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The Problem of the Standing Stones
It is the burden of anyone who supports a ritual basis for MH to prove that the standing stones are not features which, among the other stones of the walls, meant to keep in the sheep rather than keeping out evil spirits! If the site was configured along the lines of proven astronomical monuments, such as Stonehenge, Callanish, etc., I would not need to say this. Such sites immediately strike one's eye -- they are not functional habitation or subsistence features, yet their builders expended inordinate amounts of energy to set them up impressively. They were constructed to be evident astronomical and ritualistic markers.
Mystery Hill, on the other hand, has stimulated so much controversy that it is evident that it is not evidently anything! Perhaps this controversy would have been less had the site's stones been larger and more regular, not low and irregular, and if they had been part of precise site geometries, not uneven ones. The fact is, most ritual sites bear marks of evident rituality. Size, method of construction, geometry, and decoration are some of the markers of rituality; serious researchers must ask themselves why MH shares in few of these definitions. The following sections of this report examines each of these factors.
The Form of the Standing Stones
A study of the form of the standing stones addresses one of the major points cited by interested laypeople. What sets MH apart from the usual stone walls and root cellars of New England is the degree to which large slabs are incorporated into the constructions. It is often stoutly expounded that New England farmers simply did not construct stone walls of this kind. The "odd" stone walls also incorporate some slabs that, in many people's eyes, evidence purposeful shaping by human hands.
I might devise a hypothesis to test the ritual/nonritual bases of the site by examining the consequences of each possibility. For example: If colonial or post-colonial farmers built Mystery Hill, then we will not find evidence of purposeful shaping of stone slabs -- they would save time and energy by using natural, stable slabs as uprights, and laying all others within the stone walls. I could also state this in the reverse: If ancient Europeans or Indians built Mystery Hill for ritual purposes, then the components of the site should evidence regularity and symmetry to signal the rituality of the site -- thus the builders would be inclined to choose natural slabs of close dimensions, or to fashion natural slabs into regular components. Since it is unlikely to find regularized natural slabs, the fabrication of slabs into site components is the most likely consequence of rituality.
We can test either of these hypotheses by examining slabs in a natural state and comparing them with the form of the uprights to see if the uprights are natural or fabricated. I will discuss below how the shapes of the standing stones come as no surprise; similarly, we may find that a farmer could have a good reason to incorporate heavy slabs in his walls.
Availability and Form of Materials
Slabs are a naturally occurring building material at MH. The hill is like a laminated dome. Layers of metamorphic rock exfoliate from the surface like the layers of an onion. As a result, the builder has a quantity of large slabs with which to build. Thus it comes as no surprise that there are dozens of slabs within the stone walls, as well as the more familiar glacially shaped and deposited boulders.
Given the fact that slabs are abundant natural features of the hill, we must ask, "Are the slabs that form the cultural component of the hill in a natural or fabricated form?" Since many of the slabs incorporated into the chambers and stone walls are relatively square at their base-- and thus somewhat stable when set upright -- and since many of the standing stones are 'pointy' at the top, it is sometimes claimed that someone dressed the stones. The conclusion that is implied is this: a farmer would not spend time shaping slabs of stone for his stone walls, and, therefore, the constructions must have been made by other builders for another, perhaps ritualistic, function -- the hypothesis we must test.
A survey of naturally occurring slabs that lie on the site's eastern slope helps test the hypothesis. Here, many slabs of stone are breaking from the bedrock and are sliding downslope, often hastened by the growth of trees whose roots exploit the cracks and drive a wedge between slabs and bedrock. There is general tendency for the slabs to break off from the bedrock along their long axis (i.e., they appear to move "sideways" down slope). The fractures on the uphill (or fresh) side tend to be thick and often "square edged" (i.e., could form a stable base as a "standing stone"). The downhill, "leading" edges tend to be wedge-shaped and often fractured. The fractures are often characterized by 'cupped' depressions that mimic the concavities of small stone tools. In addition the concavities often alternate sides along the edge of the slab, i.e., a foot or so of the edge is slanted toward one side of the slab, and then a foot or so is slanted toward the other side.
