Zeno’s paradoxes are ancient mind games that undermine common-sense assumptions about reality. In the most famous, “Achilles and the Tortoise,” a fast runner and a tortoise start at the same time toward the same goal, the tortoise with a head start — say it must cover 10 meters while the runner must sprint 100 to the finish line. Can the runner overtake the tortoise and win?

No, says the paradox, since when the runner reaches the tortoise’s starting line, the tortoise will have moved to point A. When the runner reaches point A, the tortoise will have moved to point B, and when the runner reaches point C, the tortoise will be at point D, ad infinitum. But would you bet on a tortoise against Usain Bolt?

In Takeshi Kitano’s new film, “Achilles to Kame (Achilles and the Tortoise),” the runner is a hapless artist named Machisu, the tortoise the art he is seeking to master and, later in life, the success he is trying to win.

Achilles to Kame
Director Takeshi Kitano
Run Time 119 minutes
Language Japanese
Opens Now showing (Oct. 3, 2008)

In a private joke, all the art on the screen is Kitano’s. Also, Kitano plays the artist in late middle-age, whose every attempt to catch the shifting winds of art world fashion ends in ridiculous failure.

This may be a private joke as well, since Kitano’s own attempts to win international honors for what might be called the “Kitano trilogy” — “Takeshi’s,” “Kantoku Banzai! (Glory to the Filmmaker!)” and “Achilles to Kame” — have finished in disappointment, if not outright failure. Festival juries have not exactly showered awards on these films, with their self-referential, self-sabotaging focus on Kitano’s public vs. private image (“Takeshi’s”), directorial struggles (“Kantoku Banzai!”) and artistic doubts (“Achilles to Kame”). It’s as if, instead of making “City Lights” and “Modern Times,” Charlie Chaplin had spent his middle years filming in-joke excursions into the psyche and celebrity of a perfectionist director with a thing for teenage girls.

Not that Kitano is a Chaplinlike genius, but his poison-tipped tongue and unbuttoned mind have rightly made him the king of Japanese TV comedians, while his cheekily unorthodox, thoroughly Kitanoesque approach to filmmaking — every frame being unmistakably his — once made his films, from “Hana-Bi” to “Zatoichi,” among the most interesting coming out of Japan.

By comparison, “Achilles” is a schizoid wreck in search of an identity — or at least a coherent story line. The film begins channeling 1950s studio melodramas about family dissolution. Sad-sack young Machisu (Reo Yoshioka) is the pampered son of a wealthy businessman and Western art collector (Akira Nakao) who encourages his boy’s budding interest in art. When Daddy’s business goes bust, poor little Machisu is cast into the cold, cruel world, like a Dickens orphan, stubbornly clinging to his art as to a lifeline.

Switch to the ’60s, when Machisu, now a lugubrious not-so-young man (played by 45-year-old “Takeshi Army” veteran Yurei Yanagi), is still banging away at his art, while working day jobs as a newspaper delivery boy and print shop hand. At the latter job he meets Sachiko (Kumiko Aso), a pretty office worker who is supportive of his artistic ambitions. He is thwarted, however, by a hard-to-please gallery owner (Nao Omori) who urges him to try something more contemporary than the conventionally realistic (and, as it turns out, eminently salable) harbor scene Machisu shows him.

So he slogs off to art school where he meets a wild crowd of conceptual artists whose idea of painting is riding a bicycle hung with paint buckets on the handlebars into a huge white canvas, splatting the paint — and the rider.

So far so fun. But Machisu ages into a middle-age hack (Kitano) who enlists the ever-loyal Sachiko (Kanako Higuchi), now his wife, in ever more hair-brained attempts to make saleable conceptual art, from flinging paint onto a canvas with a small catapult to having Sachiko drown him in the bath so he can paint his near-death visions. But nothing pleases the gallery owner. Then his fed-up teenage daughter (Rei Tokunaga) leaves, followed eventually by Sachiko. Having sacrificed his family and artistic soul on the altar of art-as-business, Machisu is seemingly left with one choice: death.

This third part has next to nothing to do with the first two, being little more than a series of mildly funny sight gags. The banally cynical, boringly downbeat conclusion: The modern art world is a sham, with poseur dealers making fortunes from nonsensical garbage, while scorning and exploiting sad fools like Machisu, who play along but never quite get the hang of the hustle.

In “Achilles,” Kitano falls into not only self imitation (much is familiar from the 1995 comedy “Minna Yatteruka (Getting Any?)” and the 1999 road movie “Kikujiro no Natsu (Kikujiro)” especially) but also the tired sentimentalism and rambling incoherence that reliably signal directorial collapse. I had a similar feeling when I saw “Madadayo” (1993), Akira Kurosawa’s last and worst film: The game is up. Is it too late for a reset?

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