Tuesday, April 14, 2015

Review of Some Research by Hively and Horn, with maps 2011

In 2011, I produced some review documents of a pending Hively and Horn article, submitted for publication to Mid Continental Journal of Archaeology,  regarding the Newark earthworks and what those authors call the “zero-degree hypothesis”. This present document contains portions of those reviews that were transmitted between myself, Hively and Horn, and the editor of Mid Continental Journal of Archaeology. These analyses are heavy on GIS analysis.
The author grants permission to reproduce text, tables, maps, or images included herein, provided that the author is cited as Turner, Christopher S.,  year of article, name of article, conference event and date (if applicable to the paper), page, and source, and provided that use of any text, tables, maps, or images included herein is for non-commercial, academic purposes only.


Review of Some Research by Hively and Horn, with maps
Christopher S. Turner
2011

Here I will present a detailed analysis of the primary sightline from authors’ backsight locus H1. As noted herein, the viewshed of this sightline is obscured by local terrain with respect to the Fairground Circle, but from H1 the Octagon group can be seen. It is this latter sightline I will be examining.
I quote here in full the authors’ premise concerning the methodology that forms the basis of the Hz model (i.e. the “zero degree horizon model”):
The HZ hypothesis makes a very specific prediction about each linear Octagon feature that is aligned to a zero-altitude standstill direction: if a line is extended backward from the Octagon feature along the line of the standstill, it will ultimately pass over a prominent elevation from which the zero-altitude alignment could be conveniently observed.” (page 27 of manuscript, italics authors’).
They continue:
The valley in which the earthworks reside is surrounded in all directions by the Appalachian foothills.  Consequently, the prediction that any line would pass over a commanding overlook was likely to be satisfied by chance alone.” (page 28).
The chance of these loci randomly occurring would be much less if the authors insisted on the extended sightlines traversing a peak feature in the topography. If plotted using the authors’ data, none of the four “H” points are on peaks. H2 and H4 are quite close however. H1 is on the incorrect side of a salient area, and H3 is on the incorrect side of a ridge. (By incorrect, I mean that the authors’ proposed viewsheds are not realized from these loci.) I suspect that the four “H” backsights would plot nearer to or even upon peak features if the authors had used a finer grained mapping system.
In any case, if these suggested backsights are not at discrete geographic peaks, it can be argued that the authors selected the sites to fulfill the demands of the model that they function as dual backsights for lunar maxima and minima sightlines.
Preceding now with the analysis of locus H1, if we follow the model as quoted above, we will extend the sightline backward (i.e. to the southwest) from the axis of the octagon earthwork. As noted by the authors in their 1982 paper, the azimuth of this line is 52.0. This is based on a combination of methods: their own field survey, the Middleton / Fowke data, and aerial photographs. I also surveyed the axial azimuth in the field (in 1982), and obtained a figure of 52.1. Using essentially the same methods as the authors, I can concur that the figure they arrived at is acceptably accurate. Let the azimuth figure then for the axis of the octagon and circle earthwork equal 52.0 degrees for this analysis.
It should be recalled that circa 1980, the best maps available for these analyses were USGS topographic 7.5’ quadrangles. As I recall, a millimeter on these maps was equal to 78 feet (in Chillicothe). I used to utilize a 1/64” ruler and a jeweler’s loupe to gain the best accuracy possible in map analyses. Compared with the software that is presently available, these methods now seem primitive.
In 1982, the authors’ calculations were based on the first gleam event of the moonrise, whereby in computations the factor for semi-diameter that represents this quantity (q) is set to (q = -0.26 degree). As such, the authors found that the axial azimuth at the octagon (A = 52.0) yielded a resultant declination that was two-tenths degrees in error.
It can be shown that if the authors had used a value of (q = 0), [rise event for central bisection of the lunar disc, i.e. the moon half risen], then the sightline would have been exactly perfect for the event in question (i.e. the north lunar maximum rise for circa 1AD).
As such, I will present the remainder of these analyses with the q-value set to zero (i.e. for central bisection of the rising moon, that is, for the moon half-risen).
Following the authors’ premises, the visible horizon as seen from the elevated backsight H1 has a lower apparent angular height. It can be shown that the angular height along the sightline with azimuth = 52.0 is in fact near zero degrees as the authors suggest. This is a full half-degree lower than the same value as seen from the Observatory Mound as posited in the authors’ 1982 paper for the same sightline. This changes the resultant declination as viewed along the sightline.
 Using the q-value of zero, the resultant declination as seen from H1 is +28.4, or four-tenths degree in error from the lunar maximum. Even if the q-value is speciously “tweaked” to try to obtain a “best fit”, the error is still present and is two-tenths degree.
The question then becomes, what azimuth produces the correct sightline as seen from the authors’ H1 point? It can be shown that the correct azimuth is 51.4 if the q-value is left at zero.
In the diagrams that follow, it will be noticed that the sightline if so plotted from H1 misses the axis of the octagon entirely. At the location of the connecting neck between the octagon and the circle, it misses by 78 meters. The lateral shift in the locus of the horizon foresight is 162 meters.
These “errors” may be the results not of an incorrect model, but on the low scale plotting of the locus of H1 by the authors.
I will include this present document and that from yesterday describing the use of the “q-value” in a complete analysis of the H1 backsight.
My next step will be to re-analyze the sightline from alternative locations of H1. My guess is that the incorrect locus as provided by the authors is due to the low scale nature of their maps. This plotting may also however reflect a desire on their part to have the proposed sightline function as a “dual backsight” with regard to their proposed Fairground Circle sightline. The more exactly these backsights can be plotted, the more precisely a location can be suggested for archaeologists to investigate. It would be preferable as regards hypothesis testing at these sites that their locations be predicted in advance with the utmost care and precision.





Figure 1. The yellow line from H1 lies along the azimuth of 52.0 degrees, and passes axially through the octagon and Observatory Circle with reasonably good fit at this map scale. It should be remembered that this value of 52.0 degrees was calculated using survey data collected circa 1885 and by using paper maps, so some error should be expected at a finer scale when plotted using ArcMap. This is especially so when the line is extended many kilometers from its origin at the authors backsight H1.


Figure 2. Here is the environs of the landform which hosts the authors’ proposed backsight H1. The distance from H1 to Point D is about 210 meters.





