<div dir="ltr"><div class="gmail_default" style="font-family:"courier new",monospace"></div><div class="gmail_default"><div class="gmail_default"><font face="courier new, monospace">On Thu, Aug 2, 2018 at 3:13 AM Robin Woolley <<a href="mailto:robin@robinw.org.uk">robin@robinw.org.uk</a>> wrote:</font></div><div class="gmail_default"><font face="courier new, monospace">> If I have read Don’s comments correctly, it could be interpreted as</font></div><div class="gmail_default"><font face="courier new, monospace">> preferring Pudsey as the extension of Cambridge and the current</font></div><div class="gmail_default"><font face="courier new, monospace">> extension path would not have been allowed.</font></div><div class="gmail_default"><font face="courier new, monospace"><br></font></div><div class="gmail_default"><font face="courier new, monospace">No, I'm afraid you have not read them correctly. My observation is that this line</font></div><div class="gmail_default"><font face="courier new, monospace"><br></font></div><div class="gmail_default"><font face="courier new, monospace"><a href="http://www.ringing.org/method/?title=Windsor+Treble+Bob+Major">http://www.ringing.org/method/?title=Windsor+Treble+Bob+Major</a></font></div><div class="gmail_default"><font face="courier new, monospace"><br></font></div><div class="gmail_default"><font face="courier new, monospace">looks a lot more like Kent Minor to me than do</font></div><div class="gmail_default"><font face="courier new, monospace"><br></font></div><div class="gmail_default"><font face="courier new, monospace"><a href="http://www.ringing.org/method/?title=Obnoxious+Treble+Bob+Major">http://www.ringing.org/method/?title=Obnoxious+Treble+Bob+Major</a></font></div><div class="gmail_default"><font face="courier new, monospace"><br></font></div><div class="gmail_default"><font face="courier new, monospace"><a href="http://www.ringing.org/method/?title=Twatt+Treble+Bob+Major">http://www.ringing.org/method/?title=Twatt+Treble+Bob+Major</a></font></div><div class="gmail_default"><font face="courier new, monospace"><br></font></div><div class="gmail_default"><font face="courier new, monospace">or</font></div><div class="gmail_default"><font face="courier new, monospace"><br></font></div><div class="gmail_default"><font face="courier new, monospace"><a href="http://www.ringing.org/method/?title=Meyrick+Treble+Bob+Major">http://www.ringing.org/method/?title=Meyrick+Treble+Bob+Major</a></font></div><div class="gmail_default"><font face="courier new, monospace"><br></font></div><div class="gmail_default"><font face="courier new, monospace">Do you really disagree?</font></div><div class="gmail_default"><font face="courier new, monospace"><br></font></div><div class="gmail_default"><font face="courier new, monospace">> Following Don’s argument,</font></div><div class="gmail_default"><font face="courier new, monospace"><br></font></div><div class="gmail_default"><font face="courier new, monospace">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.</font></div><div class="gmail_default"><font face="courier new, monospace"><br></font></div><div class="gmail_default"><font face="courier new, monospace">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.</font></div><div class="gmail_default"><font face="courier new, monospace"><br></font></div><div class="gmail_default"><font face="courier new, monospace"><br></font></div><div class="gmail_default"><font face="courier new, monospace"><br></font></div><div class="gmail_default"><font face="courier new, monospace"><br></font></div><div class="gmail_default"><font face="courier new, monospace">-- </font></div><div class="gmail_default"><font face="courier new, monospace">Don Morrison <<a href="mailto:dfm@ringing.org">dfm@ringing.org</a>></font></div><div class="gmail_default"><font face="courier new, monospace">“Goodness consists in feeling delight where one should, and</font></div><div class="gmail_default"><font face="courier new, monospace">loving and hating aright.” — Plato, /Poetics/, tr Ernest Barker</font></div><div style="font-family:"courier new",monospace"><br></div></div><br><div class="gmail_quote"><div dir="ltr">On Thu, Aug 2, 2018 at 3:13 AM Robin Woolley <<a href="mailto:robin@robinw.org.uk" target="_blank">robin@robinw.org.uk</a>> wrote:<br></div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex">
<div bgcolor="#FFFFFF">
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.
<p class="MsoNormal"> The usual extension – 34x34 – denoted 1CD - is
the same
extension PATH as used by York S at all stages.</p>
<p class="MsoNormal">The extension having 34x34.8.56x56 – denoted
1BC – is the
same as used by Cambridge S at all stages.</p>
<p class="MsoNormal">The extension having 56x56.8.56x56 – denoted
4BC – is used
by <span>Manuka<span> </span>S</span></p>
<p class="MsoNormal"><span>The
extension 56x56
– denoted 4CD – is the extension used by Pudsey.</span></p>
<p class="MsoNormal"><span> 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.</span></p>
<p class="MsoNormal"><span> 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.)<br>
</span></p>
<p class="MsoNormal"><span> Suppose
that a TD6
method has 34 made with the treble in 5-6. Norwich is such an
one.</span></p>
<p class="MsoNormal"><span> 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).<br>
</span></p>
<p class="MsoNormal"><span> Available
extensions
(via RAS) of Norwich are:</span></p>
<p class="MsoNormal"><span>2DE/5EF -34-4-2-3-34-3-34-1,1
(8 [2] 60)</span></p>
<p class="MsoNormal"><span>2CD/2EF -34-4-2-36-34-5-56-1,1
(8 [2] 60)</span></p>
<p class="MsoNormal"><span>2BC/2EF -34-4-256-36-34-5-56-1,1
(8 [2] 60)</span></p>
<p class="MsoNormal"> none of which follow Don’s idea.</p>
<p class="MsoNormal"><br>
</p>
</div>
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</blockquote></div><br clear="all"><div><br></div>-- <br><div dir="ltr" class="gmail-m_-9219489070050675925gmail_signature">Don Morrison <<a href="mailto:dfm@ringing.org" target="_blank">dfm@ringing.org</a>><br>"After all these years I have observed that beauty, like happiness,<br>is frequent. A day does not pass when we are not, for an instant,<br>in paradise." <br> -- Jorge Luis Borges, _Los Conjurados_, tr Willis Barnstone<br></div></div>