mark at snowtiger.net
Sat Jun 7 10:30:18 UTC 2014
> Think of all those people defiling themselves by ringing impure peals
> on 8 or more. Disgusting, I call it.
I think you are still thinking of the wrong definition of the word
"pure", John. In mathematics, a "pure" concept is one that is simple,
elegant, and uncontaminated by unnecessary or unrelated factors.
In terms of our discussion, the contamination is that of base 10. A
number such as 5000 appears neat, whole and round to most people's eyes,
because we are used to counting in base 10. But base 10 is just a way -
one of many ways - of representing a number in symbols. Counting in tens
has no relationship to the underlying mathematics of changeringing, so
to impose it on our definition of a peal is in a sense impure.
5040 might not look like such a nice round number, and may look
certainly no better than 5000, but in fact it is your base-10 prejudices
which lead you to conclude that.
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