[r-t] Method symmetry

Alexander Holroyd holroyd at math.ubc.ca
Wed Aug 22 22:14:22 UTC 2012

On Wed, 22 Aug 2012, Mark Davies wrote:

> "A well-formed path is one in which the hunt bell has the same path if it is 
> rung backwards and is symmetrical about two places made half a lead apart."
> If you interpretation "place" as an actual place being made, rather than just 
> a position within the lead, then the definition excludes the Evil/Good-style 
> reflective symmetry.

Right - I think "places _made_" is the key phrasing.  It seems that this 
is intended to exclude Evil-type paths, otherwise there would be no need 
for the "and is..." at all.

> It is of course difficult to imagine how the working bells could follow 
> reflectively-symmetrical paths with this type of treble path (whilst 
> preserving truth, anyway).

In particular that would seem to necessitate an asymmetric method, 
therefore it would in particular answer my original question.  Again, 
there are some silly examples such as
3478.1478.1258.1256.1456.3458 (which is true).
but I doubt whether there is anything more sensible.

I still think there should perhaps be some nice answers to my original 
question: asymmetric methods with all blue lines symmetric.

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