The example of this that has long fascinated me is the case of the American astronomer Percival Lowell and his Martian canals. He dedicated his entire life to mapping out the elaborate (and non-existent) canal system he thought he saw through his telescope. He painstakingly mapped literally hundreds of individual canals and even named all of them. He built a first-class observatory for this work with his own money. He published detailed books and gave lectures. All over an illusion.
Only two things are infinite, the universe and human stupidity, and I'm not sure about the former.
Albert Einstein
Albert Einstein