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Episode 111 - 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. (Note: This episode is inended as a companion to the video, also in the podcast feed and on YouTube, by the same name. It is stand-alone, however.)

Puzzler for Episode 111: There was no Puzzler in this episode.

Q&A: There was no Q&A in this episode.

Additional Materials:


Claim: The claim, on its face, for this episode is reasonably straight-forward and simple: There is a region of Mars, called "Cydonia," which has some features that display special geometry and numbers that are encoded within them. And, the only way those numbers and that geometry could be there is if it was created by some sort of intelligence, as in aliens.


This episode is meant to be a companion to the movie that was released into the podcast feed and on YouTube on May 31. The movie is 15 minutes and 45 seconds long and describes the claim, the evidence for and against it, and ultimately concludes that the claim is false, or at the very best, the layout of the Cydonia region's features are indistinguishable from random chance.

The claim itself is based on mathematical arguments, so while I tried to make the movie understandable, it does get into math that some have found confusing.

The claim itself is based on mathematical arguments, so while I tried to make the movie understandable, it does get into math that some have found confusing.

Hence, this episode which, as I said, is meant to be a companion to the movie. I'm going to get into some more detail, more explanations, and a few things that didn't make it into the movie. You should watch it first. Then listen to this episode. Though I already did the spoiler and told you what the conclusion is ...

I'm going to assume that you've watched it, so there won't be as much background as usual in this podcast episode.


Pretty much all of the evidence for the claim originated from an analysis by Richard C. Hoagland and Erol O. Torun back in the 1980s. It's also argued by many others, in many different permutations, but for the sake of keeping it to the original folks, their argument is the one I'm going to focus on.

Among other places, the argument was featured in Richard's book, "The Monuments of Mars," which has, to-date, undergone several printings. The argument is also in a lengthy essay on Richard's website, "The Enterprise Mission."

You can read it for yourself if you really want to, but the non-conspiracy, non-conjecture, and most objective evidence that is claimed is that many of the features that they indicate as appearing possibly artificial (1) are laid out in mathematical relationships that indicate their artificiality, (2) are positioned in a place on the planet that is a mathematical symbol of their artificiality, and/or (3) the features themselves show internal geometry - like the angles that the feature makes - that indicates their artificiality.

The primary signal to them that they are artificial is that various angles of the features are equivalent to special numbers. Or, that if you take one angle of the feature and divide it by another angle, that the result - that ratio - is equal to a special number. Or, that if you calculate the trigonometric value of any of these angles, they are equal to a special number. It's unimportant for this discussion what the trigonometry is, just know that it's related to the angles of a right triangle, where a right triangle is a triangle where one of the three angles is 90°.

In their work, they refer to features in the broader area of Cydonia - a region of Mars, but they also focus on the D&M pyramid, a feature that in low-resolution and low-quality Viking Orbiter data from the 1970s looks like a pyramid. See Episode 104 for more on that.

They focus on the pyramid because the claim is that several of its angles show their special numbers, either by themselves, in ratios of each other, or by the trigonometric functions. And that the latitude of the pyramid is special. All of the values in the pyramid - the claim goes - are also shown in the broader Cydonia region, hence why they refer to it as the "mathematical Rosetta Stone of Cydonia." This is a reference to the Rosetta Stone which contained the same text in several different languages, finally allowing for the deciphering of Egyptian hieroglyphs. That's why, while the movie is about the Cydonia region as a whole, most of the time is spent on the D&M Pyramid, as it will be in this episode.

The final bit of the claim needed at this point is what these "special numbers" are. I'm not entirely sure why Richard and Torun picked the values they did, but they are the square-roots of small numbers like 3 or 5, the math constants e and π, square-roots of those, and ratios of any of those, like e divided by the square-root of 5.

e is an important number in mathematics, it's used in things like calculating compound interest. It's roughly equal to 2.72. It's irrational, meaning that it cannot be expressed as a simple fraction and that none of the digits repeat.

Same as with π, which is the ratio of a circle's circumference to its diameter. It's roughly equal to 3.14.

Why These?

In investigating the claim, one of the first things we have to do is understand it. There are two parts to the claim -- first, that these features are important, and second that they are important as indicated by these special numbers.