Figure 3. This is the horizon foresight locus for the sightline with azimuth 52.0ᵒ as seen from H1. It lies at a distance of 15428 meters from H1. The pink shaded areas are visible from H1 according to the ArcMap viewshed analysis.

Figure 4. Here is the sightline where it passes near vertex E of the octagon.
Figure 5. Here is the sightline where it passes through the connecting neck at the same earthworks. This image is a combination of 1/10 meter elevation contours, the Middleton / Fowke plat for the octagon, the Holmes map for the circle, and some plotted points from the Middleton / Fowke survey (green dots). 

Figure 6. The H1 sightline at the Observatory Mound.

Figure 7. A wide view of the same sightline: 1/10 meter elevation contours. This line with azimuth of 52.0  degrees originates at authors’ backsight H1 some 7000 meters from the Observatory Mound. Over that distance, the skew of the azimuth relative to the local axis of the octagon becomes apparent. The azimuth of 52.0 degrees is functionally correct within the local confines of the earthwork, but is relatively inaccurate over large distances.

Figure 8. The red line is the sightline with azimuth of 51.4ᵒ as seen from the authors’ H1 backsight locus. This sightline conforms to the north lunar maximum rise declination as seen from H1 for the semi-diameter value (q = 0). If the q-value were set to (q = +0.26ᵒ), i.e. for the tangent rise event, then the sightline with the azimuth corresponding to a declination for north lunar maximum rise would lie midway between the two lines as shown and would still miss the connecting neck entirely (i.e. said line would have an azimuth = 51.7ᵒ).
Figure 9. Detail view of Figure 8. Sightlines are 78 meters apart at the location of the neck. The sightline plotted for a semi-diameter value of (q = +0.26ᵒ) and a resultant lunar rise azimuth of +28.8 degrees would still be offset from the yellow line by 39 meters, missing the neck entirely.                 


Figure 10. Location of horizon foresights for sightlines from H1: red line azimuth = 51.4ᵒ, yellow line A = 52.0ᵒ.  Corresponding declinations for (q = 0) are +28.8ᵒ and +28.4ᵒ.  



The goal of this phase of analysis was to obtain the most accurate axial line with regard to the octagon and Observatory Mound combination. The process was quite tedious. First, I had already converted all of the Middleton / Fowke survey data points from “azimuth-distance” figures to an X – Y grid. (I arbitrarily used vertex B as the (0,0) origin). The outline of the octagon in ArcMap was created using these data points. They were merged into the extant map layers as based on the UTM coordinates.
Middleton and Fowke had measured the width of the connecting neck between the two polygons, and these reference points were the most crucial in determining axiality at the enclosures. These four points are labeled 1, 34, 36, and 37 in their survey. They also measured the midpoint of the neck at the circle, labeling this as point 0.
 I had to create a corresponding midpoint for the neck where it meets the octagon by measuring halfway between points 36 and 37.
It was these two points, the one I created midway between 36-37, and the Middleton / Fowke point 0, that formed the central basis for my analysis of the true axis of the earthwork group.
There was a great deal of trial and error as I shifted the extreme ends of this line at its southwestern terminus near the original H1 locus, while alternating with nudging the northeast terminus of this axial line at the horizon foresight area. After repeated iterations, I managed to get the line within 0.01 meter of each point along the central axis of the connecting neck at the earthworks.
Once this line was generated, it was checked relative to other indices of axiality. For instance, the line misses the centroid of the Observatory Circle by only 0.23 meters.
It is much more difficult to know with any certainty where the exact center of the Observatory Mound is located. The line passes over the highest contour lines in the ArcMap display, but reconstructions of this earthwork make this index unreliable. I measured three other centrality indices of this mound: the midpoint of the flat top of the mound, the midpoint of its base, and the midpoint of the two fork features that extend out the mound to the southwest. These three centers so measured are in close agreement, and a point that approximates the three of them is 1.7 meters from the axis as determined by the Middleton / Fowke points in the connecting neck.
Lastly, there is the location of the axial line as it passes through the octagon vertex E. Again, it is quite difficult to gain an accurate measurement of the embankment features with any certainty, but simple visual inspection of the display in ArcMap shows a very good fit to the vertex.

Once the true axial line was determine in this manner, the most likely backsight and foresight loci were plotted and measured. The astronomical data were computed and the resultant lunar declination was determined. The intervisibility of the points was checked using the ArcMap viewshed function. Following are the explanatory graphics.

Figure 11. Detail of neck with Middleton / Fowke points 0, 1, 34, 36, 37, and the corresponding midway point between 36 and 37. The axial line passes through the latter point and point 0 to within 0.01 meter of each point, exceeding the accuracy of the survey data themselves. (Note: the Holmes and Thomas plats were not used as regards point placement: they are for visual orientation only.)

Figure 12. Detail view of vertex E and axial sightline with scale bar.

Figure 13. Observatory Mound. As noted in the text, three indices were measured to determine the center point of the mound’s long dimension. The major axial line of the earthwork group (black) passes within 1.7 meters of a best fit line of these three measures. Contours are 1/10 meter.

Figure 14. This is the backsight of the axial line (green dot). Authors’ original H1 is red dot. The Octagon – Observatory Circle azimuth determined graphically using the method described above yields a value of A = 51.47 = 51.5 degrees. Following this line, the location of the backsight is so determined as the locus of the green dot. This point is 11 meters from the attendant peak feature center as measured in ArcMap.
Figure 15. Backsight area in USGS 7.5’ format with scale bar. Note houses on peak with proposed backsight point. Green dot at elevation of 341 meters.

Figure 16. Foresight of axial sightline. Yellow dot at terminus of line with azimuth of 51.47ᵒ that runs through axis of earthwork group. Blue dot is the location of the sightline from H1 with azimuth = 52.0ᵒ as proposed by authors. Red dot near top is second possible locus of foresight if the axial sightline is extended. Pink areas are visible from backsight locus (as shown in Figure 19). Peak feature near red dot (11 meters apart) has elevation only 1 meter greater than that of yellow dot. Distance from backsight to yellow dot = 15860 meters. The yellow dot is at elevation of 345 meters, effectively creating a “zero degree horizon” along this sightline as from proposed backsight.
Figure 17. Foresight area USGS 7.5’ view with scale bar (detail).
Figure 18. Horizon foresight - USGS 7.5 wide view with scale bar.
Figure 19. Wide view of entire axial sightline. Pink shaded areas are visible from the axial sightline backsight (green dot, lower left). Both the octagon group and the Fairground Circle are visible from the axial backsight.

