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The paper analyzes the Stonehenge Phase 3 II Architecture, modular structure, and their connection to the sun-induced cast-off shadows from its sarsens, and the motion of the shadows over the course of a day and throughout the year. It establishes that a direct link exists between the size of certain shadows and the design of the monument. It further documents that besides the summer solstice sunrise alignment, the vernal and autumnal equinox alignment was a major one in the monument's design. Moreover, the paper demonstrates that the Trilithons sarsens ensemble's quasi-elliptical form is a type belonging to an extension of the Alexander Thom's classification of stone enclosures.
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On Stonehenge and its Moving Shadows
Dimitrios S. Dendrinos
Emeritus Professor, School of Architecture and Urban Design, University of
Kansas, Lawrence, Kansas, USA.
In Residence at Ormond Beach, Florida, USA.
Contact: cbf-jf@earthlink.net
March 14, 2017
Stonehenge in 2014.
Source: By Diego Delso, CC BY-SA 4.0,
https://commons.wikimedia.org/w/index.php?curid=35323153
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Table of Contents
Abstract
Introduction
Basic Principles in Shadow Dynamics
On the Architecture of Stonehenge
The sarsens’ outer ring vitals
The Trilithons ensemble
The mathematical modulus at Stonehenge
The Trilithons quasi-elliptical arc
Alignments at Stonehenge beyond the summer solstice sunrise
The shadows of Stonehenge and their movement in space-time
The short sharp shadows and Stonehenge 3 II key shadow length
The long shadows and the links of the monument to its environs
Some general thoughts on the very long shadows
A lintel’s shadow
Conclusions and suggestions for further research
Notes
Note 1. Newcomb’s work
Note 2. Why lunar based monuments?
Note 3. The British Heritage sources
Note 4. More on the modulus at Kasta Tumulus
References
Acknowledgements
Legal Note on Copyright
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Abstract
The paper is set to analyze the shadows of Stonehenge Phase 3 II (circa 2600 - 2400 BC). Such a
study, the paper shows, allows one to derive plausible hypotheses regarding the design
specifications of the monument, including the height of the two sets of sarsens in both stone
enclosures, the diameter of the outer circle, as well as the inner Trilithons ensemble form and
dimensions. After some general principles regarding the dynamics of shadows are presented, the
paper examines in detail the Architecture of the monument’s two stone enclosures. The paper
does not address the two Bluestone enclosures. It identifies the form of the Trilithons ensemble
as a simpler class, of the stone enclosures classification scheme proposed by Alexander Thom.
This suggested simpler class of enclosures was detected by the author to also describe the
Architecture of Gobekli Tepe’s structure D Layer III.
A mathematical modulus is identified for the monument. It depicts key ratios among the basic
constituent elements of Stonehenge 3 II floor plan. The paper pinpoints the omphalos of the
monument as being the center of the outer sarsens circle, and the barycenter of the entire Phase
3 II structure. Further, the paper analyzes the Stonehenge 3 II shadows and finds that the spatial
(lengthwise) measure of the monument’s modulus is linked to the length of the shadow cast-off
by the outer ring’s sarsens (including their lintels) at noon time at equinox, specifically a length
of about six meters.
The paper, utilizes the work by Newcomb along with previous work by the author, as to the
importance of a phase transition in the dynamics governing the three functions describing the
cast-off sharp Sun-induced shadows’ lengths over a year. This phase transition takes place during
the vernal and autumnal equinox. Whence, the paper identifies the equinox noon time alignment
to have been significant also in the design of Stonehenge 3 II, besides the dominant and well
discussed in the literature sunrise at summer solstice alignment. The significance of the winter
solstice sunset alignment is also discussed in reference to the Trilithons ensemble.
Numerous extensions of the work are suggested, as the analysis of Stonehenge 3 II shadows
opens up a new window into analyzing the monument, its design, and possibly its culture related
roles in symbolism and ceremony at the time of its construction.
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Introduction
Shadows are part of a basic duality in monuments. That duality includes as a primal the original
structure and as its dual, the shadow it casts off due to either sunlight or moonlight. In addition,
the choreography of shadows as discussed in [1.1] adds movement to structures. Thus, it renders
life into otherwise inanimate objects, through their either cast-off or carry-on shadows’ motions.
This is particularly of import when dynamics in the monuments’ representations (reliefs and
other iconography, like petroglyphs) are imprinted onto these monumental structures.
In a set of previous papers, see references [1.1], [1.3], the author analyzed the manner in which
shadows of monuments behave in space-time, at the micro as well as macro scales. Furthermore,
the author has examined the role shadows’ spatial and temporal macro-dynamics have played in
the very architectonic design of Neolithic monuments. He has proposed and demonstrated this
role in the specific cases of two Neolithic monuments, see the case of Le Grand Menec in [1.2]
and Gobekli Tepe in [1.4].
The author, basically through the paper in [1.1], composed a General Dynamical Theory of
Shadows in Neolithic monumental Architecture. There, the macro-dynamics of the behavior of
shadows were proposed and initiated, and the main tenets of that General Theory were
discussed. These tenets were stated in summary form in the Introductory section of the paper in
ref. [1.3]. Moreover, the micro-dynamics of shadows were stated and formalized in [1.3], where
the Mathematics of fuzzy shadows were presented. For brevity purposes these subjects will not
be repeated here. The reader is directed to these papers for details. Some more elaboration of
points, first raised in both [1.1 and [1.3] but not fully laid out, will however be elaborated here,
with Stonehenge Phase 3 II employed as a study in empirical verification of the General Theory.
Hence, what is outlined in this paper is a new view on Stonehenge’s Architectural Design. Besides
the application of the General Theory of Shadows, an extension by the author of Alexander
Thom’s scheme of stone enclosures is also employed. This is at the core of Stonehenge Phase 3
II, a phase in construction involving the sarsens circle and the Trilithons’ quasi-elliptical
structure. The author in references [1.2] and [1.4] has extended the A. Thom’s theory of
classification of stone enclosures found in reference [2.1]. Taking off from the insightful Thom’s
classification of the enclosures, the author has added a temporal dimension to them, suggesting
that simpler stone enclosures were succeeded by more complex in design. Hence, it was
suggested by the author that dating of monuments could be pegged to their design complexity –
a basic evolutionary rule, which has Evolution as obeying an “increase in complexity” principle.
Moreover, in what was found to be the simplest one of all was a type of enclosure detected by
the author in [1.4] as being the one responsible for the design of Gobekli Tepe’s oldest structure
D in Layer III, of the entire (excavated thus far) Gobekli Tepe complex. In this paper, the author
establishes that this same design is found in the Trilithons quasi-elliptical shape and its
approximate dimensions, both in floor plan design and also (maybe even more importantly) in
the size (height, width and thickness) of the Stonehenge trilithons and the Gobekli Tepe pillars
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and orthostats. The author has extended also the A. Thom classification scheme by suggesting a
simpler, and thus more primitive, class of stone enclosures. It was that simpler scheme that was
found to be applicable in the case of structure D, Layer III at Gobekli Tepe. We show here that
this simpler scheme is also present at the Trilithons ensemble quasi-elliptical arc.
Central notion in this context and point of the Stonehenge Phase 3 II structures is the omphalos
of the monument, the barycenter of the entire structure – which is the center in fact of the outer
sarsens circle. It is through that point that the relevant and numerous monument alignments go
through. And it is with the alignment of noon time at equinox that the key to the monument’s
modulus is to be found.
If one were able to establish a mathematical modulus for Stonehenge 3 II, involving basic ratios
among the key elements of the monument, and go even further and link these ratios to the
shadows of a key orthostat, at a key location of the monument, at a key hour and date of the
year, then a potentially strong linkage can be suggested that existed between shadows and the
monument’s Architecture and Design. This is firmly established in this paper’s three sections.
Specifically, that key is found as shadows are cast by the Southernmost upright sarsen at noon
time during equinox. There, the key of the design modulus is found.
The paper is organized as follows: the first section offers a set of principles of the General
Dynamical Theory of Shadows to be applied in this empirical study on Stonehenge; the second
section addresses the Architecture proper of Stonehenge Phase 3 II; while the third and final
section looks at the structure’s shadows and their dynamics, and locates the key shadow’s length.
Work on Stonehenge has been extensive and from many sources and angles. The objective here
is not to either survey or duplicate any of that work. The focus of this paper is on the innovative
manner that shadows enable one to look into Stonehenge. Before we do that, and derive a new
Architecture and Design based approach to Stonehenge 3 II by way of shadows, some selected
general principles from the dynamic theory of shadows suggested by the author will be briefly
listed and elaborated to an extent. As Stonehenge 3 II is a complex 3-d structure, and the
mathematics of the General Dynamical Theory of Shadows are stated in terms of a simple linear
gnomon and its style, some simplifications are required due to the immense complexity a 3-d
structure with free standing monoliths and lintels on top of them entails in its study of shadows
cast. At various aspects of combinatorial programming and computer simulations needed to fully
address the various issues involved and connections possible among all stones of the monument
are hinted.
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Basic Principles in Shadow Dynamics
In what follows, the basic principles to be employed in analyzing the Stonehenge shadows’
macro-dynamics in space-time will be presented. On them, the manner in which Stonehenge is
to be approached here will be framed. It is noted at the outset that the General Dynamical Theory
of Shadows, as found in [1.1], is stated in terms of a linear rod, the gnomon of a sundial, and most
importantly its style (the top point on the gnomon). This gnomon could be a menhir (obelisk,
pillar, orthostat or column). In other words, the General Theory was stated in terms of a linear
(or cylindrical) configuration.
Moreover, in [1.3] a fundamental equivalence (the basics of which were analyzed in [1.1]), was
stated: the azimuth-clock equivalence for limited spatial horizons, involving a perfectly flat
terrain and a perfectly horizontal ground, see Figure 1. As pointed out in [1.2] the hourly angles
are equal only for cases where the clock’s flat plain is an equatorial sundial. However, at all
locations (no matter the latitude on the Earth’s surface), the 12midnight/12noon and 6am/6pm
axes are identical to the 0/180 and 90/270 azimuths.
On an equivalence between a location’s plane where azimuth angles are shown and computed,
and the annual calendar, in fact for an azimuth-calendar-clock equivalence, much more is
necessary to be said and drawn, having to do with sidereal time. It must be emphasized that this
equivalence has nothing to do with the pseudoscientific claim that the Neolithic builders
employed a 366-day calendar, or a 366 (and not a 360) division of a circle into degrees. This
issue will not be explored here further. On the topic of sidereal time see also Note 1 and the work
by Simon Newcomb [2.3]. More on this is also supplied in Note 4, regarding the Kasta Tumulus.
