When you think of impossible images, M. C. Escher usually comes to mind. To the left, one of his iconic drawings.

If you do a web search on the terms [impossible images] or [impossible pictures], and then click on "Images", you'll find all sorts of interesting stuff.

These images are sometimes created by computer manipulation, often using the popular computer program Photoshop. Sometimes, a real three-dimensional object can appear to be "impossible" when photographed from a precisely chosen viewpoint.

For example, here's an actual construction in cardboard on which small balls appear to roll uphill. But the illusion, by Koukichi Sugihara, can only be seen from one particular viewpoint. The link takes you to a YouTube video which first shows the illusion, and then reveals the secret by rotating the construction to show it from the opposite side.

The problem with an image is not always obvious. For example, the picture just below is impossible. It has been tampered with. Can you see what's wrong with it? Think about it. The answer is given further down in this entry.

My other examples come from the works of my wife Margie, who after obtaining a Master's degree in biology, proceeded to become a social worker, and then eventually an artist. Now, an artist isn't constrained by reality - he or she can draw or paint anything (as did Escher). But if a departure from reality is accidental, it sometimes offends my engineer's sensibilities.

Consider, for example, Margie's Family Cow:

It's called the "family cow" because it has the initials of all the members of our family on it. Margie's initials MK are in the middle, and the first initials of our two daughters are on the rear end and the head. My first initial, L, is relegated to a front leg. So of course, there really isn't a cow like this. That doesn't bother me at all - it's just artistic license.

But there's another problem with this cow that makes it anatomically incorrect, and that bothers me a bit. Do you see what it is? Again, the answer is further down in this entry.

By the way, you can see Margie's website at http://margretkrakauer.com/. You can just click on that link to get to it. But if you ever want to type the URL yourself, note that her first name is spelled in an unusual way. It's "Margret" instead of "Margaret", so be careful when you're trying to find her website. The painting Family Cow can be seen on Margie's site, under GOUACHE.

Margie's site was designed and built by my sister Alice. Obviously, I'm capable of creating a website myself. But Alice has a more artistic eye, and I think she did a more attractive layout than I would have done on my own. In addition, there was an awful lot of work reformatting the many photos to the proper size, each with a full-size version and a thumbnail. It was easier for me to hire Alice to do the job, and Margie and I were very pleased with the results.

Here's another of Margie's paintings that runs counter to reality:

Can you see what's wrong with it? I don't mean that there really aren't any fish that look exactly like the ones shown - that's just artistic license again. I mean it's got a problem that runs counter to the laws of physics. Again, you can find the answer further down in this entry.

The picture above is one that's not shown on Margie's webpage. It's actually one of a group of four related pictures which hang in our entry area. If you're interested, click the next link to see all four paintings, as they are hung on our wall (return with your "Back" button).

And now, the answers. Don't scroll down beyond this point if you want to think about the images yourself a bit more.

The problem with the picture of the crescent moon: the two stars shown within the crescent. I've circled them in red in the picture to the right. Any stars in that position would be blocked by the rest of the moon, which is still there, even if you can't see it.

This was pointed out in a letter to the Boston Globe, when a similar image was shown in an earlier story (scroll down to "ACTUALLY, MAYBE IT IS ROCKET SCIENCE", the third letter).

I have to admit that I stared at a similar image in the Globe and didn't immediately notice the problem. But below you can see an un-edited copy of the original image I used above on this page, which makes it quite clear why there can't be any stars inside the crescent:

Any stars in those positions would have clearly been behind the moon (way behind the moon).

What's wrong with the "Family Cow"? It has five teats on its udder. That's not possible; cows always have four. I've actually mentioned this error previously, in a footnote to my entry English noun phrases (Note 2, at the bottom of the page).

Another previous entry, Why do women have two breasts?, is also relevant.

The picture to the right shows what's wrong with the fish painting - actually, there are two things wrong. The problem that struck me initially is that two separate streams of bubbles are flowing from the fish's mouth, so that all the bubbles are not following the same path. This is clearly impossible. Why would some bubbles go one way and others go in a completely different direction?

In writing this blog entry, I also noticed, for the first time, that the streams of bubbles are going behind a smaller fish which is itself behind the fish emitting the bubbles. How could that be? If the larger fish is in front of the smaller one, then the stream of bubbles also needs to be in front of the smaller fish.

I think Margie is rather amused that these small departures from reality bother me. After all, these are a fanciful cow and fanciful fish. They don't exist anyway, so why should I care if their udder or bubbles are not depicted accurately? But somehow, a violation of basic biology or basic physics bothers me in ways that other departures from reality don't. And Margie has a Masters degree in biology - how could she paint a cow with five teats?

Have you ever noticed an interesting impossible picture?