# [r-t] Symmetry, bluelines and differentials

Alexander Holroyd holroyd at math.ubc.ca
Thu Feb 22 03:04:18 UTC 2007

```> Presumably there is some relationship between the usual symmetry of
> the changes and some kind of symmetry in the blueline(s). What is it?
> Is it perhaps
>
> All sub-bluelines are either symmetric, or appear in pairs that are
> reverses of one another?
>
> Or is it something more complicated than that?

Unless I misunderstood something it seems clear that symmetric methods
have exactly this property.  Symmetry means that if you reverse the
sequence of place notations you get the same method (perhaps started in a
different place).  Hence each bell's blue line is the reverse (possibly
started in a different place) of some bell's blue line, perhaps the same
bell or perhaps a different one, and there is a one-to-one pairing between
original bells and reversed bells.

> half a lead apart. There's not reason both such reflections couldn't
> and the other about a change. Are there any expected properties that
> break down in either or both of these cases?

The most notable property that breaks down is truth.  A symmetry point at
a row means two consecutive place notations are the same, so with the
exception of two-changes-in-the-plain-course aberrations like Cross
Differential, the plain course is false.

See Martin Bright's article on method symmetry at
http://www.boojum.org.uk/ringing/index.html