These characteristics arise from erosion. The leading edges of the slabs are often thinner (and perhaps more susceptible to fracturing) because downhill erosion has smoothed the bedrock (see Figure 5). The trailing edges are thicker and straighter by comparison because of the relative freshness of the breaks. Slabs that have moved a distance from their fracture points are difficult to comment upon. Gravity and weather have shifted them from their positions, and the relationships between their thicker, straighter sides with their fracture points has been lost. We can assume that these slabs originated in a way similar to their relatives, which are still in the process of breakage and downslope travel. See Figure 6 for some diagrams of the slabs from this part of the hill.
Many slabs have about four or five sides. Notably so, many of the slabs are elongated and often 'pointy' towards one end (see Figure 6 above). It becomes increasingly clear that the standing stones on the site resemble the natural slabs laying close to their provenance. The ideally square, stable bases that supposedly characterize the standing stones are natural features. If it is found that a higher percentage of the standing stones have stable bases, it is simply probable that the builder of the walls selected the stablest natural slabs in the vicinity of his construction.
The features noted above are notable only because similar features at the site are sometimes cited as the work of human hands. All such features result probably from the unequal structural characteristics that arise from erosional variations. Even a cursory observation of the natural slabs shows similar features already in existence or in the process of appearing; the possibility of purposeful shaping by humans is not likely.
We may also examine ritual/nonritual possibilities by noting the unequal forms of the standing stones. Some of them, the "February 1 sun set stone," for example, are barely tall enough to form a recognizable astronomical marker. Others, such as the "winter solstice stone," are ideal markers because they are “pointier” at the top and stand out better from the fieldstone walls. If the builders were concerned with astronomical alignments, why did they not select/fabricate equally impressive and functional markers for their rituals?
The slabs incorporated into the stone walls offer additional evidence. One may hear that New England farmers did not use slabs within their stone walls. The fact that MH offers somewhat divergent building material -- natural slabs -- is often not considered in these claims. Also never considered is the form of the slabs that are laid horizontally -- a great many -- in the walls. I performed a simple survey of one wall on the site.
Approximately 50 percent of the large, horizontal slabs (the sample included only those of a minimum 4 inch thickness and 3 foot length) in the walls were characterized by "sharp" edges -- edges that could not possibly have offered a stable base, even if propped upon other stones. The remaining horizontal stones have either one significant side with a 90 plus/minus degree base (optimally stable) or a base with a roughly 70 degree angle -- one which I considered stable when matched with a slope in the ground or when propped upon "filler" stones. If one does not include the latter type within the "stable" definition, then, at a conservative estimate, only thirty percent or less of the horizontal slabs can form a stable, upright component of a stone wall.
We are left with the conclusion that the builder of the walls selected the stablest slabs for upright placement. Slabs of doubtful stability were laid horizontally, and when the walls headed down slope, the slabs were cambered horizontally, relative to the slope, to prevent slippage. Thus the slabs were used quite sensibly, and, quite to the contrary of popular belief, a farmer may well have chosen to set upright slabs in his wall -- to save himself time and energy by using one large slab to take the place of many small boulders. A large, stable slab may offer enhanced stability throughout seasonal temperature changes. As anyone knows who has skinned an ankle while walking on stone walls, the boulders are often precariously balanced. Frost heaves can and do tumble portions of a stone wall -- an event common enough for Robert Frost to immortalize in a poem. Using a stable slab in place of many small boulders is simply capitalizing on simplifying a construction, which makes it more reliable.
Perhaps it is surprising that more slabs were not given the chance of having a squared-off edge or that uniformity among the standing stones was not maintained, since the slabs actually modify quite readily with the aid of a 40 or so pound boulder thrown from overhead. Yet, this is not evident at the site. In fact, the slab forming a wall for the "chamber of the lost souls" (not my designation) has an uneven edge made more stable with small "filler" stones. One might expect that this component, which supports a quite heavy roof slab, would have been treated with more care if the builders had tended to fashion the stones -- but evidently the time and energy involved in such shaping was not considered useful. The builders of the site have saved time and energy whenever possible -- this fact extends to the use of reasonably stable, natural building materials that are peculiar to Mystery Hill.
