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Metamagical themas : questing for the essence of mind and pattern by Douglas R. Hofstadter

George H.-W.’s Review for the 510 Club | April 2026

 

The anthology Metamagical Themas (1985) is a necklace of mathematical, artistic, and philosophical beads, tied together by a thread of Hofstadterian zaniness, so self-referential it even received a positive review in the 510 Club. Taking over anagrammatically from Martin Gardner’s Mathematical Games (1957-81) column—the column that brought you just about all of recreational mathematics—Hofstadter continues to deliver on the head-scratchers and pen-clickers front, but the focus is on art, society, and cognition. 

 

There are 33 columns in total, split into seven sections. I recommend reading them in whatever order interests you, perhaps keeping a record of what you’ve covered. As magazine columns, many problems originally invited creative solutions from Scientific American readers; in the anthology, these responses are discussed at length in detailed postscripts, giving the book a nice interactive element.

 

In fact, my favourite section is probably VII, concerning Prisoner's Dilemma scenarios. What would you do if you received a letter in the mail asking you to cooperate or defect in a real-life one-round 20-player Prisoner’s Dilemma? If you were Hofstadter’s friend in the 80’s, your answer to that question, and feeble rationalisations thereof, may have been forwarded to thousands of subscribers in the column “Irrationality Is the Square Root of All Evil”. Several further experiments were discussed, including one involving thousands of Scientific American readers and a potential million dollars. In this column, Hofstadter introduced the concept of super-rationality—a kind of unstable equilibrium that fully leverages the assumption that others are reasoning just as you are.

 

I tend to think there are two types of people: those who enjoy games, and those who enjoy game-theory puzzles. Along with columns 28 and 29, there’s plenty in section VI for both. (In fact, I suggested one such puzzle to Rata for the newsletter a few months ago.) I also enjoyed the allegorical short story “The Tale of Happiton”, which probably alludes to the environmental crisis and nuclear arms race. Another highlight, discussing the mechanism of the biological information, is the column “The Genetic Code: Arbitrary?”.

 

Douglas Hofstadter is best known for the Pulitzer Prize-winning book Gödel, Escher, Bach (1979), a book which—contrapuntally, through various jokes, puzzles, formal proofs, dialogues, computer programs, patterns, everything besides plain exposition—explores the nature of cognition. It was a lot of people’s favourite book when they were 15. Metamagical Themas feels like a more focused and refined continuation of those ideas.

 

My least favourite section, Section I, is about self-reference. It begins with two entire columns on self-referential sentences (“Quines”), followed by a column which played a significant role in popularising the idea of memes, and introducing the game Nomic about self-referential law. Section II is on the opposite side of the abstract-concrete spectrum; the first two columns about scepticism and the latter two are about gendered language. My favourite columns here are “On Number Numbness”, about estimating large numbers, and the guest article by one “William Satire”. 

 

Section III is more artsy, beginning with rhythmic patterns in Chopin and a then-timely discussion of Polish Solidarity. Another column explores a kind of maths-art called “parquet deformations”, and offers plenty of design inspiration.

 

Some of the interest in the book is purely historical: section IV begins with an introduction to a new-fangled toy called the “Rubik’s cube” and a fancy programming language called “Lisp”. However, many interesting puzzles and computer science concepts are discussed which might be new to you. My favourite column of this section is number 16, on strange attractors. 

 

The book may even be a victim of its own success: some topics it popularised now feel overfamiliar. For example, column 20 on the many-worlds interpretation of quantum mechanics, and much of Section V on artificial intelligence, are interesting less for their subject matter than for Hofstadter’s broader epistemological concerns.

 

Why not take your pick from Metamagical Themas?

 

 

WHAT IS THE 510 CLUB?

The 510 Club is named after the Dewey Decimal classification for Mathematics. It is a book recommendation project facilitated by Mathateca in collaboration with Christchurch MathsJam. Each month we feature a mathematical book recommendation, whether that’s a novel, articles / essays, a puzzle book, textbook, biography... just as long as it features maths in some way. Read the above book at your leisure then feel free to comment your thoughts below, or come along to the following Christchurch MathsJam sessions to join in an informal maths/book chat with the reviewer.

We're always looking for suggestions! If you're interested in contributing a book rec one month, please email christchurch@mathsjam.com to sign up.