On several occasions, Eliezer Yudkowsky has compared certain religious people's minds to the paintings of M. C. Escher (though the idea can apply to non-religious minds). The basic idea is that a mind can hold elaborate contradictory beliefs that it can't notice.

Quotes

From a blog post in March 2009:¹

I recently spoke with a person who… it’s difficult to describe. Nominally, she was an Orthodox Jew. She was also highly intelligent, conversant with some of the archaeological evidence against her religion, and the shallow standard arguments against religion that religious people know about. For example, she knew that Mordecai, Esther, Haman, and Vashti were not in the Persian historical records, but that there was a corresponding old Persian legend about the Babylonian gods Marduk and Ishtar, and the rival Elamite gods Humman and Vashti. She knows this, and she still celebrates Purim. One of those highly intelligent religious people who stew in their own contradictions for years, elaborating and tweaking, until their minds look like the inside of an M. C. Escher painting.

From a second blog post in March 2009 (written one day after the previous blog post):²

This is why intelligent people only have a certain amount of time (measured in subjective time spent thinking about religion) to become atheists. After a certain point, if you’re smart, have spent time thinking about and defending your religion, and still haven’t escaped the grip of Dark Side Epistemology, the inside of your mind ends up as an Escher painting.

From a January 2010 interview:³

As far as I know I’m the only one in my family to give up religion except for one grand-uncle. I still talk to my parents, still phone calls and so on, amicable relations and so on. They’re Modern Orthodox Jews, and mom’s a psychiatrist and dad’s a physicist, so... ‘Escher painting’ minds; thinking about some things but always avoiding the real weak points of their beliefs and developing more and more complicated rationalizations. I tried confronting them directly about it a couple of times and each time have been increasingly surprised at the sheer depth of tangledness in there.

In addition, chapter 13 of Harry Potter and the Methods of Rationality contains the quote:⁴

Trying to navigate the halls of Hogwarts was like... probably not quite as bad as wandering around inside an Escher painting, that was the sort of thing you said for rhetorical effect rather than for its being true.

A short time later, Harry was thinking that in fact an Escher painting would have both pluses and minuses compared to Hogwarts. Minuses: No consistent gravitational orientation. Pluses: At least the stairs wouldn't move around WHILE YOU WERE STILL ON THEM.

References

Eliezer Yudkowsky. "No, Really, I’ve Deceived Myself". March 4, 2009. LessWrong. Retrieved October 3, 2018.↩
Eliezer Yudkowsky. "Belief in Self-Deception". March 5, 2009. LessWrong. Retrieved October 3, 2018.↩
curiousepic. "Transcription of Eliezer's January 2010 video Q&A". November 14, 2011. LessWrong. Retrieved October 3, 2018.↩
Eliezer Yudkowsky. "Chapter 13: Asking the Wrong Questions". Harry Potter and the Methods of Rationality. Retrieved October 3, 2018.↩

Escher Painting Mind