For proponents of Mystery Hill's possible ritual function, the 'least energy investment' hypothesis is important. The relative ease with which slab material can be found and processed at MH is at odds with the site's generally random lay out. The extra time and energy expenditure required to 1) lay out the site symmetrically and 2) choose or fabricate equally impressive/ symmetrical/functional standing stones would not have been extraordinary. If ancient Indians or Europeans built the site, they sacrificed a feasible site-symmetry that characterizes astronomical sites the world over; a ritual basis for MH is not supported.
In closing this section, some mention must be made of a 'quarry site' that researchers have examined away from the main site. A large slab rests upon a smaller stone, presumably for the purpose of making the shaping of the stone easier (Stewart-Smith:1982:2). At first glance this feature does look conspicuous, especially since several flakes lay before and under the slab as if thy had been knocked off. However, a tree appears to have sent its root to lever the stone upward, and the appearance of purposeful lifting upon the base stone may be a deceptive one. In addition the edge-wear of the slab appears to be natural, i.e., it is far too sharp, as if the 'quarriers' were fashioning a stone knife ten feet long! My experience with slab-bashing makes me uneasy -- modification of slabs with a heavy 'throwing hammer' proposed by the quarry site researcher does not tend to produce such a uniform, sharp edge. My assessment is that this 'quarry site' is a ‘trick’ by nature on sincerely curious humans. Other quarry sites are claimed to exist at MH. I have not seen them, although descriptions make me believe these others are simply zones where natural slabs have been pulled from exfoliating bedrock by gravity, freeze-thaw action, and root action.
The Distribution of the Standing Stones
I have examined naturally and 'culturally' occurring slabs and have found no evidence of purposeful modification. Now it is time to consider the larger picture -- the distribution of individual standing stones throughout the site. As noted earlier, the standing stones are components of rather ordinary stone walls. The stone walls themselves delineate 1) a large area around the top of the hill, 2) several smaller fields within the larger boundary, and 3) what appears to be a lane or wide path across the hill top. These features are in keeping with other stonewalls in the New England region, except for the number of slabs used.
The site is often thought of as once having been used for astronomical rituals, stripped of the stone walls, with the lone upright slabs and chambers remaining on a bare, grassy hilltop (a 3D model reconstruction in the tourist lodge suggests the effect). Presumably the later colonials built the house foundation and the stone walls. I wish to stress again two points: 1) the roads and fields delineated at MH appear completely logical -- or at least in keeping with other features that do not conjure any mention or ‘alternative’ theories, and 2) the standing stones of note are components in these walls. Thus if we are to assume that colonials built the walls between the standing stones, then we must assume the farmer(s) delineated property by constraining themselves to lines drawn between standing stones. The farmers were, then, very lucky fellows to have found a hill where someone had set up standing stones that corresponded to the field layout the farmers required for property demarcation and subsistence! It must have saved them time to take the ancient advice and simply string troublesome stones between the standing stones.
This picture appears ludicrous, and it does not support a ritual basis very well. Of course, we may stretch our imaginations to devise explanations for the apparently silly formulation -- but this is scientifically inefficient. The simplest explanation is this: postColumbian colonials built MH from scratch. The natural building materials -- slabs and boulders -- were moved into the stone walls. And when the slabs were stable enough, they were used as uprights as described above.
But there are those alignments. How do we explain them? I do so by remaining with the simplest hypothesis and assuming the standing stones were set there by colonials. More importantly any alignments we find do certainly exist -- but they are meaningless in regard to ritual function.
Therefore my hypothesis is this: that alignments between standing stones and astronomical events are quite real but exist only because upright stones roughly distributed along a north south axis -- that is, perpendicular to the ecliptic -- will naturally align to the events and appear to define an astronomically aligned 'site.' If you chose the backsight to these upright stones, you can also “choose” your alignments. I outline a method for testing this hypothesis below.
