[r-t] Practical Extension

[Don Morrison]

On Thu, Aug 2, 2018 at 3:13 AM Robin Woolley <robin at robinw.org.uk> wrote:
> If I have read Don’s comments correctly, it could be interpreted as
> preferring Pudsey as the extension of Cambridge and the current
> extension path would not have been allowed.

No, I'm afraid you have not read them correctly. My observation is that
this line

http://www.ringing.org/method/?title=Windsor+Treble+Bob+Major

looks a lot more like Kent Minor to me than do

http://www.ringing.org/method/?title=Obnoxious+Treble+Bob+Major

http://www.ringing.org/method/?title=Twatt+Treble+Bob+Major

or

http://www.ringing.org/method/?title=Meyrick+Treble+Bob+Major

Do you really disagree?

> Following Don’s argument,

My argument, at least as far as I intended to make it, is spelled out in
full, above. Perhaps you’d best explain what you think my “argument” was,
as I can see no way that anything I’ve written can be construed as
necessarily having any of the consequences you attribute to it.

Your message of a few days ago implied you were only talking about
“extension above the treble,” though as I responded that was not clear to
me in your original message; have you perhaps reverted to that context? I
have certainly never advanced any argument about how extension above the
treble works, as I believe it is *methods* that are extended, not their
works above and below independently. The currently blessed algorithm favors
treble dominated methods, and appears divide things into above and below,
but that is not fundamental to extension, it is merely a tool chosen for
one particular view of how extension might or might not work. And it is an
exceedingly unhelpful one for methods that are not treble dominated. In
fact, I’m skeptical that it is all that helpful for treble dominated
methods with unusual hunt paths.




-- 
Don Morrison <dfm at ringing.org>
“Goodness consists in feeling delight where one should, and
loving and hating aright.”    — Plato, /Poetics/, tr Ernest Barker


On Thu, Aug 2, 2018 at 3:13 AM Robin Woolley <robin at robinw.org.uk> wrote:

> A few thoughts of Don's thoughts about extension above of Kent by way of
> reviewing the extensions of Kent TB ‘above’ the treble with a comparison of
> extensions of Cambridge S.
>
>  The usual extension – 34x34 – denoted 1CD - is the same extension PATH as
> used by York S at all stages.
>
> The extension having 34x34.8.56x56 – denoted 1BC – is the same as used by
> Cambridge S at all stages.
>
> The extension having 56x56.8.56x56 – denoted 4BC – is used by Manuka  S
>
> The extension 56x56 – denoted 4CD – is the extension used by Pudsey.
>
>  If I have read Don’s comments correctly, it could be interpreted as
> preferring Pudsey as the extension of Cambridge and the current extension
> path would not have been allowed.
>
>  The Extension rules are fully symmetric - what you can do on the back,
> you can do on the front. (In fact, I find it easier, by hand, to extend
> 'above' by considering extensions 'below' then inverting.)
>
>  Suppose that a TD6 method has 34 made with the treble in 5-6. Norwich is
> such an one.
>
>  Following Don’s argument, an extension having just 56 places made under
> the treble in 7-8 with none (under) in 5-6 would be (subjectively)
> preferred to those having both 34 and 56 or 34 and 34. (If you do not
> accept 56x56.8.56x56 above as an extension, you cannot accept x34x1x34x
> below on symmetry gounds).
>
>  Available extensions (via RAS) of Norwich are:
>
> 2DE/5EF -34-4-2-3-34-3-34-1,1 (8 [2] 60)
>
> 2CD/2EF -34-4-2-36-34-5-56-1,1 (8 [2] 60)
>
> 2BC/2EF -34-4-256-36-34-5-56-1,1 (8 [2] 60)
>
>  none of which follow Don’s idea.
>
>
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-- 
Don Morrison <dfm at ringing.org>
"After all these years I have observed that beauty, like happiness,
is frequent. A day does not pass when we are not, for an instant,
in paradise."
        -- Jorge Luis Borges, _Los Conjurados_, tr Willis Barnstone
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