I couldn't find any explicit statement in any of their writing as to what exactly constituted a special number. I took the examples they give and made it simple: The whole numbers 1 through 5, the irrational numbers e and π, and any ratio of those or the ratio of the square-roots of those. And all the positive or negative values of those. Once all those values were calculated, there are 47 possible special numbers, though you can double it when using positive and negative, which they do, like -SQRT(3).

But why those? There are other important numbers in mathematics, and even more important numbers in architecture on Earth.

For example, the Golden Ratio, which is irrational and approximately equal to 1.62. It was used a lot in classical Greek architecture. It's defined as being when the sum of two numbers divided by the larger number is equal to the ratio of the larger divided by the smaller number. Anyway, the definition isn't quite as important as its aesthetic appeal, which is why it's used in architecture, painting, music, and even book design.

One might think given that information, that the golden ratio would be looked at by Hoagland and Torun, but it appears to be completely missing.

Personally, I think it seems pretty arbitrary what numbers they are considering important or special, other than the 19.5° which they find in round-about ways and I talked more about in Episode 26.

Then, the other part of this is the features selected. In Richard Hoagland's version of the D&M Pyramid, there are 9 angles specifically shown, though one of them is exactly half of another, so there are only 8 somewhat unique angles. But as I show in the movie, there are 35 possible angles to choose from in the pyramid shape. Why only those 9 were selected over all the others, OTHER than just because they match the special numbers, and what is special about half of one of them, is not discussed.

In other versions of the D&M Pyramid diagram from other people, I found folks drawing all sorts of other angles, like taking one of the lines from the center to the edge, and then the difference between that and due East, and saying that angle was special therefore the pyramid was designed.

The same is the case with the broader Cydonia region: There are really countless features to chose from, but in most maps I have seen around 10-25 different features called out. Then, it's the angles between them, usually, that are said to be important, and they match the angles within the D&M Pyramid. Or sometimes it's the ratios of various distances between otherwise random features.

But again, why those? There seems to be no explanation as to why those positions or angles were selected in particular as opposed to countless others, OTHER than those features seem to yield the numbers they think are special.

But even if this weren't the case, one scene that didn't make the cut in the movie is that even if everything they claimed were true, I think that at least Richard Hoagland was sloppy in doing a copy-and-paste job. In the versions of his diagrams that show the D&M Pyramid and Cydonia, he identifies the exact same angles, the exact same ratios, and the exact same trigonometric values in each. Yes, those angles are in the D&M Pyramid, he diagrams them, showing where they are. But, only about half of them are shown to be in the broader Cydonia region. As in, they're labeled in the legend, but not shown at all in the diagram. And the legend is exactly the same between the two images.

Seems somewhat suspicious to me, but then I have a somewhat cynical nature.

Let's Say They're Right, What Is the Data Quality?

But let's say, for the moment, that they are completely correct, that these specific angles and features - for whatever reason - are the only ones that were designed by an intelligence and are therefore special. Let's give them that for the sake of argument right now.

Now we have to look at whether the angles are actually what they have claimed the angles are.

The data that Richard and Erol had were Viking, with a pixel scale of about 45-55 meters per pixel, or about 145-180 ft. That means that each pixel is the footprint of a fairly large house. It's the area equivalent of about 21,000-32,000 square-feet, or 2000-3000 square-meters, which is 45-70 times the size of my first 1-bedroom apartment, and 25-40x the size of my next 2-bedroom apartment.

That's each pixel. As in, the smallest piece of information you can glean, assuming every pixel is perfect.

Now-a-days, we have imagery of the site at about 6 meters or 18 ft per pixel. Meaning that each original pixel can be filled by 70 of the new ones. Much better data resolution.

Not only that, but the digital cameras offer significantly better data quality. So even though each original pixel can be filled by 70 new ones, if you scaled the new ones to the resolution of Viking, the quality would still be better in the new images. I show what the difference in resolution is at about the 8 minute 45 second mark, and it's striking.

That's a very lengthy way of saying that the data now are better, and that any old analysis is subject to revision with the new data, which is what I did.

Originally, the claim was that the precision - the level to which the angles they found matched the special numbers - was three significant figures. In the movie, I say there are a couple different interpretations of that. It could mean that the first two digits must be the same, and the third can be one off. Usually it means that the first three digits are identical. It could mean that if you divide one by the other, then they have to match to 1% tolerance or better, which is what I code as yellow in the movie. Or, it could mean that they have to match to 0.1% tolerance or better, which is what I code as green in the movie. Regardless, I try to cover my ass and give the results to either 1% or 0.1%, so you can see how well stuff matches, and I also give the values so you can compare the actual numbers.

