For most Americans, who now wish we had never invaded Iraq, the notion of expanding that extraordinarily lethal mistake into neighboring Iran and Syria must seem insane. Yet those same brilliant neoconservative strategists who brought us the war in Iraq and constantly urge its escalation exist in their own special reality. They speak of military hostilities against Iran and Syria with anticipation rather than apprehension.

As we should have learned over the past four years, their dreams often turn out to be our nightmares.

For four brief hours on Memorial Day, however, the neoconservative drive toward a wider conflagration in the Middle East stalled, when ambassadors from the United States and Iran met in Baghdad.

That meeting’s historic significance should not be underestimated, even though U.S. officials emphasized that no further meetings would necessarily occur. Convened under the auspices of the Iraqi government, the Monday encounter represented the first substantive bilateral discussion between American and Iranian officials in three decades.

Relations with Iran have been poor ever since the mullahs seized power from the U.S.-sponsored shah in 1979, but in recent months the increasing strains between us and them have brought armed conflict closer. Longstanding grievances against Iran’s sponsorship of terrorism in the region have been exacerbated by the prospect of an Iranian nuclear arsenal and allegations about Iranian agents supplying weapons to the insurgents in Iraq.

As these problems worsened, American policy toward Iraq has vacillated between “containment” and “regime change,” with applications of economic sanctions and threatening rhetoric — and not much success. Iran has become more aggressive and more influential in the region as a direct consequence of the violent regime change that we inflicted on Iraq. Over the same period, Iran has elevated leaders such as Mahmoud Ahmadinejad, who are more religiously conservative and more hostile to the United States and its allies, especially Israel.

What we have not tried, until now, was talking with the Iranian leaders. By breaking that taboo, the Memorial Day meeting pointed toward a saner policy — just as the Iraq Study Group urged six months ago, when its report highlighted the need for regional talks including Iran and Syria.

Naturally, such signs of sanity were immediately met with furious denunciations that echoed the shrill attacks on House Speaker Nancy Pelosi, who dared to visit the Syrian leadership in Damascus. When the Pelosi trip was followed by overtures from Secretary of State Condoleezza Rice to both the Syrians and the Iranians, it signaled that U.S. policy-makers were considering a sensible shift. Rice’s exploratory gestures provoked angry editorials in The Weekly Standard and The Wall Street Journal, which accused the State Department of undermining the White House “strategy for victory” in the Middle East.

The real danger is that whenever we start talking with our enemies, we may discover potential areas of compromise or even agreement. Progress would undermine the arguments of politicians and pundits who prefer permanent war.

But we already know that both Syria and Iran have cooperated with us in the past when they believed that their interests coincided with ours. In the aftermath of 9/11, the Syrians were obliging enough to accept a Canadian citizen whom we deported, and to torture and interrogate him on our behalf. (Unfortunately, he was innocent.) Meanwhile, the Iranians helped in western Afghanistan when the U.S. and its allies overthrew the Taliban.

There is no reason to exaggerate those exceptions — or to pretend that the Iranian and Syrian regimes are anything but deplorable. Yet it is also true that those governments and the societies they control are more complex than our warmongers would tell us. Close observers of Iran, for instance, believe that our threatening attitude actually weakens the democratic forces in their struggle with the mullahs — and that improved relations would strengthen reformers.

Would negotiations with the Iranians or the Syrians today lead to any worthwhile result? Our friends and allies in the Iraqi government — whose survival we have ensured with American lives and dollars — certainly think so. The Iraqi diplomats talk with their counterparts in Damascus and Tehran every day.

Those facts won’t dissuade the neoconservatives from maligning any gestures toward realism. They continuously seek to stir hysteria about Iran and to discredit any diplomatic and political alternatives to military action.

We are still living with the terrible consequences of the last great neoconservative triumph — namely the war in Iraq — and the enhanced power that their errors have bestowed so ironically on Iran. In coping with that reality, it is long since time that we learned to ignore their bad advice.

Joe Conason writes for the New York Observer.