The Case for Random Alignments
Here I address the chance for random astronomical alignments. Previous researchers in Britain have also been plagued by possibilities of error and random alignments (see Hitching:1977:158, Cornell:1981:57ff), and I think this is the most important question that can be asked about Mystery Hill. This part of my research may dismay those who have devoted large amounts of time to the astronomical theories of the site. But we must not use devotion and investment of resources as an excuse to avoid a fundamental question: why does Mystery Hill not look like an astronomical site? -- that is, why must we use our imagination to 'see' the site?
If Mystery Hill were a regularly dimensioned site of 1) standard-sized standing stones, 2) 'filled' alignment positions, and 3) consistently distanced features (from a center), then many scholars would be less inclined to picture the site as a random scatter of slabs set in mundane stone walls. Instead, the site is 1) composed of various-sized 'markers' -- a mix of slabs and boulders of various sizes, 2) composed of some tentative alignments, some of which are not really marked by an obvious stone (such as the 'November 1/Lunar Minor North' alignment), and 3) composed of so-called astronomical markers that, if their matrix stone walls were stripped from them, along with tourist trails, signs, and the observation tower, they would appear to be an asymmetric scatter of slabs and boulders. This is in contrast with less questionable astronomical sites whose design is regular and purposeful relative to natural features.
The Requirements of Ritual
For perspective let us discuss aspects of human ritual behavior before returning to the subject of the form of the site. Rituals are defined by Rappaport (1971:62) as behavior composed of conventional moves or postures, performed at regular intervals (calendrically, or on specific occasions), affective value, and are non-instrumental. Rappaport sees rituals as "transducers" which transmit, among other things, information from one cultural subsystem to another (Rappaport:61). If a communication is to be effective, it must be distinguishable from ordinary communication -- instrumental communication that serves practical, 'every day' needs but not ritual needs. Thus, the more "bizarre" the ritual posturing is, the more easily it is recognized as ritual (Rappaport:63). This aspect of ritual communication shares fundamental requirements with information transfer in the most basic sense as defined by the Theory of Information (see Campbell:1982). Now let us apply this definition to monumental structures.
The "bizarreness" to which Rappaport refers is a fundamental in symbolic behavior, of which some megalithic sites are a part. Rappaport speaks of ritual in its human context: particularly, of its manifestation in tribal courting dances. But ritual posturing is in effect permanently solidified in megalithic 'temples', which are unusual, impressive features relative to natural features or instrumental cultural features (practical structures like houses, barns, and kilns). Further, the characteristics of other ritualistic artifacts defined by anthropologists -- status paraphernalia -- are useful in identifying rituality in monuments. To be symbolic, to be impressive, to function as an object of religious beliefs and rituals, an artifact should be characterized by A) an impressive investment of time and resources and/or B) an impressive, peculiar form (Binford:1983:228, and Haselgrove:1982:82). Such things as headdresses made from feathers of exotic birds, 'voodoo' masks, the Egyptian and South American pyramids, and megalithic monuments are all symbolic artifacts and all share in one or both aspects of the 'bizarre' definition.
Ritual Requirements and Mystery Hill
We are constrained by theory and by precedence to define a ritual monument as one recognizable from natural features and from cultural features, that, however, do not function directly toward supporting basic life functions according to Rappaport's definition (a 'voodoo' mask does not directly support a life function: it is ritualistic; a scythe, however, allows food to be efficiently harvested to fuel the human body and is non-ritualistic). In addition a ritual monument must be characterized by bizarreness in form and/or energy investment. Were we to test a hypothesis stating that MH was a ritual construction we would have to test it against the consequences of rituality defined above -- and we would have to falsify that hypothesis, for Mystery Hill does not readily fall into the definition.
MH does not look like a ritual site possibly because its diagnostic features, the standing slabs, were placed in their positions randomly in relation to important azimuths. For example, assume that the hill-top was once littered with naturally occurring slabs; assume further that a farmer needed to clear the field as farmers all over New England had to do. This farmer was a practical fellow -- he didn't want to work more than he had to -- so as he cleared his fields and built his walls from the troublesome debris, he stood many slabs upright as a way to save himself time, as discussed earlier.
