Landforms are past (or present) interpretations within a landscape which enable the land to represent meanings found within astronomical time or ideas about the ordering within any centre and its environs. There is evidence for the widespread use of landforms in prehistoric and ancient cultures.
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17 July 2017
The fields of ancient Greece were organised in a familiar way: strips of land in which a plough could prepare land for arable planting. Known in various languages as furlong, runrig, Fr. journel, G. machen etc, and in Greece there was a nominal length for arable strips which came to be associated with the metrological unit of 600 feet called a stadia. The length of foot used was systematically varied from the foot we use today, using highly disciplined variations (called modules); each module a numeric ratio of the Greek module, whose root foot was the English foot [Neal, 2000]. These modules are found employed throughout the ancient world, lengthening or reducing lengths such as the stadia, to suit geometrical problems; such as the division of land into fields (figure 1). The English furlong is a stadia of the Saxon module whose root value is 1.1 feet, hence it is 660 feet long and remains one eighth of the English mile (5280 feet), the mile being defined in ancient metrology as 5000 feet.
Figure 1 The land area of an acre x 15 considered the amount of land tillable by one ox in a ploughing season
The Distribution of Land
The word stadia became implicit in our sports stadiums because ancient Greeks used field areas as racetracks for their competitions. Their greatest games was held at Olympia’s racetrack, site of a pan-Hellenic Games now re-instituted (since1886) as today’s Olympic Games. Whilst the modern Olympics are competitions between states, racing was mythologically significant in ancient Greece. The original stadia were simply field-shaped runways; to an endpoint about a furlong (or "fur-rows long") away. Later two straight tracks were joined together by a two semi-circles (or sperium) allowing indefinite lengths of race, and giving us the modern type of stadium.
Figure 2 The Racetrack at Olympia
A 600 feet long field became a racetrack by turning it into a wide road of fine hard standing, around 100 feet wide (figure 2). Low stone ridges sometimes marked the starting, ending and intermediate lines and these starting and ending ridges have allowed exact lengths to be measured (John Neal. 225). In both arable and running strips there were boundary stones at the corners and sometimes balks bounding the perimeter. Where rectangles could not fit marginal land areas, half rectangles and other rectilinear shapes were used because their areas could be calculated more easily. Most arable strips started as simple rectangles and were later adjusted, using rectangular geometry. This allowed for split inheritance within clan families. Fifth century Greek historian Herodotus proposed geometry came about in order to measure the field areas of Egypt and it was certainly used there in the building of their temples.
Figure 3 from Thomson. 1949.
In ancient Greece the distribution of land between families, amongst other matters, were decided by lot - hence our word allotment and parking lot. A clan or village, would quantify the known land area as strips and then, "by fate" families would pull notes or objects, representing individual strips of land (their lots), out of a container or play dice for them (figure 3). When allocated in this way, family land was scattered amongst that of other families and, by using this method, the gods were seen as giving the land through "chance" or fate. Greek field games were dedicated to the gods and some arable strips were allocated "to the gods"; and it is for this reason that the dimensions of racing tracks came to have the same format as an agricultural field were given. In any case, agricultural fields belonging to a village could become "playing fields", when put to pasture. Fields given to the gods could also become sacred spaces such as groves and temples which, from at least 800 BC, were evolving to suit the arable dimensionality of allotted fields.
Figure 4 Model of early Heraion Temple House, Argive.
Jeffrey M. Hurwit wrote on the probable evolution of the Greek temple and in particular the Haraion on the Island of Samos [Hurwit. 1985. 75-77]. Small shrines to the god would employ a normal dwelling-like temple house (figure 4). In the case of the Heraion of Samos the house was elongated to 100 feet long of common Egyptian feet, and later a peristyle of columns around the building using wooden tree trunks (figure 5), perhaps echoing the sacred grove, belonging to the world of the gods. A statue of the god was placed, looking towards the entrance from the rear. Known as a "hundred-footer" or Hekatompedon, this became the norm for such rectilinear temples, the Parthenon at Athens being one hundred feet in width (of 81/80 feet [Berriman, 117-9]) rather than a length of 100 feet. (see also my analysis of the Haraion).
