Connie -- Thanks! The DRH thread seems to have reached a point where I must
try to sign off (not that I expect that to stop the wadges of material he keeps
visiting on me, much of it in fact interesting about writers who clearly do base
themselves on neat predetermined patterns). His latest messages, agreeing that
his numerical patterns can't be demonstrated to be significant by recurrence
(and are therefore only to be seen as significant if one has pre-determined that
they must be, not that he'll take that point), and making an ex cathedra 
declaration about "the bases" which one must "look first always for" (not that
he will see that anyone might doubt his magisterium), really leave nothing more
to pursue. So the fact that I mustn't quote you as rejecting his recruitment of
you won't be too distressing -- Duncan (stet patientia, presumably, on the
other matter?)
David -- Nobody has suggested that you are slow to answer. But you tend not to
answer the questions that were asked. Most notably in our recent exchanges
about the "'wif' in the middle". I asked in my e-mail of 22 June for an
explanation of what exactly this means, and how your argument proceeds from
it (I re-raised the point in my e-mails of 29 and 30 June). Your e-mail of
29 June asserts that you "were telling me exactly how you arrived at your
perception of the structure, beginning with the references to the 'wif'"
but in fact you have never done so. (My quote not verbatim from your e-mail,
but merely adjusts a pronoun or two).

As to "suggesting that a feature you have adduced in any text is not there",
if I may expand to "is not there, or is there only by such careful selection
of evidence as amounts to misrepresentation", then I have suggested in my
e-mail of 29 June that the feature "in 6 and 6' the Chronicler relates promises
in a, the terms offered in b, and the responses in c" is not there, for it is
only in the second half of 6c that "response" appears, the first half being
occupied by a feature which is certainly not "response", so that your statement
suggests a degree of parallelism between 6 and 6' which is not there.
    I mentioned that one, as illustrating the difficulties I was finding,
because it bore on the third person pronouns in "7 &t;a gebead he him..."
(your 6a and on), on which we had been in disagreement. But for that I might
instead have suggested, without the expansion, that the feature "The Chronicler
refers to his [Cynewulf's] loyal subjects in B2..." is not there; your B2
refers to a point in Cynewulf's reign at which he wished to expel..., breaking
off before specifying whom he wished to expel (certainly no "loyal subject").

I'm sorry; I have now to be away for a fortnight, and to prevent unmanageable
cluttering of my mailbox I shall have to set myself NOMAIL. We shall have to
leave these - alas - so far quite unprofitable exchanges for the present.

Dear Sarah,

I've now put another long posting on the net But to try to reply to your
"what on earth is he talking about":

He has told us what, in net postings. There were classical prescriptions for
how to write an elegant structure, involving the proportions into which its
divisions should fall, the use of direct and inverse parallelism, the device
of placing key-words at regularly recurring intervals, and so on. Writers
were recommended at least to check that they had fulfilled these prescriptions
by counting words, syllables or letters, and some writers composed by count.
These prescriptions would have been known to educated men in Anglo-Saxon
England. They would naturally have been led to consider whether these features
could or should be preserved in translation. They might well have considered
applying them to original vernacular work.
    DRH has found (or manufactured; I wish I were sure which) so much evidence
that they did so that he appears to me now to approach any medieval text with
a mental template which he lays over the work, reading only what shows through,
rather as examiners of multiple-choice questions lay a specially-prepared grid
over the scripts for marking purposes - laid over a script written in
accordance with instructions the grid shows sense through, but otherwise
nonsense.
    He will not engage with the fundamental question "How many different
possible ways are there of dividing a passage on these principles, and how
fully and precisely must it conform to them; therefore what is the probability
that a passage not thus composed will by chance prove able to be fitted to
some one of them?". Or with the particular question "what is a word in Old
English?"
    His choice of features to establish connections is often selective, and
at times twistily phrased. Look at "The Chronicler refers to Cynewulf in B1
and B'1" in his long posting on the 755 annal - he is referred to as the
principal actor in B1, but merely as learned by the principal actors to be
dead in B'1.
    He studs his analyses with technical terms, some having a precise meaning
("extreme and mean ratio"), some I suspect merely used to give a spurious
appearance of precision ("crux"), but all protecting his analyses from attack
except by those who have first laid out a great deal of time in learning the
stuff.
    He reminds me of those who offer cryptographic evidence for the authorship
of Shakespeare. I think he suffers from academic monomania. This is a pity,
because the rhetorical prescriptions he bases himself on exist and were
followed.