And there's the rub: The first thing I did was USE THEIR ANGLE MEASUREMENTS, and I just repeated the math. No new analysis of my own, no angle measurements, no new data ... I just checked their math. I found that only about 2/3 of the values that they claimed were significant, actually were when you used the 1% tolerance definition of three significant figures. In other words, it didn't matter what I measured, what data I used, or anything else at that point -- just using their angle values, their claim was over-stated.

Then, when I made the measurements myself, I found that in light of the most recent data, only two of the originally claimed 29 significant angles on the D&M Pyramid actually matched to 1% tolerance of the special numbers. 1 matched to 0.1%.

And, it was about as bad with the broader Cydonia region.

But then, we get back to this issue of data quality and the features themselves. They are not perfect. The "pyramid" is far from perfect, for no wall is straight, and they do not even converge at the same apex point. I measured it three times, and each time, I got a slightly different value that meant my angles changed by several percentage points. Meaning that when I then went to compare them with the special values, one that matched before wouldn't, and one that didn't match before now did.

And then you factor in data quality and resolution. I show in the movie that if you just shift those end points a little bit, which is several pixels in the data I used but is practically within the SAME 2000-3000 square-meter pixel that they used originally, you get different results.

In other words, it almost doesn't matter what tolerance we want to say the numbers have to match -- under any reasonable measure, you could get them to match just by tweaking the spacing a teeny bit because the data quality and the feature shapes themselves are so poorly defined for this kind of claimed high-precision work.

Null Hypothesis and Monte Carlo Simulations

That's why I then talked about the null hypothesis: How many of these angles would match our special numbers IF they were, in actuality, completely random? After all, it was starting to look like you could kinda get your special numbers or not just based on how you felt that time you were drawing your pentagon or choosing your features in the larger Cydonia area.

But, this isn't a test that "debunkers" or skeptics should just be using. This is something that you do in good scientific practice. If you want to show that a phenomenon is happening, you have to understand what the background level should be for that phenomenon. Otherwise, how can you know if your findings are unusual?

In the movie, I did this in both an informal way and a more formal way. The informal method was shown for both the D&M Pyramid and the features in the Cydonia region, where I had each vertex or important feature, then adjusted them by a small random number every half-second, and re-did the angle analysis.

The point there was to demonstrate what I had said earlier: That when you consider any reasonable uncertainty in the data quality and resolution - even in the better data today - and how they contribute to the uncertainty of where these features are exactly, that the angle you measure or ratio or trig result you get varies by several percent.

That means two things. First, that regardless of how careful Hoagland and Torun were when they did this in the 1980s, it is simply impossible for them to be accurate to the three significant figures level they claimed, regardless of the exact definition of three significant figures. Second, this implies that the special numbers could be found simply based on how you draw the shape that particular day.

That led into the full-fledged Monte Carlo simulation I did in the movie with the rapidly dancing pentagon and the histograms that were built up, around the 9.5-minute mark. In physics, the concept of a Monte Carlo experiment is something that usually a first-year physics undergraduate will learn in lab class.

It's where you do a numerical simulation with random numbers to try to understand a phenomenon. A good, non-physics example would be the Monty Hall problem. It goes like this: You're on a game show, there are three doors, behind two of them is a goat, and one has a much better prize, like a $million. You're asked to pick one that has the $million. After you do, the host opens one of the doors you DIDN'T choose with a goat. The host then asks if you want to change your guess. Should you change your guess or should you keep it?

Most people, even after it's explained, still don't quite understand that you should ALWAYS switch your choice, because then you have a 2/3 chance of winning the money, but you only have a 1/3 chance if you keep your answer the same.

To prove it to yourself without a bunch of fancy statistics, you could run a Monte Carlo simulation. You would have a random number generator pick which door has the money. You then have the computer, at random, choose your door for you. You then have the computer be the host, and open one of the doors that has the bad prize. You then have the computer switch your door to the other one that's still closed, and then see if that's the one with the good prize. If it is, add one to the tally. And then repeat this, say, 1 million times. From that simulation, the final tally should be close to 2/3 of a million.