Figure 5 The Heraion of Samos: 8th century BC evolution of the peristyle temple [Hurwit. 1985. 76]
Whatever other symbolisms were in play, the racetrack and the temple were fitting into the nominal dimensionality of arable land distributed by lot between families belonging to village communities and their gods. All three forms of land use display units of length belonging to an exact metrological system, parts of which are relevant today (Neal. 2000 and 2016). That such a system of exact measures existed in the ancient world was enthusiastically explored by nineteenth-century scholars but suppressed by twentieth-century scholarship. Metrology is as if forgotten by later generations, perhaps avoided by twenty-first century academics because it could require history to be somewhat rewritten.
Symbols of the Gods
If fields, racetracks and temples were related structures in ancient Greece, can their design be assumed arbitrary? Why did racetracks come to be associated with the gods and why were idols of goddesses placed within temples sharing the rectangular format found in fields; for example: Hera, in the case of the Heraion, and Athena in that of the Parthenon. These goddesses appear to have arisen out of regional agricultural cults, appropriate to fields, fertility and the plough, whilst Greek races came to be seen as something entirely masculine.
Figure 6 The Pelopenese
The Pelloponese racetracks of Olympia and Epidauros, southwest of Athens, have a sacred setting. Both face mountains to the northeast, in the general direction of the midsummer sunrise: in fact 20 degrees north of east, rather than to the midsummer solstice sunrise on a flat horizon which is 30 degrees north of east. They could be aligned in common for various reasons:
1. A sacred hill or distant mountain, raising the horizon, caused the midsummer sun to rise further south.
2. Epidaurus could have sought to imitate Olympia in this respect.
3. Games might have been linked to the sun rising from behind the hill above the end of the racetrack.
The Olympic games came to be held every fourth year, the time taken for the sun to reappear at exactly the same place on the horizon, whether raised or not, because of the quarter day extra each solar year. This loosely ties it to a solar calendar in which every four years there are 365 x 4 = 1460 plus one full day. I say that such a solar period can be loosely achieved since by observing the sun rising at exactly the same marker on the horizon every four years, 1461 days have passed and hence four solar years.
Figure 7 Common alignment of Epidauros and Olympia as 20 degrees north of east
It seems likely that societies using a loose solar calendar of four years would also have been observing the helical rising of the zodiacal constellations. This, as the name suggests, observes the constellation rising above the mountains in the north east, before dawn and at the solstice; this would have been Gemini or "the twins". At the feet of the twins lies Orion, still submerged below the celestial equator (zero degrees declination) due to the precession of the Equinoxes. In many traditions, the barley or corn god dies but is resurrected through his seed form, providing an agricultural metaphor for the eternal struggle between order and chaos, seen in periods of relative light and darkness within the year. And the twins are often shown engaged in or associated with competitive sports.
Figure 8 The location of the MSSR sun (altitude 6.5 degrees) at local sunrise for Olympia racetrack. At dawn on the true horizon, the Gemini twins stand above the Hill as symbol of the Games. At Epidaurus racetrack, the sunrise is later (altitude 8.625 degrees) to similar effect.
I therefore propose that around 800 BC Gemini was known by its helical rising before the midsummer point of the Ecliptic, within a loose solar calendar, and that a sacred hill enabled that constellation to appear at dawn above the hill. The most familiar myth of the celestial twins lives on in the Greek names of Gemini's brightest stars: a semi-divine Castor and a divine Pollux. The inequality of the twins is an ancient theme, first recorded 5000 years ago in the characters of a Sumerian king Gilgamesh (two-thirds divine) and "wild man" or hunter Enkidu (one-third divine), in the epic tale Gilgamesh. At its heart was the theme of competition between men born to a world in transition, from hunting and gathering, to the neolithic pastoralism established by the end of the Age of Gemini in Mesopotamia.
