[r-t] Jump change notation

[Andrew Johnson]

> From: Don Morrison <dfm at ringing.org>
> On Sun, May 17, 2015 at 2:47 AM, Glenn Taylor
> <gaataylor at blueyonder.co.uk> wrote:
> > FWIW, when Cambridge Jump was first published in the RW in about 1979 
the
> > notation used was along the lines of:
> >
> > -3-(4.2)-2 etc.
> >
> > the "novelty" being that the bracketed part indicated that the next 
row was
> > the end result of applying 14 followed by 12. Whilst less mathematical 
and
> > perhaps a little more cumbersome than the notation used for 
permutations and
> > cycles, it does have the benefit of retaining current notation (apart 
from
> > the need to understand the purpose of the brackets) and thereby being
> > "accessible" to the non-mathematical interested party.
> 
> Thank you. I'd completely forgotten about this.
> 
> It has the virtue of being entirely clear how to go from the notation
> to a permutation. On the other hand, it seems exceedingly unclear how
> to go from a permutation to the notation! For the simple treble jump
> cases it works easily, but for more arbitrary jump changes you end up
> having to compose more than two ordinary changes. In general do you
> not have to assemble a sort of mini-composition or mini-method to get
> between two arbitrary rows? And in general do you not have a host of
> alternative possibilities to choose between (infinite, I think, though
> you could undoubtedly come up with some rules that at least bound
> things, probably to no more than N-1 ordinary changes to be composed,
> where N is the stage)? Is there an obvious choice for a canonical
> representative among them?
> 
> I'm intrigued by your implication that it is more accessible than the
> alternatives. Ander's version simply names the bells (well, places)
> that jump. That seems perfectly accessible to the naive user. Is it
> that it is unclear how to figure out what the other bells do that
> makes it seem more "mathematical" to you? And the brute force of
> simply writing down the permutation seems well within the normal scope
> of what ringers do--it's the same as dealing with a lead head, course
> head or coursing order--what am I missing that makes that less
> accessible?
> 
> Anyway, as part of seriously considering this fourth possibility, does
> anyone have a suitable algorithm for going from an arbitrary
> permutation to something in this notation? The opposite need as in
> schemes (2) and (3) in my previous message.
> 
The obvious algorithm is have a change where you swap bells which are out 
of order (starting from the front just to make the choice definitive), 
then see what you get and repeat the process until you get to the target 
change. It even works for non-jump changes.

E.g.
13572468 -> 17432865
13754286 = 12
17345286 = 1678
17432586 = 1278
17432856 = 123458
17432865 = 123456

You can also put the place notation into a non-jump change aware program - 
it might be false, but it will end up at the right row.


Andrew Johnson




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