BECKET — The vibrant, very much living members of the Bill T. Jones/Arnie Zane Dance Company are surrounded by ghosts in “Story/Time.” In a general way, this is not so unusual; contemporary dance often bears a proud aura of its ancestral shadows. But Jones, the creator of “Story/Time,” has long performed with his own, particular ghosts — Zane, Jones’s lover and co-director, who died in 1988; his parents, Estelle and Gus; the dancer Demian Acquavella — who are at times faintly discernible in his work, at other times front and center.

And now John Cage makes his posthumous debut with the company, the composer’s 1958 “Indeterminacy” serving as inspiration for “Story/Time,” which is presented this week at Jacob’s Pillow. In one version of “Indeterminacy,” Cage read a series of wry one-minute stories while parts of his compositions were played by the musician David Tudor: Neither component was staged to complement the other, thus creating an oxymoronic event of purposeful randomness.

Like Cage, a composer (here Ted Coffey) performs live while Jones reads from his own series of one-minute stories; a third layer of dance happens all around Jones. The technology-loving Cage would surely have been tickled by the fact that the order of the stories, 70 of them chosen out of more than 150, and the dance phrases, 35 snippets from the archives of Jones and Zane works, is shuffled every few performances by the website Random.org.

And a random sampling of these topics shows that Jones — a world traveler who has often proclaimed his love of telling stories — doesn’t lack for variety. Snakes, deer, and squirrels make cameos, as do sex workers in Amsterdam, a concentration camp near Prague, and spilled champagne in New York City. Of course Estelle, Gus, and Arnie appear, as well as a parade of celebrities and taxi drivers. True to Cage’s example, Coffey’s improvised score mostly forges off on its own, ambient and soft or clanging and shrieking, sometimes even drowning out Jones’s narrative.

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As for the dance, bits of Jones’s “D-Man in the Waters” (1989) are unmistakable in “Story/Time” — those exuberant solo runs and diving leaps into a waiting crowd — while other phrases remind us, boldly or obliquely, of a variety of works. Here, too, in a lovely way, Jones’s current stable of terrific dancers evokes other kinds of ghosts, the earlier casts of those dances.

How poignant those afterimages are, how important that audiences remember, Jones may be saying. In one story, Jones quotes his father — “You live and learn; you die and forget it all” — then states his own version: “You live and learn; you forget it all and then you die.”

And thus, for a piece that’s so framed by linear time — for the first third or so of it, a digital clock counts down the minutes and seconds — it seems that Jones is instead wandering through the fractured, unreliable, but far more poetic time of memory and dreams. At the beginning of the opening-night performance, Jones addressed the audience, explaining the unusual nature of the piece, and suggested that we “get rid of the glue”; that is, that we allow a little chaos in. Though it took some time for me to settle in to “Story/Time,” when the clock reappeared in the last minute-and-a-half, I found I wasn’t ready to leave these fragments of a life so soon.