New Research Suggests Artificiality

Copyright © 1996 by Stanley V. McDaniel

Introduction

The McDaniel Report argues that planetary SETI research (the search for signs of extraterrestrial intelligence on planetary surfaces) should be an interdisciplinary task. Sciences that study culture, language, and symbolic communication ought to be involved when attempting to evaluate possible messages or artifacts of extraterrestrial civilizations.

NASA's approach to SETI does not appear to recognize this interdisciplinary requirement, and confines itself to "radio SETI" in the belief that no signs of extraterrestrial intelligence are likely to be found within the solar system.[1] Dr. Carl Sagan, a member of the NASA Viking team and de facto spokesman for the NASA viewpoint, has indicated that "archaeologists and the like" should be called in only after planetary scientists (geologists and astronomers) have determined that an object is artificial (see The McDaniel Report, page 151) -- but geologists and astronomers are perhaps the last persons suited to recognize possible cultural artifacts.

After the failure of the Mars Observer spacecraft in August 1993, scientists interested in the Mars Anomalies were faced with the possibility that no new images of the Cydonia region might be obtained for some time to come. Attention was turned toward the existing data to explore previously overlooked, or only partially investigated, features. In this renewed effort by independent scientists, several avenues of approach have been employed: geological, archaeological, image processing, and geometric measurement.

Drs. Carlotto and Strange are reporting their results this month (May) in papers before the Society for Scientific Exploration at its meetings in Charlottesville, VA. Geologist Erjavec's paper appeared in an earlier update of this newsletter. Dr. Crater's initial findings were reported at the Society for Scientific Exploration meetings in Huntington Beach, California, in June 1995.

Since then, I have collaborated with Dr. Crater on expanding this research. Dr. Crater, a physicist at the University of Tennessee Space Institute, has developed a careful methodology and run computer simulations in order to obtain probability estimates. My contribution has been to look for possible cultural significance in the geometry analyzed by Dr. Crater. Presently Dr. Crater and I have submitted updated research results to the Journal of Scientific Exploration for possible publication. (An earlier draft report on this research is also available in Europe from the UK Mars Network.)[2] Below you will find a summary of this potentially significant new research. It is indeed a scientific detective story with interplanetary implications.

The Problem of Geometric Measurements

After cartographer Erol Torun proposed that the object called the "D&M Pyramid" may have originally had a coherent geometric shape, science writer Richard C. Hoagland made a series of measurements on the Cydonia plain. Hoagland claimed that the geometry of relationships between a number of the landforms reiterated the geometry proposed by Torun. Unfortunately, most of the objects involved in Hoagland's measurements were large and different in character, making the identification of geometric reference points appear somewhat arbitrary. And in some cases the points of reference used by Hoagland were unclear or the measurements were in error (see Revision of Some McDaniel Report Evaluations).

However, Hoagland also made some tentative measurements of the geometric relations among a number of smaller features which, because of their relatively small size and uniform shape, do not suffer from the same problem of ambiguous or arbitrary reference points (see The McDaniel Report, page 122). In 1994 Dr. Crater turned his attention to these smaller objects. Crater's results, benefiting from a more careful methodology, differ from Hoagland's findings.

The Small Mounds

The area of interest on the Martian Cydonia Plain includes a cluster of seemingly related formations that has been called for convenience the "City" (although no one claims that the grouping actually is a city). This group is shown in the center left area of Figure 1 below. The larger objects are about 1 mile across. (Please use your best screen resolution to view these images.)[3]

Figure 1. Area of the

Figure 1. Area of the "City" at Cydonia (from NASA Viking Frame 35A72)
Within the "City" and also on the open plain to the south, there are several relatively small features that have been called "mounds." These objects are about 300-700 feet in diameter and perhaps 100 feet high. They stand out from their surroundings because they are fairly uniform in size and brightness, they are much smaller than the surrounding landforms, and most of them appear to cast shadows that come to a point. With the exception of a small group of four in the center area of the "City," they are not clustered tightly together but are separated in some cases by as much as 3 kilometers. All told there are not very many of them -- about six on the open plain and perhaps ten more within the "City." For research purposes we have given most of these mounds letter designations as shown in Figure 2 below.

