INVERSIONS is a book you can judge by its cover. At the top is the book's title, written in an ornate, gothic-looking script. At the bottom, in the same script, is the author's name. Scott Kim. Now turn the book upside-down--the cover is unchanged. It still says "inversions" and Scott Kim." Someone has gone and figure, out a way to write the book's title so it spells the author's name upside-down.

That someone, it turns out, is Kim himself, and in Inversions, he has created an entire book of words written in a fashion that visualizes their meanings--"calligraphic cartwheels," he calls them. "MIRROR" has left-to-right symmetry; so does "DYSLEXIA."" upside down" reads the same when rotated 180 degrees. The letters of "EGG" fit together to form an oval. "SYMMETRY" has rotational symmetry. (On the same page, neatly enough, "ASYMMETRY" has none.)

The list goes on; there is no word, it seems that Kim cannot invest with self-reference. "HORIZON" divides into two equal shapes--along its horizon. "LEVEL" contains infinitely regressing repetitions. The E's of "TREE become T's, out of which new "TREES"s grow. "INFINITY" is written endlessly in a single spiral so that it reads clockwise and counterclockwise.

Kim devotes an entire section to Great Names in the annals of symmetry and self-reference. "MARTIN GARDNER" and "ASIMOV" both preserve their shape upside-down. Read "BORGES" a second time: It's "JORGE" written over "LUIS." And in a tip of the hat to Inversions's literary soulmate, Douglas R. Hofstadter's Godel, Escher, Bach, Kim has created a series of appropriate representations of those three names.

There is something enormously appealing about these exercises. They elicit the same awe and pleasure as the discovery of NINA's in a Hirschfeld cartoon, or the realization that Bow and Arrow Streets in Cambridge describe the shapes they form. There's nothing to solve in Inversions--no clues to disentangle or mazes to penetrate. The satisfaction of Kim's "inversions" comes from finding new significance and new wit in the seemingly commonplace.

KIM HAS accompanied his images with a set of elegant essays on related subjects: symmetry, vision, the alphabet, the technique he uses to create inversions, and the analogies to his inversions that exist in music, art, and linguistics. Staying clear of jargon and specialized knowledge, these essays deftly challenge a great deal of what we take for granted about reading, and seeing in general. For instance, Kim poses the following "classical conundrum":

Why does a mirror reverse right and left, instead of up and down? If you extend your right hand while standing in front of a mirror, your reflection will extend it left hand--right becomes left. So why doesn't you head become your feet? Take a minute to puzzle this one out. Even if you understand the answer, you will probably have difficulty explaining it to anyone else.

In his essay on the alphabet, Kim throws another curveball. "Why do we call 'G' and 'g' the same letter when their shapes are so different?" he asks. "Look around at the alphabets in books and signs. If you think you understand what they all have in common, just try explaining how to recognize the letter 'G' to a non-Roman-alphabet-using person. Can you explain it without using pictures?"

For sheer cleverness, the flashiest section of Kim's text is his discussion of the linguistic equivalent of the calligraphic inversion--the palindrome, a word or sentence that reads the same backwards and forwards. Starting with the most familiar type of palindrome, at the letter-level ("Able was I ere I saw Elba" is the best known of these), Kim goes on to write about word-palindromes (his example is "So patient a doctor to doctor a patient so") and, most fascinating of all, phonetic palindromes, which sound the same run backwards through a tape-recorder ("we revere you" and "ominous cinema" are Kim's two examples).

From time to time, Kim loses control of himself. A handful of the inversions themselves border on the illegible, and one or two of his propositions in the accompanying essays are just plain ridiculous. It's hard to take Kim seriously when he suggests that "creating a design on your own name can be a powerful experience in defining your own identity." He sounds like a crank when he writes, "There is so much to be learned from playing with letters--why isn't more of this taught in schools?" Most disturbing of all is the statement by Kim's friend Jef Raskin, who wrote the "Backword" to Inversions, that he legally shortened his first name in order to be able to write it symmetrically.

But these lapses aside, Inversions fulfills the promise of its remarkable cover. For Scott Kim has brought off a rare trick: He has combined diversion and subversion. We are entertained, and we will never again think the same way about words and letters.