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Tuesday, 29 December 2020
Monday, 28 December 2020
The White Goddess, and Apollo's Golden Mean
Date: Sun, 25 Apr 1999 13:47:10 -0400 (EDT)
From: ......@westerncanon.com
Subject: Lecture Hall Message 18
Dated : April 25, 1999 at 13:47:09
Subject: Re: The White Goddess
>I am a junior at Malone College in Canton, OH and I am taking
>Modern British Writers. For our final project, the professor has
>asked us to analyze a poet and his works. My friend and I are going
>to do a type of interview situation, where he is Graves and I am
>the interviewer. We want to focus specifically on "The White
Goddess"
>and "Succubus." If anybody has any information or comments on
either
>of these poems, please share them with me. Also, share what types of
>questions you might ask Graves about these particular poems.
Nicole,
You have given yourselves a very tall order by focussing on
two important poems by Graves, the first of which is of central importance to
the second part of his life. I can however give you a number of pointers about
"The White Goddess" which might help you to narrow down your target.
Another of Graves important poems, "To Juan at the
Winter Solstice", begins with the lines:
There is one story and one story only/That will prove worth your telling
From the mid-forties onwards, much of Graves' prose and
poetry was shaped by this belief. Interestingly there is a passage in "The
Shout", a short story written in 1924, which prefigures this approach:
"My story is true", he said, "every word of
it. Or, when I say that my story is 'true'", I mean at least that I am
telling it in a new way. It is always the same story, but I sometimes vary the
climax and even recast the characters. Variation keeps it fresh and therefore
true".
Graves' stated opinions about the White Goddess, which
resulted in the poem and the book of the same name, should be looked at the
same way. Both Graves' prose and poetry attempt to retell his understanding of
a truth by recasting detail and character. The specific reference is (according
to Graves) always the same, but the incidentals change and the details blur and
intertwine. The poem "The Clipped Stater" for example, can be read in
terms of its references to Alexander, which are explicit, or to the phenomenon
of the Incarnation of Christ, or even to the transformation of T. E. Lawrence
into "Aircraftsman Shaw". In fact it should be read in terms of (at
least) all three: if there is "one story and one story only", the
real focus of Graves' interest is beyond the incidental details of the poem,
and the blurring and braiding of detail allows us to look at the real subject,
as it were, slantwise.
The first two lines of "The White Goddess" [the
version in "Selected Poems", ed. Paul O'Prey, 1986] express Graves'
view that his subject is one uncomfortable to the reasoning mind: and thus a
subject which the dominant forces in European civilization over at least the
past two and a half thousand years have tried to reject ("All Saints
revile her"). Very quickly however (line 3) the poem is about a voyage in
search of the Goddess: this is particularly interesting as Graves' views on
ancient matriarchy surfaced first in "The Golden Fleece" [pub 1944]
(US: "Hercules, My Shipmate" [pub 1945]), and Graves' was working on
his translation of the story of the voyage of the Argo immediately before
writing his monumental study: "The White Goddess" (to which a version
of the poem is prefaced "in dedication"). The sailors sail to find
her "in scorn" of those "ruled by the God Apollo's golden mean".
This might be read as a re-interpretation of the real mission of the Argo, or a
metaphor of Graves' own studies, or more broadly as a characterization of any
attempt to escape from (as Graves believed) the rigid, plodding patterns of
Cartesian thought sanctioned as "valid" by our civilization (the
version prefaced to "The White Goddess" speaks in the first person).
The second stanza continues the speaker's identification
with the crew of the ship:
It was a virtue not to stay/To go our headstrong and heroic way
The following three lines describe the extremes to which
they are prepared to go to find the elusive Goddess. Paradoxically she is then
given a precise physical description, clear enough to pick her out of a crowd.
That it might not be wholly healthy to actually encounter her is suggested by
the striking description of her brow as: "white as any leper's".
