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  Orthoteny as a World Grid and the Intra-Ocular Impact Test

Donald A. Johnson, Ph.D.

In the Spring 2000 issue of IUR I published an article entitled, "New lines in UFO research: Orthoteny revisited" (1) in which I reviewed the evidence for three great circle routes in France apparently used by UFOs: BAVIC, AUPER, and CAMAC. These three lines appear to have upwards of 50 UFO reports each falling along their paths that intersect at a single point in Puy de Dome, France. In the Autumn 2000 issue of IUR Claude Mauge responded with a critical review entitled, "Orthoteny: Lost cause, or a redeemed one?" (2)

I welcome the critical response that Claude Mauge wrote to my article on orthoteny as a serious topic for UFO research; I would rather have these ideas criticized than ignored. I look forward to a continuing dialogue on this stimulating topic. Here I will respond to each of his points, but I also intend to shift the direction of the argument away from some of the original notions about the "straight-line" mystery developed in the 1950s by Aime Michel (3). This shift in thinking is crucial because it will render moot most of the objections raised by Mauge.

First we must refine and agree upon our terminology. His first objection is centered on the definition of what constitutes a straight line. In non-Euclidean geometry all parallel lines on the surface of a sphere do indeed intersect at two points. These lines are straight lines or great circles because they define the shortest distance between two points. A great circle is a circle upon the earth's surface formed by the intersection of a plane passed through its center. Meridians of Longitude are great circles, formed by the intersection with the earth's surface of planes perpendicular to the equator and passing through the poles. All meridians are equal in length and meet at the poles. Distances along the meridians between any two parallels are equal.

The lines that denote latitude are not in fact parallel lines even though they are called "parallels" because they do not intersect. Latitude lines are not the shortest routes between two points. Parallels of Latitude are "small circles," formed by the intersection with the earth's surface of planes parallel to the equator. The length of the parallels decreases from the equator to the poles. At Latitude 60o, the circumference of the parallel is one-half the circumference of the equator.

The fact that a latitude line is not the shortest route between two points can easily be demonstrated on a globe: although Los Angeles and Tokyo are at approximately the same latitude, the shortest route between these two cities does not follow the 35th parallel but inscribes an arc passing well above the 45th parallel and just south of the Aleutian Islands. These shortest-distance routes are great circle lines. All of the lines defined in my IUR article, and the orthotenic lines defined by Michel and Saunders that intersect near Puy-de-Dome (BAVIC, AUPER, and CAMAC), are great circle lines.

Mauge objects to my construction of great circle lines that do not fall within the same 24-hour period. He correctly points out that this is contrary to the original definition of orthotenic lines used by Michel. I contend that the date of the occurrence of the UFO sightings or close encounters is irrelevant because the great-circle alignment is not a one-time event. Reports fall along these lines repeatedly in wave after wave of UFO reports.

Furthermore, I contend that whether these great circle routes were first discovered in data from 1954 or 1947 or 1973 is also not terribly important. The important thing is that the pattern reappears. If you were to discover surveyor stakes running in a straight line in the forest or field behind your house, and a week later you find more stakes, some conforming to that original line and others running in a straight line perpendicular to the original set, would it not be reasonable to conclude that some construction project will likely follow, either a set of roads, power lines, or building lots? The date on which the stakes first appear is not important, unless you hope to stop the project; in which case the sooner you discover the stakes the better. To carry the analogy a little further, if you proceed to remove the stakes and some short time later someone puts new ones in their place, does that not tell you something about the persistence and the importance of the phenomenon?

Likewise, whether Michel had his dates wrong or not, and whether or not you choose to include any of the original six sightings that he used to define BAVIC (the Bayonne to Vichy great circle route), BAVIC does exist! It is defined by UFO cases that have occurred subsequent to 1954, and even by cases that occurred prior to that time.

Mauge criticizes my choice of UFO cases, in that any reliance upon 1954 cases requires that one rely upon newspaper clippings about sightings and close encounters that were never properly investigated. I agree that any mapping and grid system should rely upon high quality cases to the furthest degree possible. I have pondered this problem and how best to address it for a long time. It is a frustrating fact that most case files on UFO events lack bits of information that would be necessary to categorize them as "high-quality."

On the other hand, relying solely upon the highest quality UFO cases would result in a serious bias in the data because one would be forced to include only those cases from affluent societies where trained and competent UFO field investigators live nearby and have invested the time and money necessary to do a thorough investigation. Nearly always this means the presence of a determined volunteer network, because rarely have governments or NGO's (non-governmental organizations) sponsored or funded such work. With the exception of a couple of European governments providing minor support for UFO research, whenever there has been government-sponsored work, their motives have quickly become suspect and likewise the information from their resulting reports.

One compromise approach I have developed is to plot only the high-strangeness UFO cases, focusing particularly on those cases with claims of physical effects and the presence of aliens. Not all close encounter reports are well investigated, but they are less likely to be caused by mundane phenomena such as weather or the misidentification of aircraft, satellites, or astronomical bodies. They also are likely to have more than one citation in the literature.

In my analysis using the UFOCAT database I have filtered out those cases that were flagged by the primary investigator as either explained or probably explainable. The other rule I have adopted is to only plot great circle lines that have four or more close encounter cases, because lines with fewer than four map points are much too likely to be due to chance alone.

The mapping software I have been using is Microsoft Map Point 2000. I have verified that it does an accurate job of inscribing great circle lines up to nearly halfway around the globe. It represents quite an increase in productivity and reliability over hand mapping geographical coordinates because it will plot a few thousand coordinates in a matter of minutes. It also does a better job of eliminating honest mistakes that would occur if the process of exploring possible great circle alignments were left entirely to the imagination and hand plots of the researcher.

