This sounds very much in the vein of the book I'm currently reading, Gödel, Escher, Bach: An Eternal Golden Braid by Douglas R. Hofstadter. The book is a bit dated, 1979, so I did a quick search to see if Hofstadter has revised much and found this article from last year that has some similarities to the link you shared.
More about Hoftadter's Gödel, Escher, Bach
[goodreads.com]
Loved that book! Thanks for posting the article. I'll check it out.