Figure 2. Mound Letter DesignationsFigure 2. Mound Letter Designations

The Isosceles Triangle

In 1992 Richard C. Hoagland reported that three of these mounds -- those we have lettered A, E, and D -- appear to form an almost perfect isosceles triangle (having two sides of equal length). This triangle is shown in Figure 3.

Figure 3. The Isosceles TriangleFigure 3. The Isosceles Triangle of Mounds
Taken by itself the presence of a symmetrical triangle among various apparently scattered formations is of no particular interest; however, after Dr. Crater made careful measurements of the angles in this triangle he discovered an odd coincidence. The angles within the triangle (to close tolerances) in one way or another involve the value "t" or 19.5 degrees -- an angle that cartographer Erol Torun claimed to have found in the "D&M Pyramid," and also an angle that Richard C. Hoagland claimed he had found among several larger objects in the area. 19.5 degrees is the so-called "tetrahedral latitude," which is the latitude on a sphere at which the base of an enclosed tetrahedron touches the sphere, when the apex of the tetrahedron is at one "pole" of the sphere. (See The McDaniel Report, page 102.)

The Tetrahedral Cross-Section: lrr

To be exact, the angles within the isosceles triangle formed by mounds ADE, within very close tolerances, are (in degrees) 70.5, 54.75, and 54.75. Expressed in terms of "t" (19.5 degrees) and the right angle (90 degrees), these angles are:

70.5 = (90 - t)
54.75 = (90/2 + t/2)
In reflecting on this particular set of angles, we found that this triangle is identical to the cross-section of a tetrahedron, represented by ADE in Figure 4. (NOTE: Diagrams are for illustrative purposes only and should not be used for measurement.)

Figure 4. Tetrahedral Cross-Section

Figure 4. Tetrahedron, Showing Cross-Section ADE
Dr. Crater assigned lower case letter designations to these angles, l = 70.5, r = 54.75. Thus the tetrahedral cross-section could be referred to as an lrr triangle.

The Right Triangle: prs

Richard C. Hoagland had also noticed that mounds AEG appeared to form a right triangle. Dr. Crater measured this triangle and found angles matching the following right triangle within very close tolerances: (in degrees) 90, 54.75, 35.25. Again there was a surprise. The angles in this right triangle also involve the tetrahedral angle t. Expressed in these terms the angles are: 90, (90/2 + t/2), (90/2 - t/2). The letters assigned to these angles were p = 90, r = 54.75, and s = 35.25. Thus the right triangle could be referred to as a prs triangle.

The Tetrad

The two triangles discussed above share a common side, the line drawn between mounds AE. Furthermore, one of the two triangles internal to the four mounds ADEG -- the triangle formed by mounds AGD -- happens also to be a prs triangle; that is, it has exactly the same angles as those in triangle AEG. Using analytic geometry, Dr. Crater found that an ideal figure having the shape closely approximated by the tetrad of four mounds is geometrically unique. All of the internal angles of this tetrad are either the right angle or can be expressed by means of the right angle and the tetrahedral angle t. The mystery: why was the tetrahedral angle t showing up so consistently in this figure? And how is the cross-section of a tetrahedron involved?

Figure 5. The Tetrad of MoundsFigure 5. The Tetrad of Mounds
Turning attention once more to the tetrahedral cross-section, we discovered that the prs right triangle, found twice in the tetrad, matches one of the two triangles inside the cross-section of a tetrahedron (when the cross-section is cut by the meridian of the tetrahedron). You can see this prs triangle in Figure 4 as triangle AXE. The other triangle in the cross-section, EXD, is a plt triangle (angles 90, 19.5, 70.5). This latter triangle is also visible in the tetrad as an internal triangle formed by the crossings of lines AE, GE, GD (with the 19.5 angle at G).

In other words, in the four triangles defined by this tetrad of four mounds:

The Pentad of Mounds

Seeing this apparent regularity based in some way upon the geometry of a tetrahedral cross-section, Dr. Crater next brought the single remaining mound to the south, mound B, into consideration. Measurement showed that the triangle formed by mounds ADB is once again a prs triangle.

