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Video 01 - The Cydonia Region of Mars

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Recap: Explores claims made by "Mars anomalists" that the Cydonia region of Mars (the region with the "Face on Mars") was constructed, designed, or arranged by intelligent aliens. This episode takes you through the context of the claim, some of the math behind it, an exploration of the "null hypothesis" (what the results would be if it were purely random), and draws conclusions based on the latest orbital imagery of Mars.

This movie has also been released to YouTube.



With the dawn of the space age, we have been able to study the planets in unprecedented detail, including Mars. One of the early Mars probe findings is that the southern hemisphere is ancient, bearing the scars of intense cratering; while the northern hemisphere of the planet is relatively smooth, meaning it was resurfaced only a few billion years ago.

But the strangest difference between the two is that the elevation of the northern plains is about 6 km below the southern highlands.

Between the two lies a transition region, a weird area with places called "chaos terrain," and it shows massive mesas, buttes, knobs, and infilled and eroded craters and other features that we think formed when at least a kilometer of crust was rapidly eroded away, over 3 billion years ago, possibly due to water draining from high to low elevations.

Scientists over a hundred years ago named vast regions of Mars based on subtle color or brightness differences they saw in telescopes from Earth. One area within the transition region is called "Cydonia." It is here in Cydonia that there is a mesa that looks like a face, and people calling themselves "Mars anomalists" have looked around the face and seen pyramids or entire cities.

In this video, I examine a claim that the mathematics of this region show evidence for it being artificially constructed, supposedly by an ancient advanced civilization. The anomalists have claimed that the site shows various mathematical constants "redundantly encoded in the fundamental geometry of the layout of the 'anomalous features' at Cydonia."

Specifically, in the 1980s, Richard C. Hoagland and others published images that showed Cydonia and its features with various angles and distances they measured, claiming that they represented various mathematical constants, functions, or ratios, such as the square-roots of small numbers, the constants e and π, various ratios thereof, or that trigonometric functions of the values yielded these special numbers. In other words, because they found these mathematical numbers, they claimed that only intelligence can produce them, therefore these features were designed by an intelligence.

This may appear convincing ... at first. In science though, we have a specific set of questions: What is the prediction being made and so can be independently tested? What features are considered important and so show this geometry? What is the tolerance of these numbers matching - as in, how close do the measurements need to be to the special numbers to count? Or, did one simply look at a lot of different things, choose some that matched any number of mathematical values, and claim intelligence?
Let's look first at the "D&M Pyramid," so-named for Vince diPietro and Greg Molenaar for their work in the 1980s on the so-called "face" on Mars. This feature allegedly shows special geometry and has, by some, been termed the "Mathematical Rosetta Stone of Cydonia."

But, how do we measure it? Sure, one or two sides seem to be fairly straight, but at least three are curved. No two sets of edges converge at the same apex point, regardless of how you trace the curved edges or try to straighten them. Remember: The claim is that these precise angles are present, but already we have a problem with being precise.

Let's take an average for lack of anything better, with the apex at about 40.405 to 40.411°N.

In Richard Hoagland's work in conjunction with with Erol Torun specifically, 9 angles were measured, 9 ratios given, and 10 trigonometric functions of the angles. Out of those 29 values, 24 were claimed to be significant along with the tangent of the latitude of the D&M Pyramid. At the very least, the latest Mars coordinate system defined by spacecraft orbiting Mars using lasers shows the pyramid's latitude is not where it was claimed before - new data has revised it - so that is now ruled out as a significant number. Using the old latitude is like using old maps of Earth that show California as an island.
While Mr. Hoagland and Torun measured 9, how many angles do we actually have? In a pentagon, there are five triangles, each with 3 angles. With two vertices between each adjacent triangle, there are another 5 angles. In the apex in the center, there are 5 angles, but we can combine sets of 2, or 3, or even 4. I count 35 different angles. Why did they choose only 9? In fact, there are 70 angles using their criteria because angle E is simply half of angle D.

