Washington ? In 1967 Lyndon Johnson added yet another piece to the jigsaw puzzle of national perfection: The Corporation for Public Broadcasting was born. Public television was a dubious idea even when concocted as a filigree on the Great Society. Why should government subsidize the production and distribution of entertainment and, even worse, journalism? Even if there were — has there ever been? — a shortage of either in America, is it government’s duty to address all cultural shortages?

Today, with iPod earphone cords dangling from millions of heads and movies flooding into homes where they jostle for plasma screen time with video games, Americans are entertaining themselves into inanition. Furthermore, journalism and imitations of it have become social smog. Even in airport concourses you are bombarded by televised human volcanoes verbally assaulting each other about the “news,” broadly — very broadly — defined to include Kobe Bryant’s presence on Michael Jackson’s witness list.

In 1967, public television did at least increase, for many people, the basic television choices from three — CBS, NBC, ABC — to four. Not that achieving some supposedly essential minimum was, or is, the government’s business. In today’s 500-channel environment, public television is a preposterous relic.

The Public Broadcasting Service recently tried an amazingly obtuse and arrogant slogan: “If PBS doesn’t do it, who will?” What was the antecedent of the pronoun “it”? Presumably “culture” or “seriousness” or “relevance.” Or something. But in a television universe that now includes the History Channel, Biography, A&E, Bravo, National Geographic, Disney, TNT, BBC America, Animal Planet, The Learning Channel, The Outdoor Channel, Noggin, Nickelodeon and scads of other cultural and information channels, what is the antecedent?

Now PBS is airing some HBO films. There is a nifty use of tax dollars — showing HBO reruns. Which contribute how to “diversity”?

In 1967 public television’s enthusiasts were ahead of the curve of cultural inanity, making frequent use of the d-word, which required several more decades to become the great signifier of cultural correctness. The chairman of the Federal Communications Commission hailed public television’s promise of “more diversity” and a Carnegie report foresaw increased “diversities.” Thirty-eight years later, 500 channels mock public television as crucial to diversity.

The recent spat about Buster, PBS’ cartoon rabbit, visiting two lesbian parents quickly became a second spat about the Education Department’s threat to stop financing Buster. But a third spat should have been about why the Education Department (a fourth spat: Is that department necessary?) is paying for any of Buster’s adventures. Is there a desperate shortage of television cartoons? Is Buster to other cartoons as Beethoven is to Bon Jovi?

Public television, its supporters say, is especially important for poor people who cannot afford cable or satellite television. But 62 percent of poor households have cable or satellite television and 78 percent have a VCR or DVD player.

Public television is akin to the body politic’s appendix: It is vestigial, purposeless and occasionally troublesome. Of the two arguments for it, one is impervious to refutation and the other refutes itself.

The impervious argument is: The small size of the audiences for most of public television’s programming proves how necessary public television is. The big networks gather big audiences by catering to vulgar cultural tastes, leaving the refined minority an orphan, because any demand the private market satisfies must be tacky.

The self-refuting argument is: Big Bird. Never mind that the average age of PBS viewers is 58. “Sesame Street” — see how its merchandise sells, and Barney’s, too — supposedly proves that public television can find mass audiences.

But the refined minority, as it sees itself, now has ample television choices for the rare moments when it is not rereading Proust. And successes such as “Sesame Street” could easily find private, taxpaying broadcast entities to sell them.

President Johnson, no slouch at the “progressive” rhetoric of platitudinous gush, said the prospect of public television should fill Americans with “the same awe and wonderment” that caused Samuel Morse, when he successfully tested his telegraph, to exclaim, “What hath God wrought?” But by 2002 PBS president Pat Mitchell was warning: “We are dangerously close in our overall prime-time numbers to falling below the relevance quotient.”

Public television’s survival, with no remaining rationale, should fill students of government with awe, wonderment and melancholy. Would it vanish without the 15 percent of its revenues it gets from government? Let’s find out.