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Often we hear arguments for fantastic claims based on a long list of coincidences very unlikely to happen by chance. Yet frequently they are all chance occurrences. Why is this so when the odds were against it, and how can we keep from being fooled by such circumstances?

I will mention just two common causes of deceptiveness among many known to science. The first is selection effects. You go to the airport for a trip, and while sitting there, you have a premonition that something might happen to the flight. Still, you board anyway. En route, an engine catches on fire and the plane makes an emergency landing. You remember your premonition. Isn't this near proof of a supernatural occurrence?

It turns out that you, like most people, probably have such premonitions almost every time you go to an airport and think about your mortality and how your fate will be in the hands of others. But such thoughts are quickly forgotten after all normal, safe flights. We remember them and transfer them into long-term memory only if some event reinforces the thought and causes you to ponder it.

In general, we are much more likely to remember improbable events and associations than normal or frequently occurring ones. So our memories contain many "selection effects" caused by forgetting most of the normal data and remembering only the abnormal data. It's the same if you think of someone and they call soon thereafter. Was it "psychic", or a selection effect? The latter explanation is usually the simpler and therefore the preferred one.

The second common cause of deception is also based on seemingly unlikely statistical coincidences. In any truly random data set, many regular patterns can always be found. For example, if we have a star chart with a million stars, we might find an unusual shape formed by stars that has less than one chance in a billion of happening by chance. So are some mysterious super-beings moving stars around? This is not as likely as the simpler explanation: In every random data set capable of forming billions of random patterns, it is virtually certain that some 1-in-1 billion pattern will be found formed by chance.

In general, we tend to be deceived because our minds often do not recognize how truly vast is the number of possible coincidences that can occur. So when a few of them do occur, as they must if the odds are right, we tend to be amazed simply because the odds against that particular coincidence were very great. The odds against a flipped coin coming up tails ten straight times are 1024-to-1 against. But if we make several thousand attempts, the odds become pretty good that it will happen one or more times.

In science, an improbable event that has already happened is called "a posteriori" (after the fact), and generally is taken to have no significance no matter how unlikely it might appear. By contrast, if we specified a certain specific highly improbable event in all its detail "a priori" (before the fact), and it happened anyway, that would be significant, and we would be obliged to pay attention.

As all this pertains to the "Face" on Mars at Cydonia, the discovery of the face-like object was an a posteriori event. No one predicted it, nor could they have done so based on known facts. But once our attention was called to a particular object in a particular place on a particular planet as possibly being of artificial (constructed) origin, anything else found out about it that is highly improbable but related to the artificiality question becomes a priori. We can safely ignore a posteriori claims, but not a priori ones.

At Cydonia, almost everything we see in the new, high-resolution "Face" image fulfills highly unlikely a priori predictions. So when we found a "nostrils" feature, that was impressive. The fact that the relative size, positioning, and orientation is also correct for nostrils makes it a significant a priori prediction. The additional fact that no other nostril-like features can be found nearby means that our minds are not free to pick and choose such face-like features we may want to see. Because it is a priori, that single feature would be strong evidence for the artificiality hypothesis by itself.

But when we consider the perspective, lighting, and contrast Limitations of the new image and use old Viking images to fill in missing items, we now see that a priori predictions for a "pupil" and an "eyebrow" are also fulfilled. These are a priori even if no one had verbalized them because the face hypothesis implicitly predicts such facial details before the fact. And each feature is unique on the mesa and its surroundings, and properly shaped and positioned relative to the face with the right relative size and orientation. All this makes the a priori probability of chance operating vanishingly low.

But there is much more. The eye socket is a well-formed 3-D cavity and not in any way shaped by shadows. The mouth is smooth and regular with inner and outer portions, curled just below the nose, and continues to the opposite side. Viking shows reasonable bilateral symmetry, although the Mars Global Surveyor image cannot because of its low viewing angle. The headpiece is smooth, regular, and symmetric. It is crowned with a huge crest feature just north of the mesa. The "enclosure" or headdress feature is smooth, symmetric, and right-angled, and is complete expect for a small possible "entranceway" or break in one corner. The facial decorations are smooth, linear or symmetric, and appropriate for their relative locations with respect to a face.

Before seeing this new image, we knew that "fractal" content implied a natural origin, while regularity, angularity, and symmetry indicated artificiality. I see almost no fractality with the exception of the nose bridge, the feature least protected from wind erosion. I do see smooth lines and curves, right angles and corners (including one in the "furrowed" eyebrow), and lots of symmetry, especially detailed symmetry in the headdress enclosure. And that symmetry is not simple symmetry, as when duplicating a profile, but full 3-D symmetry. For example, the enclosure wraps all the way around with both its inner and outer boundaries, yet remains of uniform height and symmetric shape. Nowhere does the mesa overlap or get confounded with this boundary.

The whole amazing "Face" mesa stands isolated in a totally flat, barren desert. It's not as if there are lots of natural formations around, and this one just happened to look like a face. And all of this says nothing about the rest of the strip image, which also contains some surprises. Even the other major formation in the strip image, although it doesn't look like any recognizable shape, does appear far too non-fractal and regular to have arisen as a natural formation. Although its boundary has an irregular outline, it wraps all the way around. The uniform parallel white strips that appear to radiate from the southeast boundary also have no precedent among natural features in the solar system.

The reason I have concluded that the case for artificiality of the "Face" is well-established is the fulfillment of so many a priori expectations, combined the lack of extraneous features that might allow us to see patterns that might arise by chance. We have almost no degrees of freedom, yet everything in the image appears to work. Each of the new a priori points such as the nostrils, mouth curl, pupil, and eyebrow has individually only very small chance to occur at all, let alone with the correct relative size, shape, location, and orientation. Each such feature by itself indicates artificiality at perhaps 1000-to-1 odds (some much more) just because of their a priori nature. Collectively, they say "artificial" beyond a reasonable doubt.

It is not the odds of occurrence of these features that is convincing, because even a long list of 1,000,000-to-1 a posteriori coincidences has no persuasive ability. It is the low probability of these features combined with their a priori nature that makes them persuasive. Real faces do have just such features, and all major facial features are present in the Martian "Face". In truth, the thought never crossed my mind before the fact that the Face should have eyebrows, nostrils, pupils, and a lip curl. But of course, if it is a real face depiction, it should have those features. Anyone could have predicted those things, but most of us dare not hope for so much. Now we have them!

SUMMARY: Based on the best available high-resolution, contrast-enhanced Mars Global Surveyor image and the best old Viking images, the "Face" mesa contains regularity, angularity, symmetry, and the fulfillment of a priori predictions based on the artificiality hypothesis such as the appearance of nostrils in the nose, mouth shaping just under the nose, an eyebrow over the eye socket, a pupil in the eye socket, a separated vertical enclosure of the whole mesa with near perfect symmetry and corners, a crest over the headpiece, and the almost complete absence of extraneous or non-contributing features. These enhance earlier findings of bilateral symmetry, 3-D contouring, a lack of fractal features that are the trademark of natural objects, plus a culturally significant location on the old Martian equator and a culturally significant upright north-south orientation. In my considered opinion, there is no longer room for reasonable doubt of the artificial origin of the face mesa, and I've never concluded "no room for reasonable doubt" about anything before in my 35-year scientific career.