A NEW NATIONAL POLL conducted jointly by NBC News and the Associated Press has just shown that half the American people do not want President Carter to run for re-election in 1980, compared with 38 percent who do. Among Democrats, half the members of the party would like Mr. Carter to run, whereas the other half breaks down into 39 percent against, 11 percent undecided. On the Republican side, 26 percent say go ahead, and 66 percent don't. All of which is fascinating, if we can figure what it means.

Half the Democrats would like the president to run again. That's easy. But how do we read the 39 percent who would not? It is probable that 39 percent of the Democrats don't want Mr. Carter to run again because they will lose with him. But it is possible that they do not wish to win with him (some Democrats are principled). Come to think of it, the 50 percent of the Democrats who do want him to run may want him to lose (some Democrats are unprincipled). In the same vein, how do we read the Republicans? The 26 percent who want Mr. Carter to run may wish him to lose; and the 66 percent who do not may fear that he'll win. Then there's that 11 percent of undecided Democrats.What are they undecided about? What are the 8 percent of remaining Republicans undecided about?

We go on:

The new poll shows that "more than a third" of those who voted for Mr. Carter in 1976 do not wish him to run again. What if that figure includes Republicans? Then we not only have the problems suggested above, but we also have the problem of not knowing who has changed his or her mind in the past couple of years. If, on the other hand, the "more than a third" exactly includes the 39 percent of disgruntled Democrats, it means that Republicans are just as happy with Mr. Carter as they've always been. But does that means? What is happiness to a Republican?

To continue:

The poll also shows that public trust in Mr. Carter - his "trust rating" as distinguished from his "job rating" - has risen again this month, and in fact has been rising steadily since the start of the summer. When asked, "How much of the time you think you can trust President Jimmy Carter to do what is right?", 13 percent responded "just about always?; 34 percent, "most of the time"; and 42 percent, "some of the time." What have we here? It would seem we are dealing with an inverse proportion, to wit: As trust in a president's ability to "do what is right" increases, trust in his ability to govern decreases - unless doing right has nothing to do with governing, which is an interesting philosophical question in itself. In any case, it seems that if Mr. Carter wishes to serve four more years, he should become less trustworthy, at least in the public mind. But there's a wrinkle here, too. Conceivably, Mr. Carter could strive to become absolutely untrustworthly - and still fall in the polls.

Which brings us to Richard Nixon:

According to the new poll, Mr. Carter's job rating is below the rating that the public now gives Mr. Nixon for his years in office. Mr. Nixon is, of course, the polestar of all polls, so one naturally assumes that anyone in Mr. Nixon's boat must be sinking. But here again, is it not possible that the people (who have a way of forgetting) now rate the Nixon years rather highly - at least for liveliness? In which cases, might not Mr. Carter, who seems on the way down, be on the way up?

Time (and the polls) will tell.