The Kurdish regions of Syria and Iraq are linked by a thin and fragile thread, a two-lane highway that passes camps filled with refugees from the wars ravaging these lands. The road is bisected by the Tigris, the international frontier that separates not only Syria from Iraq but also Kurds from Kurds. This was the border that first took shape one hundred years ago this week with the Sykes-Picot agreement between Britain and France—the first of a series of negotiations aimed at dividing the former Ottoman territories of the Levant between the two European powers. And while ISIS has made its hostility to the Anglo-French map well known, it is arguably the Kurds who have been most affected by the modern state system that has emerged from it.

Just how divided the more than 30 million Kurds continue to be was made clear to me this spring, when I crossed this border from Iraq to Syria. The crossing itself is not difficult: on the Iraqi side, an immigration officer of the Kurdish Regional Government in Erbil checks with her supervisors, fills out a form, and gives the green light. The whole procedure takes less than fifteen minutes. A small boat then ferries you across to Syria, where an employee of the newly-minted Autonomous Administration of the Syrian Kurdish region enters your information, and gives you a stamped piece of paper attesting to your right to enter. You are then free to drive westward to Qamishli, the first major Syrian Kurdish town. On neither side of the border can one find evidence that the sovereign governments in Baghdad and Damascus are exercising their authority here.

Easy procedures, yet complex politics. The Kurds may have thrown off central rule in Iraq and Syria but the border is still there: despite the Kurds or, perhaps more accurately, because of them. The Kurds have long talked of reuniting their people in a greater Kurdistan, but today their population is carved up between not only Syria and Iraq, but also Turkey and Iran, which have sizable numbers of their own. These different national populations have discovered over time that what sets them apart may be more significant than what they have in common: differences in dialect, tribal affiliation, leadership, ideology, historical experience. And Kurdish parties on both sides of the Syria-Iraq border are reaffirming these differences every day with remarkable bureaucratic fastidiousness. What’s more, the Kurdish parties seem to have internalized the very nation-states they scorn: in Syria, their leadership and members are almost exclusively Syrian Kurds; in Iraq, Iraqi Kurds; and in Iran, Iranian Kurds. Only the Kurdish movement in Turkey, which has pan-Kurdish ambitions, includes Kurds from neighboring states, though the top leadership is from Turkey (and some only speak Turkish).

All this is apart from the deep political divisions that exist among the respective national populations. In Iraq, for example, the Kurdish leadership has developed strong relations with Turkey, which has become a principal source of investment and trade; while in Syria, the dominant Kurdish party, the PYD, is a sworn enemy of the Turkish government through its close links with the PKK, the militant Kurdish movement in Turkey that is now at war with the government. And within both Kurdish regions, the dominant parties face strong opposition from a number of other factions.

Here is the quandary in which the Kurds find themselves when they make their claim for independence: Whose claim exactly? And how to realize it? To what territory, and under whose authority? As these questions remain unanswered, the old borders are proving stubbornly persistent—by the Kurds’ own hands.

In many ways, Syria’s Kurds today appear to be reliving what their Iraqi counterparts experienced at the end of the Gulf War in 1991: the same economic desolation; the same combination of military control and security provided by rebel Kurdish parties that are prized for their ability to maintain law and order but enjoy only lukewarm local support; the same deep relief that a hated regime no longer has much say in their affairs; in both cases, a measure of unexpected support from the US; the same upswell of hope now that they are finally achieving some autonomy; and the same nagging fear that an oppressive central government—whether the current one in Damascus or a future incarnation—will return to impose its will.

But looking across the Tigris, Syria’s Kurds regard their Iraqi compatriots’ twenty-five-year-old experiment in self-government as only a partial success. The Iraqi Kurds’ opportunity arose from serendipity: Saddam Hussein’s invasion of Kuwait and subsequent defeat there left a political vacuum, but the regime rebounded, brutally suppressing their rebellion. Then, the United States and its Gulf War allies bailed them out, establishing a safe haven. Freed of the regime, the Kurds ruled their quasi-independent enclave for twelve years. After the 2003 invasion, Washington compensated them for their loyal support by securing them a place in Baghdad and helping them consolidate their autonomy. Oil and gas exploration and trade with Turkey and Iran gave the Kurdish region’s economy an enormous lift. Looking at the troubles to their south, Kurdish leaders called themselves “the other Iraq.”

But amid this remarkable progress, there have been continuous setbacks. Between 1994 and 1998, the two main Iraqi Kurdish parties, Masoud Barzani’s Kurdistan Democratic Party (KDP) and Jalal Talabani’s Patriotic Union of Kurdistan (PUK), fought a civil war in which Barzani opened the gates of Erbil, the region’s capital, to Saddam’s forces in order to defeat Talabani. The conflict was brought to an end by US mediation in 1998, and the two parties agreed to form a unity government in 2005. This brought stability and prosperity, but also allowed the two ruling families to split up the oil bonanza between them. Economic growth came with rampant corruption, which, when oil prices plummeted a year ago, has landed the two parties in a profound crisis of legitimacy. Instead of progress, Kurds have suddenly faced drastic reductions in public-sector salaries, while their protests have been suppressed or preempted through intimidation by the KRG’s party-led security police.