Since so many upright slabs exist, we can arrive at the site and draw astronomical-event-lines (azimuth lines) through the slab and into the center of the field. Thus a random scatter of slabs around the perimeter of the farmer's property would offer curious observers the chance to 'discover' astronomical alignments if they stood at a certain point in the field from which he could observe the primary astro-events (sun rising and setting) over several of the tall stones along the fields perimeter. In this case we have no obvious backsight or observation platform where we would know where to stand to observe these events (as at MH). Let me stress again that the observer must find that point in the field where she can view, ideally, many or all of the primary solstice or lunar events. A person might, if he were very lucky, accidentally discover this point while wandering the field during the midwinter sun rise, let us say. Curiosity piqued, he might remain at that spot until sunset and view the setting of the sun over another stone on the other side of the field. Of course, this is unlikely. What is more likely to happen is that the observer would become curious seeing the odd standing stones in the stone walls, then go home, draw a map of the field, and use a compass to calculate field alignment, then solve an alignment equation (see Aveni:1980:120ff). Then she would find that azimuth lines drawn between events and standing stones sometimes cross in close proximity -- and close to that point one could view several of the astro events taking place over the stones. As at MH, not all of the lines from all of the stones converge at a convenient central point -- but the fact that many of them do is enough, and he is excited at having discovered an astronomical site.
Figure 7 schematizes this possibility in a simple way. In the drawing I have delineated a generic field site as a simple rectangle with the longest sides directed to north and south -- an approximation of Mystery Hill. I distributed 11 points randomly around the perimeter that represent standing stones in a stone wall matrix. I used a computer graphics program to create 'azimuth' lines for a hypothetical winter solstice sunset and sunrise at that latitude. The computer duplicated these lines precisely (i.e., at precise angles) and I could move them around the field area and line them up with the standing stones. In this simple model there are already some random alignments between two stones: line A. Line C and B come close to aligning. Thus it could seem to a worker who has solstice azimuths for that latitude at hand that these stones are markers and backsights -- when they are nothing more than random alignments.
As a better comparison to MH, assume we are made curious by these possibilities, and since no clear 'site center' exists, we look for a point near the center of the field where several alignments might culminate (of course, the center of the field is a definition biased by the placement of the colonial-era stonewalls, which may make us find a center to a 'later version' of the site). We are also assuming that an observation platform might have been destroyed over the years (i.e., the site’s “stone robber” argument stemming from supposed quarrying activity). After plotting all the stones on sunset and sunrise azimuths, we find several places where one can stand and view both events marked by separate stones. These points are where the azimuth lines cross in the drawing. We are faced by many site centers, certainly. To narrow down the possibilities, we might find that point which also aligns to a standing stone in the north of the site -- assuming that the ancients 'calibrated' their site to true north. A point exists, labeled point C, where both solstice events can be viewed over separate markers, and where the point also aligns to a true north stone.
In this example not all of the stones fall on convenient azimuth/site center lines. What of these? Perhaps they are alignments that we have not yet calculated. Perhaps they are nonaligned stones with some other mysterious ritual function. Perhaps the farmer who owned this land took them from other aligned positions in order to build his stone wall. ‘Of course,’ says our theorist, ‘there is a lack of symmetry to the solstice-observation site, but so what? Colonials certainly did not set up slabs in their walls, so this site must be ritualistic. No doubt ancient Europeans built the site for solstice observations!’ In the end we can rationalize site anomalies in several ways and leave ourselves the possibility that we have 'discovered' an astronomically aligned site. I think that this situation can arise from a random distribution of upright slabs in a stone wall.
The above example is a quick, simple demonstration. It is a scheme of what may be happening at MH, where there are 1) many standing stones, some which align nicely between events and an observation point that has been inferred, 2) curious asymmetries in site layout, and 3) stones that do not align with events. To test the 'random' possibility we must simply make the above situation simulate more closely the scope of the MH site.
What we do when we examine MH for alignments is try to define backsights or site centers since no material site center exists. We can discover astronomical alignments by 1) first finding possible markers in sight of the horizon where an astro-event would occur and 2) if the horizon does not offer a notch or peak on the horizon as a marker, we must look 'backwards' for an observation point or 'back sight' (see Figure 8).
