[r-t] Extension

[Robin Woolley]

Hi All,

Let us be clear on this, method extension is a very easy concept. Any 
problems which have arisen in interpretation of the Decision is due to 
putting an easy concept into formal language and then trying to 
understand the formality. It is rather like this - how would you explain 
the colour blue, as in the sky outside my window as I write this, to 
someone blind from birth.

Extension is based upon some simple concepts which were laid down in the 
early post-war period. I do not wish to go into historical arguments as 
to why Ipswich S8 is not a formulaic extension of Ipswich S6 and I have 
no problem with historical anomalies. Some of these basic concepts are 
preservation of class (surprise always gives surprise), preservation or 
not of PB lead heads and what might be called contiguosity. This means 
that you would expect an extension of Cambridge to have 2nds place made 
somewhere below the treble and 3-4 places made above the treble in 
Oxford, as examples.

Further, these concepts were based upon what had been rung and claimed 
as extensions at the time. I've remarked elsewhere that it might have 
happened that the 'antients' might have rung what we call Yorkshire S10 
and called it Cambridge instead. It is quite easy to justify this.

As is always the problem with 'simple' concepts, it is translating these 
into some sort of formula and back again. The man who knows most about 
the formula is the man who generated it in the first place. It's the 
rest of us who have to try to understand it.

Strange as it may seem, some of us on the Methods committee have 
concerns over the requirements in (G)B. I wonder about the desirability 
of (G)B1 - if only for practical reasons. (G)B5 is one which has caused 
comment in the past, w.r.t the extension of Surfleet S6 for example. 
Speaking from memory, RDB remarked that there is an extension at every 
stage but is regular only at stages divisible by six. (I haven't checked.)

Tim Barnes asks about (G)C2(b)i.  Consider the extension of Writtle TB6 
- which is Kent TB with additional 3-4 places made when the treble is in 
5-6, so the work below the treble is x2x1.34.2.34.1. These two parts of 
the Decisions allow: x2x1.34.2.34.1.34.2.34.1  or 
x2x1.34.2.34.1.56.2.56.1 or x2x1.34.2.34.1.36.2.36.1 or x2x1x2x1.56.2.56.1
but not x2x1x2x1.34.2.34.1

Also, (G)B6 is designed to stop the extension of a method which has at 
most two blows in any one place becoming three blows - see Beverley S8

In a case like this, examples are everything - a criticism which could 
be made of mathematics text books. I revised the Extension document some 
time ago - we just haven't got around to publishing it although one 
member of this list did receive a copy by request - didn't you?!

This drew on a complete set of extensions of both TD and Plain six-bell 
methods given to me at least ten years ago and this is acknowledged in 
the document. In the set, there are thirteen formulaic extensions of 
Surfleet S. Minor, six which terminate and the rest are *thought* to be 
indefinite. Two start at stage 10 and increase by four, two at 12 by 
six, one at 12 by eight, one at 18 by 12 and the one Tim asks about to 
28 and then 52.

It is worth why this process was started in the first place. To stop 
arguments by giving an objective rule for extension. By and large, it 
has achieved that purpose.

b.t.w, if you try extending Single Oxford B6 to seven, you will readily 
see the efficacy of (G)E

Best wishes
Robin