Figure 20. Wide view of entire axial sightline. Green shaded areas are visible from foresight locus. Note that the octagon is not visible from the foresight.

These are the UTM data for the backsight and foresight of the plotted axial sightline:

backsight (green dot in figures):
370414.58
4429722.384

foresight (yellow dot in figures):
383012.28
4439368.673

Elevation are 341 and 345 respectively (meters)
Corrected angular horizon height = (0 – 0.58 + 0.95) = +0.37
Azimuth = 51.47ᵒ 
This results in a declination of +28.8 for q = 0  (bisection of rising moon). This is exactly correct for north lunar maximum rise circa 1AD.

It should be noted that the Fairground Circle is shown as visible in the ArcMap viewshed analysis from the proposed backsight (Figure 19).
My next step will be to check the data on the Fairground Circle sightline as seen from the axial sightline backsight (marked point C in Figures 2 and 31).
That should be the last step to reanalyzing the H1 locus backsight.
It appears that both the backsight and the foresight as defined by the axial sightline are at or on peak features, unlike Hively and Horn’s proposed locations, which are on sloping areas This is likely due to their use of low scale maps.

_________________________________________________________


Using the backsight point C as defined by the axis of the Newark Octagon, here I analyze the sightline through the Fairground Circle as seen from the same backsight. This backsight is 406 meters to the south-southwest of the authors’ proposed H1 backsight. This backsight is 11 meters from a local topographic peak feature, and is at elevation 341 meters.
A line is created in ArcMap made to run from this backsight so defined through the centroid of the Fairground Circle. The centroid of the Fairground Circle is only 2.46 meters from the “center” of the Fairground Circle as defined by the Eagle Mound and the sub-mound postmolds as mapped by Greenman. This difference in the two loci is nominal.
The sightline is extended in ArcMap to the northeast through the Fairground Circle centroid till it encounters elevated landforms that create the visible horizon as seen from the backsight locus. Using the viewshed analysis feature in ArcMap, the foresight is defined along the sightline that is visible from the backsight.
The horizon foresight so defined lies at 20930 meters from the backsight locus point C. It actually has an elevation that is lower than the backsight!  I checked for other foresight loci out to a distance of 38 kilometers none were found. There are likely very small sections of more distant horizon that merge together forming the visible horizon as seen from the backsight locus. These would be impractically distant from the backsight for prehistoric use, and the effective angular horizon height of these distant foresights would not differ from the one selected at 20930 meters. All of these areas effectively present a “zero degree horizon” as seen from the backsight locus.
The positional data of the proposed foresight were obtained using ArcMap, and these data were analyzed for astronomical significance. 
The following graphics illustrate the results.









Figure 21. Wide view showing sightline through centroid of Fairground Circle from backsight of axial octagon sightline. Pink areas are visible from backsight.




 Figure 22. Detail view of foresight. Red dot lies 20930 meters from backsight. Smaller yellow dot lies a further 705 meters distant. Both are at elevation of 321 meters. Pink areas are visible from backsight. These are the positional data on the “red dot” foresight: 389516 easting, 4438277 northing. “Yellow  dot” foresight = 390159 easting,  4438565 northing.  Elevation contours = one meter.


Figure 23. Wide USGS 7.5’ view of foresight area.



Figure 24. Detail USGS 7.5’ view of foresight area with scale bar.

Figure 25. Google Earth image of foresight loci. Note how both possible foresight loci are still in tree cover. They may have greater archaeological integrity than many of the other potential foresight loci in the Newark area.





Figure 26. Mills map showing six mounds in three pairs in vicinity of foresight area. I have never been able to determine the meaning of the symbol Mills used - the triangle with a small tick mark at upper right - but I have always interpreted this as a signal mound (?) as based on the elevated location of many I examined on the maps. The Mills catalog has been derided as highly inaccurate, but I was surprised to find a good match between plotted features in ArcMap and known features on the Mills map. Specifically, the axial sightline for the octagon passes directly through the axis of the octagon on his map. The sightline from point C through the Fairground Circle centroid line misses the middle of the circle as marked on Mills, but does pass through the circle itself.



Figure 27. Same display scale as prior figure showing Mills features as plotted against the 7.5 USGS topo. Since I am uncertain which portion of the triangles represents the locus of each earthwork, I have made each symbol hollow. The upper right of the six mounds is in the wooded area as mentioned and may serve as a reference to the degree of accuracy of the Mills format if these mounds could be located. Each triangle as plotted is about 400 meters wide at the base and encloses about 15 acres.


Figure 28. Detail of the Mills map in Newark. Note that the plotted axial sightlines through the octagon and the Fairground Circle are correct in his map, especially that through the octagon group. The line passes directly through the connecting neck, though the distance placement is in error (the pairs of green dots mark the connecting neck). Note that I refer to the original placement of the enclosures in Mills map as shown with tick marks, not those as shown with heavy bold line which appear to be later additions. I have also found there to be good agreement between road features and water courses in the Mills map when georeferenced into layers in ArcMap. In a conference paper by Bill Dancey from the 1984 SAA meeting, he suggests that “an archaeologist would be foolhardy to try to use the Atlas as a guide to site locations” and that “..it is virtually worthless as a source of specific locational data” (p 11/12). But on a positive note he points out that “..included sites appear to have been verified by a field check”. I noticed in a brief inspection of the Licking County map that for instance the well known Fairmount Church mound is not marked. Conversely, mound sites that are indicated at the locus of a discrete landform such as an isolated hilltop may in fact be accurate.

Figure 29. General view of sightlines as seen from point C: axial octagon line, Fairground Circle line from same backsight.





