LEPENSKI VIR: At the Iron Gate of the Danube - Prof. Lyle Borst
Lyle Borst is a professor of physics at the University of New York at Buffalo. His findings relating to research carried out at ancient sites in Britain can be found in Megalithic Software (Part1): a book we highly recommend (see advertisement elsewhere in this issue). The article here has been assembled by your editor from work in progress material supplied by Professor Borst.
The Danube River forms a whirlpool: Lepenski Vir, near Orsova. Large fish come up the Danube to eat the little fish, confused by the currents, and men have founded a colony to eat the big fish. The small community by the river is protected by hills and the stream, and no defence works have been identified. The community is small and the houses appear triangular! A careful statistical study was made, and this follows.
Lepenski Vir is unique in conferring upon the inhabitants monopoly control of a durable, reliable food supply: the fish which come to the whirlpool to feed. The site is difficult of access and apparently defensible, and has no man-made fortifications. Its occupation, given by Srejovic, from c.5400BC (L.V.I-a) to 4600 BC (I-e) shows cultural continuity. Proto-Lepenski Vir appears to be a different culture and L.V.111 is identified with Starcevo.
Quantitative sources are limited to numerical values and illustrations in the English translation of Srejovic's book: New Discoveries at Lepenski Vir. The scales of the drawings are assumed to be accurate and the direction of north is assumed to be true.
Figure A shows a histogram of the sizes of structures. There is only one dimension which stands out: 4.6-4.7 metres. Less well defined clusters occur elsewhere. To determine the unit of length used, the design of the structure must be reconstructed. Figure B shows a large foundation plan of building #37 (L.V.I-c,d). Srejovic has properly identified as an equilateral triangle. In Western Europe, among sites perhaps as early as 3000 BC, the equilateral triangle is uniformly represented by two right triangles with sides 15,26 and hypotenuse 30 units. This approximation cannot be used at Lepenski Vir for it does not give a coherent design. The position of the altar, which we believe to be an omphalos, just beyond the hearth is at a distance of 1/4 the base. An isosceles triangle with altitude on fourth the base is usually formed from triangle 17,34,38. The two triangles are then not compatible, for the base of one should be 2 x 34 whereas the base of the other should be 2 x 15. They could be used only is separate units were used. In religious structures in England, such as Canterbury and Westminster, Charlemagne's Chapel, Aachen and in the Emperor's Mausoleums of Japan, there are examples so such pairs of isosceles triangles with a common base. In every case the unit is the same or doubled for each triangle (Canterbury:2(34,17,38); 2(17,17,24), Westminster:2(12,12,17)2; (45,24,51), Aachen 2(12,5,13)2; 2(50,10,51).
It is clear that triangles 2(7,4,8); 2(4,8,9)1/2 have the correct relation, for all dimensions become integral and the bases are equal. We therefore assume that the unit of length for the equilateral triangle is 1/8 the length of the base, and for the altar, 1/16. The length of the unit for building #37 is then 0.86 metres (as compared to 0.83m found in many sites in Europe and Asia) Figure B in addition shows an oval stone off axis beyond the altar. In other buildings this is matched by a symmetrically placed sculpture on the opposite side of the axis. The center the oval stone forms a 3,4,5 triangle with the altar and axis, and it is presumed that in other structures the isosceles triangle is complete 2(4,3,5) The unit of this triangle in building #37 of 0.19 metres is unique and is not found in any other neolithic or bronze age site.
If the other structures of L.V.1 are based upon the same geometry, the unit is 1/8 of the width of the building. This gives for the peak of the histogram 4.65 divided8 = 0.58 metres as the unit. The Babylonian cubit has a length of 0.545 metres, and it is evident that although Babylon and Mesopotamia are not contemporary with Lepenski Vir, the cubit is anticipated. The unit of the 3,4,5 triangle is one third of this value, and the oval stone is one cubit from the axis. Little can be said about the other structures, for the unit varies from 0.225m (building #49) to 1.33m. (building #57)
A statistical treatment of the dimensions of the hearths is not possible with available data. They are characterised as about one metre long with a length-to-width ratio of 3:1 or 4:1.
