[r-t] Rows and changes

[Mark Davies]

Several people writes stuff like,

> You are correct in that we usually omit either row 0 or row 5040.  The
> issue is that we don't have to omit either of them, or we are free to omit
> both.

No oh dearie me no! :-)

Touches are round blocks. They have the same number of rows as (changes
between rows).

Consider the extent on three:

123
213
231
321
313
132
123

This has six rows and six changes. That's not obvious because I've written
it out on the wrong sort of plane. Because it's a round block, the beginning
and end join up. Write it out on a strip of paper, cut it to the right
length, then join up the ends so the beginning rounds and ending rounds
overlap, and become the same row. That's your touch. That's a round block.

Basically, a round block needs to be written out on a cylinder to show its
true nature. The beginning and ending rounds aren't just the same sequence
of bells, they are *the same row*, at the *same point in time*.

I guess it's a bit like a closed time-like curve. If you've ever rung a
touch which has come round, you are forever ringing that touch. Hopefully a
nice thought! ;-)

MBD