The azimuth of the line from the axial octagon backsight through the centroid of the Fairground Circle is A = 64.81 degrees.
The effective angular horizon height along this line is that of a “zero degree horizon”. As such, the corrected horizon height hc = 0.37 degrees.
The resultant declination along this sightline is = +19.3 degrees for a q-value = 0 (bisected rising moon).
This is in error from the declination of the north lunar minimum rise by 7/10 degree, or 1.4 moon widths.
This is an appreciable error and should not be discounted, especially in that the sightline through the octagon axis is exactly correct for the north lunar maximum rise event.
The authors at various points in their manuscript suggest that errors of 0.5 degrees are insignificant. Degrees of precision with such great error ranges are unacceptable. With a higher precision treatment of the data, use of a mapping system that can afford such precision, and by rigorously maintaining a fixed use of a particular q-value (preferably q = 0), the precision of resultant data becomes possible.
The Newark Octagon and the Fairground Circle are the two best preserved Hopewell geometric enclosures, and afford the best chance at determining high precision sightlines. By using remote sensing as has been employed at the Hopeton site in Chillicothe, similar degrees of ground accuracy can be obtained. The recent availability of USGS 1/9” DEMs further augments the ability to produce precision analyses of sightlines, vitiating any validity of claims that we need be satisfied with declination values of wide ranging uncertainty.
The authors are imprecise as regards their use of error range and just what constitutes an error. It is difficult to follow whether they are referring to an error in the resultant declination value when referring to a sightline, or in the error of the specific azimuth of the sightline. The two are not mutually interchangeable.
For instance, in the calculations for the Fairground Circle centroid sightline, the azimuth value used is 64.8 degrees. Consider the same equation for the two azimuth values 64 and 65 degrees. The corresponding declinations are +19.9 and + 19.1, a difference of 8/10 degree resulting from a one degree change in azimuth. This 2/10 degree difference may seem like a trivial amount until it is remembered that the target object in question, the moon, is itself only 0.5 degree in diameter.
More rigorous control of error tolerances must be demonstrated and maintained.
At one point in their manuscript, specifically referring to the locus of backsight H1, the authors suggest that a change in the ground locus of this backsight of 60 meters is acceptable! They suggest that this would alter the resultant azimuth value by up to 0.5 degrees, and they suggest that this is acceptable! 
Many of the error tolerances cited by the authors as regards their 1982 paper are due to systematic errors. The authors employ a spurious non-parsimonious method of defining what constitutes a sightline. Part of their argument uses the spine or ridge of given octagon embankments to define astronomically significant azimuths. But, in other sections of their 1982 and 1984 (and in the present) papers, they define these astronomically significant sightlines as being defined by the edges of the vertex gateways or gaps. These “gap edge” sightlines form a major thrust of the authors’ argument of “deliberate distortion” of the otherwise geometrically regular octagon (see page 14 manuscript and the 1982 article), and are not trivial in importance or frequency.
It can be shown that the sightlines that the authors have chosen to define as existing along the spines or ridges of the embankments can also be as accurately defined by the vertex gateway or gap features, and their corresponding edges.
It is these sort of sightlines that the authors’ themselves define in key examples at the Newark octagon (1982), and at the great majority of their sightlines at the High Bank earthworks in Chillicothe (1984). The authors are in essence choosing again which set of data fit which desired computational outcome, as has been demonstrated to be the case with their varying use of the q-value factor.
As with the q-value factor, the most parsimonious procedure would be to adhere to one and only one framework within the model. Because the embankment ridgeline azimuths can be as effectively generated with the gap-to-gap interpretation by the same data, but not vice versa, it follows that the authors should abandon the ridgeline or embankment spine model and adhere to the gap-to-gap interpretation. From a scientific and experimental viewpoint, it cannot be had both ways.
This issue is not without importance as pertaining to the citing of error ranges and values. Because the authors claim to maintain an adherence to the ridgeline azimuth model, they are forced to cite high error ranges of 1.7 degrees in their 1982 paper. (Actually the error they cite in 1982 is 1.3 degrees, but it is cited elsewhere as 1.7 degrees).
It is this error value which compels them to commend the new Hz or “zero degree horizon” model. Now, after reviewing their premises, I am convinced, with some corrections, that they have discovered a valid model that was used by the Hopewell in designing and constructing the Newark Octagon. The issue here I am addressing is rather that of error tolerances, not the Hz model itself.
The authors state in their manuscript that the Hz model still produces errors of 1.6 degrees, or a 1/10 degree difference from the model on which they were trying to improve! Note here how it is difficult to determine if they are referring to azimuth values or declinations values, as they do not rigorously define these.
In effect, by citing a resultant error range of 1.6 degrees for a model that they consider to be valid, they are asserting that such a great error is acceptable in the analysis of astronomically significant sightlines. It is this point I would contest specifically.  An error of 1.6 degrees is over three moon widths. Also recall that the authors do not rigorously treat the use of the q-value, which can introduce a further 4/10 degree range in citable resultant declination values.
Elsewhere in the manuscript, the authors suggest that the combination of the Middleton / Fowke survey data when assessed with their topographical analysis should produce an accuracy of 0.1 degree in azimuth values. (page 28 of manuscript)
Inasmuch as the authors suggest a precision value of 0.1 degree, it seems to be entirely implausible on the other hand to accept as valid astronomical sightlines that result in error values as high as 1.6 degrees.
In my own present analysis of the lunar minimum sightline as defined through the center of the Fairground Circle centroid as viewed from the locus of the octagon’s axial backsight, point C, the declination error along this sightline is 7/10 degree, or 1.4 moon widths. To me this seems unacceptably large itself to be cited as anything approaching validity within the model. This is especially true when we consider the high degree of precision (essentially perfect) in the axial sightline of the octagon as I have demonstrated regarding its indexing of the lunar maximum rise.
In their present paper, the authors cite errors of similar magnitude in their analysis, and claim them as valid astronomical sightlines, or “alignments” as they call them.
The authors seem to want to have it both ways. They assert claims of precision of 1-meter for the Middleton / Fowke survey data. They cite topographic azimuth accuracy of 1/10 degree. But when their proposed sightline declinations are off by 0.5 to 0.9 degree or more, they brush such errors aside as being due to imprecision in the method of analysis or to the imprecision of the observations made by the Hopewell.
 To make such suggestions is to ignore the means by which we can improve the handling of these data, and anthropologically it smacks of an ethnocentric assessment of the observational acuity that was manifested and employed by the ancients.  Actually, many of the authors’ proposed errors can be shown to be a result of poor modeling, insufficient map accuracy tolerances, misuse of the q-value, or a combination thereof.
As an important side bar: I completely reject the authors’ claim that the azimuth of the rising point of the moon can vary laterally due to refraction by as much one degree (see page 12 manuscript), or even by a total of +/- one degree depending on how one reads this sentence. I have been observing the sky for 40 years and I have never experienced such a wild range of refraction effects. Such an effect would be plainly visible while observing the rising of a bright star.
The authors have suggested the Hz model by the following premise: we take the extant sightlines at the octagon and reverse the azimuths till we arrive at salient features in the topography. I have done just that, as accurately as possible assessing the axial value for azimuth of the Newark Octagon group. This line does not eventuate in the locus of H1 as defined by the authors. It rather culminates within 11 meters of a peak feature, and the resultant declination from that peak area as pertains to the north lunar maximum rise event is exact.
Furthering with the author’s model, when the sightline for the Fairground Circle centroid is tested from this same backsight, it fails to demonstrate astronomical significance. It misses the declination in question by 1.4 moon widths, an unacceptably large error given the treatment of the data.
The authors assert that the selected backsight locus of H1 is unto itself topographically salient and that they have not chosen this locus speciously with regard to satisfying the criteria of their model. However, the location of H1 is in fact on the slope of a ridge feature, at a non-salient location. The Fairground Circle is not even visible from H1. There is no logical reason to choose H1 as the backsight locus as opposed to others that may lie along this particular azimuth.
When tested using ArcMap, the authors’ proposed sightline from their H1 backsight to the Fairground Circle is obscured by local terrain. The azimuth between H1 and the Fairground Circle does approximate the location of the north lunar minimum rise however. As such, it appears as if the authors have chosen this placement for this proposed backsight H1 more with regard to meeting the needs of their model than as to having objectively followed their own criterion as defined for placing these elevated backsights. Of all of the possible locations along their proposed sightline that they may have placed this backsight, they chose the one that “worked” with regard to the Fairground Circle.
Figure 30. The red dot is the authors’ H1, and the yellow line is that to the octagon vertex E. Why did not the authors locate H1 at any of the salient areas at the  pink crosses indicated? What makes the location that they chose for H1 to be independently significant? Can we can consider the results to be objective when they selected a locus that satisfies the requirement of their model that the backsight also functions with regard to the lunar minimum event as seen through the Fairground Circle? These are questions that any perspicacious review of their paper should consider.
Having said this, I would like to state that I still believe that the authors have discovered a valid geographic set of (approximate) locations that were used by the Hopewell in designing and constructing the Newark Octagon. I believe that it can be shown that peak features were the preferred loci of these backsights. I think that the errors with regard to the authors’ proposed locations of these elevated backsights are due to their use of low scale mapping and can and should be improved
















