[r-t] Complexity of extents

Richard Smith richard at ex-parrot.com
Wed Jun 19 22:51:47 UTC 2013

> Mark Davies wrote:
>> Find a way of writing out the extents in a standard way 
>> (perhaps the expanded place notation), and compress them 
>> using a tool like gzip.

The problem with that is that most general-purpose 
compression programs (certainly including gzip) don't 
understand a string occuring once forwards and a second 
time backwards, e.g. "abcdefghijihgfedcba".  Clearly that 
string has structure, but gzip doesn't spot it.

Matthew Frye wrote:

> Yes. Clever. The choice of how to "write out" the extent 
> clearly becomes key, perhaps even moreso than the choice 
> of compression.

Indeed so.  And we've already made one such choice that 
no-one has commented on.  Everyone here has been talking 
about extents written as sequences of changes, not as rows. 
In other words, we've decided to notate a three-bell extent 
as "" instead of "123 213 231 321 312 132 123". 
The three-part structure is far more obvious in the former 
representation than the latter.

> I think it's important to keep the relationships you might 
> notice while ringing in this description. e.g. for spliced 
> St Simon's and St Martin's doubles, around the half-lead 
> the back work is the same despite the difference in 
> frontwork, but place notation mangles recognition of that.

The similarity you notice between St Simon's and St Martin's 
isn't just a superficial similarity that helps learn the 
methods.  It's also key to the reason why you can splice 
them in the first place.  I'm not sure I'd go so far as to 
say the "place notation mangles recognition of that." 
After all, their notations are really rather similar:

   St Simon's   &,2
   St Martin's  &,2

But then, so is:

   Plain Bob    &,2

What we're perhaps saying is that the 3 and 23 changes are 
in some way more similar than either is to 1.  But that's 
not really true, is it?  23 is a just a swap different from 
1, as it is from 3.  The reason we can splice St Simon's and 
St Martin's in the way we can is because of the particular 
bells that stay together on the front.  (In fact, St 
Martin's and Plain Bob do splice together, but it is a 
course splice, not a two-lead splice.)

> With any simple, linear description you can get issues 
> like this but if you were to "write out" the method in 
> some 2-D format (e.g. a grid) and then directly compress 
> that by some means it may be more satisfactory.

My immediate reaction is that we don't need to think about 
the internal structure of change, and instead we should be 
thinking in terms of what bells are where at the points 
where the sequence of changes varies.  Effectively we'd be 
thinking in terms of (generalised) Q-sets.  That has the 
advantage of being closer to the concepts that are 
responsible for making the compositions work.  That seems 
desirable if we're interested in the complexity of an extent 
as a mathematical object, rather than its complexity as 
something we might consider ringing.  And, as I read 
Philip's opening email, it was the former that he was 
trying to assess.


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