[r-t] The null change

[Don Morrison]

On Wed, Dec 31, 2014 at 3:48 PM, Graham John <graham at changeringing.co.uk> wrote:
> A compromise, therefore,  is to accept the use of the null change to
> generate another row, but not count it in the number of changes rung.

This is attempting to solve a non-existant problem, and in the
process would foment no end of new, pointless confusion.

We only count "changes" in the sense that folks that aren't of the
sort of turn of mind that subscribes to this list use the word as
synonymous with "rows". If you ask most ringers "how many distinct
changes are there in an extent of minor?", you'll get the answer
"720", even though for most methods the correct answer is in the
single digits. Try again, leaving the word "distinct" out: "how many
changes are there in an extent of minor?" Even some fairly
sophisticated ringers will answer "720", missing the subtlety that it
really only requires 719 changes to connect up those 720 rows.

The basis for all the numbers of "changes" we're looking for is the
number of permutations of a given number items (and, by the way,
includes the identity!). And those N! permutations are all rows.

What ringers ring is rows. All the sweat and effort is making the darn
bell swing around to make a noise, which is part of a row, not a
change. Our effect on the surrounding universe is the sounds of the
bells, which are part of rows, not changes. We measure the time it
takes to ring those rows, which is typically in the 1.5 second-ish
range; a change is an abstract thing in our heads and has no duration.

If you write yourselve a piece of software to prove peals I'd be
shocked if when you printed out the length, what you hadn't counted
was the rows you checked against one another for distinctness.

We really count rows. Yes, there's the slight complexity of whether to
count the rounds at the beginning or at the end, but that's just convention.
But let's not fool ourselves: it's the rows we count.



-- 
Don Morrison <dfm at ringing.org>
"If a philosopher advances a philosophical argument to show that
we do not in fact ever see trees and books and human bodies,
despite the fact that in a variety of familiar situations we
would ordinarily say that we do, then our philosopher is almost
certainly wrong."     -- Paul Grice, _Studies in the Way of Words_