Suppose someone came up with a device that would allow mental images to be projected on a screen. And suppose he asked a cross-section of Americans to project vignettes from their Ideal America.

Could you, by looking at the screen, tell whether the image was that of a conservative or a liberal? A man or a woman? A northerner or a southerner? A black or a white?

Clearly the various subsets of Americans espouse different methods for achieving their ideals. One would give government the power to make us behave; another would get government off our backs. One would be more concerned with attitudes, another with actions. One would seek peace; another would prepare for war. But the point, in every case, would be toward an ideal. Are the ideals really so different?

Would a southern conservative, for instance, suppose that an ideal America must be segregated by race? Or is his present-day support of segregation mere pragmatism based on his assumption that in a less-than-perfect world it's better for everybody to keep the races apart? Don't both hawk and dove long for a world at peace? Isn't the argument between them over the best way to achieve peace?

Would anyone's idealized projection depict an America in which some were exploiters and the others exploited? Or wouldn't both big-government and free-trade advocates see a system in which all transactions were freely undertaken and mutually beneficial?

There would be some obvious differences, no doubt. Men might be more likely to see an ideal America in which husbands earned the family income while wives managed the home. Women might be more likely to see the blurring of sex lines in the workplace, with females no less prevalent than males in the managerial ranks.

If the projection showed a Sunday morning congregation that was essentially white with a smattering of bright- faced black families, you would probably guess that it was a white doing the projecting. If the congregation was thoroughly mixed, you might guess it to be the image of a minority. If the minister is female, you'd suspect the vision emanated from a woman. And what if the priest were a black woman?

Would anyone's idealized vision include neighborhoods segregated by race? By income? Or would there be a random scattering of colors and professions, with mansions and cottages intermingled? Would there be exclusive schools based on anything other than ability? Would friendships cross lines of race and ethnicity? Would marriages?

Surely there would be no poverty in anyone's ideal projection. But would there be servants? And would they be of a different color than the one doing the projecting?

Conservatives may demand, in the real world, bigger and better jails, while liberals may feel more optimistic about the potential for crime prevention and non-prison rehabilitation. But since the ideal vision of both would be of a society without crime, would either include police officers and jails?

Would the neighborhood bar be racially or sexually segregated, or would it be more like a scene from a TV beer commercial? Who would own it?

If the image involved people who were not racially identifiable, just vaguely people, would you attribute the projection to a white or a black? If a particular scene included a fair number of Asians or Latin Americans, would you suppose that an Asian or a Hispanic was doing the projecting?

While the approaches we take to solving our various social problems tend to depend on our own circumstances and ethnicity, how different are our visions of what the country would look like once the problems were solved? In other words, are the crucial differences between us based on disparate goals, or only on contradictory methods for achieving them?

I'd guess the latter. I don't doubt that some of the scenes projected by our magic machine would be traceable to those doing the projecting. But I suspect a lot of us would be surprised to find the projections more alike than different.

Except, perhaps, for the American Indians.