The problem with the principle of even-numberedness is that people count differently.

Research shows that while people think of their own actions as the consequences of what came before, they think of other people’s actions as the causes of what came later.

Volunteers remembered the causes of their own statements and the consequences of their partner’s statements.

What seems like a grossly self-serving pattern of remembering is actually the product of two innocent facts. First, because our senses point outward, we can observe other people’s actions but not our own. Second, because mental life is a private affair, we can observe our own thoughts but not the thoughts of others. Together, these facts suggest that our reasons for punching will always be more salient to us than the punches themselves — but that the opposite will be true of other people’s reasons and other people’s punches.

But research suggests that these claims reflect genuinely different perceptions of the same bloody conversation.

Legitimate retribution is meant to restore balance, and thus an eye for an eye is fair, but an eye for an eyelash is not.

When the European Union condemned Israel for bombing Lebanon in retaliation for the kidnapping of two Israeli soldiers, it did not question Israel’s right to respond, but rather, its “disproportionate use of force.” It is O.K. to hit back, just not too hard.

The researcher began the game by exerting a fixed amount of pressure on the first volunteer’s finger. The first volunteer was then asked to exert precisely the same amount of pressure on the second volunteer’s finger.

Although volunteers tried to respond to each other’s touches with equal force, they typically responded with about 40 percent more force than they had just experienced.

Each time a volunteer was touched, he touched back harder, which led the other volunteer to touch back even harder. What began as a game of soft touches quickly became a game of moderate pokes and then hard prods, even though both volunteers were doing their level best to respond in kind.

Neither realized that the escalation was the natural byproduct of a neurological quirk that causes the pain we receive to seem more painful than the pain we produce, so we usually give more pain than we have received.

Research teaches us that our reasons and our pains are more palpable, more obvious and real, than are the reasons and pains of others. This leads to the escalation of mutual harm, to the illusion that others are solely responsible for it and to the belief that our actions are justifiable responses to theirs.

None of this is to deny the roles that hatred, intolerance, avarice and deceit play in human conflict. It is simply to say that basic principles of human psychology are important ingredients in this miserable stew. Until we learn to stop trusting everything our brains tell us about others — and to start trusting others themselves — there will continue to be tears and recriminations in the wayback.