-- Duncan

(28 Nov 1995)
WARNING! This, though a critique of less than half of David Howlett's
paper in the Scragg & Szarmach volume, is a quite long and detailed
posting. IF NOT INTERESTED DELETE AT ONCE.

For those who have not yet been able to see the paper, David prints
first the "prologue" of St John's Gospel (i.e. verses 1-5), in both
Greek and Vulgate Latin versions, indented and labelled to exhibit
clearly the features of structural balance which it beyond question 
displays. He divides it into four sections, three chiastic and one
parallel. As an example, the chiastic section B appears thus (for
obvious reasons only the Latin):

    B1  Omnia
     2    per ipsum facta sunt
     3      et
     2'   sine ipso factum est
     1' nihil.

The evident balance about the central "et" is maintained by word
(5 before, 5 after), syllable (9, 9) and letter (22, 22). It need
not be done exactly like that, however. In the Greek form of this
section the central word has to be included with the first part to
get the balance; in another section of the Greek the central word
is included to get the word balance, excluded for syllable and
letter. Given even so much permitted variation it is hard to see
how such structures could provide criteria for editing, which as
David understands it includes emendation to recover an author's
exact intended forms if they seem to have been corrupted in
transmission.

In other cases more extensive variation appears. In the parallel
section the "halves" contain in the Latin five words each, but to
make the syllables and letters support the division we must
divide them at the "golden section" (that at which the ratio
between the larger and smaller divisions is equal, as nearly as
may be, to that between the whole and the larger section - what
is called "extreme and mean ratio"); there are obviously two such
division points in any passage. In the Greek matters are different
again. The "halves" contain respectively seven and six words, but
David sees the seventh word as "central" in importance, flanked by
six and six. In considering the syllables and letters, however,
this seventh word gets no special treatment in exhibiting - in
this case almost - identical numbers in the "halves": 11 and 12,
26 and 25. The golden section does not seem to be significant.

In yet another type of mathematical structure which David offers
to demonstrate, the possibilities of variation are so large as to
make it doubtful if there is anything significant there at all.
The noun _Deus_, he tells us, occurs three times, the intervals
from the beginning of the passage to the first occurrence, between
the first and second, between the second and third, and from the
third to the end being significant in that all are multiples of
three: from the first word of the prologue to the first instance
9, from the first to the second 3, from the second to the third
again 9 (all inclusive), and from the third to the end 33 - but
this time exclusive of the word itself. The important verb 
_facere_ also occurs three times, but in its case the significant
intervals are multiples of four: from the first word - but not
this time "of the prologue"; the count is from the start of
section B - to the first instance 4, from the first to the second
- but this time exclusive of the instances - 4, from the second
to the third - this time exclusive of the second but inclusive of
the third - again 4, from the third to the end - and now back on
the same basis as for _Deus_, exclusive of the word (and to the
end of the prologue, not, as with the start, of the section), 20.
David's phrasing does not conceal, but neither does it draw
attention to, the shifting basis of location of the ends of the
intervals, which is of crucial importance; it is after all the
case that any interval whatever (above zero) can be represented
as a multiple of three if one can choose at both ends independently
whether to treat it as inclusive or exclusive, and three quarters
of all intervals can be represented as multiples of four.

Thus it is less happily than I had hoped that I turn with David
to Old English; I had not thought to find myself uneasy in
following him on his own ground. 

From the St. John passage, given as one that would be familiar
to any educated Anglo-Saxon, he proceeds to the statement "The
author of _Beowulf_ understood these compositional rules, which
he applied throughout the poem." In most cases such a statement
would represent a prospectus for the next part of the work, to
be read with the implied continuation "as I shall now demonstrate".
In this case it may not be; it may be a flat statement of what we
are to take as evident fact. His posting of 23 June 1995 declared
that (given that OE writers knew of these rules, and themselves
applied them when they wrote in Latin, premises that as far as I
know nobody on the net has sought to challenge) "it is absolutely
inconceivable that men who do this in a learned language do not
do it in their mother tongue". As a literal statement this can be
rebutted by a simple averral that I find it quite easy to conceive
that men already familiar with a living poetic tradition in their
native language, before they began the study that taught them rules
governing Latin poetry, should treat the two media in different
ways. But in any case, whether or not David expects our advance
acceptance of his statement, he will presumably wish to illustrate
with the clearest possible instances.