Here, a second fundamental equivalence will be stated: the alignment-shadow equivalence. Any
stone, on the basis of which any lunisolar alignment is obtained, is in fact a marker of the
equivalent cast-off shadow produced by the Moon or the Sun (or any star in the Celestial Sphere
were it possible to depict the star’s induced cast-off shadow) from the menhir. In fact, any
statement about alignments (approximations, errors and related limitations) hides in it an
identical statement about shadows. And conversely, any statement about shadows and their
conditions (thus limitations) contains within it an equivalent statement about alignments.
In view of the analysis in [1.3], see Figure 2, regarding fuzziness in shadows, it immediately follows
that these alignments are characterized by (suffering or sporting) the same (ailment or gift):
fuzziness. This ought to be kept in mind when sophisticated alignments are suggested by archaeo-
astronomers as having been implanted in Neolithic monuments – alignments requiring the use
of advanced surveying equipment (laser based theodolites) by contemporary analysts to
establish.
The General Theory can be expanded, this paper shows, to simulate the movement of shadows
cast off from a surface of a solid, rather than a menhir. It actually involves two solids – one being
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the sarsens’ outer circle, which can be viewed as the outer skin of a circle-based cylinder with a
hollow interior; and the Trilithons’ arc, involving the outer skin of a quasi-elliptical cylinder with
a hollow interior as well. The Bluestones circles will not be analyzed here; their equivalent
treatment is left to future research.
A further disaggregation can be briefly outlined, and experimentally analyzed, whereby the
sarsens and Trilithons skins can be subdivided into sectors, representing distinct stones or sets
of stones – although the shadows of all these individually considered stones to be explicitly and
individually modeled would entail a significant combinatorial and computational challenge. The
large number (60 sarsens, consisting of 30 pillars and 30 lintels, plus 15 trilithons, consisting of
ten pillars and five lintels) of stones involved, generate a very large number of combinations.
Combinatorial computing and associated computer programming of this scale render the analysis
prohibitively voluminous, to an extent intractable, and next to impossible for it to be
accommodated in a single paper. The magnitude of the combinatorial problem involved is further
boosted by the derivation of the R areas for each stone; see for the definition of these R regions
the next section, ref. [1.1] and Figure 1 below).
A parallel processing, supercomputer simulation is needed, to capture all possible motions and
all possible interactions among all these stones at different times of the day (and night) over all
days of a year. Such a computer simulation is a considerable research undertaking, albeit a very
promising one, that potentially can accommodate formal statistical analysis. It must be of course
assumed that not all of these interactions were individually computed at the time of their
construction, and that only a few were of import. Prior analyses have alluded as to which stones
among the 75 total were key in the Neolithic architects’ design, and to that not much will be
added here, except when novel findings are to be pointed out and some new stones to be
designated as of at least as much import as those already identified as important in the existing
literature on Stonehenge.
The focal point in this paper is to seek an answer to the question: what aspect of the shadow
dynamics encountered at Stonehenge is likely to have played a significant (major) role in the very
design of Stonehenge. By that, it is meant to answer the following sets of basic Stonehenge design
questions: to what extent Stonehenge shadows determined (a) why a 30-meter sarsens circle,
with 30 sarsens (pillars and lintels) of the specific sizes (height, width, length) were put in place;
(b) why were these 30+30 sarsens placed exactly at the locations placed; (c) a similar set of
questions for the 10+5 sarsens forming a five-set ensemble of trilithons. Some of these questions
have been addressed extensively in the literature, and that will not either be repeated here or
surveyed, since this isn’t the objective of this paper. Only novel aspects in the answers to these
fundamental questions will be supplied.
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Figure 1. The (sharp) lengths of shadows. Daily and annual paths of total Sun-induced cast off
shadow lengths are shown in this (macro) dynamics model proposed by the author in reference
[1.1] Arc {EA(1)D} is the style’s trajectory identified by function (1) during the day of the
summer solstice; arc {GA(2)F} is the style’s trajectory during equinoxes, function (2); and arc
{CA(3)B} is the style’s trajectory during winter solstice, function (3), at some location where the
solstices appear at an angle ω. As discussed in [1.3], various sub-regions within region R (see
paper’s narrative for its definition) identify ground based calendar and clock functions for the
menhir acting as a gnomon of a sundial with a style on its very top point. Inside the shaded area,
the menhir loses its ground based calendar indicating property, retaining only its clock indicating
capability. Of course, if another menhir is raised inside the shaded area then the calculus is
different. Consequently, for a monument with multiple menhirs, the shaded area acquires special
interest. As mentioned in the text, these functions hide in them alignment functions, due to the
alignments-shadows equivalence principle. Source: the author in [1.1].
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A shadows related question is also this: was there a role shadows played in locating the
monument (which goes by the term “Stonehenge” today) where it is precisely located, in what is
currently been referred to as “Wiltshire at Salisbury Plain” in current day Southern England (see
Note 3 for more regarding this remark). That is, were there macro-landscape, macro-topography
and macro-Geography shadow-related considerations for the spatial allocation of this
monument at its current site. Of course, there were numerous other possible considerations
which render this specific site as the most favorable, referred to as “locational comparative
advantages” in Economic Geography. Again, this question will be addressed to the extent that
novel insights can be obtained by considering shadows when they obtain huge lengths, close to
sunrise and sunset (and of course, moonrise and moonset).
For each individual Stonehenge pillar or standing stone (the 30 sarsens and the 10 trilithons), the
macro spatial and temporal dynamics of shadows with sharp edges are depicted by the author’s
diagram in Figure 1, found in reference [1.1]. For the identification of all relevant points and lines
on this diagram, which identifies the azimuths of the solstices and equinoxes at some arbitrary
location on any of the Earth’s latitudes, under a limited horizon and flat ground which is perfectly
horizontal, the reader is referred to [1.1]. Here, a closer look will be taken on the diagram, and
especially on its shaded part. It turns out that it plays a pivotal role in the design of monuments,
where shadows shaped to an extent their morphology.
It should be kept in mind that these shadows’ domains are the product of a linear menhir, of
some arbitrary height H, cast off it as a result of sunlight and traced during any day of the year,
and over the approximate 365-day annual cycle. The various areas, designated under a limited
horizon (depicted by the circle identifying the azimuth-clock equivalence), present special
interest to the extent that shadows (and alignments) are concerned.
Of course, the total area inside the region R identified by the points {O,D,F,B,A(3),C,G,E,O} is
where cast-off shadows fall on the ground from the menhir in question (of some height H) at
some latitude where the solstices occur at some angle ω. Shadows do not exist off this region
during any time of the day, any day of the year. In effect, R depicts the menhir’s market area for
shadow interaction. Beyond this area, there is no effect either from or to the menhir in question.
Stated in slightly different terms, south of the solstices radii (OD) and (OE) and north of the (3)
function, the presence of a H-high menhir, at location O, at some latitude on the Earth’s surface,
has no effect at the ground level. There are numerous sub-regions in R where some cast-off from
the menhir shadow effects are seasonal.
The calculus is different, if some other menhir is raised at some point within these sub-regions
of R in Figure 1. Among these sub-regions, the shaded area in Figure 1 is of some extra interest.
At no time of the day and at no day of the year, in that sub-region, is there a ground based
calendar function possible for the menhir in question. For the calendar function to be maintained
inside the shaded area of Figure 1, a menhir must be raised of sufficient (minimum) height,
dependent upon its location within that shaded area and the site’s location on the Earth’s surface
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(its latitude). Thus, in all cases of monuments where multiple menhirs (orthostats, pillars,
columns, obelisks etc.) are involved, this shaded area of Figure 1 acquires particular importance.
At any location, north of function (1) and south of function (2), ground based calendar
indications can only be obtained between the summer solstice and the autumnal equinox, and
the time period between the spring equinox and the summer solstice. And at any location, north
of function (2) and south of function (3) ground based calendar indications can be obtained
in the seasons between the autumnal equinox and the winter solstice, as well as during the winter
solstice and the spring equinox. And again, the calculus changes if menhirs of appropriate height
are raised within these sub-regions. Naturally, they would be of decreasing capability to act as
calendar indicators the further away they are from the shaded area of Figure 1.
Figure 2. This is a figure showing shadows of objects from different distances. It was analyzed
and extensively discussed in [1.3]. The photo demonstrates two fundamental properties of
shadows, namely their fuzzy nature and the effect distance has on them. Source: the author and
reference [1.3], Figure 3.
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Elaborating on these principles is of some further interest, as the discussion touches subjects of
scale. The height of any menhir north of the one at point O need be lower than the original menhir
at O. Any higher menhir (for calendar purposes) is unnecessary. Thus, any menhir must be
considered (calendar-wise) subordinate to the original menhir at point O, and must be lower in
height than H. On the other hand, the opposite holds for any menhir south of the original at O. It
must be taller and thus dominant over the original. These are intra-monument scale
relationships, linking heights of the monument’s various components and their sizes (as well as
distances among them). We shall see them play out in the case of Stonehenge in later sections.
Any menhir (no matter its height) to the north of R, is not relevant to the menhir raised at point
O, as it falls outside its market area. On the other hand, it must be noted that this menhir’s market
area is operable in 3-d. It is so that, a menhir to the south of R could fall inside the ground based
calendar use of, at point O located, menhir – that is, it falls within its market area, if and only if
it is sufficiently high at the specific point raised. These conditions of course depend on the
monument’s location on the Earth’s surface.
This analysis potentially ties up the latitude of a monument to its scale (size). More specifically,
if the shadows paly any role in the design of a monument, then the initial scale of some first
planned for pillar (menhir, orthostat, column etc.) in turn determines the dimensions and scale
of the entire monument. To a degree, this initial pillar’s size, or its relevant subdivision, is the
monument’s modulus. The subdivision is directly related to the distance and size of the other
components (menhirs) of the monument, and their relative distance from the base menhir.
A brief note is necessary at this point to demonstrate the relevance of the above finding,
regarding another Neolithic monument. In view of the above analysis, one can now understand
the shape of the strings of stones at Le Grand Menec, at Carnac, discussed in reference [1.2] and
also in [1.5]. More specifically, the menhir discussed on p. 24, shown in the sequence of Figure
A4.1-3 of [1.5], could be instrumental in identifying the location of at least three strings of stones
to the North (and both East and West) of it, as falling within its “market area” at different times
of the day over possibly three different (key?) days of the year.
