City Slicker

• Introduction to the City
• How Many Angles Can Dance on the Head of a Pin?
• The Numbers Game
• Conclusions

Introduction to the City

The reason has to do with where the "Face" is on Mars. It sits in a plain called Cydonia. There are many interesting geological features in Cydonia, as there are for most places on Mars. I won't go into them here, but you can find more info on Cydonia at the Mars Orbiter Camera webpage about it.

There are lots of big formations in this region; the "Face" is just one of them. They are reminiscent of mesas and buttes, and are, according to the MOC page, probably heavily eroded remnants of the uplands to the north.

In a nutshell (haha), Hoagland claims these features are the remnants of a city. He bases this on images which do not have the resolution to support the claim, but even aside from that, his supposition rests on what he claims is a mathematical relationship between the objects in that "City". This relationship is so extraordinary, so special, he says, that it forms a new type of "hyperdimensional physics " that opens up the mysteries of the Universe. This is the drum he has been beating for some time. This hyperdimensional physics rests solely on the relationships he sees in the "City". As you'll see, his claims that these relationships are special are totally bogus.

How Many Angles Can Dance on the Head of a Pin?

Hoagland took an image of the Cydonia region, found his objects, then connected them with lines. He then measured the angles between the objects and manipulated them mathematically. He took ratios (dividing one angle by another), performed trigonometry (taking the sine, cosine, and tangent of the angles), and then went about seeing if those numbers have any special significance. And he found that they do indeed appear to relate to one another! In the image above are some of the relationships he found; click on it to see a high-res version that is easier to read.

He found that some of these numbers correspond to such mathematical constants as e (the base number in the natural logarithm system, equal to about 2.718), pi (3.1415), and multiples of simple square roots (like square root of 2 = 1.414, square root of 3 = 1.732). Amazingly, he seemed to have found an intricate relationship between the placement of these objects on Mars.

If true, this could not have happened naturally. There must be some intelligence behind the "City". Hoagland claims that over time he became so convinced that the relationships in the "City" cannot be coincidence, and represent an artificial structure, that he all but abandoned his claims about the "Face". As he says himself:

But simultaneously, we do not want anyone to lose sight of the fact that the Face, at a more fundamental level, has almost become a secondary part of this debate for many years; Hoagland's Geometric Relationship Model for Cydonia -- with its potential for quantification and testing of the foundations of the "intelligence hypothesis" itself, in the form of specific predictions made by the Hyperdimensional Physics theory derived from that alignment Model -- has clearly stepped to the forefront of the debate over the artificiality of Cydonia of late. Because of this quantifiable basis for the Model, the Face itself ("But, what does it look like?") has been relegated to a secondary, "confirmatory" status -- rather than the linch-pin around which all decisions vis-Þ-vis the artificiality of Cydonia must (or should) be anchored.

So if the math he did turns out to be wrong, then his claims -- really, all of them-- are wrong too.

Guess what?

His mathematical analysis is so full of holes, flaws, and misdirection that it is completely worthless. This not only destroys his claims about the "City", but by his own words, everything else he says too. Why? How specifically is he wrong?

The Numbers Game

First off, his claims of measurement accuracy are too high, given that he measured these angles off a photograph. This throws off his amazing relationships. He claims one angle is exactly 120 degrees, but if his ruler is off by a tiny bit, then his angle might be 119 or 121 degrees. This in turn completely negates all the fancy math he then does before he even turns on his calculator.

Second, by picking and choosing which features to use (he uses a hill in one spot, but not another very similar hill next to it) he ups the odds of finding what he wants. A suspicious person might assume he initially drew lines from all the available features, and only kept the ones he liked. That makes the mathematical relationship seem a lot stronger than it really is.

Third, even if he didn't pick and choose, the odds of finding relationships are extremely high, even with random numbers. For one thing, he had lots of measurements to choose from. He only shows a few connections in his drawing, but in fact, given that he shows 17 points, there are literally thousands of angles he could have used. Don't believe me? Draw 3 points on a piece of paper, and then connect them. You made a triangle, of course, and there are three angles. Now, draw 4 points randomly on a piece of paper (don't make a square). Connect every point to every other point. You'll have six lines (the outside four, and two connecting opposite vertices). How many angles do you have? I count 16 when I do this, but some of the angles are equal due to geometry, so really there are 14. And that's with four points! The numbers increase very rapidly. By the time you draw 17 points, as Hoagland did, the numbers of angle to choose from is staggering. Some of them are bound to be close to special values, simply by chance.

But even that isn't everything. Fourth, by taking ratios of these angles, and using trig functions, he is forcing lots of his measured numbers to be in a small range of values, mostly between 0 and pi. The numbers he then chooses as a comparison (like, say e/square root(5)) are all in that similar range. Besides his huge number of angles to choose from, he has a huge number of mathematical constants to choose from as well.

Using the square roots of the numbers between 1 and 5 gives you 5 numbers, of course: 1, 1.414, 1.732, 2, and 2.236. But then if you allow multiples of those numbers, like 2 times the square root of 2, then you start getting vast amounts of numbers to fiddle with. If you allow multiplying by, say 1-5, then each number suddenly becomes 5 numbers, so you now have 5 x 5 = 25 numbers. Allowing division of those numbers (square root of 2 divided by 2) yields 5 more sets, for a total of 50. You can also do numbers divided by square roots, making a bigger set. Add e and pi into the mix, and you wind up with hundreds of numbers to play with, roughly between 0 and 4. Some of these numbers are too big (like multiples of the square root of 5) but those are more than made up for by the hundreds or even thousands to choose from that are in the right range.

Suddenly, Hoagland's "magic" relationships aren't looking so hot. In fact, given his accuracies, it would be amazing if he hadn't found any near hits to mathematical constants. Given enough random numbers, you can always find lots of coincidental numbers that are close to mathematical constants involving square roots, e and pi.

How do I know? Because someone did exactly this! Mathematics professor Ralph Greenberg at the University of Washington stumbled on Hoagland's claims one day, and set about showing how what Hoagland is saying is, to be polite, full of it. Read it for yourself. Dr. Greenberg's analysis is as beautiful as it is thorough, and it totally trashes Hoagland's claims. Even more wonderfully, Greenberg sets up his own experiment using telephone numbers to show that any set of random numbers, when played with as Hoagland has, will generate mathematical relationships. In fact, using random numbers, Greenberg did even better than Hoagland did with his numbers.

Greenberg didn't stop there. He tried to contact Hoagland, who ignored him. He also called Art Bell, who mentioned this to Hoagland on the "Coast to Coast AM" radio show. According to Greenberg, Hoagland was dismissive, if not rude about the analysis. Greenberg has even directly challenged Hoagland to debate this math, emailing and faxing Hoagland and Art Bell. Given that Hoagland loves to get airtime, and also bases nearly his entire "research" on the math he did, one would think he would jump at the chance to defend it. In fact, he has ignored these calls to debate. That's not terribly surprising; reading Greenberg's analysis shows conclusively that Hoagland's claim that these relationships indicate the "City" is artificial is completely and utterly wrong.

I will be fair, and note that just because these relationships can be found in any random numbers does not mean the "City" isn't artificial. After all, if you did this analysis using buildings in downtown Washington, DC you'd see similar patterns. What I am saying is that Hoagland is claiming the "City" is artificial because of these relationships. That is clearly a bogus claim. Since the relationships turn up in random patterns, they cannot be used as an indication of artificiality. And since the "Face" is also clearly just a hunk of rock, he cannot use that either. So, in the end, I can confidently state: