When he finished his classic work on democracy in America 150 years ago, Alexis de Tocqueville peered into the future with uncanny foresight--and foreboding.

"There are, at the present time, two great nations in the world which seem to tend toward the same end, although they started from different points," he wrote in the 1830s. "I allude to the Russians and the Americans."

All the other nations had nearly reached their natural limits, he said, but the Russians and the Americans were still in the act of growth, "proceeding with ease and with celerity along a path to which the human eye can assign no term . . . . Their starting point is different, and their courses are not the same. Yet each of them seems to be marked out by the will of Heaven to sway the destinies of half the globe."

Tocqueville was worried. His concern was that these two nations, so much alike in raw physical energy, frontier youthful exuberance, natural resources and sense of national mission, but so dissimilar in collective cast of mind and method of functioning, eventually would come into fateful collision.

Which remains, of course, the overriding question today, especially as the Soviet-American arms race accelerates and we slide back into a renewal of Cold War tensions.

Walter Lippmann's famous admonition about the dangers of stereotypes has never been more appropriate. As Lippmann put it, we are all trapped by the pictures we carry around in our heads. We believe that the world we know and see is the world that exists. And the world that will be.

That's certainly the case when it comes to present Soviet-U.S. attitudes. Each side holds a frightening mirror image of the other. Each side betrays a sometimes astonishing lack of understanding of the other's history and present point of view. Each appears trapped in dangerous illusions formed by those imperfect, if not distorted, pictures in their respective heads.

The president travels to Florida and speaks of the evils of the Soviet system with messianic zeal before a gathering of fundamentalist Christians. He urges them not "to ignore the facts of history and the aggressive impulses of an evil empire . . . . " Then he goes before the nation on TV with his charts about the Soviet threat rising like a tidal wave around the globe. He conjures up a vision of some futuristic encounters in outer space, and summons the scientists to work toward redressing the military imbalance once and for all.

His intention may well have been eventually to reduce the threat of nuclear war, but his words and timing surely only serve to confirm the dark suspicions of the Soviets about the United States.

Even before his recent speeches, Soviet specialists on American life were warning their leaders that the United States was embarking on a new, more menacing period. They were saying this was a deliberate public campaign to divert attention from America's economic woes and presumed loss of place in the world.

And while the president employs biblical language to warn about the evils of the Soviet empire, the Russians add their own old pet Marxist phrases about the growing dangers from the "American power elite" and from "U.S. imperialism." They continue to predict the inevitable triumph of socialism over capitalism.

All this adds up to a chilling portrait of a deteriorating state of relations between these two superpowers which now indeed hold sway over the destinies of the earth, and in fearsome ways never imagined by Tocqueville.

By curious coincidence, the current spate of Cold War rhetoric comes just as the official views of Georgi Arbatov, chief adviser to the Kremlin on American affairs, have been published in the United States. ("The Soviet Viewpoint" by Arbatov from interviews by Dutch journalist Willem Oltmans.) Among other things, Arbatov has been a consultant to Soviet leader Yuri V. Andropov and longtime director of the Institute of USA and Canadian Studies in Moscow.

Much of Arbatov's opinions sound like more of the familiar Soviet party line propaganda about the United States. But his words are worth pondering for the insights they give about top-level Soviet thinking today, and for his expressed concern about beginning an infinitely more dangerous "second edition of the Cold War" in the 1980s. As George F. Kennan, the former U.S. ambassador to the Soviet Union, remarks, "One does not have to agree with many of Mr. Arbatov's views, or even with his understanding of historical events, to recognize that this is a uniquely revealing and significant record of the way Soviet-American relations look to one highly placed Soviet personality."

Arbatov has been an advocate of detente. Not, as he makes clear, out of fuzzy idealism, but hard realism: "Detente . . . has no acceptable alternatives if we are to avoid doomsday."

He speaks in similar vein about Soviet-American relations. "While an improvement for relations between Moscow and Washington is not a panacea for all troubles, unrestrained hostility between the two can lead to the extinction of our civilization."

And he is capable of giving voice to disturbing eloquence:

"The overwhelming mutual interest between the USSR and the United States is indeed survival. It makes peaceful coexistence between us imperative. Whether one likes it or not, we are chained to each other on this planet. Neither side can leave the globe. We are here. Americans are here. We've got to learn to live in peace. If we succeed, we will not only survive, but may be able to establish relations that could bring benefits to each other and to the world as a whole. Our well-being and the world's well-being depend to a large extent on whether we spend more on peaceful endeavors or continue to squander our resources through the arms race. There could be tremendous benefit to all humanity in the cooperation of the two biggest economic and scientific-technical potentials of the world. Finally, we are faced with growing global problems that can only be tackled in a peaceful atmosphere.

"If we allow ourselves to slide down into uncontrollable hostility, we can expect, at best, a quite drab and bleak existence, and, at worst, a nuclear incineration of life on this planet."

As Lippmann would have said, one of the ways to guard against that unacceptable alternative is to change some of those pictures we carry around in our heads.

Postscript: Last night, after hearing himself lampooned and his military policies spoofed at a Washington hotel, the president of the United States joined his critics onstage in a conga line and delivered his own song-and-dance reply. All in good fun, and all before an audience that included many of the nation's political, economic and military leaders.

Among the invited guests to the Gridiron Club's annual dinner was Soviet Ambassador Anatoliy F. Dobrynin. One wonders what he will report back to Moscow, and whether that picture of presidential good will and humor changes any previous impressions.