remember investigating this about 15 years ago - I have a vague memory 
concerning St. Lawrence LB6 - but maybe not. Whatever - this Decision 
depends upon the 'antients' deciding that Little B8 retains the treble 
to 4ths and not 6ths.

I have not the skill/time to program the Decision - but at least I can 
generate candidate extensions by hand. I also suspect that PABS ideas 
would be much more difficult to understand!

PABS:

"So far ... I don't see that that would be an improvement."

Quite!

:

"(c) is also a problem if extensions by a single stage is permitted: 
Ashford Little Bob Minor would be 36.16-14-14-16 ..."

Extending S. Oxford B6 to seven gives 12 blows at the back for the seventh.

Tony Cox & GACJ:

'Ordinary' people - non-mathematicians - have difficulty with something 
happening zero times! I remember someone having this problem with 
extension of Alliance methods - but that's 15 years ago, also. It came 
down to this. What is 'nothing' above the treble?

There are many good ideas here of which some have been around for years 
- counting down to 'small' numbers as in Bristol, for example. It's nice 
to see PABS agreeing with me about Cambridge, Yorkshire, Albanian, etc.. 
When I've said this years ago, some idiots told me I didn't know what I 
was talking about so you can see my reluctance to make the Extension 
document public.

It has been said that the Decision on Extension is difficult to 
understand - don't make it even more difficult!

Best wishes
Robin