I oversimplified the situation outlined above in order to introduce this new method of studying Mystery Hill. Obviously, the case for random alignments must rest on an important factor -- the relationship between the perimeter of the site and the number of suitable slabs that could function as astronomical markers. The more densely packed is the area, the more of a chance exists for random alignments to delineate a site center or to provide individual backsights. What we must do is look at the site to decide if enough standing stones exists to provide coincidental alignments.
We may analyze the case for random alignments best by 1) simulating the general configuration of the site's stone walls and 2) superimposing it with a grid system for plotting random points. The random points will be the standing stones in the quantity that is presently existent at the site. For example, about 100 large or standing-type stones are marked on the site map. Let us assume that these are peculiar stones out of place in the standard New England stone-wall type and possibly of a ritual purpose. We must then randomly plot a hundred points in a grid composed of blank points equally spaced that correspond to the stone wall layout -- for standing stones at MH are predominantly found in the stone walls. The points must be numbered, and a hundred random numbers corresponding to 100 standing stones must be generated. The random numbers are then matched with the grid points to form a MH with 'new' standing stone arrangements.
The invariable factors in this study are, of course, the azimuths of certain astronomical events for a given epoch. Let us assume for the moment that the azimuths calculated for MH are correct for an epoch (i.e., “1200 BC”) that has been selected with sound archaeological reasoning. If we can draw lines through the azimuths of the astronomical events and the standing stones, and if these lines all culminate at some central point or if single alignments culminate at a second marker (a platform or second standing stone), then we can justify the site as an astronomical one.
Results of the Total Point Scatter: 100 Points
A colleague generated 100 random numbers on a computer. They are presented in Appendix A. I chose 100 points for this first experiment because the published site map of MH marks about 100 major slabs and boulders; I took this number as the quantity of stones likely to have been dragged from the field and set up as markers. Possibly these represent the best (in form and stability) of the stones for upright placement. There is a fault in this approach, which I discuss in the next section.
I used graph paper to set up a coordinate system and placed the random points as shown in Figure 9. Figure 10 shows these points connected for the two solstices, and I indicate 28 paired or tripled alignments. In other words, the azimuths for both solstices (rise and set) passed through two or more simulated standing stones for a total of 28 possible alignments. In several places one can notice where the symbols of each alignment overlap -- this means that some points that function as backsights for one alignment azimuth are also backsights for other astronomical events. We might think of such points as possible 'site centers.' The point that is a backsight for the most events could be the most likely site center (but what to do with the other less likely “alignments” would remain a problem!). If this center falls near some other site feature, such as a foundation or slab chamber, we might be further willing to claim this point as the center of an astronomically aligned site -- as has been done as MH. In addition, some of these centers have standing stones due north of them or due east -- for true north or equinox alignments. Such evidence might add further to our definition of the center.
Though these results are interesting, the scatter field does not adequately represent an MH-type site. For the standing stones at MH are predominantly features of matrix stones walls; since the uprights are constrained linearly, (thus, to a small overall area) this probably changes the chance for alignments in some way. I used the square grid discussed below as a better model.
Figure A [note 1/2007: seems to be damaged after transferring between various systems over the years; I believe it once was a MacDraw file] -- Simple illustration of a random-scatter experiment. The square box symbolizes a field defined by a stone wall. The grid marks represent the average width of “standing stones.” The black circles are stones randomly inserted into the grid through some random-number method. Thus the schematic represents a thought-experiment: “What if a patch of land had a number of unusually sized stones among all the other stones, and a farmer used both typical and unusual stones when making the stone-wall around his property. Let us assume he inserted the unusual stones without knowing or caring that they might or might NOT align with astronomical events if he stood somewhere in the center of his field and sighted over the stones. Given this situation, what is the chance that I could “discover” by wandering the field that some point existed in the field that could form a back sight from which one or more astronomical events could be viewed?” If I found one point where several astronomical events could be viewed from over the standing stones, then we might be tempted to say the stones were part of an ritual astronomically aligned site. Or we might say that enough large stones existed in the area that it is highly probable that we could find such points in any field built with that kind of material, and that the alignments are a chance. Such a possibility is enhanced when we find that some, even many, of the unusually large stones do not seem to align with any known, culturally significant, astronomical event. In a nutshell, this is my test for the significance of the alignments at Mystery Hill.
