A sidenote on Marian apparitions

In one of the places I used to live, I observed the following phenomenon. There was a building with a brick facade. On some days, approaching sunset, the filtered light of the declining sun projected an image of the cross on the side of the building. It took the form of contrast between the sunbeam, and the darker facade. The sunlight cast an image of a cross, surround by the shaded facade. The cross was centered in the facade. The image was well-defined.

This wasn't a figment of the observer's imagination. That shape really appeared on the side of the building.

However, the religious significance of the image was a psychological projection. To recognize the religious significance of the image, you had to be familiar with elementary Christian iconography.

Moreover, the significance wasn't intentional, unlike a cross in a church. Rather, it was a random occurrence, based on a combination of natural variables which sometimes lined up in a particular way: the position of the building, the angle and level of the sunlight, and the position of certain trees nearby. A combination that was bound to happen every so often. So even though the image reminded a Christian observer of the Christian cross, that association was completely incidental to the image. 

What many lay Catholics take to be Marian apparitions commit the same fallacy. I'm not suggesting that all purported apparitions can be explained that way. I'd add that while purported apparition at Knock is approved for widespread liturgical veneration, that example is analogous to my comparison.