[r-t] Doubles Principles

H C Pumphrey H.C.Pumphrey at ed.ac.uk
Wed Feb 16 09:08:51 UTC 2011

Samuel M. Austin wrote:

> Is it possible to have a Doubles Principle consisting of 10 or 20 
> changes per section?

That depends on what you mean.

I became interested in whether there were any other doubles principles so I 
hacked together some scripts and my dodgy homebrew proving program to look for 
some. I found lots and lots. But when I tried to generate a 120 from them I 
found that it was always impossible, whatever calls you chose.

I have not tried 10 or 20 changes / section, but I have tried 6, 8 and 12.

With 8 changes per section, 1-3-5-3-5-3-1-3- is a double principle with a 
40-row plain course. Two singles will double this to 80 rows but I can't find 
a 120. There are a number of others like this.

With 12 changes / section there are lots of possibilities, even if you 
restrict yourself to methods that never have more than 2 blows in one place. 
But the only pure-doubles principles (where 2 singles guarantees a 120) are 
Stedman, reverse Stedman, Carter and reverse Carter. Most of the others won't 
give a 120, a few (e.g. wiggle) give one that is really a single every lead -- 
not terribly satisfactory.

With 10 and 20 changes / section you would have plain courses of 50 or 100 
changes. My guess (before I try it) is that it would be possible to find such 
a principle. But it seems very unlikely to me that you will be able to obtain 
the extent of 120 easily with such a principle.

The observation that it is easy to find unrung and un-named principles but 
hard to generate an extent from them seems to be true on 6 bells as well as 5.



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