We conclude this section of the paper with a reference to the long distance (from a macro-
landscape, macro-topography, or macro-Geography, that is macro-spatial) interaction linking the
specific site of a monument to its broader surrounding Environment. These linkages, if they exist,
come about from the very long lengths of the shadows close to the points B, C, F, G, D, and E of
Figure 1. Along the arcs defined by these points, arc (BD) and arc (CE), and at the extended
horizon (as the radius of the circle with center at point O, and delineating the horizon, increases)
the various skyline features found at the end of the horizon are touched by the very long shadows
cast off by the menhir at point O. Thus, these points on the horizon act as the bridges linking the
monument to its large-scale surroundings. This is directly related to the alignment-shadow
equivalency discussed earlier in this section.
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On the Architecture of Stonehenge
Much has been said and written about the Architecture of Stonehenge, and this section’s aim is
not to either repeat or survey that extensive literature. The objective here is to add a new angle
to that body of work, an off-shot of the author’s extension of Alexander Thom’s theory on the
design of Neolithic stone enclosures. Under this new angle, we will link the contents of this
section to the paper’s main goal, which is the study of the Stonehenge’s Sun induced cast-off
shadows, their motion during the day and throughout the year, and the role these motions very
likely played in the design of Stonehenge’s two key structures: the sarsens circle, and the
Trilithons quasi-elliptical arc.
There are numerous sources where data and especially the floor and site plans containing the
Architectural detail of Stonehenge can be found, one being the English Heritage reference in [2.2]
and its cited references. The generally accepted site plan for Stonehenge is that of Figure 3. On
it, a numbering of stones also generally accepted is found – a numbering which involves the
sarsens of the outer circle, the quasi-elliptical arc of the Trilithons, and the two Bluestone rings.
Moreover, in the legend, a breakdown is offered according to their current state by stone type.
A very quick description, of the basic two components (the sarsens outer circle and the Trilithons’
arc) of Stonehenge that we shall address in this paper, follows. This diagram will be used as a
blueprint in the present study. Consequently, the accuracy of the findings critically hinge upon
the accuracy of the floor plan in Figure 3.
Stonehenge Phase 3 II (circa 2600 2400 BC), contains a circular system of 60 sarsens out of
which 30 were erected as orthostats (pillars), supporting another 30 sarsens as a ring of lintels.
An open research question exists, as to whether the entire circle was ever completed, or that it
was ever planned (and designed) to be completed as described; see this issue being discussed in
the author’s paper [1.6]. This question is of direct relevance here, for the following reason: if the
outer ring was completed at a different time than the inner arc of the Trilithons was erected in
the two centuries period, then the inner quasi-elliptical enclosure must had been erected first
and then the 60 sarsens circle were raised. This sequence becomes of import, when the modular
structure of the monument is to be discussed, as it will become obvious from the analysis that
follows.
All sarsens (orthostats and lintels) had undergone by the builders of the monument “dressing”,
i.e., some form of processing. This included, as it is well documented in the existing literature, a
slight bending of the lintels to follow the overall circular structure, and the slightly upwardly
widening of the orthostats to correct for ground perspective. Architectonically, both of these
forms of dressing were construction innovations at the time this Phase of the monument was
constructed. Bending of lintels is of course encountered in the case of the earlier Maltese
Temples; but correcting for ground perspective is a significant innovation that occurred at
Stonehenge 3 II.
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Figure 3. Stonehenge sarsens: the outer and Trilithons rings and the Bluestones circles. The floor
plan and its legend are due to Antony Johnson (who holds a 2008 copyright on it, see [2.1]). The
stones’ numbering follows the conventional F. Petrie 1880 system. Numbers 1-30 depict the
sarsens outer ring orthostats; 101-130 the sarsens lintels; 51-60 the standing Trilithons; 51a-55a
the Trilithon lintels; 31-49 the outer Bluestone circle; and 61-72 the inner Bluestone circle. The
two Bluestone circles are post 2400 BC additions (constituting Phases 3 III and IV). The central
point (barycenter) of the monument is exactly where the cross is at the diagram above. However,
as the diagram in Figure 4 shows, the center of the Trilithons’ quasi-ellipse is not at that point. In
the above diagram, tone indicates state of the stone (standing or fallen) and stone type.
14
The sarsens’ outer ring vitals. These standing stones form an approximate 33-meter in diameter
(i.e., with a radius of about 16.50 meters and a circumference of almost 103.70 meters) perfect
circle, with its center being the omphalos of the monument, see diagram in Figure 3. That circle
is drawn going through the very center of the standing sarsens. The average standing sarsen is
approximately 4.10 meters in height above ground (in total, they measure about 5.50 meters in
height), 1.10 meters thick, and 2.10 meters wide. Thus, the standing sarsens form the skin of a
hollow cylinder with inner surface diameter of about 31.90 meters and an outer skin surface of
about 34.10 meters in diameter. The lintel ring has a thickness of about .80 meters (each lintel is
3.20 m x 1 m x .80 m), thus the total height of the structure above ground is close to five meters.
How the structure is currently envisioned by the consensus of archeologists is shown in Figure
N1 in Note 3 (see section on Notes at the end of the paper).
With a perimeter (at the skin’s center) of about 103.70 meters, an average length (at their center)
of about 2.10 meters, and assuming completion of the circle, the sarsens are spaced on the
average at a distance of about 1.36 meters. The fact that the existing surviving in situ distances
among the standing sarsens is slightly more than a meter, adds more questions as to whether
the monument was designed to be precisely built and completed as described. A note-
parenthesis is warranted here, no matter the speculation regarding original intent by the
architect(s) of Stonehenge Phase 3 II. The length of 1.36 meters is precisely the modulus found
by the author to have been used in the Kasta Tumulus perimeter wall construction, see reference
[1.7]. In Note 4, more elaboration is provided on this issue. The Note amends and extends the
work on this topic found in the author’s prior papers on the subject.
In Figure 4, the N-S and E-W axes from the very center of Stonehenge are drawn. On them, the
current azimuths can be estimated. It is noted that due to shifts in the Earth’s axis of rotation
(declination), the current azimuths are off from those at the time of Stonehenge Phase 3 II
construction by approximately 1 to 2. Actually, no one is exactly sure what precisely is this
deviation, see Note 1. More on this topic in a bit, following the brief outline of the Trilithons.
Finally, it is noted that on the surface of sarsens #3, #4 and #5 carvings of axe-heads have been
found. The importance of this will be further discussed when the alignments of that section of
Stonehenge will be addressed a bit later.
We now turn to the Trilithons’ quasi-elliptical arc. We shall attempt to reconstruct this part of
the structure, and by doing so an innovative perspective on Stonehenge emerges.
The Trilithons ensemble. Let us review what is known about the Trilithons arc, drawn from the
previous sources as well. The specific quasi-elliptical morphology of this arc will be analyzed
shortly, after the vitals of the stones contained herein are presented. The Trilithons ensemble is
organized so that there are five sets of three sarsens, placed so that each trilithon set contains
two standing orthostats with a lintel on top, i.e., each set forms a triple, which is commonly
referred to as a “trilithon” (ΤΡΕΙΣ-ΛΙΘΟΙ). Hence, in total, there are fifteen sarsens in this quasi-
elliptical arc, organized in a symmetric pattern, aligned on an axis and facing towards the summer
solstice at sunrise and at the back end facing the winter solstice at sunset.
15
Figure 4. The N-S and E-W axes of Stonehenge, at present azimuths with the center of the plane
determining the azimuths at the very center of the outer ring circle – this being the monument’s
omphalos. The possible azimuth of these two axes at the time of Phase 3 II construction is also
shown. The N-S and E-W axes are critical in discussing the layout of the broader site (and floor)
plan and in specific stones #4, #12, #19 and #57. See for more discussion on this topic the section
of the paper on azimuths, as they were then and now, and Note 1. Source: the author.
16
The height of the ten upright stones belonging to this ensemble is not uniform. The tallest two
orthostats are found at the south-western trilithon set of the quasi-elliptical Trilithons ensemble;
they would have had a height of about 7.30 meters above ground (with a total height of about
ten meters), although at present the only standing sarsen of this set is about 6.70 meters in height
above the ground level. Whereas the two pairs of upright sarsens at the north-easternmost
triples have a height of approximately six meters. The pair of the triple between the two has a
height of about 6.50 meters. How shadows are linked to this height differentials would be of
interest to ponder. No average thickness or length measure is available for the ten uprights.
The mathematical modulus at Stonehenge. Obviously, given the basics of the design in Phase 3
II, one concludes that the monument at this stage was built on the basis of number 2 and the
prime numbers 3 and 5, and of course their multiples. The number of sarsens in the outer ring is
3x5x2x2; the number of sarsens in the inner Trilithons ensemble quasi-ellipse is 3x5. We hence
must conclude that the beginning of a modulus is present here, based on the prime numbers 3
and 5. The small axis of the quasi-elliptical Trilithons ensemble inner skin (about 15 meters) is
half the outer ring’s inner skin diameter of approximately 30 meters. It is noted that the total
height of the outer sarsens circle (about five meters) is one sixth (2x3) of the circle’s diameter.
Moreover, the total height of the shortest sarsen in the quasi-elliptical arc of the Trilithons
ensemble (six meters) is about one fifth of the outer ring’s diameter as well. The tallest sarsen
(estimated to have been about 7.30 meters above ground) is close to about one fourth its
diameter, and about half of the quasi-elliptical arc’s minor axis. These ratios are central in
understanding the basis on which the monument’s Phase 3 II was constructed. How this modulus
was linked to the cast-off shadows at Stonehenge, and hence how shadows (and thus,
alignments) played into the very design of the monument is addressed in the next section of the
paper, following the presentation of the new findings about Stonehenge’s Architecture.
The Trilithons quasi-elliptical arc. In Figure 5, The blueprint of the Trilithons arc design is shown.
That design consists of two almost perfect semicircles, separated by a distance of about 3.50
meters. The diagonals (AB) and (CD) of these approximate semicircles run parallel to each other.