His first is of the first three lines of _Beowulf_, which he sets
out thus, as a parallel structure (in exhibiting structures from
the poem his practice is to give significant words, not the whole
text):

    A1  in geardagum
     2    [th]eodcyninga
     3      [th]rym
     1' [dh]a
     2'   [ae][th]elingas
     3'      ellen

"The poet speaks of 'days gone by', of 'kings', and their 'might';
'then', of 'princes', and their 'strength'." Two things leap to the
eye. First, "[th]eodcyninga" does not stand alone in the poem; it
is part of the phrase "Gardena [th]eodcyninga", split by "in
geardagum" in a way that OE idiom readily allows, so the neat
parallelism disappears. Second, as recent exchanges on the net
have made clear, the parallelism requires a sense for "[dh]a"
which would not otherwise seem the likeliest; moreover it surely
requires "[dh]a" to be stressed, where the alliteration suggests
otherwise.

David supports his contention of careful deliberation of structure
by pointing out that if these three lines are divided by extreme
and mean ratio - by lines, by words, and by syllables - the division
in all cases falls neatly between the "halves". This appears more
impressive than it is. The line division, 2 and 1, is certainly as
close as it could get to mathematical extreme and mean (which is
more exactly 1.85 and 1.15), but since three lines cannot be
divided otherwise than 2 and 1 all that has effectively been
said is that the division occurs at a line-break. The word division,
8 and 5, is very close, but these are editorial words. The manuscript
clearly divides "[th]eod cyninga". It divides "gear dagum" too; this
could be held compensated for by its uniting of "ingear", but if
that is to be considered so must the uniting of "hu[th]a" in the
other half of the structure. If one is already convinced that the
words must divide by extreme and mean between the "halves" one
will of course simply feel confident that the editor has restored
the author's intention, but the prime evidence from the words is not
solid. The syllable division is good, but one notices that David
does not mention a letter division: there are 73 characters, which
divide by extreme and mean ratio at 45 and 28, putting the division
between the first "n" and the "o" of "gefrunon".

This passage, then, is far from the clear specimen one would like. 

David next proceeds to lines 4 to ll, which few will doubt form a
unified group, and a group with a clear internal structure. I would
describe it as tripartite, based on three words/phrases of time.
"Oft" introduces Scyld in his prime; "sy[dh][dh]an" goes back to his
time of weakness but the section then advances through his recovery;
"o[dh] [th][ae]t" returns us to the original time and presents
Scyld's power again, but viewed in the other direction, action
by surrounding peoples, not upon them. The final half-line appears
to be a coda, summing up the whole. There is this much manuscript
support for such a structure, that there is a point before "o[dh]
[th][ae]t" (as well as at the end of line 11). The manuscript, in
passing, seems to support treatment of "o[dh] [th][ae]t" as two
words, as in other cases where the second element is represented
by a barred thorn, in contrast to cases where it is spelt out.
This is David's display:

    B1a     Oft Scyld Scefing
      bi      monegum m[ae]g[th]um
       ii       meodosetla
       iii        egsode
       iv           [ae]rest wear[dh] feasceaft funden
      c               weox
      d                 under wolcnum
      d'                weor[dh]myndum
      c'              [th]ah .
      b'i     [ae]ghwylc
        ii      ymbsittendra
        iii       hyran scolde
        iv          gomban gyldan
      a'    [th][ae]t w[ae]s god cyning .

It will be seen that he views the passage as basically a chiasmus
(abcdd'c'b'a'), though a less tidy one than those in the St. John
passage, since the subsections of  b/b' are seen as related in
direct parallel, not reverse. I think it will also strike many
readers that whereas every pair of sections marked as equivalent
in St. John can be seen at a glance to be so, that is not the case
with a single one of the pairs here, even though there has here
been extensive pruning of distracting elements (such as the "ofteah"
which attaches to bii "meodosetla", while there is no equivalent
attached to b'ii "ymbsittendra") - no such pruning was required
in St. John. Of the pairs as presented, the least obviously
equivalent would seem to be bi and b'i, biv and b'iv. These David
justifies thus: "The poet refers ... to retainers in i, ... to
Scyld's destitution at first and his riches at last in iv ..."