"The Boxers" from Akrotiri image: Carole Raddato from FRANKFURT, Germany [CC BY-SA 2.0 (http://creativecommons.org/licenses/by-sa/2.0)], via Wikimedia Commons
When the Bronze Age collapsed suddenly around 1200 BC, cultures were re-integrated by iron age tribes. At the time of the Greek racetracks, agriculture was losing its matrilineal roots due to patrilineal Indo-European tribes, most notably the Dorians. Conquest often left fields, communities and habits intact, with some religious and economic changes. This explains the gender ambiguities and naming anomalies and found in the Greek myths; such as that Zeus is clearly an Indo-European name whilst Hera local and, more naturally, the wife of the hero Herakles: "Her temple at Olympia, the oldest on the site, cannot be dissociated from the tradition that the Games were founded by the Argive Herakles " (Thomson. 1949. 281-2.). Hera has no children by Zeus, who came to dominate the Olympia racetrack and religious complex. Instead she gives a virgin birth (parthenogenesis) to Hephaistos the Smith, who later relieves Zeus of his "headache" (having swallowed matriarchal goddess Metis). Splitting Zeus' head open with his axe reveals Athena: a transformed snake goddess, by another parthenogenesis. The goddess Athena had come from Troy, and her palladion (cult image) said to protect Troy. It survived Troy’s destruction and was taken to Athens, and later to Rome. Athena appears on the cap of Zeus, just as the Minoan serpent goddess had a cat on her cap.
Figure 7 (left) Serpent Goddess, Herakleion Museum, case 50, 63 Image: Richard Heath (right) from George Thomson, 1949
Traditions of the Twins
The Maya of Mesoamerica had Hero Twins, whose father was the maise (corn) god Hun Hunahpu (Diane Wirth, 2003), probably the constellation Orion below the twin's feet . The twins defeat the Lords of Death (who killed their father) by dying then to be reborn, rather like the English story of John Barleycorn. The story of the twins relates to many other myths of resurrection, and Minoan Crete knew the story of Osiris (Orion), his brother Set who killed him and of his son Horus who defeats Set. The Pharaoh is Horus reborn and it is evidently the competition between two principles, inherent to the universe, which can be expressed in competitive sport and war.
Figure 8 [Wirth. 2003]
A god who must die only to be reborn is metaphorically presented in three ways: the resurrection of life within the arable field, the heroism of competition presented on the racetrack, the fertility of the young mother goddess who brings forth the twins: so as to link fields, racetracks and temples to the goddess. Two genders were being expressed and celebrated in the Greek fields given over to the gods: racetracks expressive of a divine contest and temples to the matriarchal goddesses expressive of fertility and new life.
Figure 9 Mother Goddess and twins
Herwit, Jeffrey M. The Art and Culture of Early Greece, 1100-480 B.C.. Cornell: Ithaca 1985.
All DoneWith Mirrors. Secret Academy: London 2000.
Ancient Metrology: vol. 1: A NUMERICAL CODE. Squeeze Press 2016. 225-243, analyses some of the stadia that can still be measured, most in the Peloponnese, in terms of ancient metrology.
Thomson, George. The Prehistoric Aegean. Lawrence & Wishart: London 1949.
Wirth, Diane E. PARALLELS: Mesoamerican and Ancient Middle Eastern Traditions. Stonecliffe: Utah 2003. see Chapter Two.
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In researching the Minoan civilization of Crete (2nd millennium BC) I have been studying the anthropology of tribal groups focused around women**. It is a surprisingly rich and interesting subject which has found itself in a turf war with archaeology. Archaeologists study the past "through the spade" whilst anthropologists study living tribal groups. On occasion, studies of the sexual organization of human groups can be seen to bear upon ancient myths and hence on the social organization of tribes from the late Stone Age onwards. Perhaps archaeology has not taken studies of tribal organization to heart because they involve alternative modes of sexual reproduction, of ownership and belonging. The myths, iconography and legends of first millennium BC Mediterranean cultures indicate that human groups always organize themselves on two principles: what they have to do to eat and how the genders become organized for that work and sexual reproduction.
** For this I returned to William Sullivan's The Secret of the Incas ,
and found the extraordinary The Prehistoric Aegean by George Thomson
In the landforms of Iceland we see an unusually self conscious preoccupation of a new land, to establish its foundation myths alongside circular landforms with a numerical structure. In that case 36 godar were defined, commensurate with our 360 degrees within a circle, each then containing ten degrees. If the oak leafed decagon of west-southern Britain is considered similar, its divisions contain 36 degrees so that the two circular structures are complementary within a shared scheme of 360 degrees, a system of division as old as the Sumerians of 3000 BC.
John Michell (Twelve-Tribe Nations) found a widely distributed twelve-tribe tradition "from Iceland to Madagascar, from Europe through the ancient East to America" - and the most natural cause might be found within the tribal politics of its prior human groupings. That is, human groups may have an invariant preference for order according to the divisions natural to its early gens (breeding groups) which can, according to taboo, intermarry. These groups, transformed into a state with a leader and specialist institutions, then manifest the pre-existing notion of tribal divisions geographically.
