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<div class="moz-text-flowed" style="font-family: -moz-fixed;
font-size: 14px;" lang="x-unicode">Hi All,
<br>
<br>
A brief history of indefinacy.
<br>
<br>
In the old days, indefinacy didn't matter so no problem there.
<br>
<br>
At the time of the first big revision of Extension rules circa
mid-90's, a comparative new idea that Extensions working at more
stages would be preferred to one working at fewer stages - within
the space available, of course, which has practical limit of c20.
<br>
<br>
Then, in the early 2000's, all valid extensions had to be
indefinite.
<br>
<br>
At the time, I went on record against this on the grounds that (i)
extensions above a certain stage would never be rung and (ii) I
couldn't see how indefinite could be proved in general.
<br>
<br>
As regards (i), no peals above stage 22 still have never been
rung.
<br>
<br>
As regards (ii), it is possible that a given method only has a
valid extension at, say, every 50 bells, i.e., n = 22, 72, 122,...
and I couldn't see anyway of demonstrating this theorectically -
or every 100 bells, etc....
<br>
<br>
On this latter point, I was assured by certain list-members that
it would be theoretically possible to show indefinacy. However,
these persons have decided since that they were wrong in this
case. (I have no doubt it is in some cases, but not all.)
<br>
<br>
To cut a long story short, indefinacy has been redfined in the
framework:
<br>
<br>
"There is no known approach for demonstrating mathematically that
a given extension construction will work indefinitely. Therefore
the following practical test is applied:
<br>
An extension construction is deemed to work indefinitely if:
<br>
(1) It has been tested up to stage 32;
<br>
(2) At least one valid extension is produced in the range of stage
25 to stage 32.
<br>
E.g. an extension construction of a Royal method that produces
valid extensions at stages 18 and 26 is deemed to work
indefinitely."
<br>
<br>
This seems an ideal compromise and is ideal for computer
implementation, although there are extensions which work in much
greater increases. There is one of Surfleet which increases by 24
bells each time.
<br>
<br>
Best wishes
<br>
Robin
<br>
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