Foreword

“You know, people think mathematics is complicated. Mathematics is the simple bit. It’s the stuff we can understand. It’s cats that are complicated.”

— John Horton Conway

Type TRUE + TRUE into an R console. You get 2. Why? R is not doing arithmetic on the word “true.” It converts a logical value to the number 1, twice, and adds. That conversion follows a rule, and the rule traces back to a design decision that predates R by sixty years and programming itself by two decades. Where did it come from?

In 1936, a logician named Alonzo Church defined booleans as functions that choose: TRUE picks the first argument, FALSE picks the second. No special boolean type, no if keyword — just functions calling functions. John McCarthy built a programming language from that idea in 1958 and called it Lisp. Guy Steele and Gerald Sussman distilled it into Scheme in 1975. John Chambers designed S at Bell Labs in the 1980s with Scheme’s scoping rules in his head, and two statisticians in Auckland built R from S in the 1990s. The TRUE + TRUE in your console still carries Church’s fingerprint, and so does nearly everything else you type into R.