Hardly "retainers" in i in any case, but to make b'i refer to the
same surrounding peoples as bi does "[th]ara ymbsittendra" has to
be added to the mere "[ae]ghwylc", thus absorbing b'ii, which
David needs as a distinct element to make a parallel with bii
based on the presence of the root "sit/set" in both. Also if he
had not pruned from bi the "scea[th]ena [th]reatum" which is a
clear structural parallel to "monegum m[ae]g[th]um", the
enormously greater weight of the complete bi than of b'i as
stated would thrust itself on the attention.  His explanation of
iv is highly selective in the aspects chosen to demonstrate
equivalence. The other uses of "feasceaft" in _Beowulf_ do not
suggest chief reference to lack of wealth, it is not at all clear
that the main sense of "gomban" is abundance of wealth, and the
close parallelism of b'iv with b'iii is absolutely not present
in biv and biii.

Perhaps the most serious way of all in which the structure has
been adjusted in David's display, one might almost say
reconstructed, is the removal of the important "he [th][ae]s
frofre gebad", which forms a parallel to the cd/d'c' phrases,
for it is vital to the structure as presented that cdd'c', with
its own little chiastic structure, should also be at the centre
of the main chiasmus, and re-insertion of "he [th][ae]s frofre
gebad" spoils that. David uses the phrase later, certainly,
together with two phrases that do appear in the display, in
presenting a wider structure that links lines 1-11 to lines
12-15, but if 1-11 is to be analysed for itself the phrase must
have its place at that level.

David does so analyse 1-11. With cdd'c' placed as the "crux", at
the centre of the main chiasmus, he is able to claim a numerical
centrality - not for it as a whole, however, but for its first
word: "The central twenty-first word ... is the beginning of the
crux of the chiasmus, _weox_." The twenty-first word is not in
fact the central one of a passage of 40 words (again, of course,
editorial words, including the disputable "o[dh][th][ae]t" as
one); what is in effect being said is that the passage balances
in respect of words provided all and only line 9 is taken as 
the central element, and counted in with the second half (note
that when central elements were counted in in St. John it was
with the first). David does not look to syllables or letters
here; with the same treatment of line 9 the syllables are
divided almost evenly, 39 and 38, the letters not so closely,
116 and 110. If of course "he [th][ae]s frofre gebad" is joined
to line 9 at the centre none of this remains. Support for cdd'c'
as crux is also claimed from the manuscript: "punctuation points
mark both the crux and the end". This time it is of course the 
end of the crux that is marked.

By this stage I was tending more and more to conclude that
David was certainly demonstrating extensive structural features
in _Beowulf_, using parallelism both direct and reversed (which
however nobody was doubting), but that as to a mathematical
basis for this structuring he was demonstrating only that if one
is convinced in advance that it must exist, it will always be
possible with a little snipping and stretching to fit one
mathematical scheme or another to whatever part of the poem
seems worth the effort.

I have tried to be scrupulously fair in my use of evidence; if
I have anywhere erred I beg correction from my colleagues. The
labour even so far has been considerable; for the present I must
move to other tasks. I hope others of us have also been looking
at David's important propositions, preferably continuing the work
further. I would be most grateful, and so I think would be the
scholarship of the subject, for well-based agreement with, or
rebuttal of, my provisional conclusions.

-- Duncan Macrae-Gibson (macg@abdn.ac.uk)

John -- Thank you. I hope that perhaps you, some at least of those
who repond, will feel they can do so on the net. What has happened
in the past when I have tried to refute some of David's analyses
is that (i) David himself has ignored me, (ii) I have had private
messages of support, (iii) Karen Foster has put on the net a
vigorous if rather imprecise posting in support of David's position
and condemning me for a mis-aimed and uncalled-for attack. The
impression to those merely reading net postings is one I am unhappy
about. -- Duncan Macrae-Gibson (macg@abdn.ac.uk) [and in fact this
time the debate became general. Some is saved in "goldsec"]