More GIS review of H1 properties
I begin with the authors’ value of H1 as noted in the article, i.e. latitude = +40.0123, and longitude = -82.5150. (page 29 of manuscript)
Figure 31.
H1 is the authors’ locus = lat +40.0123, long -82.5150 as provided by authors on page 29 of their manuscript. These values were converted to UTM zone 17 coordinates 4430012 and 370697 for the NAD 1927 datum,  using the website http://www.rcn.montana.edu/resources/tools/coordinates.aspx , then the location was determined and plotted using ArcMap 9.3
Points C and D are considered below as alternative loci for the authors’ proposed backsight.













Figure 32. This is the line plotted from authors’ H1 backsight to vertex “E” of the octagon



Figure 33. This is the line (purple) from H1 through the Fairground Circle center. The white line is the approximated axial sightline for the Fairground Circle.

Figure 34. The yellow line is also plotted from H1, but now intentionally made to go through the center of the gateway. At the Eagle Mound location, the lines differ by nearly 9 meters separation. One wonders to what extent Greenman may have rebuilt the Eagle Mound in the wrong position, though 9 meters seems like a rather large error as such.  [The white line is the best fit line through the center of the Eagle Mound and the center of the gateway.]
Notice how the authors’ suggested sightline (purple) is skewed relative to the axis of the center and gateway of the Fairground Circle. The authors argue that the enclosure is an imperfect circle and as such does not have a true “center”, so that there is room for variance in this regard. While the enclosure is not as geometrically regular as the circle at the nearby octagon, it has a distinguishing feature unlike most such Hopewell enclosures. I refer to the central mounds. These four low mounds are known collectively as the “Eagle Mound”. Greenman excavated this mound group around 1930, and uncovered as series of post molds that are consistent with a rectangular structure whose long dimension is collinear with the axis defined by the gateway.
Figure 35. The red dots are Greenman’s postmolds. They are plotted with regard to the features of the Eagle Mound, since they lack absolute positional data  Regardless of any imperfections that the large circle may have relative to geometric circularity, culturally speaking it is evident that the Hopewell considered this location to be the de facto working “center” of the enclosure.
One has to ask certain questions regarding the authors’ interpretation of the sightline shown above in purple. They note that from the point H1, the two lines, one to the octagon and one to the Fairground Circle, define the north lunar maximum and the north lunar minimum rise points respectively.
As for the line to the Fairground Circle, it has only an imperfect fit. One has to ask, given the exactitude and construction ability demonstrated by the line to the octagon: “Why isn’t the line to the Fairground Circle more accurate?” It can be defined as crossing the Eagle Mound in the center, or as passing centrally through the gateway, but not both. Why would the builders not place the Fairground Circle’s gateway in a more accurate location?
Also, and this is very important, there are issues of landscape phenomenology that need to be addressed. These methods of investigation, developed by British archaeologists, are largely ignored within Hopewell archaeoastronomy.
At this point in time, the best evidence suggests that the construction of the Fairground Circle preceded that of the octagon. Brad Lepper and other archaeologists excavated a section of the wall at Fairground, and obtained datable material which suggests a construction date early in the Middle Woodland period, around 100BC. Lepper was also involved in obtaining datable material from the octagon site, and these dates are much later, around AD 300.  Even given vagaries in dating, these dates suggest that the construction of the Fairground Circle preceded the construction of the octagon.
The Fairground Circle also has been suggested by several researchers: Carskadden and Morton, myself, and later Byers, to in essence be a Late Adena circle. This is based on its morphology. The great majority of Hopewell enclosures do not have interior ditches, but Fairground notably does. Its singular opening to the northeast is also an Adena trait. One could even suggest that its geometric irregularity may be indicative of an early placement in the chronology of Hopewell enclosure construction. The exactitude found at the octagon can argue for its later construction.
Now, to return to landscape and phenomenology, and to châine opératoire reasoning. When humans observe the sky, it must be that first sedentism is occurring for horizon calendars to develop. This is nearly an axiom in archaeoastronomy. Mobile groups use the zenith passage or heliacal rising of stars to mark the seasons, whereas sedentary groups use the sun’s motion along the horizon. The reason is obvious: if you are mobile you will not grow accustomed to the location of celestial objects as they rise and set along a specific local horizon.
There is also a lineage defined by the dictates of the sky itself regarding the order in which events become known to observers. Humans recognize the solstices before anything else within the corpus of solar and lunar motions. There are citable papers on this topic. In this regard, it is accepted that human observers would need first a deep familiarity with the solar motions before they would ever notice the more subtle variations of the lunar rise locations. This is why it is fairly common to find evidence for solstice observations across the world, whereas the lunar indices that the authors discovered at Newark are much rarer.
The least salient of all of these lunar horizon loci are those of the lunar minimum events. Whereas the lunar maximum rise and set points exceed the locations of the sun along the horizon, the lunar minimum points are within the range along the horizon of the sun’s movements, and indeed they are contained within the range of the moon’s azimuthal range along the horizon. As such, they would be the most difficult to observe and index definitively.
Hence, the notion that indices to the lunar minimum would precede those to the lunar maximum is fallacious. Yet that is what must be suggested in declaring the H1 sightline to the Fairground Circle to be a lunar minimum line. If the dating and apparent cultural chronologies regarding the Fairground Circle and the octagon are correct, it is very unlikely that the authors’ interpretation can be valid. The idea that the sightline to the Fairground Circle from point H1 was delineated intentionally with regard to the lunar minimum rise point must be reexamined.
It would be possible to suggest that the Fairground Circle already existed and was used by the Hopewell as a foresight target when they began to make their observations from the authors’ proposed elevated backsight loci. The more I consider the scenario the more I think this was what happened.








