[r-t] "X above, Y below"

Alexander Holroyd holroyd at math.ubc.ca
Wed Aug 2 01:47:08 UTC 2017

I think these kind of things are much more likely to be true if they 
are defined in a time-symmetric way.  E.g. one can declare that method X 
will be rung for all the _changes_ where the 2 is swapping with the 
treble.  (Or even have a different rule according to where in the row they 
are swapping).

That way, it is impossible for two differnt "courses" starting from 
differnt rows to coalesce.  Different starting rows will produce distinct 
round blocks, aiding truth. (Still, in general it is possible for 
different blocks to be false with each other, e.g. at a snap versus a lead 
end, or even false with themselves).


On Wed, 2 Aug 2017, tuftyfrog at gmail.com wrote:

> On 2 Aug 2017, at 00:34, Don Morrison <dfm at ringing.org> wrote:
>       On Tue, Aug 1, 2017 at 4:10 PM, Pip Dillistone
>       <tuftyfrog at gmail.com> wrote:
> > With Bristol below and Double Dublin above you get a 2-3
> > differential with 2 and 3 both hunt bells:
>> >https://complib.org/method/32289?accessKey=f8fac86bb06c104f84fdb9201f26a7ea
> 0bef08c6
> The Composition Library, via this link, says this method is
> asymmetric. Given the rule for generating it I'd naively thought it
> would have the usual, palindromic symmetry. What happens to break
> that? Presumably there must be some other, but still related and
> succinct, way to describe its reverse?
> -- 
> Don Morrison <dfm at ringing.org>
> "Great theories don't simply appear in someone's head as if by magic,
> but take time to blossom. The so-called 'eureka' cry is more an
> exclamation of mental relief than a cry of sudden revelation."
>           -- Marcello Gleiser, _The Dancing Universe_
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> Sorry, this is my mistake in transcribing the method ? as far as I can tell it
> should indeed be palindromic. 
> I chose to define "over" to mean "the 2nd is over the treble in this
> particular row". Since the path of the 2nd is determined by the rule from
> the outset, this made the most sense to me at the time. It's remarkably
> fiddly to work out what to do when the 2nd is dodging with the treble, and
> it's here that I've made the mistake ? just after the halfway point there
> should be a 34 instead of a 14 in the notation, for example. 
> Pip

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