[r-t] Principles
Mark Davies
mark at snowtiger.net
Wed Jul 6 21:02:04 UTC 2011
Ander writes,
> By definition this is true for n=1 and n=stage, but I'm guessing that's
> not what you mean. I don't at present see why it must be true for any
> other n.
Nor I, but all the examples seen so far appear to be so.
> I don't understand this - what is the reduction you are talking about?
I'm just trying to get this straight in my head. How about putting it
this way: there is a "de-winking" transform for these methods; a pair of
bells (for n=2; triplet for n=3, etc) acts in a way analogous to a
single bell at stage M/n.
Consider the behaviour of the front four of an 8-bell method of your
type. Only certain sets of place notation are allowed. This is OK:
1234
2143 x
2143 1234
1234 x
Because it keeps the (12) and the (34) pair quite separate. The two
pairs can therefore be considered to be two single bells ringing one
change, in which both make a place:
ab
ab 12
Where a is equivalent to the 12 pair and b the 34.
It is also possible to make (12) and (34) hunt through each other, like
this:
1234
1324 14
3142 x
3412 14
This again reduces to the single pair a and b, this time crossing with
each other:
ab
ba x
This transform (if it is such) applies to both Ander's and Frank
Blagrove's methods. They both reduce, in this sense, to a Minimus
principle with half the lead length but the same number of leads.
I have a feeling that any method which exhibits this property, which I
shall call "slide self-similarity", or "slideyness" for short, can be
constructed from a true principle at a lower stage, by winking up, or
whatever the reverse of my reductionist transform is called.
But I don't know that for sure. My question is, are there slidey methods
which cannot be constructed in this way?
MBD
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