The semicircles have a radius of about 7.80 meters, measured at about the middle point of the
Trilithons’ sarsens skin. Whereas the South-western semicircle is quite obvious, the North-
eastern isn’t quite as obvious, thus its detection has escaped the architectonic analysis of the
ensemble so far. However, the presence of the North-eastern semicircle is hinted by the slight
inward bending of the Northernmost sarsens in the Trilithons ensemble, stones #51 and #60. In
Figure 5, the center of the outer ring of 30+30 sarsens (upright orthostats and their lintels) is also
the barycenter of the entire Stonehenge Phase 3 II monument. This is the omphalos of this
section of the monument at Stonehenge. For design purposes, it is far more important than the
spot where the so called “altar stone” is located – in front of sarsens #55(a), now fallen, and #56
(still standing).
17
Figure 5. The major alignments with O as the monument’s omphalos. The Architecture and
Astronomy of Stonehenge Phase 3 II contains the sarsens circle and the Trilithons’ quasi-elliptical
morphology. The Trilithons’ stone enclosure configuration consists of two semicircles with
parallel diameters (AB) and (CD) separated by a distance of about 3.50 meters. It contains the
structure’s main alignment (the summer solstice sunrise) as its major axis. It is similar to the stone
enclosure identified by the author as the blueprint of Gobekli Tepe structure D, Layer III, see [1.4],
[1.8]. Both are simpler versions of the Thom’s stone enclosure classification scheme for Neolithic
monuments in Brittany and the British Isles found in [2.6]. Source: the author.
18
Upright stone #52 and (down) stone #59 (broken into three pieces - #59a, b, c) serve as the (two
parallel) links between the two approximate semicircles. Of note is the location of these
semicircles’ center: the one to the South-east, lies at about the very barycenter of the entire
monument (as shown in Figure 4) and slightly to the South-west, off by a small distance from the
diagonal (AB). Due to unavoidable approximations in composing the basic site plan by the British
Heritage, and construction imperfections, plus the time that has elapsed and the effects of wear
and tear of the monument over the millennia, there is no reason to doubt and reason to accept
that the center of this semicircle was intended to be at the diagonal shown in Figure 5. Whereas,
the center of the North-eastern approximate semicircle is found exactly on the diagonal (CD).
Hence, we detect in the Trilithons ensemble a familiar pattern, from the Thom’s classification
scheme: two separated but linked semicircles forming a quasi-elliptical structure. This quasi-
elliptical form has as a minor axis (diameter of the constituent circle) of about 15.10 meters, and
a total length (major axis) of about 18.90 meters. Notice, the total length of the major elliptical
axis is short by a small fraction of the sum (2x7.80+3.50=19.10) due to the factors already
mentioned. Although the Trilithons ensemble is positioned so that it is symmetrical in reference
to the summer solstice azimuth line, it isn’t symmetrically located in reference to the barycenter
of the entire structure, point O in Figure 5, the monument’s omphalos. However, the omphalos
is at the same location as the center of the 30-sarsen outer circle because the density of Trilithon
ensemble sarsens isn’t uniform along the quasi-ellipse.
The outer edge of the Trilithons stone enclosure is at a distance of about 3.5 meters from the
inner surface of the sarsens circle (at its minimum approach) in the North-east; it is at about and
no less than six meters away from the inner surface of the sarsens’ outer ring at the other end
(South-west). It turns out that this 6-meter distance is a key length for the entire Stonehenge 3
II design, as it will be pointed out in a bit. It is also noted that the so-called “altar stone” laying in
front of the Southwestern trilithon set is parallel to the winter solstice sunrise – summer solstice
sunset axis at the 130 to 310 azimuth line (see, p. 1 in [2.7]).
The design has deep roots in stone enclosure morphology. Alexander Thom and his son Archibald
S. Thom in reference [2.6] offered an insightful and general classification scheme for stone
enclosures encountered in the British Isles and Brittany. This scheme was extended by this author
in [1.4] and [1.8], so that it acquired a temporal dimension, based on the principle of increased
complexity in the Evolution of Form. Simply stated, simpler forms must have appeared before
more complex versions (of a particular form) came about. Furthermore, certain time periods
must elapse in the formation of complex variations of an original simple form, the more (or higher
degree of) complexity requiring proportionally longer time periods.
Moreover, the author recognized the presence of similar stone enclosures falling under the
Thom’s classification scheme in other Neolithic sites, including Gobekli Tepe and Malta.
According to this (theoretical, involving temporal dynamics) type perspective, it was gauged that
Layer III, structure D (the oldest thus far excavated enclosure) at Gobekli Tepe was a late
Mesolithic to early Neolithic structure, and that Gobekli Tepe was buried sometime around the
19
beginning of the Bronze Age (the approximate time of Phase 3 II at Stonehenge), see [1.8]. In
addition, trilithon formations (the subject of interest in this subsection) are encountered in the
Maltese Hagar Qim temples of the Ggantija Phase on the island of Malta, see [1.6].
It is established that the pattern (and not only, as stone sizes as well as enclosure dimensions are
very similar too) as discussed here for the Trilithons ensemble at Stonehenge, is what the author
described structure D, Layer III at Gobekli Tepe to be, see references [1.4] and its precursor [1.8].
This finding is a major one, since it directly links the Architecture of Stonehenge to that of the
Fertile Crescent. This connection in design has been initially explored in [1.6], where it was
suggested that the morphology of the Trilithons ensemble was consistent with a Bull Cult design.
That Crescent Moon and bull horn combination design pattern has been imprinted in the
architectonics of all structures bearing the shape of an arc (or apse), since early Mesolithic. It has
been identified in a multiplicity of contexts, such as the early Natufian Fertile Crescent
Architecture, the Maltese Archipelago Neolithic megalithic Temples of the Ggantija and Tarxien
phases, to the River Boyne passage tombs (Newgrange), down to Stonehenge.
In the Trilithons ensemble, we find a NE-SW main (long) axis of the quasi-elliptical arc at an
azimuth of 50 (the blue line in Figure 5). This line cuts across right in the middle the distance
between stones #1 and #30 at present, bisecting the entire monument. It intersects at exactly
90 the (AB) and (CD) minor axes. In Figure 5, the 45 azimuth line is drawn; it touches off the
very southern point sarsen #30. Thus, the window defined by the azimuths 45 and 52 is the
summer solstice sunrise window at Stonehenge. The fact that this event is still possible to
observe, offers strong support to the proposition that the azimuth movement (the precession)
since the construction date of Stonehenge Phase 3 II (about 4.5Kya) has been minor (possibly no
more than 1 to 1.5, possibly less, according to A. Thom in [2.5]).
The reader should keep in mind that one-degree of azimuth is about the width of two Sun disks
at the horizon. The reader should also keep in mind that the current azimuths have moved
clockwise from the Neolithic ones. Putting it slightly different terms, the Neolithic N-S axis was
slightly to the left of the current N-S axis. Finally, it is noted that the extension of the azimuth for
the summer solstice sunrise, is the winter solstice rays at sunset. Consequently, at the South-
western quadrant of Figure 5, one sees the directions and azimuths of the sunset at winter
solstice. It follows in reverse the paths outlined for the sunrise rays at summer solstice (the
sunrise azimuths plus 180).
Similar carvings to those on sarsens #3, #4 and #5 from the outer circular enclosure, a “dagger”
and fourteen axe-heads have been found carved on stone #53 of the Trilithons ensemble. Given
the relatively good condition of this sarsen relative to its neighboring to the south sarsen #54,
one may speculate that on both there could be carvings. The import here is the location of stone
#53 (and potentially #54) in the context of the alignments involved at Stonehenge’s inner
sanctum – in combination with stones #3, #4, and #5.
20
Alignments at Stonehenge beyond the summer solstice sunrise. The midsummer solstice date’s
sunrise is not the only (although the most important given the monument’s overall morphology
of floor and site plan) alignment marked by the Architecture of the two sarsens’ rings-enclosures
at Stonehenge. Although it may have justifiably attracted the overwhelming attention of the 20th
century Stonehenge analysts, it certainly was not the only one, although clearly (given the site
plan of the monument, see Figure N1, as well as the specific floor plan of the Phase 3II stone
enclosures, shown in Figure 3) it might have been one among the two most important ones.
Work in the second decade of the 21st century has offered new insights into the nature proper of
Stonehenge. Since the work by Gerald Hawkins, C. A. Peter Newham, Fred Hoyle, Alexander Thom
– and for an entertaining review of this literature see R. Hill [2.11] and for a more recent analysis
about “solving Stonehenge” see [2.12] – much new work has taken place. This new work, see for
example T. Maeden [2.7], [2.9], and the group in [2.8], does not focus on the potentially excessive
claims of these early archaeo-astronomers, regarding complicated lunisolar cycles – cycles that
require both mathematical and astronomical sophistication clearly beyond these Neolithic
architects and astronomers’ capacity for record keeping. Along with work by this author [1.1],
[1.2], [1.3] etc., this work isn’t largely based on the intangible notion of an “alignment” or the
extraordinary approximations required to accommodate its claims.
Instead, although of equal mathematical and astronomical rigor, this new work focuses on
tangible subjects which leave little doubt as to their potential role in the monument’s design:
their cast-off shadows and the shadows’ choreography during the day or night. As this paper
asserts, there are of course strong connections between shadows and specific major and obvious
alignments imprinted into the monuments’ architectural design. This new work does employ
some major features from the early archaeo-astronomy literature however, like for example the
Thom’s classification scheme of stone enclosures. More on this subject of course is found in the
next section of this paper.
A closer look at the East-West and the North-South axes allows for a deeper appreciation of the
barycentric point O and these two axes, and the other solar-related alignments at Stonehenge.
Although in the current literature on Stonehenge, the altar stone in front of the Southwestern
trilithon set is considered to be the omphalos of the entire monument, the import of barycenter
O should not be underestimated. In effect, the axis of the equinoxes, reveals that the current
equinox sunrise rays hit stone #4, and do not penetrate the inner sanctum of the Trilithons
ensemble for an observer standing at ground zero, point O, Stonehenge’s barycenter. To this end,
upright #4 outer surface must had held some significance for the architect(s), engineer(s),
astronomer(s), builder(s) and craftsmen of Stonehenge 3 II. Here we may recognize the
importance of the carvings on that particular sarsen, as well the neighboring stones #3 and #5.
However, red line in Figure 5 holds some critical information; going through the monument’s
barycenter (point O), it reveals that by an approximate 3-deviation to the North (an angle quite
close to the then equinox azimuth), through stone #3 and #4, touching the orthostat #4, the
sunrise rays would pass to the North of sarsen #51, bypass orthostat #57 and penetrate just off
21
its Southern tip the entire set of two stone enclosures. This alignment of uprights very likely
isn’trandom, and offers some (albeit weak) support to the argument that the obliquity of the
ecliptic in that 4.5Ky time interval may have resulted in such a 3 angular change in the equinoxes’
azimuth.