Figure 36. Authors’ H1 is the green dot at lower left. The lime green areas are calculated by ArcMap as “viewshed” from H1. Because of the intervening topography immediately to its northeast, the Fairground Circle not visible from H1,  the authors’ suggested dual backsight locus.
Figure 37. Areas in blue are the viewshed from Point C. The Fairground Circle is visible from this point, but a large swath of the valley remains obscured. Note variations in viewshed coverage as compared with Figure 19, which uses a lower scale DEM in analysis.

Figure 38. Areas in rose color are visible from Point D. Note that there is more complete visibility of the Fairground site, and that the entire valley is in general more visible. The mottled appearance of urban Newark is due to the high resolution Lidar-based DEM which shows modern street features.


Figure 39. Detail of Fairground Circle: rose colored areas are visible from Point D.
Figure 40. Lines of sight from Point D
Code: green = visible, red = invisible from Point D

 
Figure 41. Lines of sight from authors’ H1.  Red line and red dot at Fairground site indicates invisibility. Inset shows detail of H1 locus: black dot = authors’ point H1, dark blue circle = Point D locus, dark blue dot = “obstruction point” generated by ArcMap. All of the above viewshed and line-of-sight analyses are modeled in ArcMap for an observer 2 meters in height.   

                 
Figure 42. Sightline from point D
Figure 43. Although the most complete viewshed is seen from Point D, the “fit” to the axis of the octagon is not quite as accurate as from authors’ H1 backsight.

Figure 44. The sightline from Point D as it passes through the center area of the Eagle Mound, shown in purple. The line remains skewed relative to the gateway.






Figure 45. Idealized sightline through Fairground Circle gateway and through Eagle Mound


Figure 46. An idealized axial sightline through the Fairground Circle is shown in purple. Note where the “best fit” Fairground Circle sightline (Figure 45) (purple) crosses the Octagon sightline (yellow). This would approximate the “best fit” area for the authors’ proposed multiple backsight point when considered for enclosure axiality of sightlines. The distance from Point D to the crossing point of the two lines is 1430 meters, from authors’ H1 locus the distance is 1620 meters.
The three analyzed backsight points are shown at bottom of figure: H1 (green dot), Point C (turquoise circle), and Point D (blue circle).





Calculations testing authors’ proposed sightline to Fairground Circle from H1
Authors  give location of their point H1 as : +40.0123 latitude,     -82,5150  longitude
These convert to (UTM Zone 17) =    4430012 northing    370697 easting
After conversion to the form degrees-minutes-seconds, these figures can be entered into the online azimuth calculator found at
giving an azimuth value of 65.91ᵒ between authors’ H1 and the center of the Fairground Circle.
I checked the horizon features using ArcMap. The horizon as seen from H1 along this azimuth lies  21.8 km distant. I checked as far away as 37 km finding no other likely horizon loci.
The elevation of H1 is near 332m , whereas the horizon terminus of the sightline has an elevation of 315m. The difference is negligible at this distance, and hence the horizon is effectively a “zero degree horizon” along this sightline as the authors suggest.

For calculation purposes, these are the positional data for the horizon locus:                                                                              
Horizon foresight of Fairground Circle (center) sightline as seen from authors’ backsight H1
UTM (Zone 17 NAD 1927)             decimal degrees                               degree, minutes, seconds
391051                                                  +40.09310                                            40   05   35.2  N
4438663                                               -82.27804                                             82   16   40.9  W






Using the standard equation to obtain declination, the results are:
sin δ = (sin φ)(sin h) + (cos A)(cos δ)(cos h)
where    δ = declination
                φ = latitude
                A = azimuth
                h = corrected horizon height
i.e.           h = (h₀ - r + p ) +/- q
where    h₀ = true horizon height
                r = corresponding refraction value for that height [for h₀ = 0ᵒ ,  r = (-0.58ᵒ)]
                p = parallax value (for moon p = 0.95ᵒ, negligible for sun = 0.002ᵒ)
                q = +0.26ᵒ if for tangent event
                q = -0.26ᵒ for gleam event
                q = 0ᵒ for bisection of disk of sun or moon
Results show that for q = 0,       δ = +18ᵒ.5 
The declination value for the north lunar minimum event circa 1AD was +18.6ᵒ, hence this line is within accuracy guidelines. Remember though, the sightline is actually obscured by terrain, and the circle is invisible from H1.