In the third stanza it is clear that there have been (and
will be) good times for the Goddess, when all recognise her and the
universality of her significance:
The green sap of spring in the young wood astir/Will celebrate the Mountain
Mother
However the crew of the ship are gifted to recognise,
"even in November", her "nakedly worn magnificence". Thus
the ability to discern the Goddess in her elusiveness is given more importance by
Graves than her mere celebration. Here Graves alludes to the different
qualities required of devotees of the Goddess in secular (i.e., modern) times,
to those qualities required in times when her reality is taken for granted.
The penultimate line reveals that the sailors have
undertaken the voyage, not in ignorance, but in full knowledge of the dangers:
since they have experienced "cruelty and past betrayal". They have
met her before, in one form or another. They are also, like those in love:
Heedless of where the next bright bolt may fall.
"Bolts" are of course more commonly associated in
Greek Mythology with Zeus, king of the gods. But Graves regarded Zeus as a
usurper, and believed that real power belonged to the Goddess (See for example
"The Greek Myths" 9.7: Zeus and Metis, where Graves quotes Jane
Harrison who described the story of Athene's birth from Zeus's head as 'a
desperate theological expedient to rid her of her matriarchal conditions').
Graves more and more came to regard the White Goddess as the
real source of inspiration for poets, so that he began to view poetry written
for any other reason as fakery. In his study "The White Goddess" he
describes her in similar terms to those used in the poem:
...a lovely, slender woman with a hooked nose, deathly pale
face, lips red as rowan-berries, startlingly blue eyes and long fair hair; she
will suddenly transform herself into sow, mare, bitch, vixen, she-ass, weasel,
serpent, owl, she-wolf, tigress, mermaid or loathsome hag. Her names and titles
are innumerable. ... I cannot think of any true poet from Homer onwards who has
not independently recorded his experience of her. The test of a poet's vision,
one might say, is the accuracy of his portrayal of the White Goddess... The
reason why the hairs stand on end, the eyes water, the throat is constricted,
the skin crawls and a shiver runs down the spine when one writes or reads a
true poem is that a true poem is necessarily an invocation of the White
Goddess, or Muse, the Mother of All Living... [TWG: Ch. One, "Poets and
Gleemen"]
Hence it is that Graves' concept of the White Goddess is
entwined with the craft of poetry: poetry is an invocation of the Goddess, and
to write "true poetry" the poet has to love someone in whom the
Goddess temporarily manifests. Graves' book on the White Goddess has to be read
therefore as a braid, made up of a historical reconstruction of poetic grammar,
as well as his personal experience of the Goddess in his association with Laura
Riding, and possibly also his mother, Amalie von Ranke Graves.
The Graves Interview:
You are going to have to do a lot of research to do this
properly! You can find most of what you need in three books: Robert Graves
"The White Goddess" for Graves own account of his ideas; Richard
Perceval Graves: "Robert Graves and the White Goddess 1940-1985" [pub
1995]; and "Robert Graves: The Years with Laura Riding 1926-1940"
[pub 1990]: these last two volumes give the relevant details about Graves'
collaboration with Laura Riding, and his later muse poetry. Other information
about Graves' picture of ancient matriarchy can be found in his novel
"King Jesus" [pub 1946] and "Seven Days in New Crete" [pub
1949] (US "Watch the North Wind Rise"). Some useful critical remarks
about the thesis of "The White Goddess" can be found in Martin
Seymour-Smith's "Robert Graves: His Life and Work" [1982; expanded
edition pub 1995]
Saturday, 26 December 2020
Wednesday, 23 December 2020
The Wider Scope of Ancient Mathematics (letter to an American Scholar)
Avebury Circle, photographed in 2001
Dear.....,
Hi. I became aware of your short book [.......................] relatively recently. I wish I’d known it earlier.
I have a strong interest in the idea and function of the concept of limit in antiquity. My main object of study at UCL was ancient Assyria (mostly the text corpus). Like the Greeks, they had a strong interest in the idea of limit, which is illustrated on the walls of their buildings, and is also represented in their images of the sacred tree. Limit also serves an important function in setting up their gods in heaven (I’ve written about both Assyrian and Babylonian rituals for this).