Dimensions of rectangular altars given in Srejovic's book show concentrations around a length-to-width ratio of 1.2 (FigC). The width of the altars show less variation than the length. The average of fifteen altars from 14 to 17 cm is 15.3cm. The most frequently used unit in house dimensions is 0.58m, and one quarter of this is 14.5cm. slightly less than the average alter width of 15.3cm. Three altars all from L.V.1-c buildings (#45 and 37) show ratios of 1.75=7/4, suggesting two 4,7,8 triangles with a common hypotenuse. The unit then is between 3.5and 5 cm. Approximately 1/4 of the altar width. Since building dimensions use multiples of four it is not surprising to find 1/4 of this unit in the altar width and a further reduction of 1/4 x 1/4 = 1/16 as a useful unit in proportioning the alters. If a width of four units is accepted for the altars, the length to width ration should be 1.25, not far from that observed, with a unit of about 3.6cm.
The position of the altar seems to be the focus of the building design. For this reason we believe this to be an omphalos. Figure D (a) shows the pattern of these positions for L.V.1-a. Buildings 36,54a, 58 have axes which intersect at a common point. The axis of #36 passes through the centre of 34. We have also drawn lines through alignments of three or more centres. L.V.1-b(b) shows one strong alignment of which five points are retained from L.V.1-a. The indicated azimuth is 168 degrees (as compared to 166 degrees for L.V.1-a). This is not likely to be a stellar alignment, and so, for the present is unidentified. A prominent fiducial mark on the horizon, however, may be involved. L.V.1-c) retains the 166-168 degree alignment, measured as 165 degrees. Three points are preserved from L.V.1-b but none from L.V.1-a. The alignments are similar to those found at El Mina, north of Mecca, Arabia, and alignments in England. In the case of Lepenski Vir the date is established whereas no exact date can be assigned to the other sites.
Lepenski Vir 1-e (not illustrated) shows a very different pattern. The axes of the houses are nearly parallel and point north of east. Thirteen houses in the north half of the site have a range of 54-72 degrees with an average azimuth of 65 degrees. None of these is present in L.V.1-d(not illustrated). The clustering around 65 degrees is not strong, so a celestial alignment is not expected.
Information on the first settlement is mostly by inference. Hearths from proto-Lepenski Vir have survived, but house size and form can only be suggested from the pattern of debris remaining. The hearths were well constructed of slabs 'usually 30x25x10cm have lengths of 0.8-1.0 metres and show a ration of 3:1 or 4:1 Again the width seems to show least variation (0.2-0.25m); and this width is not far from the unit of the 3,4,5 triangle of building #37 (0.19m). The form of the buildings was not triangular. Srejovic suggest a length of 3,4-4.0 metres, and an egg shaped form.
Such an egg shaped form is common throughout Europe. The trilithos of Stonehenge are tangent to an inferred oval. Many oval sanctuaries, both pagan and Christian, have been found throughout Europe. The inner horseshoe of Sarmizugetusa has such a form. Predynastic graves in Egypt and Palestine of the same age result from the same geometry. We would expect the 3,4,5 triangle to be set out in half megalithic yards (0.83/2=0.415m), as at many other sites. The position of the hearth is suggested. The length of the oval would be 4.15m and the maximum width, 3.32m.. There may be the same variation in size found at the later site.
The foregoing analysis strongly supports Srejovic's inference 'that the builders of Lepenski Vir possessed quite definite mathematical knowledge which they employed skillfully in measuring the terrain and fixing the proportions, shapes and dimensions of the houses' (164,P.51). The culture was using the cubit 2-3000 years before it appeared in Mesopotamia. The use of Pythagorean triangles is well supported.
The non-random alignment of house altars again suggests a coherent plan not evident from a cursory inspection. The alignment with an azimuth 165-168 degrees in L.V.1-a,b,c is apparently significant. It cannot be a solar alignment. It may be an attempt to establish a N-S meridian, but the error is great. Its most probable explanation is that the alignment is upon a prominent feature on the skyline.
We have noted a cluster of houses around a single point (L.V.1-a) The altars of houses 36 and 54a as well as the curved end of 58 are equidistant from this point at a distance of about seven metres. We suggest no explanation.
We have noticed with interest, as has Srejovic, the frequent use of the integer four. This appears in the dimensions of houses and the position of the altar and sculptures, in the dimensions of the altars and hearths. This seems to be a very special number.
Our geographical discussion has largely ignored chronology, for this does not come immediately from our analysis. We have assumed that most of our sites are third millennium BC or later.