BOOK REVIEW : Beautiful and Silly Poetry Is a Game the Reader Can Play : MADOC A Mystery<i> by Paul Muldoon</i> Farrar Straus Giroux $14.95; 261 pages

There is something in “Madoc” of the game in which one child names four disparate things--a year-old egg, the Czar’s slippers, a teen-ager getting ready for a date and the planet Neptune--and the other makes up a story that somehow tugs all four in. It can be silly and anarchic, and it stretches the spirit.

Paul Muldoon’s “Madoc” is, and does. It is a book-length poem, ostensibly narrative, and much of the poetry is beautiful and arresting. Yet the poetry is better reached if you use “Madoc” as a game to be played rather than a book to be read. Its rules are to be taken lightly, as if Muldoon had added only a few as an afterthought and was agreeable to letting readers make up a few of their own.

Muldoon, a young and prodigiously talented Irish poet, subtitles it “A Mystery,” and that’s not to be taken seriously either. It is a puzzle, at most, or a hide-and-seek whose main purpose is to get you out and running among the opportunities of a sunny morning.

His sunny game has quite a few more than four items. There are the poet Coleridge; his fellow romantic, Southey, who later went starchy and orthodox, and, fleetingly, Byron, who mocked Southey and was in turn denounced by him as a Satanist. There is Coleridge’s and Southey’s scheme to set up a Utopian community somewhere in Pennsylvania.

These are facts. “Madoc” invents a descendant of Southey who lives somewhere in the near future and who imagines the two poets actually carrying out their scheme. They round up their Bath and Bristol fellow Utopians, bring along Southey’s wife, Edith, and her sister, Sara, and make their way up the Susquehanna Valley. The party includes Cinnamond, a dubious guide who dresses in human skin, and Shad, a black servant.

A settlement is made, which Southey rules with increasing stuffiness. Sara is abducted by Senecas, Coleridge goes to find her, meets various Indian chiefs and ends up crossing paths with the Lewis and Clark expedition out West. He is mistaken for a “white” Indian, descendant from an early settlement supposedly made in America by the Welsh chieftain Madoc.

Thomas Jefferson is brought into the picture; so is Aaron Burr, with his plot to set up a kingdom in Louisiana. We encounter Coleridge and Southey, not only while they are floundering around America but also while they are simultaneously conducting their real lives and literary feuds in England. Everything, needless to say, blurs, entwines and goes back and forth in time and space. Dream and historical fact wink in each other’s pockets.

The real game is not the puzzling, shifting story but the verse that holds it together. This is set out in more than 200 short poems, 10 to 20 lines long, usually, or as short as one line. Some of these verselets are lovely lyric or descriptive poems, some are mysterious fragments, some are bawdy and scurrilous, some are comic gibberish. And each bears the name of a thinker, going back to Pythagoras and coming forward to the likes of Robert Nozick and Noam Chomsky.

The particular philosopher and the particular verse usually have no seeming relation to each other; but odd lights are cast by their very disparity. A disconnection suddenly becomes a weird connection. Overdosed, Coleridge is dumped into a cold bath; the verselet is entitled “Epicurus.” The next verselet reads in its entirety: “Coleridge leaps out of the tub. Imagine that”; and is headed: “Archimedes.”

The effect is partly ironic. “Madoc” manages to skewer the histories of philosophy, literature and American settlement. But irony isn’t all. Playfulness is more important, the kind of playfulness that suddenly sparks a leap of the imagination.

Thus, “Madoc” will use a seemingly silly rhyme to take out a pretension. It is particularly apt to use “de-dum” as a rhyme in the straight historical passages or, sometimes, “tsk-tsk.” The verselet under the name of the Medieval theologian Anselm is a single line: “De-dum, Te Deum, de-dum, Te-Deum, de-dum.” And then, unexpectedly, another silly rhyme takes on an elusive enchantment: “Coleridge follows a white Spaniel/through the caverns of the Domdaniel,” cutting back from the harsh American wilderness to Coleridge’s dream territories.

Some of the verselets are glowing poems in themselves. Their beauty ambushes us out of the playfulness, as if a treasure hunt offered--so erratically and unexpectedly as itself to be a kind of play--real diamonds. A prefatory poem, “Cauliflowers,” for example, is a brilliantly moving lyric.

More than anything, “Madoc” sets its game of narrative and narrative-scrambling to music. The music is partly verbal and partly the twists and springs of Muldoon’s lines and rhythms. Even the disassociations, the breaks of thought, the harsh logical and narrative juxtapositions, furnish a kind of idea-music--cymbals, drums--that is more important than what they say or conceal.

Next: Judith Freeman reviews “Glad Rags” by MacDonald Harris (Story Line Press).