When calculating ratios, we could do this for sets of those 35 angles, for a total of 595 ratios (if we allowed halvsies as they do, there are nearly 2500 ratios). And, with three normal trigonometric functions - sine, cosine, and tangent - one can perform 3 functions on each of the 35 angles for 105 different values. That's a total of 735 potentially supposedly important numbers.

Then, if we allow any combination of the square-root of 1-5, e, or pi, and the ratios of any of those, there are 47 unique values that you could match the 735 numbers to, all of them between 0 and 2π, or 6.28. There are 94 when you allow for negative values, which the Mars anomalists do.

With that in mind, with so many combinations, it's odd that Mr. Hoagland and Torun claimed 24 significant matches of the 29, because we can test the basic math, like angle C divided by angle D which they say equals e divided by the square-root of 5, and claim that these are accurate to three significant figures. There are a couple ways to interpret what that means, but for this video, I'm adopting the definition that it needs to match to 0.1%, but I'm also going to show throughout this video what matches to 1%. In this case, the values are off by 1.1% USING THEIR ANGLE MEASUREMENTS. Perhaps not huge, but it is not what was claimed.

In fact, when we check the ratios, USING THEIR ANGLE VALUES, only 1 of the 9 ratios equal the claimed value to 0.1%, while 8 of the 9 are within 1% tolerance. The trigonometry fares better with half to within 0.1%, and an additional 4 are within the 1% tolerance, but the tangent of angle F is almost 2% off from π/e. Even the basic angles are off; 4 of the 9 are said to be significant constants when converted to radians, and two do match, but angle D is off by 0.36%, and angle E is off by over 30%.

At this point, while 24 of 29 angles, ratios, or trigonometric functions of angles were claimed to equal significant constants to within three significant figures, even using their angle values, only 8 of the 29 work out when we do the simple math. This is one of the reasons we do peer-review in science: It helps to catch these major math errors before publicizing them.

But let's get to the actual feature and do the angle measurements and math ourselves. When looking at the angles or ratios or trig originally claimed as important, based on my measurements of the angles, only 2 of the 24 hold up to within 1% of the mathematical constant claimed. When doing the math with ALL 735 measurements, 227 match to within 1% of any one of the 47 positive, or 47 negative possible special mathematical constants claimed to be significant in the original work. But, the original claim was 3 significant figures accuracy.

If we only allow that 0.1% tolerance, meaning that the result must be within 0.1% of the special mathematical number, 1 of Richard Hoagland's and Erol Torun's angles match. Mine drop to 17 matches out of 735.

But that's from the apex I chose, and the walls I decided to draw. Mr. Hoagland and Torun measured their angles on data that was about 10x lower resolution than mine and yet they claimed 0.1% accuracy in their angle measurements. Yet, even on this higher resolution data, when I repeated my measurements, as being shown now by just shifting the vertexes a few pixels, they were only within about 2° each time, or 3% accuracy, because this is so far from a perfect shape. And, based on the image resolutions and quality, shifting a few pixels on these high-resolution and high-quality data is still within the SAME pixel that the Mars anomalists had from Viking data in the 1970s, 80s, and 90s. So, not only do you have much lower accuracy possible than what was claimed, but if you shift things by just a few pixels - which on the data they used would be the size of a supermarket - you get different results.

But, it's actually harder than that: This analysis completely ignores the fact that this is a three-dimensional structure. That means the true angles of all these triangles are different in 3D space, we have only been measuring them as they appear when flattened in 2D space, when looking straight down on it.

So far, I've examined the pentagon shape as it looks. In science, we have a concept of a "null hypothesis," which says that there will always be some of angles that will closely match a given set of special numbers, even if those angles are purely random. For the anomalist's findings to be statistically significant -- meaning truly unusual or out of the ordinary -- then their number of "hits" needs to be significantly more than the number of purely random "hits."