The manner in which breeding groups organize is thought to arise by splitting into two parts when a group gets large enough. Gens grow and subdivide and then, according to their taboos, every gens has its own animal or other badge with which the gens becomes identifiable. Depending on whether hunting or pastoralism is primary, it may be the women whose lineage defines the child (men must live in the woman's tribe) whilst in pastoralism the reverse is true (women must live in the man's tribe). Farming tends towards monogamy since man and woman can then work together - our agricultural norm of marriage; in difficulty since husband and wife rarely farm and sexual taboos no longer regulate society. The evidence for all of this can be found in the vocabulary of human groups where familial relationships are sometimes very detailed whilst some terms, such as uncle or grandmother, are surprisingly broad in scope and hence ambiguous.
This sub-division of small tribal groups, there for the purpose of variety in breeding, inherently leads to more groups than are easily manageable through a simple confederation on one level. Complexity also arises when larger groups of gens interact with other large groups within the landscape. Larger groups can develop trade with each other, encouraging specialization within villages and towns. There can be surpluses and there would be a reaching out to other groups to exchange these for other goods. But then one has to see how technologies like metal are operating and how weapon creation is complementary with trade: it can seem easier to absorb neighbors rather than trade with them.
Sexual taboos used animal and plant badges to identify members of a genetic group, these badges often involving magical rites. Some badges appear to have survived and informed now-familiar religious icons, such as different forms of the goddess first evolved by taboo groups. Symbolic frameworks emerged out of taboo, giving inter-breeding groups foundation myths and religious notions. Any symbolic structuring of a tribe would be informed by the prior numeracy emerging from badged sub-groups, in order to form an idealized map as a framework for administrating a manageable number of parts, into ten or twelve parts - in order to act with common purpose. The nation-building process would be dividing an expanse of land into an integrated number of regions like the spokes of a wheel, as was presented in Arthur's myth of a round table of knights. Groups falling within a given region then belong to that region, which has its own center.
Because of its long and complex history, Britain is not divided or mapped like this. In any case, a regular structure would not fit it as a whole island and in fact the white-leafed decagon is about as big a regular circle one could have in Britain. If such structures arrived in the first flush of expansion by tribal groups (by coalescence of naturally dividing breeding groups) then regularity in division of a circular structure might be a simple and hence attractive decision, graspable by the pre-existing familial mind of all the tribe members and un-requiring of the complex mapping found in present day printed maps. Directions from the center locate a tribes regional affiliation without a map. Such a structure is attractive also to autocratic or bureaucratic needs, whilst integrating prior mythic or religious structures, now relating to the overall pattern - as occurred in the establishment of Iceland.
The people of the North appear to have preferred organization according to twelve, as is seen in Iceland etc. and this may relate to an Indo-Europeans desire to incorporate prime number three rather than prime number five. In reading George Thomson's description of the Roman state, one sees that units of ten and one hundred were popular. If the Roman model of ten (300 units in all forming the Roman state electing a king or rex) then could the white-leafed decagon's organization (if it is a tribal state structure) be a division chosen for the post-Roman Anglo Saxon state of Alfred or was it pre-Roman? It is quite likely that post-Roman governmental structures could have evolved from the Roman organization of Britain or at least from Roman ideas in contrast to Norse norms and one notes that the Anglo Saxons were organized according to Hundreds (of tribes) in their administration.
This theory departs from my own "monoculture of thinking" about landscape structures having to be the product of number specialists wishing only to stamp shapes or their elite knowledge onto the land. The simple notion of a circle representing the earth and human groups upon it is natural to tribal groups. Using a convenient number (ten or twelve) to regionally locate and allocate tribes, created an efficient means for organizing tribes upon the Earth. The anthropology of human groups, their invariant evolution and natural modes of work and reproduction, needs to be considered in understanding otherwise enigmatic landscape geometries.