In the application to the Mars / Cydonia / D&M Pyramid problem, the Monte Carlo approach is to create a bunch of random pentagons, and then measure the angles, and see how many of them or their ratios or their trig functions match the significant numbers. In a simulation like that, you can check everything to an arbitrary precision, which is why I did it both to matching the 1% and 0.1% levels.

At this point in the movie, I had also left the idea that the particular 9 angles out of the 35 were the ones that were important. After all, the purpose of this simulation was to get an idea of how many of the angles, ratios, or trig values would match the special numbers as a whole, not just the ones that Hoagland and Torun chose. That's why I analyzed all 35 potential angles that were present as opposed to focusing on the 9 they selected.

The way I got to 735 different numbers to compare to the special numbers was to take the 35 possible angles, plus 3 times that for the sine, cosine, or tangent of those angles, and then add up all the possible ratios, like angle 1 divided by angle 2, or 3, or 4, or 5, up to angle 35; then angle 2 divided by angle 3, 4, 5, and so on.

I think by the point in the video that I had shown all the different possible numbers - we're talking 735 possibly important numbers, or actually over 2800 if you consider half-angles, which they did - it may have become apparent to those with a more critical eye that the analysis was unlikely to end well for Richard Hoagland, Erol Torun, and others who followed their lead. Just by the shear numbers there, and all of them are generally between 0 and about 6.3 because of how the problem is set up ... just by the shear hundreds of possible values, it's pretty darn likely that some of them are going to match the special numbers - also between 0 and 6.3.

Hence the point of the Monte Carlo simulation, to see how many did. I ran the simulation on 15,000 random pentagons, and even though this was done in animation software, it really was a random simulation, not deterministic with something pre-programmed in as the end result. Each time I rendered the scene, the results were slightly different, but they all had the same distribution. That's the point of the Monte Carlo process. Just like if we go back to the Monty Hall problem, if you run the simulation 100 times, you're not going to win exactly 67 times; it may be 55, then 70, then 74, then 63, and so on. But, the more you run it, the closer you'll get to that 2/3 value.

When I ran it on 15,000 random pentagons, I think the result was pretty telling: An average of 214 of those 735 possible angles, ratios, or trig results matched any one of the 47 positive or 47 negative special numbers to 1% accuracy. And, 22, on average, matched to 0.1%. That means that if you were to pick any random feature on Mars that looks sort of like a pentagon, and then measure all your angles, you can expect 22 of those to match those special numbers.

And, that's of course assuming you do the math right, which as I show in the video, isn't actually the case, with Richard being over 30% wrong in his simple division of e by π. It's 0.887, not 0.61.

Anyway, Richard and Torun claimed that 29 numbers were significant to three significant figure accuracy. Let's pretend that they are correct, even though, as I just mentioned, their math was off. But, again, let's say they're correct. Then the question is, what is the likelihood of them finding 29 significant matches when our average was 22?

This is something else that comes out of the Monte Carlo simulation. While you get an average, there is a distribution of results. Each simulation has a slightly different number of matches, as shown in the histogram in the movie. You can do some basic statistics when you calculate the average and also calculate a standard deviation. Pretty much any analysis, graphing, math, or other software that calculates averages will also calculate standard deviations, including Microsoft's Excel.

IF the data are distributed in what physicists refer to as a "Gaussian" distribution, and what statisticians normally refer to as a "Normal" distribution, and what every high school student fears as the "Bell Curve" -- it's all the same thing -- then the standard deviation represents where 68.3% of the data are. Why it's 68.3% has to do with calculus and other things, which is unimportant for this conversation.

What is important is that you take the average, subtract the standard deviation, and then take the average and add the standard deviation. In that range, 68.3% of the data lie. Which means that 68.3% of the time, just by pure chance, you can expect to get that many significant numbers. Also meaning that the inverse is true: 31.7% of the time, you can expect to get more or less than that many significant numbers.

In the video, I went to 2-sigma, meaning that I went plus or minus 2 standard deviations from the average, where 95.5% of the data are. Meaning that there's only about a 2.3% chance of finding more, and 2.3% chance of finding less than that range. As I discussed in Episode 82, the gold standard in physics is 5-sigma, meaning that there's less than 1 in a million chance of finding that value by random chance alone.

