[r-t] Practical Extension

[Don Morrison]

On Fri, Aug 3, 2018 at 1:04 PM Robin Woolley <robin at robinw.org.uk> wrote:
> Don said he preferred the 56x56 extension of Kent to, inter alia, the
34x34.1.56x56 or the 56x56.1.56x56.

No, that’s not what I said at all. I said that the major method denoted

56x56.1x2x1x2x1x2x1,8 [m]

looks a lot more, to me, like the minor method denoted

34x34.1x2x1x2x1,6 [m]

than do the major methods denoted

36x36.1.56x56.1x34x1x34.6.5,8 [j]

34x34.1.56x56.1x2x1x3456x3,8 [h]

or

56x56.1.56x56.1.34x34.1x2x7,2 [b]

I continue to believe that it is methods whose extension we care about, not
short fragments of place notation.

> Marple D6 is &x34x4x2x1.34x34.1,1.
>
> It has four decision compliant extensions (RAS):
>
> 2DE/2FG -34-4-2-1.34-34.1.56-56.1,2 (8 [2] 60)
> 2DE/5FG -34-4-2-1.34-34.1.34-34.1,2 (8 [2] 60)
> 2BC/2FG -34-4-256-6.34-34.1.56-56.1,2 (8 [2] 60)
> 2BC/5FG -34-4-256-6.34-34.1.34-34.1,2 (8 [2] 60)

I could be persuaded otherwise by a cogent argument, but right off the top
of my head I think it unlikely that a seconds place method, which all four
of your extension are, would ever seem to me to be an extension of a sixths
place method, which is what state you are trying to extend. Though, as I
say, I may be missing something and could be persuaded otherwise.

> The first question which arises to me is, given these are the only
> compliant extensions, would you say that Marple is inextensible?
> (Yes or no would do very well here!) Why?

If it is indeed true that these are the only compliant extensions, I would
say it cannot be sensibly extended using the currently blessed algorithm,
but that there might be other sensible ways to extend it; but I am
skeptical that what you have proposed are compliant extensions, given the
lead end change being so different. But maybe that’s something else I don’t
understand about the current scheme.

I will try to find some time to look at these more carefully, and see why
you think they are extensions, and if, indeed, the lead end change is
covered by the current rules, as I, perhaps mistakenly, believed.

> b.t.w., when you mention the 4-colour problem, what was the context of
this?

It is yet another example of an endeavor in which small pieces can be done
by hand, but that the totality of an operation is too tedious for a human
to do, and so is more conveniently automated: an example of something that
cannot (yet, someone may come up with a cleverer scheme) be tractably done
by hand, but, someone who, by definition, can’t do it by hand, understands
enough of the bits and pieces to program a computer to do the whole job.



-- 
Don Morrison <dfm at ringing.org>
“I was the Cheshire Cat....But they moved the county boundaries,
so technically speaking I’m now the Unitary Authority of
Warrington Cat.”   — Jasper Fforde, /Lost in a Good Book/
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