# [r-t] Re: Proofs

Robin Woolley robin at robinw.org.uk
Tue Sep 28 08:21:33 UTC 2004

```I'm beginning to wish I hadn't got along with Philip's suggestion. This is
perhaps why there is very little published and that which is is so obscure.
I was trying when I wrote this to make it as easy as possible to
understand - bed-time reading, if you like. It is also bound to suffer from
missing the initial 13 pages of explanation.

Firstly - it looks a lot better in Word, - I'd rather use power of -1 but
this is plain text so I used INV instead.

X(AC) here means just the falseness between A & C - no 'direction' is
intended but having decided on the rule 'inverse of second of the pair
operating on the first of the pair', we're stuck with it.

My wife, who, to save her from ennui, is currently doing
an M.Math course at the Open U (M336) confirms my recollection from 30 years
ago that the convention (then and now) is that 'ab' is 'a operating on b'
or, if you like as I say sotto voce when I write it down, 'a of b'.

In fact, the whole analysis is just as valid the other way round, C.inv(A),
except that it might be less natural when starting from first principles.

The definition of J in words is the permutation  for a seconds place lead
end so:

> e = rpJ => rp = J
>
>Here you meant to type "e = rpJ => pr = J" I suppose

No! - since J is self-inverse, it makes no difference: J = pr = rp.

Anyway, I said in the pre-amble:

"An asymmetric section may also have just one falseness group."

Inspection of the appropriate collection will show that it is usual for any
asymmetric section to lead to  two distinct falseness groups. Indeed,
Wollaton has all its sections asymmetric and has eight distinct falseness
groups. If I can find an asymmetric section with just one, then I will have
either proved the statement or disproved the converse of the first statement
(as you prefer), -

"A symmetric section only has one falseness group associated with it"

In fact, the method 34x5678.12 (8ths place) has just 'D' falseness.

b.t.w., the eight falseness ratios leading to one falseness group are X, XJ,
JX and JXJ together with their inverses where J = 12436587 or, I suppose, J
= 13254768.

Can we have an explanation of geoetrics, please? You'll remember the
original msgs for Clarrie & Graham. I'll add my name to this. Most
importantly, can this technique deal with incidence? This is probably more
important to composition than falseness groups themselves.

As every good schoolboy, 'without loss of generality', knows, Middleton's
should be false to Cambridge. Fortunately, the 'E' falseness in the
composition appears in the 'middle' lead whereas the 'E' falseness in
Cambridge is between the first & last leads. I could give chapter & verse in
the comic as to where other methods have been tried, but fail to give
incidence.

Best wishes
Robin.

```