In the end of the Monte Carlo experiment, I point out that when I measured the D&M Pyramid's angles, I found 17 matches to 0.1% of the special numbers. That's right at about 1-sigma from the average, meaning that I had a really good chance - 68.3% - of finding that number of matches purely at random.

Texas Sharpshooter Fallacy Wrap-Up

When all was said and done, the movie was a way of illustrating the Texas Sharpshooter Fallacy, which is where you have a bunch of numbers, see where they cluster, and draw a target around it.

I can't read minds, I have no idea if that's how they went about it in the 1980s, but even if there was a genuine intent of a true scientific analysis, Mr. Hoagland and Torun - to put it bluntly - failed. In a non-exhaustive list of reasons ...

For one, they made basic math errors.

Second, they failed to clearly state their criteria for when a match was considered important. You have to know this in order to evaluate the claim independently.

Third, they showed only a few angles, or a few points, and said that those ones matched their significant numbers, but they did NOT show the inverse, that choosing other points did not match their numbers, or that they even tested other features or configurations.

Fourth, they dramatically over-estimated the quality and fidelity of the data to make the kind of analysis they did, especially on the D&M Pyramid feature, for just shifting your points within a single pixel of the original data can change the results by more than 1%.

Fifth, they failed to actually state their criteria for what I've been calling a "special number." I tried to be objective in my interpretation of what they mean, based on their diagrams and listing of some of them, but without being clear, they make it very difficult for someone to replicate their findings -- one of the key requirements for this to be accepted, except perhaps by late-night radio hosts and an uncritical audience.

Sixth, they failed to estimate - by any method - how many matches they should find even if the shape were completely, utterly random, which I did by a Monte Carlo simulation and which they could have done by more primitive methods that don't require a computer. After all, it was the '80s.

Seventh, decades later, with much better data, Richard Hoagland hunkered down and insisted that his analysis was correct, even claiming that a reason one of his "walls" on the D&M Pyramid that was now not in shadow in the images and in an entirely different place than they thought in 1989, actually should still be where they thought it was in 1989 because it simply collapsed. And it shows 19.5° in it ... somehow or other.

And finally, a point that a member of my test audience pointed out should be emphasized much more than I did because it shows the entire analysis they did - and even I did - is flawed, is that the D&M Pyramid is a three-dimensional structure. Every analysis has been done looking down on it as a 2D projection. But because it's a 3D structure, every single angle that we measure in the 2D projection is wrong. Everything at the apex is smaller than we measured, and everything around the sides is larger. And so all of the angles are different. And if your Rosetta Stone turns out to be gibberish because you're reading it on its side, then your reading of the language - the broader Cydonia region is just as flawed.

Provide Your Comments:

Comments to date: 5. Page 1 of 1. Average Rating:

Chris L   Colorado, USA

12:27pm on Sunday, June 15th, 2014 

What you did was explain in clear and concise language what it is Hoagland and company have been actually doing all these years. The so-called evidence that they go on about is just a combination of poor images and statistical fishing. Great work Doctor.

Tuatara   New Zealand

11:23am on Tuesday, June 3rd, 2014 

What a great episode. As mentioned by the others, the video was a very effective way to show just how much fishing for significant numbers Hoagland is guilty of.

Really appreciate the effort you went to and the efforts of those who helped.

Stuart R   Lyons, CO, USA

12:50am on Monday, June 2nd, 2014

James– Thank you. And yes, I've spent the last seven weeks working on this, probably around 130 hrs.

Paul– Thank you, also. I worked hard on trying to make it as understandable as possible, and a big thanks to my test audience for helping with that. And all comments on this website are moderated.

Paul   LA

12:37am on Monday, June 2nd, 2014 

Bra-f***ing-vo. Stuart that video was amazing. Not just from a visual perspective but for showing the data (so large and mathy) in such an understandable way. Now granted as a fellow scientist I'm familiar with confidence limits and significant figures already, but I think it would be understood even by a layperson the way the data is behaving and what that means for the face on cydonia hypothesis.

They won't accept it of course, but they'll be really really mad at the cognitive dissonance they will have to experience manuevering around and rationalize away.

James   UK

1:36pm on Sunday, June 1st, 2014 

Excellent episode and video. You've really shown with this comprehensive demonstration that Hoagland et al are just fishing for hits to random numbers and committing many fallacies in the process. It must have taken a while to plan & run all those computations! Well done

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