[r-t] Lead-based methods [was: Poll on consecutive blows in the same position]

Don Morrison dfm at ringing.org
Tue Dec 30 04:22:58 UTC 2014

On Mon, Dec 29, 2014 at 6:49 PM, Alexander Holroyd <holroyd at math.ubc.ca> wrote:
> A method is a finite sequence of changes.

Ander's message raises a point I'd not considered, but should have.
And which is going to make some readers groan.

+Does+ a method (or perhaps more precisely, the sequence of changes a
method generates) have to be finite? On first asking myself that
question I answered "of course it does, Bozo". But on further
reflection I'm not so sure. An actual touch of the method we ring must
be made up of finite segments of the method (we ring fractional leads
of things all the time already), but it's not obvious to me that the
method itself needs to be finite. Yes, of course, the resulting
infinite set of rows arising from applying an infinite method to a
starting row will be false, but a majority of folks voting in an early
poll said that a course of a method doesn't hae to be true
(presumably, most implicitly added "so long as you use only mutually
true portions of courses of it in a touch").

Perhaps the word "finite" needs to be added to the definition of an
α-method. Or, really, I think, it needs to be something like "all the
sequences generated by an α-method, starting from any of the N! possible
rows, must be of finite length".

Also, if we allow infinite methods, then we can't demand that a method
be a round block, I don't think. Though, if we so chose, I think we
might still apply that restriction to α-methods.

Don Morrison <dfm at ringing.org>
"It is not the perfect but the imperfect who have need of love."
                                 -- Oscar Wilde, _An Ideal Husband_

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