Studying these maps on the computer screen, two linear patterns emerge. The first is there appears to be an interlocking grid with lines converging on hotspots that appear as major intersections of great circle routes. In France, this grid bears similarity to the one proposed by Garreau and Lavier (4), who plotted 202 landing cases from 1947 to 1975. BAVIC is rotated 29 from their set of East-West lines, CAMAC is rotated 29 from their set of North-South lines, and AUPER is rotated 146 from their East-West lines. I have shown the BAVIC-CAMAC-AUPER grid superimposed upon the Garreau and Lavier grid in Figure 1. These lines tend to be oriented in such a manner as to conform to natural features and landmarks. For example, lines tend to intersect with the mouths of rivers, parallel coastlines, and pass through straits and channels.

The second noticeable pattern is that there appear to be sets of two, three or four parallel lines that overlap this grid. They give the appearance of satellite trackings, and suggest that these lines are not part of the permanent grid but trace flight paths.

Mauge assumes that because the statistical tables were absent from my earlier article I have relied solely upon "play[ing] with point coordinates in a computer." This is not entirely the case. I have checked the goodness-of-fit of many lines statistically. For coordinates along a line with a length of 200 miles or less I have used least-squares linear regression and compare the predicted latitude with the observed latitude and only consider points as qualifying for a line if the predicted latitude is off by less than .15 degrees. This method works adequately for the temperate and tropical regions, but presents large inaccuracies when attempted for the sub-polar regions. For coordinates falling along a line with a distance greater than 500 miles the distortion caused by the curvature of the Earth is too great to use linear regression, and I have employed polar coordinates and the equation suggested by Haythornthwaite (5).

I agree with Mauge that whether or not orthotenic alignments exist is ultimately a mathematical question. I propose the following statistical test. What we need to judge the statistical remarkability of the alignments is some measure of the probability of observing an identical mapping from random sets of geographical coordinates of the same number. I propose that we use Bradley Efron's bootstrapping procedure (6) to generate a sampling distribution. We would repeatedly draw samples with replacement from a large universe of geographical coordinates with plausible boundaries, calculate the number of alignments obtained, and repeat the process a large number of times.

A geographical region such as the Iberian Peninsula would be a good test case because the land mass is nearly square and it has a long coastline, so if there is any merit to my hypothesis that lines do indeed intersect with rivers and bays or parallel coastlines, it will stand or fall by comparing the number of lines with five or more points to the distribution that results from the bootstrapping process. In lieu of these more rigorous statistical results, which must wait for the future completion of this computer-intensive technique, I make at this time the following two arguments that the alignments are real and not illusory.

My first defense is based upon the best statistical test that I know, the intra-ocular impact test! Does the impact of the evidence "hit you between the eyes"? Trace a few of the longer lines and count the number of cases. Without double counting the sites with multiple cases, a line from near Cadiz, Spain through Helsinki, Finland has 13 points defining it. The line from Loch Maree in the Highlands of Scotland to the Isle of Capri near Naples, Italy has 11 points defining it, and many of these are hotspots with multiple reports occurring over many years. BAVIC still has seven points that are CE-2 and CE-3 level reports, and this is just considering Europe and ignoring the additional points that define it in South America and Asia.

Are these alignments illusory? I would deem this unlikely. Does my method for developing these alignments capitalize on chance? Undeniably. But is there a pattern that is so obvious upon visual inspection that it would be hard to deny something is going on? It certainly looks that way to me. And it becomes even plainer and more convincing when you scrutinize these mappings up close. For this reason I am offering to provide the UFOCAT-2003 CD-ROM to anyone who would seriously like to independently verify what I believe to be the truth (7). The maps that can be produced on paper from the mapping software do not entirely do justice to the dramatic impact I am describing here.

My second argument is that the network of great circle lines appears to be an interlocking grid and conforms to an orderly pattern. This grid would be even less likely to be due to chance, because the degrees of freedom necessary to define the grid are reduced. I believe that the orthotenic alignments represent a navigation system, possibly tied to a propulsion system, used by the UFOs. Others have suggested the existence of a grid system, but the great circle alignments provided by mapping the UFOCAT close encounter data provide confirmatory evidence for the existence of a worldwide grid.

David Saunders suggested such a grid network as a possibility in his 1972 MUFON symposium presentation, the manuscript of which is much more detailed than what appears in the published proceedings (8). MUFON requires that the written version of the talk be available a month in advance of the conference, so the paper I have in my possession has several pages devoted to orthoteny that do not appear in print. I have sent a copy of Saunders paper to the J. Allen Hynek Center for UFO Studies.


1. Mauge, Claude. "Orthoteny: Lost cause, or a redeemed one?" International UFO Reporter, 25, no. 3 (Fall 2000): 24-28.

2. Johnson, Donald A. "New lines in UFO research: Orthoteny revisited," International UFO Reporter, 25, no. 1 (Spring 2000): 18-19, 32.

3. Aime Michel, Flying Saucers and the Straight-line Mystery. New York: Criterion, 1958.

4. Garreau and Lavier (1974) map from Claude Mauge, "Orthoteny: Lost cause, or a redeemed one?" International UFO Reporter, 25, no. 3 (Fall 2000): 24-28.

5. Haythornthwaite, P. K. "BAVIC plotted as a world circle line," Flying Saucer Review, 9 (Nov.-Dec. 1963): 17-18.

6. Persi Diaconis and Bradley Efron, "Computer-intensive methods in statistics." Scientific American, 248, no. 5 (May 1983): 116-130.

7. Requests can be e-mailed to Donald A. Johnson, Ph.D. donjohnson@ufocat.com.

8. David R. Saunders, "Some New Lines for UFO Research", (unpublished manuscript), paper presented at the 1972 Midwest UFO Network Conference, Quincy, IL.