This tells us something of the actual basis of Mesopotamian religion, which has an origin which is quite different from what we imagine.
Essentially ancient religions are transcendentalist in nature. In other words, they have their origins in a focus on abstract conceptions (limit, infinity, infinite series,completion, totality, etc). Which makes a nonsense of the idea that the Greeks were the first to grapple with sophisticated abstract thought. Clement of Alexandria created a list of civilizations which practised philosophy, and added the Greeks as the* last* to adopt the practice of philosophy.
Since you might be interested in the wider scope of ancient mathematics, I am writing to you to point you at a couple of articles which illustrate that these concerns were a feature of building projects in Neolithic Britain also. The Horus numbers are there, as the basis of establishing Euler’s number via a geometric construction. Euler’s number being the final result of a convergent infinite series.
Did they get their mathematics from Egypt, or did they develop them themselves? I have no idea. Why Euler’s number? It’s a mathematical stand-in for the extreme limit, which is infinity.
‘At Reality’s Edge’
https://shrineinthesea.blogspot.com/2020/12/at-realitys-edge.html?spref=tw%20%20# (Short article)
‘The Mathematical Origins of the Megalithic Yard’
http://shrineinthesea.blogspot.com/2020/02/the-mathematical-origins-of-megalithic.html (Long article)
Best regards,
Thomas Yaeger
At Reality's Edge
[Some notes I made while I was writing up The Mathematical Origins of the Megalithic Yard in early 2020. The notes conclude with some observations of the importance of the idea of limit in Mesopotamia, and its connection with the Assyrian Sacred Tree, and their notion of kingship. I could have finished up with a short discussion of Egyptian interest in the idea of limit, particularly since we know (from the Rhind Papyrus) that they used the same method of calculation of Euler's number as in ancient Britain. That discussion with follow later.]
***
It has been twenty two days since I started to write up the
article ‘The Mathematical Origins of the Megalithic Yard’ (mid February 2020).
In this article, I suggested that those who designed the. circles came to the
idea of the megalithic yard of 2.72 feet as the consequence of an interest in
infinite series, and particularly those which approach a limit. The most
important of these limits is the one which is known as Euler’s number, which, when rounded up from 2.7218… is 2.72.
This limit was first noticed in relatively modern times in
the context of the calculation of compound interest, but the number, and the
process by which it is arrived at, can be found in many other contexts.
Effectively, the number (when worked out to thousands of
places), is the number as it would be found at infinity. So it can stand as an
indicator of ultimate limit and of infinity. It is associated with the idea of
‘one’, as I’ve discussed in the article, and also as an irrational equivalent
of one, which is a rational whole number.
An irrational counterpart to ‘one’, in a proto-pythagorean
community, would have been easy to understand as belonging to a world beyond
this one – i.e., a transcendent reality which is more perfect than this world,
which is full of irrationality and measures which are incommensurable. The
number may have been understood as being irrational to us because it is being
represented in our finite world, and not irrational.
It also stood for the edge of our reality, and therefore
would have signified the possibility of a joining between the transcendent
reality, and our world of physical reality. Finding ways in which the worlds
could be joined, and the incommensurate made commensurate, seems to have been a
major preoccupation in the Neolithic, as it was also to philosophers and
mathematicians in Greece during the second half of the first millennium BCE.
After I finished the article, I wondered how difficult it is
to construct a series which will arrive at Euler’s number, how it might have
been done, and how long it would take to come to the result.
A little research showed that there were many ways to
construct suitable series of numbers, and a geometric calculation could produce
a reasonable approximation reasonably quickly, without enormous calculations.
We don’t know for
certain what base was used for calculations in the British Neolithic, but they
were certainly aware of base 10, since they used powers of ten in their
construction (ie, instead of a 3,4,5 triangle, they would sometimes use 30,40,
50 as their measures, knowing that the sides would be similarly commensurate
after squaring). If they were using the English foot as their basic measure, it
is likely they were counting to base 12 (ie, in duodecimal). But the
construction of a series only requires whole numbers, arranged as fractions.