It must be emphasized that a 3 change could be well accommodated by the monument’s floor
layout, for it allows the summer solstice sunrise rays to still penetrate through uprights #1 and
#30 and hit the gap between sarsens #55(a) and #56 of the Trilithons ensemble above the altar
stone, and reach the gap between the outer ring sarsens #15 and #16. Upright stones #3 and #4
in combination with stones #18 and #19 would form windows through which the vernal and
autumnal equinoxes sunrise and sunset rays would allow for light to penetrate the entire
monument. Of course, the import of recording the summer solstice sunrise has been widely
analyzed in the existing archaeo-astronomy literature and not much will be added here. The
importance however of monitoring the equinoxes is not so widely discussed. But it is analyzed in
Note 2, at the end of the paper from a novel perspective. In case the upright stone #4 was in the
way of the equinoxes’ sunrise, then its interior surface must have had a special meaning to the
builders of Stonehenge 3 II, being the receptor of the last gleam at equinox.
Finally, regarding the main summer solstice sunrise alignment, a point need be made: the
convexity of the Trilithons ensemble in receiving the first sunrays of the day, is also the concavity
of the ensemble in repulsing the winter solstice last gleam. Thus, a duality in the alignments is
detected, designating different roles played by the uprights at different times of the year.
Now, a look into the winter solstice alignments will be taken. Of course, since the summer solstice
azimuth is at about 50 (i.e., 90-40), the winter solstice must be at 130 (90+40), indicated by
the green line at that azimuth in Figure 5. Hence, the winter solstice sunset is at 230 (50+180).
For an observer at barycenter O, the sunrise rays at winter solstice would be blocked (assuming
all factors mentioned earlier being operable here) by orthostat #7. However, at present, the first
winter solstice rays do penetrate the monument’s inner sanctum, touching the southern tip of
upright sarsen #7, and likewise sarsen #52 of the Trilithons ensemble.
They continue through the gap between the Northernmost set of trilithons, South of sarsen
#59(a), and North of sarsen #58; and end up reaching the gap between outer ring sarsens #22
and #23 thus totally penetrating the two stone enclosures. The 5 angle shown by the two
green lines in Figure 5, depict the four consecutive windows allowing the sun of the winter
solstice to work its way through the monument, as at these instances the monument’s two stone
enclosures become translucent. The obvious conclusion is that the floor plan of Stonehenge
Phase 3 II was capable of accommodating all six major Sun-related alignments at the site.
Consequently, it has been demonstrated that Stonehenge 3 II has been a far more complex
monument in its design and functions, than the simple “open to the summer solstice sunrise”
monument portrayed thus far in the literature.
22
On the shadows of Stonehenge and their movement in space-time
In what follows, some use is made of astronomical information and terms, although the paper is
addressed to a general audience. The mathematically inclined reader is directed to a classical
reference from 1906 on subjects covered here, see Simon Newcomb [2.3]. For more on the
reference, see Note 1. Much has been written on Stonehenge’s Astronomy, see for a brief review
the author’s reference in [1.6]. A key body of work in this discussion is Alexander Thom’s writings
in [2.4], that has inspired a new breed of archaeo-astronomers with a special focus on Neolithic
monuments of the British Isles and Brittany (like for example, Aubrey Burl, see [2.5]).
Figure 6.a. Google Earth map of Stonehenge, taken on August 13, 2016. The photo is from an
altitude of about 600 feet; Stonehenge’s elevation is approximately 340 feet. Its (map pointer)
coordinates are: 5110’44”N, 149’34”W. This coordinate implies that at summer solstice noon
time the Sun’s angle from the horizon there is about 62 (see text for a more accurate estimate).
23
On the specific subject of shadows at Stonehenge, the reader is directed to the work discussed
in [2.8]. Of special importance is the work by T. Meaden in [2.9], where the notion of “ΙΕΡΟΣ
ΓΑΜΟΣ” is advanced as being at work at Stonehenge and Drombeg, see reference in [2.10]. A
similar condition, depicted by the cast-off shadows of the two central pillars on each other, was
identified also in the case of Gobekli Tepe’s structures C and D, and possibly other structures
within the Gobekli Tepe complex with central pillars in them, as analyzed by the author in
reference [1.4] and [1.11].
In Figure 6, a Google Earth map snapshot is shown. It was taken on August 13, 2016 according to
Google Earth map records. By using the clock-azimuth equivalence, one can infer that the shot
was taken between nine and ten o’clock in the morning. The lengths of the shadows cast by the
different stones can be measured (at some approximation from the map). Since the actual
heights and widths of the stones are known (see the subsection on the stones’ vitals), one can
estimate at what angle above the horizon the Sun was, when the shot was taken.
Of interest in this paper is the angle ω above the horizon the Sun is at, during noon time at
summer (maximum), at equinoxes, and during winter(minimum) solstice. This angle ω is of
course a function of the Earth’s axial tilt (currently estimated to be close to 2326’13”), and the
latitude of Stonehenge (5110’44”). At noon time during equinox, this angle is:
ω(E) = 90 - 5110’44” = 3849’16”;
at noon time during summer solstice, the angle is:
ω(SS) = 3849’16” + 2326’13” = 6215’29”;
and at noon time during winter solstice:
ω(WS) = 3849’16” - 2326’13” = 1523’03”.
From these angles and the known height of the sarsens outer circle, we can estimate the (sharp
edges) length of the cast-off shadow from sarsen #12 (and its lintel), albeit fallen at present, the
Southernmost upright orthostat of the Stonehenge 3 II outer ring. Given the height H including
its lintel (a total of about five meters) over the course of a year, and at these three critical dates
and at noon time, one can compute directly the sharp length L. From Trigonometry, it is known
that, the tangent of angle ω is tanω=H/L, thus (given the above-mentioned measurements): at
equinoxes, L(E)=6.21 meters; at summer solstice, L(SS)= 2.63 meters; and at winter solstice,
L(WS)=18.17 meters. The length 6.21 meters is the key here: it is almost exactly the distance
between the Trilithons’ Southernmost trilithon set’s sarsen #54 and outer ring’s sarsen #12.
This is a strong indication that the monument Stonehenge Phase 3 II was built on the basis of the
mathematical relations given in the previous section’s sub-section on the mathematical modulus,
and the above found distance L(E). These connections fully describe the monument’s design, as
the L(E) length determined the basic measures of the monument, the heights of sarsens in the
two enclosures and distances among them. The motion of this orthostat’s shadow through the
24
day, under sunlight, obeys the (2)-function of Figure 1, where A(2)=6.21 meters. In [1.1] the
author discussed the importance of the equinox (2)-function, as at this border a structural
change takes place on the 3-d -surface, regarding the forms of the 2-d -functions. We
conclude that this nodal point was the critical Stonehenge 3 II design attribute.
One can obviously carry this analysis for all 30+10 uprights in both enclosures for the three key
times of the year (for noon or any other time of the day under sunlight), and this is left for future
research and to any interested reader. More general (aggregate) analysis on these “relatively
short” (with sharp borders) shadows is next.
The short sharp shadows and Stonehenge 3 II key shadow length. First, the short cast-off
shadows of the monument will be analyzed now in some limited combinations. They are referred
to as relatively “short”, since cast-off shadows close to both sunrises and sunsets, as shown in
Figure 1, can obtain significantly long in lengths sizes. These effects will be addressed in the next
subsection. In this subsection, the effect of short in length cast off shadows from the outer ring
to the Trilithons’ ensemble, and from the Trilithons’ ensemble to the outer ring of sarsens will be
analyzed when some combinations of stones are considered.
Along with this analysis, the inter-stone cast off shadow connections will be examined, as for
example the shadows cast from the set of upright sarsens #25 to #7 onto the Trilithons and outer
ring sarsens at sunrise during the summer solstice. A series of diagrams along these lines can be
produced to demonstrate the effect throughout the daylight time (or night time under
moonlight) at a particular set of days during the year. Computer simulations can produce 3-d
moving graphics to that effect. However, the key points can be adequately made with some key
graphs, although this doesn’t preclude some additional findings as a result of the suggested
computer simulation based search.
Only two snapshots will be discussed here. One is the case shown in Figure 6.a; the other is the
case of Figure 6.b.
In Figure 6.a, the case of Stonehenge 3 II’s cast-off shadows are shown at the indicated date,
August 13. The length of the shadow is about 1.2 times the height of the upright sarsens
(including their lintel). This is the cotangent of the angle above the horizon the Sun was at the
time the photo from Google Earth map was obtained. In turn, this implies that the angle was
about 40 and the time must have been between 9:30 and 10 am (local time). What is apparent
from the photo is that the outside ring’s shadows gently touch the Trilithon’s ensemble, during
their top’s movement towards the North, as the Sun is moving (in its apparent motion) towards
the West. This gentle touch is maintained throughout the motion, as is demonstrated in the
following Figure 6.b, where the autumnal equinox cast-off shadows are shown at noon time.
25
Figure 6.b. Equinox day, noon time shadows. Stonehenge Phase 3 II and its dual, the shadow cast
by some of its Trilithons ensemble pillars and the lintels of the (completed, in theory) outer ring.
The key distance of about six meters is depicted; that is where the shadow from the outer 30-
sarsens ring structure touches the outer skin surface of the Trilithons ensemble and the distance
between stones #11 and #54 is bridged. This distance is the only variable needed to completely
specify the monument’s various components measures according to the mathematical modulus.
Source: the author.
26
The effect pf this motion becomes more evident in the selected shadows shown in Figure 6.b. It
depicts the cast-off shadows at noon during equinox. Prominent in that Figure is the lintels ring
shadow on the ground. Shadows cast by the surviving upright sarsens from the Trilithon
ensemble are also shown in this Figure that shows the duality of Stonehenge 3 II, as discussed at
the Introduction, this being an intrinsic duality shadows bestow on any object under sunlight (or
moonlight). Undoubtedly, this duality didn’t escape the architects of Neolithic monuments.
To be emphasized, is an important finding from the analysis, indicated by the cast-off shadows
at noon during the equinoxes in Figure 6.b (as it was also shown in Figure 6.a): it is the 6-meter
distance covered by the shadows of the Southernmost point of the lintels’ ring touching the
Southernmost sarsen of the inner quasi-elliptical stone enclosure (arc) of the Trilithons ensemble.
