[r-t] Rows and changes

[Mark Davies]

Don writes,

> On paper, as a mathematical abstraction, sure.
> But that's not at all what we're talking about.
> We're talkin about people actually ringing, making noises spaced out in
> time.

Yes, that's why you're confused! Rows and changes and touches *are*
mathematical abstractions. We try and recreate them in the tower, but we are
not actually producing real rows and changes, just as close a simulacra as
we can. It's a bit like a circle drawn on a piece of paper - it's a physical
simulation of the abstract mathematical object.

For example: in the abstract, all rows are the same. In the tower, rows vary
depending on what sort of bells you are ringing on, how well-struck the
ringing is, and so on. We even say we have "rung" a touch if a couple of
bells swapped over for a blow or two.

So you will get very confused if you try and work out how many rows and how
many changes there are in a peal by considering the actual physical ringing.
You are looking at the problem in the wrong domain. The touch and the rows
and changes exist not in the tower, nor even on the flat Euclidean plane of
your pricking paper, but on the surface of a perfectly abstract cylinder.

All the rules we have been discussing are about the abstract objects, with
one exception: the quality of the ringing. We could lay down a lot more
rules about how closely the physical performance must match the abstract
definition of the touch, but most of that is generally left unsaid; stuff
about "swaps must be corrected" being the main item usually voiced.

MBD