Norton Juster is famous as the author of the 1961 children’s book The Phantom Tollbooth. In that allegorical adventure, a young hero journeys from the Foothills of Confusion through the well-ordered realm of Digitopolis, intent on rescuing two princesses, Rhyme and Reason. Juster’s The Dot and the Line: A Romance in Lower Mathematics, now reissued for Valentine’s Day, is a fraction of the length of Tollbooth. It is not a story for children but a picture book for grown-ups of all ages, and whimsy for whimsy, it’s just as droll.
The plot is the traditional eternal triangle: A straight line has fallen in love with a dot, but ”she only had eyes for a wild and unkempt squiggle who never seemed to have anything on his mind at all.” While the dot and the squiggle frolic together, the line daydreams of himself as ”a leader in world affairs” (we see him as the equator), a ”law enforcement agent” (he’s the white line down the middle of the road), and ”a potent force in the world of art” (with Rubens assisting). Then, in the spirit of the Little Engine That Could, the line shapes himself up in all the ways lines have at their disposal. He’s a parallelepiped! He’s a complex curve! The next time he encounters the dot and her squiggle, the tables are turned. ”She realized that what she had thought was freedom and joy was nothing but anarchy and sloth,” and she informs the feckless squiggle that he is ”as meaningless as a melon.”
If everyone had read The Dot and the Line when it first appeared in 1963 and taken its message to heart, the ’60s might never have happened. Myself, I can’t help feeling sorry for the carefree squiggle (another great role for Jack Nicholson, if they ever make it a movie). Nowadays, with what’s been learned about fractal geometry and chaos theory, the squiggle might have a fighting chance to win back the dot’s affection, but that would be a different sort of romance. Squares of all ages will appreciate Juster’s straightforward tale (while wishing it longer) and will surely endorse its moral: ”To the vector belong the spoils.” A-