This figure of five mounds, which Dr. Crater termed the "pentad," repeated the pattern begun with the original isosceles triangle: the angles within all ten internal triangles created by lines drawn between the mounds are simple functions of the 90 degree angle and the tetrahedral latitude angle t.

Figure 6. The Pentad of MoundsFigure 6. The Pentad of Mounds
Further analysis of the figure indicated by the five mounds uncovered an even more surprising fact: if you take the shortest intermound distance (BD) as a unit of measurement, all the other intermound distances are multiples of powers of the square root of 2 and the square root of three (Figure 7 below). (NOTE: Diagrams are for illustrative purposes only. Accuracy of angles may vary depending on computer display characteristics.)

Figure 7. Intermound Distances

Figure 7. Intermound Distances in the Pentad
In Figure 7 above, line EX divides the tetrahedral cross-section ADE precisely by its altitude (see line EX in Figure 4). Triangles EXD and EXA are the tetrahedral plt and prs triangles, respectively. Simultaneously triangles EAG, ADG, EAB, and ADB are prs triangles found in the tetrahedral cross-section matching triangle EXA. This illustrates the manner in which the pentad figure is "saturated" with the geometry of the tetrahedron.

Clearly there is evidence of remarkable geometric regularity in this pattern of five mounds. What is the probability that such a configuration might occur by chance?

Probability Calculations

Dr. Crater next used three different methods, including 200 million computer simulations of random distributions and a study of 4,000 other natural objects on Mars, for calculating the probability that the pentad formation is consistent with random distribution of features as might be expected of natural geological features. The methods and formulas used for these calculations are complex and will not be discussed here.[4] The net result: the probability that the configuration of five mounds is a result of random geological action is less than one in 200 million. While this extremely low probability does not prove that the mound pattern is a product of intentional design, it clearly identifies the pattern as an unmistakable anomaly calling for explanation.

The Square Root 2 Rectangle

At this point we have a five-sided figure, defined by the pentad of mounds ADEGB, which -- within very close tolerances -- exhibits a remarkable degree of geometric regularity that clearly references the geometry of the tetrahedron, and whose chances of being a product of random geological placement are practically zero. Furthermore we have the fact that prior to this discovery by Dr. Crater, Erol Torun and Richard C. Hoagland had both claimed to have found evidence of the tetrahedral angle t elsewhere in the vicinity of the Face on Mars. Dr. Crater's discovery was entirely independent of those earlier speculations.

The question that arises is: if this placement of mounds is intentional, what might be its geometric, symbolic, technological or architectural -- in other words, cultural -- rationale?

In studying the pentad Dr. Crater had discovered, I noticed that when the lines are extended the five mounds suggest a rectangular pattern. Although there are no mounds visible at two of the corners, the mounds that form the pentad lie very precisely on five of the eight nodes (four corners and four side midpoints) of such a rectangle.

Figure 8. Rectangle Implied by MoundsFigure 8. Rectangle Implied by 5 Mounds
Inspection of the geometry of the rectangle revealed a remarkable fact. The rectangle clearly defined by these five mounds is a direct geometric representation of the formula for finding the tetrahedral value t. That formula, sin(t) = 1/3, is expressed geometrically by a triangle with a short side of 1 unit and an hypotenuse of 3 units. When four such triangles are placed together, they form a rectangle with a short/long side ratio of 1 to the square root of 2 -- and these are the proportions of the rectangle defined by the five Cydonia mounds (Figure 8). [6]

Figure 9. The Square Root 2 Rectangle

Figure 9. The Square Root 2 Rectangle
The triangle that is the basis for this rectangle contains angles 90, 70.5, and 19.5. Using the abbreviations given earlier, we would refer to this as a plt triangle.

