Some tools used in statistics courses are useful for understanding race in America. In statistics, you learn about overlapping and non-overlapping “sets.”

Black and white America are like two Venn diagrams, circles that share substantial common or overlapping space and that have some areas that do not overlap at all. In many ways, the area of common overlap is now probably larger than it has ever been. And there is good reason to expect that overlap to grow in the future to the point of becoming completely co-terminus. Whenever that day comes, America will be effectively post-racial.

Yet, the remarkably polarized reactions to the recent arrest of Harvard Professor Henry Louis Gates Jr. exposes one of those areas of non-overlapping, or unique, space. It reveals one of those acutely painful subjects where much of black and white America share all too little commonality of outlooks. It is that point of everyday interaction where race plays out in a face-to-face encounter. In particular, it involves the type of encounter involving respect for police authority on the one hand and, on the other hand, respect for the rights of citizens who happen to be African Americans.

For most blacks, this police-black citizen interaction is an acutely sensitive terrain. For many African Americans, it is a space marked by live wounds, personal and familial memories of injury and insult, and the heavy weight of group experience of injustice. For most whites, however, there is nothing so close, so profoundly emotion-laced or so fundamentally defined by an ascriptive feature such as one’s perceived racial background. It is, in short, a place where the Venn diagrams of white America and black America generally do not overlap.

As a consequence, it is one of those topics where miscommunication is not merely easy, but where potentially explosive mutual misunderstanding is quite likely. I know this in a very personal sense. A good friend whom I’ve known since high school got in touch with me following the news of Gates’ arrest on disorderly conduct charges. She passed along the initial news reports, which were based largely on parts of police reports that were inappropriately released and, at best, one-sided. To my mind, it sounded as if Gates had behaved wildly. I was as flabbergasted to hear that as to hear my friend’s conclusion that both sides had erred. I responded with, frankly, a blistering, liquid hot fusillade of facts and background as to why saying that just wasn’t good enough.

She conceded that, viewed in context, my take on the incident was probably the right one. She also said that my reaction and tone had brought her to tears. At this point, it is worth noting that she is white and I am black. We’ve probably seen one another only three or four times since her graduation from Wellesley and mine from Loyola Marymount, but we have a connection that I am certain will survive this intensely fraught moment.

I was passionate in my reaction to her “split the difference/everybody acted badly” response to the Gates arrest for three tightly interlaced reasons. First, the world at that point had heard only one side of the story, that of Sgt. James Crowley, via a leaked police report. Second, anyone who knows Skip Gates knows that he is probably the very last black person on earth to blame racial bias for what happens to him. The charge of disorderly conduct was just not credible at all. Third, like most black men, especially one living and working in a largely white environment, I worry frequently about establishing my “bona fides” and wondering who might be available to “vouch” for me, especially in a circumstance where police might be involved—a worry that I know is not a preoccupation of any of my white colleagues.

To return to the bitter disagreement with my high school friend, the larger point is that she is a person with scrupulously progressive politics and whose values and basic instincts are almost completely co-terminus with my own. But then there comes this aspect of the racial divide where, to stick with the metaphor, the Venn diagrams simply do not overlap. Indeed, not only do they not overlap but the intensity of experience and belief on my side of the circle is completely absent in hers. The distance between even good friends was almost unbridgeable.

I say “almost” because we are, of course, still friends. In this vein, I perfectly understand President Barack Obama’s decision to call the officer who arrested Skip Gates and then placed a call to Gates himself. (I do not attach much significance to who got the first call because Gates had to change his private cell phone number after it was released publicly and, as it played out, the White House had to find me on Martha’s Vineyard to get a direct, workable phone number for him). Much of Obama’s politics, and certainly his larger life experience, has been about summoning the perspective and courage needed to seek mutual healing and transcendence in the face of long-standing racial fissures of this kind. So I hope the president is successful in bringing together Sgt. Crowley and my friend Professor Gates, at least as a symbol of the possibility of racial healing and comity.

It is ironic, of course, that Henry Louis Gates Jr. should become the global poster child for the evils of racial profiling and be cast as an anti-racist agitator. Nothing could be further from the path he has trod to this point (as others, including Melissa Harris-Lacewell, writing in The Nation, have ably pointed out). Like Obama, Gates has been a dedicated and consummate builder of bridges across the racial divide. From family history, to personal biography, to a long and prominent intellectual and professional life, he has been about resisting the oversimplifications, the polarities, the easily invoked catchphrases and slogans, the totems and symbols, and the choosing of sides along a great racial divide that constitute so much of the burden of race in America. Thus, it is unfair and, frankly, tragic that so much of the media coverage of this event has treated Gates as if he has ever walked around shouting “racism” or “yo’ mama” at police officers. Absurd in the extreme.

My friend and I reached a point of intense friction over this episode. Just imagine how difficult it is for white and black Americans (and Latino and Asian and Native Americans as well)—who may not have 20 or 30 years of personal friendship to rely upon in creating the commitment to keep on listening—to do the work required to really hear a message from a place in the other person’s experience (Venn diagram) that has no immediate parallel in one’s own set of experiences. It is not easy, and the din of a media circus is rarely a good setting to bring together members of communities that are at loggerheads. Everybody is too concerned about sending symbolic messages of solidarity to those normally on “our side” (i.e., police unions, the Congressional Black Caucus) to engage in any real work of communication and reconciliation.

Yet we can, as Obama and Gates and many others suggest, take this as a teachable moment. That is what needs to happen now. My high school friend and I will remain connected. And I am confident that with the wisdom and commitment to racial understanding that Barack Obama and Skip Gates have long exhibited, we as a nation will continue the slow, difficult, inexorable work of bringing more fully together the members of two circles of lived experience, one black and one white, all heading toward that point of e pluribus unum.

Lawrence Bobo is the W.E.B. Du Bois Professor of the Social Sciences at Harvard University.