To determine how many "hits" we would expect from randomness, I've generated 15,000 different pentagons with random angles that still form a shape sorta like the D&M Pyramid. And, I've then compared the angles, ratios, and trigonometry results against the 47 positive and 47 negative significant numbers. What we see in the upper graph is how many times the numbers of randomgly-generated angles agreed within 1%, and the bottom graph shows the results to within 0.1%. From this experiment, we would expect, PURELY AT RANDOM, 214±15 out of the possible 735 angles, ratios, or functions were significant at the 1% level, and 22±5 at the 0.1% level. Those ± numbers is called a "standard deviation," or "1-sigma," meaning that 68.3% of the time, the result will be in that range.

Furthermore, this kind of analysis lets us statistically say just how rare or unusual it would be to find a certain number of "hits" or "misses." For example, we can say that for the anomalists' findings to be "of statistical significance," they should be different from 95% of the randomly generated matches, or more than 2-sigma away. That means that the anomalists or we should have found either more than 31 matches or less than 11 to better than 0.1% accuracy. Interestingly, finding VERY FEW matches is just as unusual as finding VERY MANY. However, NEITHER is the case: 17 matched, just what you would expect by pure chance. Not too many, not too few, just about right for a purely random shape, matching our null hypothesis.

Another point of this experiment is to show what is known as the "Texas Sharpshooter Fallacy," a fallacy being where the argument is logically flawed. In this case, we have a huge amount of possible values, a huge number of possible matches, and so we can select just a few to claim that there is a high level of significance. But, we ignore all of the ones that don't match, also known as "Cherry Picking." Another way of thinking about it is to look at all the data and draw a target around it; this is why a specific, a priori prediction is needed in this kind of work, as is understanding what the results would be if it were purely random.

The same thing happens when we return to the broader region around the "Face" in Cydonia. There are about 16 different features marked as significant by the Mars anomalists, but why were these particular features selected over others? Why were these angles selected over the countless others? Why were these locations on the features selected - like two random locations on the face-like feature?

If we test the original claimed angles, when I measure them with the latest high-resolution images properly controlled to the Martian geoid, only 7 of the claimed 19 angles actually match to within 1% of was originally stated, and 1 to 0.1%. But, you could easily choose a nearby feature where the angle DOES match and call it important.

And, just as with the D&M Pyramid, we can see what happens when we shift the vertexes just a few pixels. Not only do we again see that the claimed level of accuracy is impossible because shifting things a teeny bit changes the angle measurements by several degrees or percent, but the exercise shows the Texas Sharpshooter Fallacy all over again, only on an impossibly grander scale. The liklihood of finding "hits" to these mathematical relationships to an arbitrary accuracy is a certainty, only in this case, we can truly select any feature that fits the angles and call it therefore important.

With these much higher resolution and quality data, a final thing we can look at is the "City" area where features were claimed to show specific, intelligently designed geometry, including numerous tetrahedral mounds that rival the pyramids at Giza. And yet, under higher resolution images, the city square becomes an eroded mesa and the tetrahedral pyramids are simple mounds, similar to countless other wind- and water-eroded features in this weird transition region of Mars.

What this all boils down to is that the original claim appears baseless. (1) I've shown that the null hypothesis - the number of hits we'd expect purely by random shapes - is the same as what is actually found, both by the anomalists' measurements and (2) my own measurements under higher resolution data. What this indicates is that it's a good example of (3) the Texas Sharpshooter fallacy, whereby you have so much data that you can pick and choose what you want and it looks important. But, it's not, and (4) under the high-resolution cameras we have now, features that may have looked anomalous under certain resolution and lighting before, are not.

What does this all mean, and with what are we left when this is over? Mars is still a fascinating place that awaits scientific discoveries that could re-shape our views of the planet, the solar system, and how we fit into the grander scheme of things. But when exploring Mars, when investigating its surface and features upon it, be wary of pseudoscience, numerology, and similar mistakes. Mars is interesting enough, it doesn't need pseudoscience, too.

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Comments to date: 1. Page 1 of 1. Average Rating:

Malcolm Smith   UK

11:54pm on Wednesday, September 3rd, 2014 

Hi Stuart: Why not engage directly with scientists from the Society for Planetary SETI Research? Their website: it includes published papers e.g. JBIS
Cheers - Malcolm

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