[r-t] Practical Extension

[Robin Woolley]

Following on from pervsious correspondence:

Richard Grimmett asked "Are you saying there is much less significant 
improvement to be made on what was there already than previously thought?"

Isn't this inevitably true from all human endeavour? As an example I met 
only today, when I'm going on a week's ringing holiday, I like to get 
the OS maps for the area which also come with a free mobile-phone 
version. About three month ago, my usual supplier had changed their 
web-site which made it very difficult to select the maps I wanted so I 
changed supplier. Today I find the original supplier has gone bust 'due 
to some very recent & unforeseen setbacks following the relaunch of our 
website'. Not much improvement there, then.

As regards Extension, I've been interested in it for at least 25 years 
so it is comparatively easy for me to do extensions by hand. It is, 
after all, a practical subject. (Thought: if you can't do it by hand, 
how the ... can you write a program to do it?)

Everyone on this list should be capable of doing it. If you understand 
place notation, then I could teach any of you to do it within an hour - 
face to face, of course.

One point - I think it is a bit of a delusion to hope that every method 
can be extended to every succeeding stage. We should be quite happy with 
a particular method not having extensions at all. There is no 
fundamental theorem saying there must be extensions within any given 
rule-space. (Why does the name Godel spring to my mind here?).

The current rules on extension have one advantage. They are objective 
and make no value-decision on any one in a set of competing extensions.

Best wishes
Robin