When President Obama’s special representative to Afghanistan and Pakistan, Richard Holbrooke, was asked last month to define “success” in those countries, he said, “We’ll know it when we see it.”

That comment isn’t as flip as it seems (see below). But it illustrates the difficulties of explaining why we should get further involved in Afghanistan.

Even as President Obama considers whether to send more troops, public opinion is turning against the Afghan war because Americans can’t figure out what we are doing — or where we are headed.

So it’s not enough for Obama to say, “This is a war of necessity,” not of choice. If he truly believes this (as I do), he must spell out our strategy to the American people and explain why it’s worth the costs.

If Obama doesn’t take a firm lead, others will shape the debate and narrow his options, just as they have done with health care. And we’ll all pay the price.

The president should start by clarifying the strategic reasons we are in Afghanistan and what we are trying to achieve there. Americans grasp, as the president has said, that “we want to disrupt, dismantle, and defeat al-Qaida in Pakistan and Afghanistan and prevent their return to either country in the future.”

But many ask, logically, why fight the Afghan Taliban if al-Qaida is now based inside Pakistan? And are those jihadis in caves still a strategic threat to us?

What most Americans don’t know is that top Afghan Taliban are tightly linked with al-Qaida leaders and radical Pakistani jihadis.

Al-Qaida still gives strategic guidance and training to groups aiming to attack Europeans or Americans. But even more dangerous is the group’s avowed goal of destabilizing the Pakistani government and getting its hands on that country’s nuclear weapons — which it has threatened to use against the West. Strategic experts in Pakistan fear the jihadis could penetrate military or nuclear installations.

This puts the jihadi threat inside AfPak in a different category than that presented by Somalia and other unstable backwaters.

Our presence in Afghanistan is, in part, a holding action while we seek to stabilize Pakistan and persuade its military to focus more on fighting internal jihadis than on archenemy India. Were Afghanistan to revert to Taliban control, the blowback would be felt inside Pakistan, where terrorists would be immeasurably strengthened.

Critics say we could handle this threat by firing drones and missiles at jihadi bases from offshore and sending in special forces. Obama should explain to Americans why this idea is a pipe dream.

Targeting terrorists requires on-the-ground intelligence and cooperation. We would lose both inside Afghanistan were the Taliban to retake the country. Without good intelligence, we’d be left with the option of bomb, bomb, bomb the country — killing civilians with little prospect of achieving our objective. And if we left Afghanistan, our intelligence on targets inside Pakistan also would shrink.

Moreover, we’ve twice tried the minimalist approach to Afghanistan and it led to disaster. The first time, we got 9/11. The second time, after the 2001 overthrow of the Taliban, our neglect produced the mess we have now.

The president’s biggest challenge is to clarify why the Afghan war is not hopeless — and why it’s not analogous to the Soviet occupation there in the 1980s or to Vietnam. Polls have made clear that Afghans don’t want the Taliban back in power; they will tolerate a temporary NATO presence if it provides them with security and a better life and then hands over to Afghans.

Hand over to whom, skeptics ask? Indeed, the Afghan central government is weak and corrupt and may lack all legitimacy after disputed elections. And it will take years to build up a credible Afghan army.

To these complaints, Obama can offer two rejoinders. First, his Afghan war is just starting. As Secretary of Defense Robert M. Gates put it last week, this mission “has been under-resourced almost since its inception.” In other words, the Bush administration let Afghanistan go hang while it focused on Iraq. That is changing, and the new president deserves a chance to set things right, especially since he has a top civilian and military team in Kabul.

Second, there is a plausible U.S. strategy in place, which would focus immediate economic aid and military resources on limited geographical areas where the Taliban challenge is strongest. The goal: Try to create “ink spots” within which people can see that their lives are improving, and which can be expanded outward.

The broader strategy: Demonstrate that the U.S. commitment is firm, and shift the Afghan mood, which perceives the Taliban as winning. If Afghans believe the Taliban can be ousted, they will provide more intelligence to their own and NATO forces and may be willing to stand up to Taliban threats. If locals see they can get jobs, they may quit the Taliban payroll.

The strategy must be flexible. If national Afghan leaders are recalcitrant, U.S. commanders and diplomats can work with local and regional leaders, as they did in Iraq, until Kabul is forced to take notice. If the Afghan army grows slowly, the U.S. military may turn to tribal militias in the short term.

This brings me back to Holbrooke’s “We’ll know it when we see it.” As I saw in Iraq, once an ink-spot strategy starts to work, it opens new opportunities for progress. If midlevel Taliban leaders see the wind shift, they may choose to enter politics or business. If Pakistani military commanders see Americans making a firm commitment to South Asia, they may fight harder against their own jihadis, which will in turn help the Afghans. A lot of ifs, but you get the picture.

And you see why this complex strategy is tough for Obama to explain because it draws together so many pieces. But it is not impossible to do so. And the time to do it is now.