That is, the shadow cast off from stone #12 (now fallen) upon stone #54.
Here, one must also note the effects of medium in length shadows, like those cast off the heal
stone onto the sarsens outer ring at time intervals between sunrise/sunset and noon time.
The long shadows and the links between the monument and its environs. Now, the possible
effects of relatively long shadows will be analyzed, the shadows’ very large macro-scale. They
bear considerable similarities to alignments, although they are also quite different in many
respects along with the kind of information about the monument they convey. At the beginning
of this sub-section, the relatively short segment of the long cast-off shadows falling within the
floor area of the Stonehenge 3 II Phase monument will be looked at and their shapes will be
analyzed.
In the set of Figures 7.a, 7.b, and 7.c, the short distance effect of the part of the long shadows is
examined at summer solstice, equinox, and winter solstice sunrise correspondingly. That part (in
which the lintels play no role) of the very long shadows falls within the monument’s floor plan,
cast-off the still standing sarsens at Stonehenge are shown in the set of the three Figures. A
number of key observations can be made.
As a direct result of the Geometry involved, the slits among the uprights allowing sunrays to
penetrate the monument’s Eastern section of the outer ring get progressively thinner towards
North and South. The sunrays either reach the Trilithons Ensemble Eastern section of the quasi-
ellipse; or go through the Eastern part of the quasi-ellipse and them touch either the Western
part of the quasi-elliptic arc, or get to the diametrically opposing sarsens on the outer ring.
Moreover, the thickness of the sarsens’ shadows get progressively greater, so that beyond a point
(a point that depends on the day of the year under consideration) the entire Northern and
Southern section of the monument’s floor plan is under shade.
27
Figure 7.a. The Stonehenge 3 II floor plan during sunrise at summer solstice. The short part of the
very long sunrise shadows is shown inside the sarsens outer circle. Only the cast-off shadows
from still standing sarsens in the outer ring and the Trilithons ensemble are drawn. The sunrays
are parallel lines. Source: the author.
In Figure 7.a, it is shown that the main alignment of Stonehenge 3 II, the summer solstice sunrise,
allows for light to penetrate the entire floor plan from three spaces between the frontal sarsens
of the outer ring: besides the main and widest opening between uprights #1 and #30, there are
28
two more to that opening’s either side: that between #29 and #30 (to the North) and between
#1 and #2 to the South. These three slits allow for a complete penetration of the floor plan.
Whereas the next two (that between #2 and #3, as well as that between #28 and #29) are not
translucent, as sunrays fall on Trilithons Ensemble sarsens. To the North of #27 and South of #4
the floor plan of the monument is in shade.
Figure 7.b. The Stonehenge 3 II floor plan during sunrise at equinox. The specifications are as in
Figure 7.a. Source: the author.
29
In Figure 7.b, the same conditions are shown but for the sunrise at equinox. Stones #51, #52, #57
and #58 of the Trilithons ensemble now attain significant importance, as they become the main
receptors of the sunrise rays inside the monument’s inner sanctum. The importance of the vernal
equinox has already been addressed in the text, as it was the importance (and associated
carvings) of stone #4.
Figure 7.c. Stonehenge 3 II floor plan at sunrise during the winter solstice. The specifications are
as in Figure 7.a. Noticeable is the translucent nature of the sunrise rays. Source: the author.
30
Some general thoughts on the very long shadows. A number of remarks will be made here
regarding the nature of very long shadows, associated with conditions very close to both sunrise
and sunset (moonrise and moonset as well). This type of shadows has fuzzy borders, the fuzzy
nature of shadows having already been extensively discussed by the author in [1.3]. A key rule
applicable in shadows is that the further away from the object, the fuzzier the shadow gets,
implying a lower in intensity tone. Thus, very long shadows have undiscernible ends, largely due
to increasingly fuzzy borders. Moreover, they get progressively wider as they get longer (and
further away from the source). Since the very long shadows’ edges are becoming progressively
less sharp, their extent becomes increasingly difficult to gauge.
However, very long shadows are means to link distant objects upstream (sunrise) or downstream
(sunset). These connections provide ways to associate the monument’s elements to various
features of the site’s immediate or distance environment (including landscape, topographical,
geographical) features and anomalies (bumps, mounds, tells, hills, mountain peaks etc.) These
associations tie up the monument to its broader close by or distant surroundings. These features
acquire additional importance as ground heterogeneity and anomalies tend to either enhance or
depress certain of the monuments features (and shadows) by design. In combination, these
geographical attributes and how they are incorporated into the site and floor plans of a
monument link the monument to its environment’s locational comparative advantages (that is
to factors which make the site suitable for the particular monument according to the architect’s
design and plan). In turn, this monument enhances the locational comparative advantages of the
site in a positive feedback loop. Shadows are tangible traces of these locational interactions.
Alignments are more closely connected to long range (length) shadows. Since alignments are by
nature long distance interactions, very long shadows provide the means to manifest them in a
tangible way. This equivalence between alignments and shadows has been already pointed out
in the Introduction to this paper. It would be useful to check the effects of Stonehenge 3 II
shadows on the surrounding environment, as well as the effects of the surrounding environment
on Stonehenge in view of the above general thoughts. This is left to further future research.
A lintel’s shadow.
How many Sun disks would take to overcome the lintels height, and project their shadows on the
ground? This question is of both theoretical and empirical interest. When the source of light, as
is sunrise or sunset light, falls below a lintel’s level, then the lintel’s shadow is projected in the
atmosphere not the ground. Although not directly observable (unless an object gets in the way),
the mathematics of shadows described in [1.3] determine the extent and nature of that shadow
as well.
The moment of the day, and the distance from the monument at which the lintels’ shadow hits
the ground determines the “effective influence area” in space-time of the lintel carrying
monument. This extension, along the notion of an “effective in space-time influence area”
31
regarding monuments where lintels are involved in free standing stone enclosures, is potentially
an interesting direction to extend the analysis presented here on Stonehenge and the General
Dynamic Theory of Shadows, first outlined in [1.1].
Conclusions and suggestions for further research
The key finding of this paper was that Stonehenge Phase 3 II is a far more complex in Design
structure than previously thought. Whereas much has been written with reference to the so-
called “altar stone”, the omphalos of the monument is the center of the outer ring’s circle and
barycenter of the entire Phase 3 II monument (not just of the outer 30-sarsen stone circle).
Phase 3 II of the monument was designed on the basis of two (not a single) major alignments and
a key shadow, in addition to a mathematical modulus which was in turn based on ratios obeying
the sequence 2-3-5. The two alignments imprinted on Stonehenge Phase 3 II were (of course) the
summer solstice sunrise, an issue extensively (and almost exclusively) having been discussed in
the Stonehenge existing literature. However, beyond this alignment two more alignments are
found at Stonehenge 3 II, and one of them played a pivotal role in its very design specifications.
One is the extension of the main summer solstice sunrise alignment, namely the winter solstice
sunset. The other is the sunrise at equinoxes and most importantly, the alignment during noon
time at either vernal or autumnal equinox.
The equinox’s alignment is of fundamental import for a key reason: at noon time at equinox, the
cast-off shadow from the outer ring touches the Trilithons Southernmost sarsen, thus linking the
two stone enclosures (the primal and its dual). That duality is more than just symbolic: it is when
(at the primal) the site receives the maximum amount of day light (when the Sun is at the
maximum angle above the horizon); whereas, at the same time the length of the shadow (the
value of the dual) is at a minimum. At that moment, the length of that shadow is at a distance of
about six meters. That distance is the pivot into the design of the entire monument, as major
aspects and components of the monument obey ratios that can be expressed as multiples of
numbers 2, 3, and 5.
The paper analyzed to an extent the discrete (snapshot) dynamics of shadows, especially the
shorter sections of the long (and sharp) shadows during the summer and winter solstices as well
as at equinox. Some rules governing these snapshots and the motion of these shadows were
outlined. Moreover, the paper discovered that the Trilithons quasi-elliptical ensemble of sarsens
is a simpler case of those presented by Alexander Thom. This simple form falls within a set of
distinct categories, discussed in [1.8], where it was found that this stone enclosure describes the
Gobekli Tepe structurer D, Layer III stone enclosure. Hence, another strong link was established
in this paper between Phase 3 II Stonehenge and Fertile Crescent Architecture.
Numerous suggestions have been made for further research. Computer simulations in 3-d,
involving the shadows’ daily movement over a year, at the latitude of Stonehenge, and under
32
different environmental conditions, would enhance the documentation of their effects upon the
monument. Computational complexity, due to the large number of stones and their relative
positions in the floor plan, could be to an extent tackled through such computer simulation.
Bluestones and their rings were not included at this stage in the research. Obviously, they played
also a role along with their shadows in the organization and use of space at the later date when
they were positioned as it has been suggested in the literature. Work along these lines might
offer more insight into the positioning of the two Bluestone enclosures and the sequence
involved. Lastly, in terms of extensions, of course the angle of the sarsens’ carry-on shadows and
their motions is a chapter all to itself, in need of further work. One need not forget that this is
work involving Sun derived shadows. On Moon-derived shadows, much is to be still done, both
analytically and computationally.
In concluding this final remarks, something must be said about a subject little addressed here:
culture, symbolism and ceremony related connections for monuments and their shadows.
Symbolism, ceremony, cultural role of the monument as it might relate to both static and
dynamic versions of shadows is an area suggested as being of considerable interest for further
research. Specifically, in view of the interpretation of shadows within a male-female symbolism,
this type of analysis might provide suggestions as to the meaning of the two stone enclosures in
reference to each other. What do the two stone enclosures of Stonehenge Phase 3 II represent?
May be a male and female symbol, where the Trilithons ensemble stands for the male and the
sarsens circle for the female? Could the shadow (the dual) of the monument (the primal) also be
an enhancement to this primordial male-female duality? No doubt these are issues to ponder, in
view of the corresponding symbolism detected at Gobekli Tepe’s two central pillars present in
structures C and D of Layer III. Although symbolism and cultural aspects of this interconnectivity
among stones have not been part of this paper, it doesn’t follow that they are not as important.
