First: yes, there should be prize for the 400th. Doesn't Mantovano have a
merchandizing department?
Second: I have been writing recently on the question of number patterns in
Vergil. Let me see if I can convince you, in not too many words, that
there are no Golden Ratios or Fibonacci-type patterns in Vergil.
The Fibonacci series is a series that generates each successive term by
adding together the two previous terms, like so:
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, etc.
There is not a single piece of evidence that the ancients knew about this
series. 'But what about Vergil?' Well, let's see.
As the terms of the series become very big, the ratio of one term to the
next approaches a specific value: 0.618034... (it is an irrational number).
Now, Euclid describes a thing called "the section in extreme and mean
ratio" (Elements, Bk. 6, def.3), which is formed when there exist
magnitudes x and y such that x is greater than y and the ratio of x to y is
the same as the ratio of x + y to x. The ratio of y to x, in this case,
works out to 0.618... 1:1.618... is the so-called 'golden ratio'.
G. LeGrelle ("Le premier livre des Georgicques: poeme pythagoricien." LEC
17: 139-235) says that in the first Georgic, what he calls the 'body' of
the poem - the whole minus the 42 line introduction and the 51.5 line
epilogue - is divided into two portions at line 203. What he calls the
'Works' section comes before line 203 (43-203) and what he calls the 'Days'
comes after (204-462.5). Now the ratio of the Days and the Body is about
the same as the ratio of the Works to the Days; both ratios are
approximately equal to 0.618. LeGrelle claimed that this meant Vergil was
incorporating the 'golden ratio' into his poetry.
If you take a look at your text, you can begin to see how arbitrary these
divisions are, but set that aside for a second.
Anyway, there is no Fibonacci sequence in Vergil, only a ratio between the
lengths of passages whose value approximates the 'golden ratio' - a ratio
whose value can be derived from the series Fibonacci discovered, but which
the ancients would have dealt with geometrically.
George Duckworth's book 'Structural Patterns and Proportions in Vergil's
Aeneid' (Ann Arbor 1962) extended LeGrelle's argument to the whole of the
Aeneid. Duckworth claims to have shown that there are hundreds (1048, to
be exact) of passages where, with a little artful cutting and pasting, one
can get sections that make up a 'golden ratio.'
Here are some problems:
1) How good are LeGrelle's and Duckworth's divisions? Consider one of
Duckworth's typical examples. Aen. 7.1-24: take 1-4 and add it to 10-20
(giving you 15), then take 5-9 and add it to 21-24 (giving you 9). The
ratio of 9 to 15 is .625 (close to .618, no?). Why break things up that
way? It seems more than a little arbitrary. Duckworth's only criteria for
defining sections is that they begin and end at (what we print as) sentence
breaks.
2) According to Duckworth, the whole poem, on scales large and small, is
structured with these ratios. What perceptable effect could this pattern
possibly have? Vergil has written all of his poem according to the
numerical pattern of hexameter verse, but at least hexameters can be
expressed of something, such as speed. And how are we supposed to detect
the pattern? Nothing in the text prompts us to look for the pattern, after
all. The only answer usually given to the question of detection is
something like, 'one senses it unconsciously', which is really no answer at
all.
3) Shouldn't one be suspicious when one finds the same 'golden ratio'
patterns appearing in authors like Catullus and Lucretius? And in the
Fables of LaFontaine? And in Duckworth's own text?! (as Dalzell noted in
a review: Phoenix 17: 314-6)
Vergil does do some clever things with numbers. They are hardly as
elaborate as the patterns that LeGrelle/Duckworth talk about, however. For
example, Maecenas' name appears in the 2nd, 41st, 41st, and 2nd lines,
respectively, of the four Georgics. Why? No one knows. Next, as Richard
Thomas and Ruth Scodel first pointed out, the word "Euphrates" appears six
lines from the end of Geo.1, Geo. 4, and Aen. 8. Why? Well, in
Callimachus' Hymn to Apollo, the "Assyrian river" i.e. the Euphrates, also
appears six lines from the end. Then, there are some nice, simple
numerical symmetries in the songs of the Eclogues: see the introductory
remarks to Clausen's commentary on Ecl. 3.
*****
There is also a large, simple, and striking numerical ring pattern nested
in Geo. 4.116-227 - Vergil even alludes to its presence. That, at any
rate, is what I have argued in my dissertation. I would be happy to point
it out to anyone who is interested. (If you are, please email me, not the
list: [EMAIL PROTECTED] I will send you a four-page attachment.)
Phil Thibodeau
>2. This morning I rec'd the following from a producer at BBC Radio Scotland:
>
>"I am producing a half hour science documentary on the mathematician
>Fibonacci and the Fibonacci number sequence for BBC Radio Scotland. One of
>my colleagues has heard that the Fibonacci sequence occurs in the poems of
>Vergil - which were obviously written long before the time of Fibonacci.
>I wondered if you knew anything about this or could steer me to some-one who
>might?"
>
>Anyone know anything about this? Duckworth found the Golden Section
>everywhere in Virgil's poetry, but I don't recall anything about the
>Fibonacci sequence. Otfried?
>
>-----------------------------------------------------------------------
>David Wilson-Okamura http://www.virgil.org [EMAIL PROTECTED]
>University of Chicago Online Virgil discussion, bibliography & links
>-----------------------------------------------------------------------
-----------------------------------------------------------------------
To leave the Mantovano mailing list at any time, do NOT hit reply.
Instead, send email to [EMAIL PROTECTED] with the message
"unsubscribe mantovano" in the body (omitting the quotation marks). You
can also unsubscribe at http://virgil.org/mantovano/mantovano.htm#unsub
