[r-t] Principles

[Alexander Holroyd]

PABS beat me to it!

Here is another method (a shorter one) in which all bells do the same 
work (i.e. their blue lines are vertical translates of one another), yet 
it cannot be viewed as a principle (i.e. it cannot be split into leads in 
such a way that the lead-end change is an n-cycle, where n is the number 
of bells).

-123458-1238-1678-145678
http://www.boojum.org.uk/cgi-bin/line.pl?bells=8&pn=-2345-23-67-4567&lines=1&line=2&line1=b&line1c=red&line2=b&line2b=2&action.x=1

I find it fairly amazing that such a thing can exist.  Is there a general 
theory of such methods?  Can someone come up with a nice one that people 
would want to ring (preferably with a nice peal compositions available)? 
What is the smallest number of bells on which one exists?

With regard to the original query, principles seems a very sensible 
classification to me - there is a good case to be made that they represent 
the pinacle of elegance in method construction.

Now I'm very intrigued by these "fake principles" too...

On Tue, 5 Jul 2011, Philip Saddleton wrote:

> Josy Shewell Brockway said  on 05/07/2011 00:16:
>> It is not possible to construct a method without a hunt bell in which
>> all bells do the same work but the number of leads is different from the
>> number of bells.
>
> Yes it is - Simon already did. You could argue that the Plain Course is 
> exactly the same as Original, but there is nothing in the Decisions to say 
> that a lead of a method has to be the shortest repeated block (see Magenta 
> Little Place Maximus), or that two methods cannot have the same Plain Course. 
> You could play the same trick with any principle on a non-prime number of 
> bells.
>
> In any case there are examples where this is not the case, e.g. 
> &9.1.789.1.9.3.9.1.789.1.9.1.9.1.789.1.9.3,1
>
>> Because all the bells do the same work, each bell must find itself in
>> every place at at least one lead-head.
>
> Not true.
>
>> I don't know why the Central Council definition is phrased in the way it
>> is.
>
> Both conditions are necessary - it is also possible to have a method where 
> the number of leads is the same as the number of working bells, but they do 
> not all do the same work in the plain course, e.g.
> &38-,29T
>
> PABS
>
>
>