Thus the pentad of mounds at Cydonia, in a very precise and clear manner, references the geometric figure called a "square root 2 rectangle." And that rectangle, in turn, is thoroughly saturated with the internal geometry of the tetrahedron:

The Hexad of Mounds

The remaining mound that lies outside the "City" boundaries to the east is mound P. Upon measurement it became evident to Dr. Crater that again we have an example of the prs right triangle, this time formed by mounds EGP. More remarkably, triangle EGP is the same size as triangles EGA and EAB, both of which are within the pentad. This being the case, it turns out that mound P lies at one node of an extended square root 2 grid (Figure 10).

Figure 10. Extended RectangleFigure 10. Extended Sqrt 2 Rectangle
Again, two of the corners of the extended rectangle are missing, but the geometry of the rectangle is clearly implied by the distances and angles among the six mounds.

Note that mound P lies in an isolated position. There are no other mounds lying about that might offer "choices" and create an arbitrary selection. Furthermore there are only six clearly identifiable mounds at or outside the southern "City" boundaries, and the hexad involves all of them (again ruling out arbitrary selection). Of the probabilities involved in this hexad, Dr. Crater says that the likelihood of this being a random formation "is obviously less than that of the pentad by at least a factor of 1000" (Less than one in 200 billion).

Dr. Mark J. Carlotto has recently noted that even if one discounts the internal geometric properties of this rectangular grid, overall it has a rectilinear character that matches very closely the orientation of four major objects in the area: the Face, the "Fort," the "Main Pyramid" and the "Platform Pyramid."[5] Dr. Carlotto's observation is of considerable interest, since it suggests a connection, at least in orientation, between the mound formation and the larger features of interest.

The Heptad of Mounds

Upon further measurement, Dr. Crater found that mound O, which lies near the northeast corner of the "City" group, forms an equilateral triangle with mounds P and G. Taken by itself this is again not particularly remarkable. Furthermore, mound O does not lie on any further extension of the sqrt2 rectangular grid. The various triangles formed within a sqrt2 grid do not include equilateral triangles. However, the faces of a tetrahedron are equilateral triangles, and what is notable about the equilateral triangle formed by mounds OPG is that it is the same size as would be a face of a tetrahedron whose cross-section has the dimensions of triangle ADE -- which is a part of the sqrt2 grid (Figure 11).

Figure 11. Equilateral OPGFigure 11. Equilateral OPG
Thus in the context of the sqrt2 grid and the presence of isosceles triangle ADE, equilateral triangle OPG supplies the remaining "piece" of an apparent tetrahedral puzzle:

The Remaining Mounds

When Dr. Crater first put forward his findings he was immediately questioned regarding the remainder of the mounds -- those primarily within the borders of the "City." Although there is no clear extension of the square root 2 rectangular grid into the "City" mounds, Dr. Crater found that there is a preponderance beyond chance of the tetrahedral prs and lrr triangles. Altogether 12 mound structures over an area of about 62,500 square pixels, including the hexad of mounds, were studied, leaving out only the four mounds clustered tightly together near the center of the image (since the distances between them is on the order of their sizes, rendering angular measurements meaningless) and one or two others that are borderline on our criteria for the mounds.

In this study, Dr. Crater allowed the value of angle t to vary in order to see if there were possibly other triangular patterns having as high a frequency as the prs and lrr triangles. Dr. Crater reports his results as follows:

"The results show in the clearest possible terms a geometrical anomaly at t = arcsin (1/3). The z-score for t = arcsin(1/3) was very nearly five, compared to z-scores of about -1 to +1 for all other values of t. There is thus no validity to the objection that the analysis biases the results in favor of tetrahedral triangles. The data itself does, with the geometry of the tetrahedral cross-section defined by t = arcsin(1/3) standing starkly above that of all other geometries tested."

Possible Cultural Implications

As stated earlier, the fact that the mound configuration is almost certainly not a result of random geological forces does not prove that the mounds are artificial. However it is an anomaly that demands an explanation, either in terms of some unknown geological processes that could create this sort of pattern, or in terms of intelligent design.

Of these two alternative explanations, that of intelligent design would appear at present to be the more likely -- if only for the reason that the orderly configuration of mounds has been located in an area already containing several anomalous objects (Including the Face). It is certainly worthwhile, then, to speculate on the possible implications of intelligent origin.

