A few words about the Mountaintop and the Promised Land. On the last night of his life, Martin Luther King Jr. famously told an audience in Memphis that he had stood on the one and seen the other.

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“I may not get there with you.”

— Martin Luther King Jr., April 3, 1968

A few words about the Mountaintop and the Promised Land.

On the last night of his life, Martin Luther King Jr. famously told an audience in Memphis that he had stood on the one and seen the other. He did not define the Promised Land, but he did not need to. That audience of striking sanitation workers and their supporters, those long-suffering women and men who erupted in cries and shouts, already knew.

The Promised Land was where you did not have to march for your dignity. It was where you did not have to sing for your freedom. It was where there was no need for speeches to verify your humanity. The Promised Land was that sacred place where all of God’s children would stand as equals on level, fertile ground.

Friday marks 40 years since Martin Luther King was assassinated. And the search for that promised land has shrunken until it fits inside an old riddle, the one that asks whether the glass is half empty or half full.

I’m moved to this conclusion by a column published last week in The Washington Post by Shankar Vedantam, who writes on issues of human behavior. Vedantam’s piece recounted two studies. The first, by Philip Mazzocco of Ohio State University and Mahzarin Banaji of Harvard, asked white volunteers a question: If they were to be reborn black in America, how much money would they ask for to cover the lifetime disadvantages? Most gave amounts less than $10,000. To go a lifetime without TV, they wanted $1 million.

When it was explained to them that being black meant they would earn a fraction of what whites earn, suffer higher rates of infant mortality, be unemployed at a rate nearly twice the national average, be more likely to be poor and live at dramatically greater risk of being jailed or killed, whites raised their asking prices a hundredfold.

That blacks and whites live different realities is hardly news. What’s intriguing is the reason, as suggested by the second study. Yale University researcher Richard Eibach found that whites and blacks employ different measures in assessing racial progress. Whites judge it by looking at how far we have come (“How can you say there’s still racism when we have an Oprah Winfrey and a Barack Obama?”) Blacks judge it by how far we have yet to go (“How can you say there’s no racism when police keep stopping me for no reason?”)

So each side of America’s most intractable debate chooses the path of least resistance, the path that shoves the onus for change off to the other side. Thus, whites can feel justified in noting the incredible progress we have made, and blacks can feel equally justified in feeling still victimized, and it never seems to occur to any of us that both views are true, that they do not contradict each other. We never seem to realize that we are having an argument over how much water is in the glass.

I guess you can’t see that from the narrow valley of cynicism and self-interest. But in his last public exhortation, Martin Luther King called us up from there, called us up to the grand view, the big picture, the mountaintop. From there, he said, you could see the Promised Land.

Whites, Eibach told the Post, see that promised land — racial equality — as an ideal, something it would be nice to achieve someday. Blacks see it as a necessity, something you work to make manifest here and now. The urgency embodied in the one view, and the luxuriant indolence in the other, speak volumes about the cognitive distance between blacks and whites.

And explain why, rather than being inspired by the possibilities glimpsed from a mountain peak, we trudge through a valley arguing how much water is in the glass. Is it half empty? Half full?

I guess that would depend on how thirsty you are.

Miami Herald columnist Leonard Pitts Jr.’s column appears regularly on editorial pages of The Times. His e-mail address is: lpitts@miamiherald.com