# Cubes, Conic Sections, and Crockett Johnson - Johnson’s Introduction to Mathematics

Author(s):
Stephanie Cawthorne (Trevecca Nazarene University) and Judy Green (Marymount University)

Crockett Johnson (1906-1975), the author of the popular 1955 children’s book Harold and the Purple Crayon, was known before then for the 1940s comic strip “Barnaby” and for the illustrations in the 1945 children’s book The Carrot Seed, which was written by his wife, Ruth Krauss.  Crockett Johnson was born David Johnson Leisk in New York City on October 6, 1906, and died in Norwalk, Connecticut, on July 11, 1975.  Despite his death before the advent of webpages, the Crockett Johnson Homepage exists.  It is maintained by Philip Nel and includes, among other things, a short biography and bibliography.  Nel is also the author of a 2012 biography of Crockett Johnson and his wife Ruth Krauss and an editor of a new series of reprints of “Barnaby.”

Crockett Johnson was not a professional mathematician.  In fact, he was not trained in mathematics at all.  Although he drew cartoons while he was in high school, he did not become a professional cartoonist until 1934 when he published his first political cartoon for the radical news magazine New Masses.  During the previous ten years, Johnson studied art at Cooper Union, a free college in New York City specializing in art, architecture, and engineering; studied typography at New York University’s School of Fine arts; worked in advertising and art editing; did free-lance designing; and “may have played semi-professional football for the Flushing Packers” (Nel 2012, 33).  His first cartoon series, “The Little Man with the Eyes,” appeared weekly in Collier’s from March 1940 through January 1942.  “Barnaby” first appeared in the New York newspaper PM in April 1942, shortly after the U.S. entered World War II.  The comic strip has as its two main characters Barnaby, whom Harold definitely resembles, and his fairy godfather, Mr. O’Malley, who cannot be seen by the adults in the comic strip.

On May 26, 1943, mathematical symbols first appeared in the comic strip.  The previous day Mr. O’Malley had introduced Barnaby to Atlas the Mental Giant, who carried a slide rule, a tool based on logarithms that was used from the late seventeenth century until the introduction of calculators for multiplication and division of large numbers.  In some unexplained way, Atlas was able to use his slide rule and the mathematical symbols to produce words like O MALLEY and NO (see Figure 3).  While it is possible to use mathematical expressions to produce words, it cannot be done on a slide rule, which can only produce approximate solutions to numerical problems.

Figure 3. Barnaby, May 26 & 27, 1943 [Johnson 2013, 189].  (These comic strips are published with the permission of the Executor of the Estate of Ruth Krauss.)

The expressions that appeared in these early strips were not mathematically coherent and so they, like slide rules, could not have produced answers to the questions posed.  Sometime after Atlas’ appearance in the strip, Crockett Johnson learned that strings of letters could be produced by mathematical expressions; for example, $L^2$ can represent $LL.$  In January 1944, Atlas reappeared using mathematical symbols in a grammatically correct way, although Johnson still misrepresented the use of slide rules.

Figure 4. Crockett Johnson's markup for Barnaby comic strip that appeared on January 27, 1944.  (Reproduction courtesy of the Smithsonian Institution, image number DOR2012-8045. This comic strip is published with the permission of the Executor of the Estate of Ruth Krauss.)

While the expressions appearing in “Barnaby” were no longer nonsense, Crockett Johnson did not explain the difference to his audience, so only those who themselves knew some mathematics could evaluate the expressions in Figure 4 along with Atlas.  Later in 1944 Johnson’s second collection of comic strips, Barnaby and Mr. O’Malley, appeared in book form and in that book Johnson changed the nonsense expressions he used in 1943 (Figure 5).  The expressions could then be read by anyone who knew some calculus, linear algebra, and the fact that $e^{{\pi}i}=-1.$  This experience with the language of mathematics made Crockett Johnson aware of mathematics in a way that most people are not.

Figure 5. Rewritten panels from Barnaby strips in Figure 3 [Johnson 1944, 97 and 99].  (These panels are published with the permission of the Executor of the Estate of Ruth Krauss.)

Stephanie Cawthorne (Trevecca Nazarene University) and Judy Green (Marymount University), "Cubes, Conic Sections, and Crockett Johnson - Johnson’s Introduction to Mathematics," Convergence (March 2014)