Testing the Sightline from Point D through the Fairground Circle Center
If the same calculations are made for the sightline from Point D to the center of the Fairground Circle as outlined in the graphics above, the resultant declination δ = +18.8ᵒ.
This value is also within accuracy guidelines. If the Hopewell skywatchers were observing the first gleam event, this value is exact (i.e. for q = -0.26ᵒ, δ =  +18.6ᵒ).

The geographic data for sightline D are as follows:
Point D (locus proximate to H1 with best view of valley)
UTM (Zone 17 NAD 1927)             decimal degrees                               degree, minutes, seconds
370905                                                  +40.0125                                              40   00   45.0  N
4430030                                                -82.512583                                          82   30   45.3  W

Horizon foresight of Fairground Circle(center) sightline as seen from point D
UTM (Zone 17 NAD 1927)             decimal degrees                               degree, minutes, seconds
390270                                                  +40.09110                                            40   05   28.0  N
4438452                                                -82.28716                                             82   17   13.8  W

Distance of sightline to horizon is 21.12km     
elevation of D is 335 m
elevation of horizon locus is 325 m
again indicating a “zero degree horizon” effect as authors premise

Testing the Octagon Sightlines from H1 and D
H1  (authors suggested backsight for octagon axis and Fairground Circle center)
UTM (Zone 17 NAD 1927)                             decimal degrees                               degrees, minutes, seconds
4430012   (+/- 5.5m)                                        +40ᵒ.01230                                          40ᵒ   00’   44”.3  N
370697    (+/- 4.5m)                                         -82.5150                                               82   30   54.0  W
elevation = 332

Point D (salient peak locus proximate to H1  with best view of valley)
UTM (Zone 17 NAD 1927)             decimal degrees                               degree, minutes, seconds
4430030                                                +40.0125                                              40   00   45.0  N
370905                                                  -82.512583                                          82   30   45.3  W
elevation = 336

Horizon Foresight from authors’ H1:
UTM (Zone 17 NAD 1927)      decimal degrees                     degree, minutes, seconds
4439292                                  +40.09579                               40   05   44.849  N                              
383017                                    -82.37237                                82   22   20.525  W



Continuing Review of Author’s Article: (from page 27 through 30)
We then noticed that all the errors in the Octagon alignments were small and of comparable value if we assumed that the Octagon features were built along zero-altitude lines directed toward the lunar standstills as would be seen from high elevations where the altitudes of distant horizons were negligible.  The HZ hypothesis makes a very specific prediction about each linear Octagon feature that is aligned to a zero-altitude standstill direction: if a line is extended backward from the Octagon feature along the line of the standstill, it will ultimately pass over a prominent elevation from which the zero-altitude alignment could be conveniently observed.  At first we were skeptical about the likelihood of finding persuasive evidence for this idea.  The valley in which the earthworks reside is surrounded in all directions by the Appalachian foothills.  Consequently, the prediction that any line would pass over a commanding overlook was likely to be satisfied by chance alone.  Accordingly we did not initially think the possibility was even worth investigating because intentionality could never be demonstrated.  We were taken by surprise to discover that the elevated overlooks predicted by HZ for specific alignments in the earthworks were not only present in a prominent fashion, but that they had a repetitive pattern of geometrical relations to the earthworks and to one another which were unlikely to be due to chance.
Please propose the method of statistical analysis here regarding the prior phrase  “…were unlikely to be due to chance”. It is difficult to imagine the statistical format that would be used to analyze these varied multiple locations, though it must be possible.
.
In the analysis that follows the azimuths between earthwork features and positions in the local terrain have been determined using USGS 7.5 minute quads and digital mapping programs (Delorme 2002, 2004). The coordinates of earthwork features have been entered into the program using: (1) on-site GPS measurements; (2) rectified aerial photographs of the Earthworks; (3) the survey data obtained by James Middleton.   Field checks (using GPS measurements) of the azimuths obtained from the computer software suggest that unless otherwise stated the likely errors in the azimuths between earthwork features and distant locations in the local topography are on the order of ± 0°.1. 

The first and most important test of HZ is for the all-important alignment of the Circle-Octagon avenue axis to the northern maximum extreme moonrise.   When a line is extended through the center of the Observatory Circle backward along the avenue alignment at an azimuth 232°.0, we find that the line passes very near the highest point on a plateau that provides the most commanding overlook of the earthworks from the southwest.   The highest point on this azimuth which provides the best view of the valley below (known hereafter as point H1 and shown in Figure 8) is located at latitude 40°.0123 N and longitude 82°.5150 W.   The topographical profile from the Octagon center to H1 is shown in Figure 9.[i]
This is shown by above graphics to be largely correct. The octagon is visible from the authors point H1, but the Fairground Circle is not.