Phaidon's Atlas of the Greek World by Peter Levi gives a useful cross bearing on George Thomson's book from an Oxford Fellow in Classical Studies:
"A great deal was made of mother goddesses in a bold and brilliant discussion, The Prehistoric Aegean, by the Marxist scholar George Thomson. His pioneering study has not been accepted as a whole, but some pieces of it have been digested, often without acknowledgment, by later writers. The sweep of his work, which was an attempt to apply anthropology and a wide range of other disciplines to what we know of Greek prehistory, is hard to deal with; it has therefore been neglected. He identifies his Minoan mother goddess with Demeter, and if she had a name that is as good an equivalent as any. Since he wrote before the deciphering of Linear B, he could not have known that Demeter's name was not used by the Mycenaeans, but that does not essentially weaken his position. The later pantheon did undoubtedly develop out of the earlier. What is not so certain is that the early society was matriarchal and matrilinear. The anthropological model that George Thomson was using is not now widely accepted by anthropologists. Whether or not his theory that the Mycenaeans came from the direction of central Asia is correct, analogies exist there for the dominant role of women, not only among the gods but in human society, that would confirm it." [43.]
It is fair to say that George Thomson's work has not been disproved but nor could it be approved of since its publication. It has therefore become esoteric: its conclusions remain respectable yet is "not accepted as a whole"; "it remains neglected", yet in parts has been "digested, often without acknowledgement" . This note will be moved to Bibliography when other articles refer to this subject.
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In Sacred Number and the Roots of Civilization, chapter three, based on John Michell's reconstruction of the ancient model of the Earth I resolved the mean earth radius (in feet) as being only made up of powers of prime numbers 2, 3 and 7: the primes two and three are factors of twelve, 22 times 3 equalling 12, and Michell's figure of 20901888 feet for the radius is then 126 times 7 feet. The utility of this came, not least, in the ability to form the mean earth circumference as 126 times 44 feet, using a 2 x pi value of 44/7.
Figure 1 The Ancient Model of the Earth
Considering the Oakleaf Decagon of south western England and Wales, we ignore here the other value of 2 x pi (63/10) relating the mean circumference to the polare radius. Top right the rational 44 units around the circumference is also shown in the geometry of a square of equal perimeter length having sides eleven units, squaring the circle in one sense and generating the preferred symbol of the element earth as the square.
Whenever a model of the earth's mean radius is formed, this has to be through a scaling down by some factor into a smaller length. If this was done arbitrarily, without carefully choosing a desireable scaling, then the resulting length would not be a rational model but instead, any length could be said to model anything. The principle of rationality within the model of the earth requires that the scaled down length of a model also be rational in a meaningful way.
In the Oakleaf (perpetual choirs) Decagon, in line with John Michell's finding that perimeters of sacred stuctures were (a) related to the mean earth and (b) employ in some fashion a perimeter of 3168 equal units of length. In our last article, we showed that the scaling of this decagon's radius relative to the mean earth radius was 63.36, so it is important to understand why and how this scaling was chosen (through prime factorization) and achieved (through metrological manipulation) to make the decagon's radius,
Of particular interest is the fractional part of 63.36. As a rational fraction this 0.36 equals 9/25. Dividing 0.36 into 63.36 yields an integer significant to metrology, namely 176 so that 176 times 0.36 equals 63.36.
There is another interesting clue in 0.36 in that the Assyrian foot of 9/10 (0.9) feet as a double foot (1.8 feet) was seen as having 60 parts called shu-si whose length was 0.36 inches**. However, the mean earth radius is 126 times 7 feet when divided by 63.36 feet (the scaling factor) becomes the decagon's radius of 329890.9091 - not rational in feet but ideally suited to the approximation to the golden mean of 160/99 (1.6162) found between the radius and the side lengths of a regular decagon. If that radius is viewed as 512 units long then each side length is 316.8 units long so that the ten sides of the decagon will be 3168 units in all, conforming to Michell's ancient norm for sacred spaces.
**Marduk's ziggurat (the Etemenanki)in Babylon can be seen to have been built within a rational cube of 4320 shu-si or 2400 double Assyrian feet.
To see how the decagon was conceived, one needs to see the mean earth radius as a more complex factorization than 126 times 7 feet, since 20901888 feet can also be arrived at by multiplying: 9/25 (=0.36) x 176 (=63.36, the scaling factor) x 175 x 12/11 x 1728 (123) = 20901888. This factorization reveals the need, to maintain rationality, for the root Sumerian foot of 12/11 feet to measure the octagon model of the mean earth's radius, when it is scaled down by 1/63.36. The decagon radius then becomes a rational 302400 Sumerian feet long whilst the side lengths become 187110 Sumerian feet long - the length of 204120 English feet identified by Michell.