Notes
Note 1: Newcomb’s work. Simon Newcomb’s classical work, of interest far beyond its
Astronomy related material and written at the dawn of the 20th Century, analyzes at great
mathematical lengths some basic astronomical concepts of use when reviewing the design of
monuments: solar and sidereal (a time duration measured against “fixed stars” and not the Sun,
resulting in one more rotation along the Earth’s axis of rotation completed in a year as a result of
the Earth’s annual orbit around the Sun, a fraction less than the solar, 360/365.2422) days and
time, right ascension (Celestial longitude) and declination (Celestial latitude), nutation (change in
the angle of the Earth’s axis of rotation relative to the Celestial equatorial plane due to many
factors), precession of the equinoxes (due to the approximate 26Ky cycle of the earth’s axis of
rotation), obliquity of the ecliptic (the Earth’s axial tilt), ecliptic (the apparent motion of the Sun
in the Celestial Sphere, due to the Earth’s orbit around the Sun), equinoctial day (the slightly
longer time of the daylight due to the rising of the Sun’s top before the center of the Sun’s disc
33
appears over the unobstructed horizon) and atmospheric refraction (a factor slightly altering the
visibility of the Sun during sunrise and sunset due to the atmospheric conditions, varying among
various geographic locations) are some among many other key astronomical events and concepts
of relevance here. They require some advance knowledge of both Mathematics (including
Trigonometry and Calculus) as well as Earth related Astronomy.
However, three issues that a reading of this classical reference brings to the forefront, in so far
as the work here is concerned, are the following: the difference in azimuths between the 2500
BC and today; a possible reason why (among the many) lunar cycles were of import back then;
and the broader topic/problem of approximations. We shall briefly review them in turn.
In reference to the change in azimuths, on p. 232 in [2.3[ one reads that over a 350-year period
(1750 2100 AD) Newcomb estimated a change in the position of the ecliptic of less than 1;
specifically, he computed a change from about 616’ to about 77’ or 51’. Extrapolating this to a
period of four and one half millennia (2500 BC – 2000 AD), a time period which spans about one
sixth of the approximate 26K-year cycle of the Earth’s axis of rotation, produces a change of about
1245’. However, this isn’t very informative, as we do not know how much on the azimuth this
change really represents (keeping in mind that half of the cyclical motion in the N-S axis projected
on the azimuth plane is in the opposite direction of the other half of the motion). No one has
estimated the change in the ecliptic going so far back, as the computing gets quickly intractable
and computer simulations can only supply gross approximations. Thus, one is not clear on the
actual shift in the N-S axis from the time of Stonehenge Phase 3 II to today. Some, like A. Thom,
propose that it has been less than 1. With a maximum of about 6, its actual size remains
unknown. However, Stonehenge stone enclosure sarsens #1 and #30 may be informative given
the todays’ summer solstice azimuth there and may be can offer hints (explored in the main text
of the paper).
A second key aspect of Newcomb’s work, and of extreme importance for the purposes of our
discussion here regarding solar versus lunar cycles, is the note he has on p. 253 in [2.3], regarding
nutation and precession of the equinoxes. Newcomb remarks (without citations) that the
ancients estimated the length of years by either of two methods: one was that by measuring the
time interval between two equinoxes; the other was by measuring the time interval taken by the
Sun to complete a full revolution in its apparent motion among some stars (and thence, certain
Constellations must have been key in this regard). And here comes into the calculus the
importance of the Moon in the estimation of the yearly length. As the Sun is not possible to track
in its apparent revolution among stars (invisible to their naked eye when the Sun is above the
horizon), they used as a substitute, the Moon. Newcomb remarks on p. 253 (and without any
references) “At the middle of a total eclipse of the moon, the latter was known to be directly
opposite the sun, and its position among the stars could be determined. The distance of the moon
from the sun could also be measured before sunset, and from a star after sunset.”
34
It is obvious that these “ancient astronomers” Newcomb alludes to must not have been prior to
the second century BC Greek astronomer Hipparchus, whom Newcomb mentions (correctly) as
the discoverer of the precession of the equinoxes. Thus, we are left still in the dark, as to whether
the architect(s) and astronomers of Stonehenge had any knowledge of the Heliocentric system.
No evidence is there that they did, and we know that Aristarchus in the 3rd century BC was the
first to formally suggest it. Indications however do exist that the system was known at the
beginning of the 4th century BC, see the discussion on this issue in the paper by the author [1.9],
(p. 17, Note 2 on Philolaus the Pythagorean). But we are left pondering the supposition that the
use of the lunar cycles and prediction of the lunar events (phases and eclipses as well as the 18.6-
year cycle) was of necessity to them. This is a subject addressed more in detail in Note 2.
Finally, the third issue abundantly made clear by Newcomb in his classical treatise on Spherical
Astronomy is the significance of approximations in astronomical observations and the
unavoidable errors in them. Interestingly, Newcomb considers the issue equivalent to British
Criminal Law (p. 343), as he says when referring to an observatory and its observations: “the
instrument is indicted as it were for every possible fault, and it isn’t exonerated till it has proved
itself correct in every point”. It is noteworthy that according to US Jurisprudence (which is based
on Anglo-Saxon Law), one is considered innocent until proven guilty by a judge or jury of his/her
peers. Thus, one must question the validity of Newcomb’s analogy, as his dictum (or adage) is
more like Roman rather than British Criminal Law. Be that as it may, Newcomb does make a
significant point about approximations. In any case, no matter the acceptable degree of
approximations made through the use of advanced statistical methods and record keeping, use
of more perfect observational tools (telescopes), or the accounting for more factors interfering
with the accuracy of astronomical records, the errors and the level of approximation attained will
always leave something to be desired. On top of all factors which have been accounted for in the
drafting of astronomical ΕΦΗΜΕΡΙΔΕΣ, there will be always deviations, due to the eternal motion
of the bodies in the Celestial Sphere, and due to the Earth’s to an extent chaotic movements, the
result of Earth’s multiple gravitational interactions with all planets and the Sun. This is a factor
which in effect renders eventually all immobile sources of astronomical observations (as the
Neolithic monuments partially were) obsolete.
Note 2: Why Lunar based monuments? In this Note, we address more in detail the question as
to why would the Neolithic architects, astronomers, and their agricultural communities who
sustained the social elites, who in turn employed them and sponsored the construction of these
monuments, be interested in lunar cycles. Obviously, the Neolithic people needed a calendar for
a host of reasons, and a monument was an instrument for deriving calendar related dates.
It is well understood that solar cycles were of paramount import in Upper Paleolithic, Mesolithic
and Neolithic eras simply because of the agriculture related impacts that season had. Thus, from
35
a purely economic-utilitarian angle, Neolithic farmers and their elites would be interested in
tracking down as accurately as possible solar cycles.
On top of that, we understand from the Social Science angle of Archeology that Neolithic farmers
attached ceremonial, as well as symbolic meaning to the Sun and the Moon; thus, this is a reason
for tracking down lunar cycles – time markers for festivals and other related cultural activity. In
addition, as we do today commemorating significant social events, probably so did the ancients
they needed a calendar to keep track of remembering important events to them (like the
memory of the date some major social figure passed away or was born), or the remembrance of
some significant to them social event (the outcome of a raid or battle, for example).
All the above are reasons to demand a social calendar, in which the Sun played a major role, as
did the Moon – and which one was more important obviously depended on social factors beyond
the interest of this paper – as did locally important events. What this brief set of notes imply is
this: there could be monuments (and that may include also Stonehenge) where some alignments
were implanted, having nothing to do with major lunisolar cycles, pegged to social events we
simply are not at present aware. Seeking in monuments simply or exclusively lunisolar cycles is
most likely misleading.
However, beyond all these caveats, there is another reason, suggested in Note 1, why some lunar
cycles might have been of import: it was a way to track the very important spring equinox to
estimate the exact length of a year. In effect, this may have been the single most important factor
as to why lunar cycles were important to track, since these cycles per se do not impact in any
direct way agriculture. And Agriculture (Economics, that is) maybe was far more important to
them than leisure embedded in social ceremonies.
Note 3: The British Heritage Sources. In this Note, we supply some more specifics about the
monument at Wiltshire’s Stonehenge in Salisbury Plain. The site plan in Figure N1 has the
immediately surrounding part of the monument to the sarsens circle and the Trilithons ensemble
we examined here. The three major phases of the monument are indicated. The diagram
provides the location of some related stones, off the immediate section of the floor plan analyzed
in this paper, like the heal and slaughter stones – clearly informative in terms of the ensemble’s
orientation.
In the last sub-sections of the last section of the paper, the possibility was raised (and much has
been written along these lines in the existing literature) that the broader site plan’s shadows also
played a role in the determination of the Stonehenge 3 II Phase floor plan. This is consistent with
what numerous authors have pointed out while addressing the links between that Phase of the
floor plan and not only the Heal and Slaughter stones but also other features of the site plan in
terms of alignment, and also in terms of shadows, and some of that literature is cited in the Figure
N1 citation.
36
In this Note, a remark made in the main text of the paper will be further elaborated. The paper
mentioned the monument as “so-called at present” Stonehenge at a place currently called
Wiltshire at a place called Salisbury Plain. It was mentioned in such a manner of course, because
these are current terms and nomenclature regarding toponyms and monuments that current
socio-cultural conditions employ in labeling monuments and sites.
Figure N1. The three major Phases of the Stonehenge complex, with the various components of
the monument. The dark section is the part studied in this paper. Location of various stones
associated with the Phase 3 II monument orientation (heal and slaughter stones) are indicated
at the bottom diagram. The stone not shown here and of import is the altar stone, lying just in
front of the Southwestern trilithon set, at the very center where the slit between its two uprights
#55(a) and #56 is found. Source: British Heritage, https://www.britannica.com/topic/Stonehenge
37
In a paper on Gobekli Tepe, see [1.8], the author raised the point that current nomenclature on
monuments does not usually reflect the nomenclature used by the culture that built these
monuments. Similar is the case for the monument at Newgrange (as well as all the River Boyne
passage tombs), Carnac at Brittany, and the Temples of the Maltese Archipelago, to mention only
those referred to in this paper.
As a result, and to avoid unnecessarily loading a monument with the current socio-cultural
baggage, it was suggested for scientific reasons to use names for archeological sites drawn from
a system similar to those employed by astronomers in calling stars and galaxies (like the Messier
or the NGC systems, in that case). Naturally, this scientific system of toponyms and monuments’
names could co-exist with any name a local culture at any specific point in time would choose to
use to call a monument or a location, keeping in mind that these cultures change over time.