Random Scatter Constrained to Simulated Walls: 65 Points
An example of the 'book keeping' grids is supplied in Figure 11. These were computer-generated, then cut-and-pasted over the lines representing the stone walls. This is an 'idealized model' of Mystery Hill -- a rectangular perimeter crossed by internal 'walls' perpendicularly (see a reduced configuration of the square grid in Figure 11). Such a grid serves as a generic site-layout and aids a researcher in quickly finding and plotting points to test this method.
To accommodate my eyesight and my simple tools, I selected grid increments of about 1/8 of an inch. The schematized layout of the stone walls on which the increments are placed approximates the scale of the site: about 50 feet to the inch. Thus my grid allows me to place a standing stone every 1/8 inch, that is, about every 6 feet. A more precise study of this kind would use a closer increment. However, since I am using these points for drawing backsight lines and not as targets for simulated transit sightings, the large scale does not greatly affect this experiment. I discuss a more precise method later in the paper.
The 'generic grid' is an attempt to conveniently simulate a site that is defined by a stone wall perimeter and crisscrossed by internal walls. This approximates the situation of MH, though MH is considerably more asymmetric.
I chose 65 points for this and following simulations because in several walks around the site I could not identify more than 65 major slabs that are standing upright in, leaning from, or fallen out of the stone wall matrix. I used this definition for a 'standing stone': slabs 1) with at least one stable base, 2) at least two feet wide, 3) at least three feet tall, and 4) with only their broad side parallel with the matrix wall (maximally visible to an observer standing roughly in the center of the site). In addition there are about 45 stones slabs that are lying horizontally on top of the stone walls; others are buried within them. [Note 1/2007: I have digital photos I can e-mail on request] I did not consider such stones. Former MH researchers include some large boulders as markers, and in one instance include a boulder that is overlain by smaller stones in a wall (feature "E5" in the 1985-current tourist map); I do not define such stones as markers no matter how they may align. I assigned random points to the grid by using the table of random numbers supplied in Thomas (1976:428ff, Table A.2).
Since it is difficult to plot clearly at this level of detail, I plotted each alignment separately on the square grid. In other words, I made one plot for each astronomical event. I correlated all the plots by overlaying each plot with a transparent grid on which I could mark where each backsight line extended. I completed two such plots: one in which the grid extended downward (south) from a 'true north' standing stone (as has been done at MH), and one to the left (west) of this area, but unmarked by a north stone for an alternate sample. I could use this record on following grids. The result is a record of the zones where each backsight line crossed. The incremented zones represent about 100 square feet, or a square ten feet to a side -- which is similar to the accuracy of the MH plot in which two observation points are defined, one falling ten feet north of the other. Of course, this is only a small sample of the possible 'site centers' that could exist in the middle of the grid. Thus the results are conservative.
The results (Figure 12) show that a point of 5 or 6 possible alignments existed for one column of plots, and two 4-alignment zones also existed. Numerous 0, 1, 2, and 3-alignment zones also existed. For the column beneath the north standing stone there was a possibility of 7 possible alignments (including the north stone); two 4-alignment zones exist, and numerous 0, 1, 2, and 3-alignment zones exist (Since the medium is cumbersome, only a sample plotting grid is provided in Appendix B; the others may be viewed upon request. The refined random-study method outlined below is directed at improving the reproduction of primary test results from original data sheets).
Discussion of the Random Point Model
What does it all mean? The several plots, representing various ways of representing an astronomically aligned site, show that standing stones randomly placed throughout a small field or throughout the walls defining a small field can appear to define an astronomically aligned site. It means that we must be very careful in claiming that a peculiar feature of a site represents a purposeful, ritual arrangement. This is especially true when little other supporting evidence exists. It would be difficult to reproduce a Stonehenge, or Callanish, or medicine wheel arrangement by the random-point method used here. However, I have come near to reproducing Mystery-Hill-like alignments with the random method. Certainly this is an important point.