If this mound configuration is a product of intelligent design, it must reflect some kind of cultural context.What are the possible cultural connections for such a figure? Are there any parallels in terrestrial cultural history that might give a clue as to the nature of the intelligence that may have constructed these mounds?

There are indeed some known terrestrial cultural contexts in which the square root 2 rectangle has a role. In his book The Geometry of Art and Life, Matila Ghyka discusses "Greek and Gothic Canons of Proportion." in which it is said that the proportions of certain rectangles, derivable geometrically from the square, represent harmonic balance in art and architecture. These include the square root (sqrt) 2, sqrt 3, and sqrt 5 rectangles. They are called "dynamic" rectangles.

These "dynamic" rectangles were thought to produce "the most varied and satisfactory harmonic subdivisions and combinations" for use in art and architecture. In his book, Matila Ghyka shows seven different "harmonic decompositions" of the sqrt 2 rectangle, which would be used to establish a great variety of proportions perceived as aesthetically pleasing.

In a series of two articles in the journal Discussions in Egyptology (1988, 1989), John A. R. Legon presents data indicating that the layout of the three pyramids at Gizeh, Egypt (including the Great Pyramid) is based on a rectangle having as its sides sqrt 2 and sqrt 3, with its diagonal being sqrt 5. The values sqrt 2 and 3 are predominant in the sqrt 2 rectangle, and the value sqrt 5 is derivable geometrically from that rectangle. From Legon's work it would appear that the layout of the Gizeh pyramids may have been influenced by the same concepts of harmonic proportion as those discussed by Ghyka.

What is most interesting about the Legon data is that it implies an application of the "dynamic rectangle" concept to the distribution of a group of pyramids. On Mars we have, perhaps, an analogous situation: At Cydonia there is also a group of structures of relatively uniform shape, distributed according to the "dynamic" sqrt 2 rectangle.

The cultural implication may be that the distribution of mounds (if they are artificial) is simply architectural or aesthetic in intent. If so, this would be a piece of information regarding the cultural mind-set of the builders. And since the Canons of Proportion are geometrically derived -- geometry being a universal science -- there is no reason to suppose that extraterrestrial intelligence might not be responsive to the same concepts of harmonic proportion as those appreciated in the terrestrial cultural tradition.

Another possibility is that the distribution of mounds is intended as a kind of signal. Critics have said that any "message" from extraterrestrials ought to be simple and easy to recognize; that any intentional pattern would have to be "obvious." But I don't see how that is necessarily the case. It could well be that a signal was created that could only be understood by a civilization advanced enough in mathematics and geometry to interpret and respond to a more complex geometric pattern. Or it could be that the "message," if that is what it is, speaks to a symbolic and aesthetic side of culture rather than a coldly scientific one.

At the very least, the Cydonian mound configuration may be interpreted as added support for the initial speculation by Torun and Hoagland that for some reason, the geometry of the tetrahedron is an intentional factor in the landscape of this mysterious portion of Mars.

What the truth of the matter is, and whether the objects are artificial or not, humanity will never discover -- unless those at NASA (and other spacefaring nations) who are in charge of the exploration of Mars assign greater priority to the anomalies in the Cydonia region.

FOOTNOTES

1. Anthropologist Randolfo Pozos and science writer Richard C. Hoagland, organizers of the first Independent Mars Investigation (reported in Pozos' book The Face on Mars) in the 1980's, advocated an interdisciplinary approach

2. Write the UK Mars Network, P.O. Box 1814, Buckingham, MK18 3ZZ, ENGLAND. English Pounds 5.75 by surface mail, 7.00 air mail.

3. All photographic images in this article are based on an original enhancement by Dr. Mark J. Carlotto. They are for illustration only and should not be used for measurement. The original from which these images were taken is in Dr. Carlotto's book The Martian Enigmas, page 24.

4. For copies of the paper detailing the methodology, see footnote 2 or write to The McDaniel Report Newsletter, 1055 W. College Ave. #273, Santa Rosa CA 95401. Include $5.00 U.S. to cover cost of reproduction and handling.

5. See The McDaniel Report, page 77, for identification of these features.