Note 4. More on the modulus at Kasta Tumulus. In this Note more elaboration is offered on
the modular structure of a far more recent monument where a round structure was possibly used
as a calendar, the late 4th century BC Amphipolis’ Kasta Tumulus’ perimeter wall. In reference
[1.7] the author demonstrated that the perimeter of the tumulus was linked to an annual
calendar. Throughout the time period August 2014 till October 2016, the tumulus was thought
to have had a circumference of 497 meters, according to repeated and multiple announcements
by both the archeological team and the Greek Ministry of Culture and formal architectural
drawings produced and shown to the public although never published or presented in any
appreciable detail. In October 2016, the architect of the archeological team announced that the
perimeter wall had a length of 498 meters, without any documentation or explanation as to why
the 497-meter length of the August 2014 to October 2016 time period was suddenly increased
to 498 meters.
In any case, if the total length of the tumulus’ perimeter is 498 meters, then this length implies a
ratio of 366.1765 (498:1.36) given the 1.36m length of the monument’s modulus. The number
366.1765 is close to the sidereal number of days (365.22+1) a finding which would imply an
understanding of calendar time based not on solar years but on time calculated based on the
position of fixed stars in the Celestial Sphere. This would imply a new understanding from our
part of the astronomical knowledge at the period when the formation of the tumulus at Kasta, in
Amphipolis took place (currently estimated to have occurred around the beginning of the fourth
quarter of the 4th century BC and following the death of Alexander III in Babylon). For more on
this issue, the reader is directed to the numerous papers written on the subject by the author,
see reference [1.10].
With this short Note, the author amends and extends the material presented in reference [1.9]
and all associated with it prior references.
38
References
The author’s related work
[1.1] Dimitrios S. Dendrinos, 24 January 2017, “The Mathematics of Monoliths’ Shadows”,
academia.edu.
The paper is found here:
https://www.academia.edu/31101997/The_Mathematics_of_Monoliths_Shadows
[1.2] Dimitrios S. Dendrinos, 15 November 2016, “In the Shadows of Carnac’s Le Menec Stones:
A Neolithic proto supercomputer”, academia.edu. The paper is found here:
https://www.academia.edu/30164088/In_the_Shadows_of_Carnacs_Le_Menec_Stones_A_Ne
olithic_proto_supercomputer
[1.3] Dimitrios S. Dendrinos, 1 March 2017, “On the Fuzzy Nature of Shadows”, academia.edu :
https://www.academia.edu/31671102/ON_THE_FUZZY_NATURE_OF_SHADOWS
[1.4] Dimitrios S. Dendrinos, 25 November 2016, “Gobekli Tepe: a 6th Millennium BC
monument”, academia.edu:
https://www.academia.edu/30163462/Gobekli_Tepe_a_6_th_millennium_BC_monument
[1.5] Dimitrios S. Dendrinos, 21 November 2016, “A Carnac Conjecture: Neolithic
experimentation with Primitive Pythagorean Triples?”, academia.edu; the paper is here:
https://www.academia.edu/30163918/A_Carnac_Conjecture_Neolithic_experimentation_with
_primitive_Pythagorean_triples
[1.6] Dimitrios S. Dendrinos, last update 10 September 2016, “From Newgrange to Stonehenge:
monuments to a Bull Cult and origins of innovation”, academia.edu; the paper is found here:
https://www.academia.edu/28393947/From_Newgrange_to_Stonehenge_Monuments_to_a_B
ull_Cult_and_Origins_of_Innovation
[1.7] Dimitrios S. Dendrinos (with Vassilis Petropoulos), 4 December 2014, “The Modular
Structure of the tomb/monument at Kasta Hill”, academia.edu. The paper is found here:
https://www.academia.edu/10923712/The_modular_structure_of_the_tomb_at_Kasta_Hill_by
_D_Dendrinos
[1.8] Dimitrios S. Dendrinos, 19 September 2016, “Dating Gobekli Tepe: the evidence doesn’t
support a PPNB date but instead a much later one”, in academia.edu. The paper is found here:
https://www.academia.edu/28603175/Dating_Gobekli_Tepe
[1.9] Dimitrios S. Dendrinos, 17 February 2016, “The Earth’s Orbit around the Sun, and the
Tunulus at Kasta”, academia.edu. The paper is found here:
https://www.academia.edu/22103391/The_Earths_orbit_around_the_Sun_and_the_Tumulus_
at_Kasta._Update_1
39
[1.10] https://kansas.academia.edu/DimitriosDendrinos
[1.11] Dimitrios S. Dendrinos, 21 January 2017, “A Primer on Gobekli Tepe”, academia.edu. :
https://www.academia.edu/31039270/A_Primer_on_Gobekli_Tepe
Other sources
[2.1] By Anthony Johnson - Drawn by Author (AJ), a computer compilation of data from various
surveys., CC BY 3.0, https://commons.wikimedia.org/w/index.php?curid=4871482
[2.2] http://www.english-heritage.org.uk/visit/places/stonehenge/history/
[2.3] Simon Newcomb, 1906, A Compendium of Spherical Astronomy: with its applications to
the determination and reduction of positions of the fixed stars, MacMillan, New York. In
electronic form the book is here:
https://books.google.com/books?id=CAxDAAAAIAAJ&printsec=frontcover&source=gbs_ge_sum
mary_r&cad=0#v=onepage&q&f=false
[2.4] Alexander Thom, 1971, Megalithic Lunar Observations, Oxford University Press, Oxford.
[2.5] Aubrey Burl, 1976, The Stone Circles of the British Isles, Yale University Press, New Heaven.
[2.6] Alexander Thom, Archibald S. Thom, 1978, Megalithic Remains in Britain and Brittany,
Clarendon Press, Oxford.
[2.7] G. Terence Meaden, 2017, “Stonehenge and Avebury: megalithic shadow casting at the
solstices at sunrise”, forthcoming in the Journal of Lithic Studies.
[2.8] A highly specialized blog is that by the name “Do you look at shadows” found here:
http://www.megalithic.co.uk/modules.php?op=modload&name=Forum&file=viewtopic&topic=
7230&forum=1&start=100
It is hosted by the site “Megalithic Portal” found here: http://www.megalithic.co.uk/index.php
[2.9] G. Terence Meaden, 2017, “”Dromberg Stone Circle, SW Ireland: design plan analyzed with
respect to sunrises and lithic shadow-casting for the eight traditional agricultural festival dates –
and further validated by photography”, forthcoming in the Journal of Lithic Studies.
[2.10] https://www.facebook.com/groups/991876107537537/permalink/1239078399483972/
[2.11] Rosemary Hill, 2008, Stonehenge, profile Books, London. The book is also found here:
https://books.google.com/books?id=-
vWrImYK8K0C&pg=PA170&lpg=PA170&dq=peter+Newham+and+the+Station+Stones#v=onepa
ge&q=peter%20Newham%20and%20the%20Station%20Stones&f=false
[2.12] Anthony Johnson, 2008, Solving Stonehenge, Thames and Hudson, London.
40
Acknowledgements
The author wishes to acknowledge the contributions made to this paper through his interaction
with members of the Megalithic Portal website (http://www.megalithic.co.uk/index.php ). The
author wishes to thank the site manager Andy Burnham; and also, the members of the sub-group
in it “Do you look at the shadows”. Within this group, in specific, the author wishes to recognize
the contributions by David Smyth (Energyman), Neil Wiseman (Feanor), and Richard Bartosz
(Orpbit). David Smyth has been instrumental in encouraging the author to participate in that
group, and for introducing the author’s prior work to the group members.
Furthermore, the author wishes to recognize his Facebook friends and especially those who are
members of the seven groups the author has created and is administering. Their continuous
intellectual and artistic stimulation and support have been remarkable and thus a great sense of
gratitude is extended to them as well. Special mention must be made to Professor Terence
Meaden for his contribution, and especially his work on the shadows at Drombeg and
Stonehenge.
But most important and deer to this authors has been the more than 20 years of encouragement
and support he has received from his wife Catherine and their daughters Daphne-Iris and Alexia-
Artemis. Their continuing assistance and understanding for all those long hours he spent on doing
research, when he could have allotted time with them, this author will always be deeply
appreciative.
Legal Note on Copyright
© The author, Dimitrios S. Dendrinos retains full copyrights to the contents of this
paper. Reproduction in any form of either parts or in whole of this paper is
prohibited, without the explicit and written consent and permission by the author,
Dimitrios S. Dendrinos.
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... From [2. 16], and the diagram of Figure 4.1, the horizontal cross-section diameter of the 38 peristyle columns is found to be about one meter, measured from the columns' center to the top point of the flutes' edges. Consequently, we find that the variable y is about 1.67 meters (again, longer than the Vitruvius' estimate of 1.5 times the column's diameter at the base); and variable y' is about 1.62 meters, quite close to (but slightly less than) the narrow side's intercolumnium. ...
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A new survey of Drombeg Stone Circle and accurate analysis of shadow effects beginning at particular sunrises of the calendar year has led to a breakthrough in the understanding of lithic symbolism and the intentions behind the construction of this and other Irish monuments including Knowth and Newgrange that also have astronomical alignments. At Drombeg specific standing stones play critical roles at sunrise for all eight of the festival dates as known traditionally and historically for agricultural communities and as now inferred for prehistoric times following the present observation-based analysis.Crucial for Drombeg in the summer half of the year is the positioning of a tall straight-sided portal stone such that its shadow at midsummer sunrise encounters an engraving on the recumbent stone diametrically opposite. During subsequent minutes the shadow moves away allowing the light of the sun to fall on the carved symbol. It is the same for sunrises at Beltane (May Day), Lughnasadh (Lammas), and the equinoxes when shadows from other perimeter stones achieve the same coupling with the same image, each time soon replaced by sunlight. For the winter half of the year which includes dates for Samhain, the winter solstice and Imbolc, the target stone for shadow reception at sunrise is a huge lozenge-shaped megalith, artificially trimmed. Moreover, for 22 March and 21 September there is notable dramatic action by shadow and light between a precisely positioned narrow pillar stone and the lozenge stone.As a result, at sunrise at Drombeg eight calendrical shadow events have been witnessed and photographed. This attests to the precision of Neolithic planning that determined the stone positions, and demonstrates the antiquity of the calendar dates for these traditional agricultural festivals. Discussion is held as to what the concept of shadow casting between shaped or engraved stones at the time of sunrise may have meant in terms of lithic symbolism for the planners and builders. This leads to a possible explanation in terms of the ancient worldview known as the hieros gamos or the Marriage of the Gods between Sky and Earth.
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