The existence of H1 would not add much to the case for astronomy at Newark if it were not related to another major feature of the earthworks in a manner that is similar and complementary to its relation to the Circle and Octagon.  In our original paper we noted that the Great Circle had an avenue opening with avenue walls directed (66°.68 and 66°.41 according to the Middleton survey recorded in Thomas, 462) toward the northern minimum extreme moonrise (within 0°.5). The walls of the avenue are far too short (25.6 m and 29 m) and asymmetrical, however, to define an alignment to the horizon with an accuracy better than ± 1°.0. The center of the imperfect Great Circle and the center of the avenue with asymmetrical walls cannot be unambiguously located, and so a line between these two points does not produce a precisely defined alignment.  Any alignment proposed for the center of the Great Circle to the center of the outgoing avenue would be uncertain by 1° The best estimate available for that alignment would be about 69°.   So, the best that one can say from the survey data internal to the Great Circle is that its avenue points in the general direction of the northern minimum extreme moonrise (within three degrees).
This paragraph is quite problematic. First, the authors do correctly recount their assertion from HH1982 that claims that the entry walls at the Fairground Circle define a lunar minimum sightline. Yes, that is their claim in 1982. But as they acknowledge above, these walls are exceedingly short, bulky, and non-linear so as to be suggested as sighting devices. To do so sets a bad precedent in this line of research, and neither they or has anyone else followed up with such assertions.
Their statement above that it is impossible to accurately define the center of the circle is quite misleading. True, the large circle is irregular, and as such it is problematic to define an unambiguous center. But, and the authors are well aware of this, there is a small set of mounds near the middle of the enclosure called the “Eagle Mound”. It can be shown in ArcMap that the geometric centroid of the circle and the axial midpoint of the Eagle Mound are separated by less than three meters (2.46 m).
Greenman circa 1930 excavated these mounds and found postmolds beneath them consistent with a long rectangular structure having once existed there. The long axis of this structure is coincident with the axis toward the gateway of the Fairground Circle. Culturally speaking, it is evident that the Hopewell used this locus as the “working” center of the Fairground Circle. As such, it is quite easy to define the azimuth from the “center” of the circle to the gateway. The authors above say it is about 69 degrees, which is reasonably near to what I have surveyed in situ to be 68.5 or 68.6. These values can be determined mathematically from the Middleton data or graphically from the Holmes map also, and agree.
It is beyond reasonable to suggest that this sightline so established defines the lunar minimum rise point, as Romain has claimed elsewhere. As the authors admit, it is 3 degrees in error from this sightline. This error amount is far too large to suggest anything conclusive. Three degrees is six moon widths!
The authors are ignoring work that I have performed since 1982 related to this site. I have shown in several papers and many conference presentations that the axial sightline at the Fairground Circle defines the May cross quarter date, this being around May 5. I interpret this as being a solar sightline used in establishing a planting calendar. The Hopewell were beginning to depend heavily on the cultivars of the Eastern Agricultural Complex, as can be shown in the archaeological record, and it is a culturally plausible interpretation that this circle was designed by elite skywatchers who were engaged in subsistence scheduling.
It also brings to bear a key point. No one would suggest that a human observer would begin monitoring moonrises until well after they had become aware of solar sightlines. We can employ the phenomenological premises of operational sequence studies to define in what manner given celestial events would become recognized by human observers. It invariably follows that solar motions are far easier to observe and detect than lunar ones. The more subtle lunar motions would have to be preceded by many generations of observers who were marking the solar motions. There are several good journal and book articles in the archaeoastronomy corpus that develop this idea. I am surprised that the authors do not use these as guidelines, but are trying instead to suggest the preeminence of the lunar sightlines exclusively, without providing any cultural background regarding the development of this technology.

The significant observation to be made in this context, however, is that if a line is drawn from H1 to the centroid of the Great Circle or the ‘center’ of the outgoing avenue from this circle, the resulting azimuth is 65°.9 (within 0°.2 of the northern minimum extreme moonrise for zero altitude).  Since H1 is located some 7.7 km from the Great Circle centroid, uncertainties in the positions of the centroid and the center of the outgoing avenue have a negligible effect on the azimuth of this alignment.   This alignment is shown in Figure 8, and the topographical profile from the Great Circle centroid to H1 is shown in Fig 9. 
I obtain the exact same azimuth value for the sightline from the authors’ H1 point through the center of the Fairground Circle, A = 65ᵒ.91.  Recall however that this sightline is obscured by nearby foreground terrain so that the Fairground Circle is invisible from the authors’ H1 backsight.
The modeled sightline is indeed within only 1/10 degree off the lunar minimum rise point, taking the moon as “centrally bisected” at rising (i.e. q=0).
Notice the use of the word “or” in this sentence, tacitly acknowledging that a line cannot be drawn through both the center of the circle and the center of the gateway at the Fairground Circle that originates at the authors’ backsight H1: “…if a line is drawn from H1 to the centroid of the Great Circle or the ‘center’ of the outgoing avenue from this circle”…
This sentence is less than clear: “..uncertainties in the positions of the centroid and the center of the outgoing avenue have a negligible effect on the azimuth of this alignment.”, As can be seen in the graphics provided above, in no case do the avenue and the center of the Fairground Circle fall along the same line as seen from the authors’ point H1. Also, the use of the term “centroid” is superfluous, the de facto “center” of this circle would have been the locus of the present Eagle Mound, and more specifically, the structure that once stood there. The two points are only 2.46 meters apart.

Thus H1 (the most commanding overlook point to the southwest of the earthworks) (is not, but rather on slope on west side of ridge) provides a common backsight for the observation of two complementary lunar standstills.  From H1 an observer would see the Moon rise over the Observatory Circle-Octagon axis when it was at the northern maximum standstill.  The same H1 observer would also see the Moon rise over a line through the center of the Great Circle and its associated avenue when the Moon was at the minor standstill. So as the Moon oscillated back and forth between the major and minor standstills, it would (at its northern extreme rise point) move back and forth between the center of the Observatory Circle-Octagon and the centroid/avenue of the Great Circle as seen from H1.  The effects of the altitude of distant horizons on these alignments is negligible (< 0°.05) and both alignments as seen from H1 have an accuracy of 0°.3 or less. The location which might have been used for such backsight observations cannot be determined exactly from these considerations since the backsight (over 7.2 km from either circle center) could be moved by as much as 60 m without producing alignment errors greater than 0°.5.  On the other hand the position of H1 cannot be moved further than about 50 m toward the southwest without losing a direct view of the Great Circle.
Notice in the above paragraph that the authors are very careful to state that the sightline to the Fairground Circle passes “through the center” of the circle, whereas the sightline to the octagon is genuinely axial. This is a tacit admission that the proposed lunar minimum sightline does not pass through the center of the gateway of the Fairground Circle. Again, given the degree of accuracy found with the axial alignment at the octagon, this begs the question why the sightline (i.e. the gateway location) was not so constructed at the Fairground Circle.
The authors suggest above that the backsight locus H1 “could be moved by as much as 60 m without producing alignment errors greater than 0ᵒ.5.” This value of 0ᵒ.5  is quite high, and would cause the moon to rise out of line by its entire diameter. The sentence is therefore superfluous and should be deleted.
The authors also write: “On the other hand the position of H1 cannot be moved further than about 50 m toward the southwest without losing a direct view of the Great Circle.” As demonstrated in the above graphics, the Fairground Circle is not visible at all from their proposed backsight H1, and to remain as a plausible argument, the proffered locus needs to be relocated to point C or D as outlined in the descriptions appended to the above graphics.