edward.w.martin at gmail.com
Sun Aug 6 02:33:24 UTC 2006
On 8/4/06, Alexander Holroyd <holroyd at math.ubc.ca> wrote:
> Are you saying that you can prove it's always possible to get an extent in
> this way from any in-course extent? If so I don't get it. Obviously
> there are lots of ways to resolve the double changes into pairs of single
> changes, but one has to do it in such a way that the 60 out-of-course rows
> so introduced are all different. Most ways fail to achieve this, e.g.
> turning 3.1 into 3184.108.40.206 !
Well yes - as far as Doubles is concerned, but you seem to be
doubling back on yourself in what you said earlier. It was I who could
see no logioc behind the production of Crambo and it was you who
claimed that there was something.
Unless I'm mistaken, you yourself have demonstrated that it works on a
plain course of Stedman, or of Carter's or of Grandsire called pbpbpb.
Having demonstrated that it is indeed possible, why would you need
proof that it is possible or do you know of other true extents of
in-course Doubles other than the reverse of the above & rotations of
the above etc?
My original dispute with you (if we can call it that) is that I don't
think that taking a plain course of Stedman Doubles and trying to
insert the 60 out-of-course rows to get a true extent (120) of say
Crambo is in any way a process open to logic. As you correctly say
there are too many choices for say 1sts followed by say 5ths = 123 or
145 followed by 125 or 345
Again as you say, only one works but how does Ed Martin or Fabian
Stedman know which it is without trial & error? What is the logic you
I was interested that what you demonstrated regarding the backstrokes
of Crambo & the rows of Reverse Stedman coincide nicely, but I was
also surprised & interested that if you try to do the same with the
handstrokes of Crambo to get the desired rows of Reverse Stedman you
can't do it, it necessitates 3 jump changes!!! Why is that I wonders
In short, I think that there is no percievable logic behind the
production of Crambo and I am at a loss as to how Stedman discovered
it or indeed - as I mentioned - How he discovered London Pleasure
Do lets be friends - I obviously misunderstood you somehow somewhere
along the way, set me straight
More information about the ringing-theory