1 + 1/100000)^100000 =
2.7182682371923
100,000 is a lot of iterations, so it is unlikely that the
determination was done in this way. The process will result in Euler’s number
with any consistently generated series.
It can be done geometrically, which is much more practical,
and is probably the technique which was used in the Neolithic. Using a sequence
such as:
1/2 + 1/4
+ 1//8 +
1/16 + ... = 1
Those who generated such a geometrical figure did so knowing that the series converged on a limit from observing the initial results. What they wanted was to find out a reasonably accurate value for the limit itself. The square could therefore be of any size (read as the value ‘one’), and might well have been created in a large field, with the fractions indicated by small stones.
I’ve written elsewhere about the importance given to limits
and boundaries in ancient Assyria and Babylonia, particularly in connection
with sites connected with the gods, and the rituals for the installation of the
gods in Heaven. Sometimes aspects of the design of the Assyrian Sacred Tree
were unwrapped, and represented on pavings as lotuses, alternately open and
closed. Which is a way of indicating at these edge points that both
possibilities are open, and even perhaps that opposing states are commensurate
with each other in infinity.
It has already been identified that the Sacred Tree represents a form of limit, and consequently of the nature of divinity which has its true existence in a world beyond the constraints of finitude. The design of the alternating lotuses also was used to separate the registers of images adjoining the collosal Lamassu statues which guarded the entrances of royal palaces. There was an image of the sacred tree, with two winged genies behind Assurbanipal’s throne, which seems to indicate that the king was understood to embody the transcendent reality which lies behind the world of the here and now.[the identification of the king with the divine reality appears in various royal letters] He is the perfect man, and the very image of God
[March 8, 2020]
Wednesday, 9 December 2020
Revolt in Athens in the late Seventh Century BCE (A letter to SemprePhi)
At 19:12 29/11/2020, Thomas Yaeger wrote:
[.......]
Hi. I didn't mean to do any work on the DoP [Death of Pan] today, but it was a quiet Sunday,
and I decided in the morning to explore expanding the content headings into
sections. This is a much more abstract discussion than in the earlier books,
but that is how imagined it would be. So I need a lot of references to existing
articles and chapters, enabling readers to have access to real detail. The
article 'An Appetite for Knowledge' will be the basis of this, but much expanded.
So far I've argued that a great deal of intellectual and philosophical input to
Greek civilization comes from Mesopotamia and Egypt, which is the case. But
I've been arguing in terms of a sixth century BCE input, via Pythagoras, just
to open the door to an acceptance of the possibility of an east-west
transmission. Plato's determination to get hold of the three volumes concerning
Pythagorean doctrine offered for sale by Philolaus, tells us that he understood
that they contained information useful for the understanding of cult doctrine
in Greece.Something had been lost along the way.
Martin Bernal argued, on the basis of comparisons of Egyptian and Greek words,
that the Greek vocabulary was heavily indebted to Egyptian, and that the
borrowings probably dated back to the mid-2nd millennium, when there were major
population movements from Egypt and North Africa. Some of those ended up in the
Peloponnese and in Anatolia. I think that he is right about that line of
transmission.
But there is a third route of transmission. After the second millennium, but
before Pythagoras. I mentioned it in a chapter which didn't make it into SHB
for one reason and another, but which has since been published. There is an
obscure quote preserved in Eusebius, which says that the Assyrian king
Sennacherib captured Athens. This would have been around 701-700 BCE. Any
classicist reading that will find it deeply shocking. Generally I try not to
mention it.
[……………] This story is [likely to be] true because it explains a peculiarity in
Sennacherib's campaign records - half of them are missing from the archives in
Assyria. The quotation goes on to mention that Sennacherib built a temple in
Athens, which he filled with brazen statues, and that his exploits were
recorded in cuneiform on the statues. Now we know why they were missing.
It takes a while to build a temple, and to fill it with brazen statues, so
Sennacherib and his troops were there for a while.
I sent the completed chapter to Simo Parpola, and asked if he had anything else
to add to the pot. He replied *the same day* with an article he'd contributed
to a volume of conference proceedings in 2004, in which he was able to trace
the westward expansion of the Assyrians across Anatolia, from their records,
all the way to Ionia, which of course was part of greater Greece at this time.