It is important to realize that certain weaknesses in the site's features allow such comparisons to be made. In particular the fact that former researchers had to rely on an awkward twin-site-center arrangement in order to find their alignments throws doubt on the site. If the site was laid out with a central observation point, why must we move ten feet between centers to find alignments? It seems here that the site was made to fit the hypothesis. One hears at times that this had to be done since the terrain did not suit all the alignments. But builders of astro-sites usually find good terrain for their sites -- and there are other hills within a few miles of MH that are either higher or provide a good view of the horizon. Additionally the alignment markers for both centers appear both around the main perimeter and in walls that cross the main site relatively close to the centers -- and in no observable pattern. Some markers are not there, some alignments fall amidst a small grouping of slabs, and some markers are not slabs, but are boulders and in one case a corbelled chamber. My point is that there is little system to this arrangement.
Astronomical sites less questionable than MH also have many stones and can suffer from a random alignment problem. But such sites are at least recognizable as purposeful, ritual structures because of A) their 'bizarre' and/or systematic form and B) energy investment in relation to instrumental constructions like fortresses, livestock enclosures, and smaller habitations. They are recognizable as such because of an evident symmetry. Even if you had the permission and resources to string New England-type stonewalls around and between features in Callanish, Stonehenge, and the medicine wheels, you could probably easily disentangle the ritual structures from the mundane ones. But this is simply not true for Mystery Hill and other 'enigmatic' structures in New England. The difficulty and emotion we experience in trying to prove these NE sites to be ritual -- let alone astronomically aligned -- is a measure of how plausible such ideas really are.
I conclude this experiment conservatively: my results do throw into question the claimed astronomical alignments at Mystery Hill. However, my method must be honed sharper and replicated before doubts can be seen to be proven facts. The method needs to be more precise, more easily replicable, and closer to the specific circumstances. In particular I would like to account for the size of the standing stones. For example, if the stones that mark the alignments appear to be larger than the so far unaligned stones, then the possibility for randomness in the claimed alignments is reduced. With this refinement should come a recheck of the claimed alignments by a professional surveyor. A new set of alignment azimuths should also be computer-calculated to complement a survey. These are important aspects for astronomical theories and require repeatable results and insurance against errors by previous workers. What I have so far presented is a method and some tentative results that demand further substantiation and support. I discuss ways to improve accuracy below in more detail.
Improved Random Grid Analysis
[ June 2001 note -- many of the problems I note below are today solvable by advanced computer-graphics packages not available to me in 1985. ]
The goal of an improved random grid analysis is tripartite: 1) to improve the precision of scale, 2) to facilitate replicability, and 3) to facilitate reproducibility in report form. These points are explained below.
The current level of precision is hampered by the need to use easily visible grids for placing the points generated from a computer or taken from a random number table. The large grids present a confusing array of useless information after plotting. This problem can be remedied with a percentile-based plotting system. The percent-chance for a standing stone to occupy a given 'slot' in a stone wall is calculated, and a series of random numbers is generated on a computer that will correspond to a 'binary' system of standing stone generation.
For example, let us use the 65 stone arrangement. Assume a standing stone is at least two feet wide. Assume the perimeter of MH is 4000 feet. Thus there are 2000 'slots' in the stone wall matrix that a typical standing stone could occupy -- assuming, of course, that we do not allow standing stones to exist directly behind each other (within touching distance) relative to an azimuth line drawn from the approximate center of the simulated field. If 65 stones are to be distributed throughout a possible 2000 slots, then there is a 3.2 percent chance a stone would be dragged to that position by a farmer (for example) and set upright (It would be desirable to account for nonrandom processes here, such as slab availability plotted for designated zones over the hill top. Thus wall 'A' might be expected to have more standing stones if the adjacent area produced more natural slabs -- perhaps because of increased erosion in that zone -- than other areas. I do not know whether this kind of precision is possible at the site).
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