Oct 20
aside
change ringing
The art and science of bell ringing
is called "campanology". Since medieval times,
lots of churches through Europe had bells, and
finding interesting ways to ring 'em became
a serious business. The math behind these patterns
was a precurser to group theory.
See midsomer murders season 5 episode 3, i.e. 8:50 in.
background
Today it's a popular activity and competition,
especially in England. Timing, mental focus,
teamwork, ...
There is a lot of specialized vocabulary:
peal : at least 5000 changes on 8 or more bells
extent = full peal = all permutations of n bells
(With 8 bells, that's 40320 permutations,
which done in 18 hours in 1963.)
4 bells is known as Minimus;
5, Doubles;
6, Minor;
7, Triples;
8, Major;
9, Caters;
10, Royal;
11, Cinques; and
12, Maximus.
methods
The simplest "method" pattern in common use is
the "plain hunt". But that isn't enough to
get many permutations, so other tricks ("bob", "single")
are used to break alter the permutation pattern.
And here's a good explanation of the next kinds of tricks,
at
http://www.merrix.eu/BellRinging/methods/
(With 6 bells, 6! = 720 is all possible permutations,
which is (for example) the Bob-Minor on that site.)
math
Also related to juggling notation :
Jokes
your turn - let's do this
I'm trying to get some hand bells for next week's
class. Your mission: learn some of these simplest
patterns, and do some change ringing.
For a place to start :
As a class, invent your own system along these lines for
four people, calling out "1", "2", "3", "4" (pause),
with each person keeping the same number, and in each
repetition either
(a) staying in the same 1 to 4 position, or
(b) moving one place earlier, or
(c) moving one place later.
* How many permutations does "plain hunt" take you through?
* What do "generators" have to do with this?
* And how does it connect to the puzzles we've been doing?
Now, how about with 5? 6? Perhaps some subset of the permutations of 6?
Your mission for this week: read about some of this stuff,
and come to class next time ready to play around with it.