They were always aiming for Greece. He didn't know they made the mainland. But
they did.
How long were the Assyrians in Athens, and in Attica? I guessed five years or
so. But I started to look for some kind of end point to the Assyrian
occupation. I could find nothing. Parpola had pointed out in his article
that a number of features of Greek political and social organisation looked
like borrowings from Assyrian organisation, such as naming eponyms for each
year, and the institution of Archons. So I looked further, and found an
interesting account of a tyrants revolt in 632 BCE (revolt of Cilon). The Greeks
recorded tyrants often with very little detail. They were tyrants if they
opposed the established authorities. The detail we have is that conspirators
were hunted down by the Archons and killed (their grave site has been
excavated, and it isn't pretty - the skeletons are in manacles and their mouths
have been stopped up with stones).
The date is significant. The last important king of Assyria was Ashurbanipal,
who disappears entirely from the record in 632-1 BCE (the empire staggered on
till about 609). Possibly as the result of a palace revolt. We don't know. But
this would be the right time to rise up against a hated occupying force.
If the revolt and the collapse of the Assyrian empire are connected, this would
mean that the Assyrians were in Athens for nearly *seventy
years.*
[..........................................................]
I'll deal with the Assyrian occupation in a couple of papers further down the
line.
Best, Thomas
Tuesday, 8 December 2020
Mathematics and Calculation in Antiquity (letter to a Cambridge Scholar)
To: .............cam.ac.uk
From: thomas yaeger
Subject: Mathematics and Calculation in Antiquity
Dear........,
I’m supplying here the address of an article which may be of interest to you, since a) you are interested in early examples of sophisticated human cognition, and also b) in examples of ideas, languages and cultures being transmitted west to east in deep antiquity. This article addresses both of these areas.
The article took seven years before it assumed its current form. It started off as a relatively minor component in a project on the presence of abstract ideas in the ANE and the Levant before the Greeks, which resulted in my book, ‘The Sacred History of Being’ (2015).
What the article argues is that the mathematics which can be found in the vast majority of megalithic rings in Britain, France and elsewhere, show that builders had a grasp of infinite series and Euler’s number from very early on (late 4th mill. BCE onwards, up until around 1400 BCE, which is when they seem to have stopped constructing them).
The pattern of their distribution around Europe and the Mediterranean suggests the original builders travelled westwards, and then north to Britain.
One of the reasons why no-one has considered the presence of Euler’s number in these structures (2.72, supposedly first discovered by Bernoulli), is of course, why would they know this number? It is also assumed that the number would have been too hard to calculate in such ancient times, even if they did have a loose grasp of infinite series.
This is not actually the case – it can be established geometrically with a relatively small number of iterations (less than a dozen). Interestingly the procedure for doing this can be found in the Rhind Papyrus, which dates from around the 17th century BCE, but was originally compiled earlier. In a publication issued by the British Museum in the late eighties, Gay Robins and her husband identified that the Egyptians were working with an understanding of infinite series. And showed the Egyptian diagram, illustrating how it was done.
The geometric process for establishing Euler’s number can be done on the ground, using small stones. I explored the Avebury complex pretty thoroughly in 2001 and 2002, and noticed brickish sized stones collected together, on the edge of one of the circles, almost lost in the grass. I had no idea why they might be there at the time, but they may have been what they used in the geometric construction . Effectively, the small stones are telling us what the whole structure is for.
The article is at:
http://shrineinthesea.blogspot.com/2020/02/the-mathematical-origins-of-megalithic.html
The short book on the Rhind Papyrus is at:
https://www.amazon.co.uk/Rhind-Mathematical-Papyrus-Ancient-Egyptian/dp/0714109444
My book is available from CUL (and elsewhere) in eBook format.
[text correction, December23, 2020]
Best regards, Thomas Yaeger.
December 6, 2020.
Best regards, Thomas Yaeger.
December 6, 2020.
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