Meanwhile, Barzani has clung to power as the region’s president, even though his term in office has expired (twice)—and despite his failure to institute reforms. At the same time, the prospect of true independence for Iraqi Kurdistan looks agonizingly remote. This may explain Barzani’s recent renewed call for an independence referendum: more a gambit to shore up his flagging popularity than a concrete step toward fulfillment of the Kurdish dream.

For Syria’s Kurds, the lessons of Iraqi Kurdistan are in any case far from the immediate concerns of war. Unlike its counterpart in Iraq, Syria’s Kurdish population is separated into three cantons in two non-contiguous areas in the country’s north, and continues to face a constant threat from ISIS forces nearby. Also unlike the Iraqi Kurds, they are aided by their alliance with Turkey’s militant PKK, but this has brought challenges of its own. The civil war in Syria has revitalized the PKK, allowing it to effectively seize control of Syrian Kurdish areas through its Syrian affiliate, the PYD, expanding the territory under its command. But the collapse of peace talks between Ankara and the PKK last summer has meanwhile precipitated a new violent conflict in Turkey, causing the Turkish government in turn to put more pressure on Syrian Kurdish areas. (Since the peace talks broke down, Turkey has accused the PYD of sending arms across the border to support the PKK’s insurgency.) Today, the Turkish-PKK war is causing large-scale displacement in southeastern Turkey and giving no sign of letting up. It seemed paradoxical, standing safely in Qamishli in a Syria at war, to listen to the sounds of gunfire just across the border in Turkey.

Complicating matters further, while the Iraqi and Syrian Kurdish leaderships have diametrically opposed relations with Turkey, both are now allied with the US in a joint struggle against the Islamic State—a struggle in which both Kurdish regions have proven notably effective. This has presented the Syrian Kurdish PYD with a tricky strategic choice: Should it seek to replicate the Iraqi Kurdish model of using American power as a vector for Kurdish ambitions? If it does so, it knows that Washington seems likely to limit those ambitions, providing some degree of Kurdish autonomy within a Syrian state that Washington hopes to rebuild through a peace process sponsored by the US and Russia. Or should Syria’s Kurds exploit the country’s disorder to expand the territory under their control and simultaneously escalate the war in Turkey in overall pursuit of the ultimate Kurdish goal: to gather up the four severed Kurdish parts and reconstitute them into a single “Greater Kurdistan”?

Though the motivations are very different, the long-term geographic aspirations of the Kurds are oddly similar to those of the jihadists they are fighting: both seem equally intent on erasing the old borders of the post-Ottoman order. When I drew this somewhat audacious parallel in conversation with a PYD official in northern Syria during a visit in March, there was a brief, uncomfortable silence. Then he flashed a bright smile and said: “Daesh threw the first bomb. We will reap the result.”

Syria’s Kurdish leaders are frank about their willingness to use conflict and chaos to their own advantage. The PYD’s fighting force, the YPG, having gained a sense of its value, and therefore leverage, as an indispensable ally in the fight against the Islamic State, doesn’t shy away from playing the big powers in the region—the US, Russia, Turkey, the regime of Bashar al-Assad—against each other, regardless of the cost. If Washington continues to treat the YPG as little more than a private security company, a hired hand to help it dislodge ISIS from the banks of the Euphrates, and refuses to help the YPG in its territorial ambition to unify the three Kurdish cantons (which are interspersed with Arab, Turkoman, and Christian populations), then the YPG believes it can use the prospect of a defacto alliance with Russia to get more support from the US.

Kurdish leaders say that Russian officials have told them that if the YPG tries to extend the area of northern Syria under its control all the way to the shores of the Mediterranean (where, incidentally, few if any Kurds can be found), Russia will not prevent it. This may help explain the PYD’s announcement of a federal region (under its control, and with boundaries not yet established) on the eve of the Kurdish New Year in March, a statement that lit up social media and electrified opinion throughout the dismembered Kurdish realm. Another reason for the timing of the announcement may have been the PYD’s wish to draw attention to its cause after it was excluded from the Geneva talks about Syria. Of course the announcement does not create a unified region—to unify the Kurdish areas would require a major military effort against both ISIS and Turkey, and US-backed rebels north of Aleppo. But the YPG is a disciplined and accomplished military force and, unimpeded by a major power, could make significant headway in realizing this goal.

What makes such consolidation of territory particularly dangerous is the possibility that it might draw in the Turkish military. Turkey has already warned that any move to connect the Kurdish canton of Afrin north of Aleppo with other Kurdish areas further east along Turkey’s border would be unacceptable. This is not only because it cannot countenance a large area of Syria’s border with Turkey controlled by Kurds allied with the PKK. It is also because such a move would sever the only remaining supply line to rebel groups in Aleppo that are backed by Turkey. A Turkish military counter-move against the YPG, if not done by proxy, might in turn trigger Russian airstrikes, and from that point on, given Turkey’s likely invocation of its NATO membership, further international intervention could derail efforts to wind down the Syrian war.

It need not come to this. If it does, it will be because the Obama administration, the one power that has leverage with both Turkey and the YPG, is so internally confused that it cannot accomplish either one of its strategic goals: a political transition to a post-Assad era in Syria and the defeat of the Islamic State. It is pursuit of these two aims that has seen some factions in the Obama administration pressing for greater support for Turkey-backed Syrian rebels in Aleppo and along a corridor to the Turkish border; and other factions that are championing a strengthening of the YPG as the US’s most effective auxiliary in the fight against the Islamic State, which it sees as the top US priority. The two approaches cannot be successfully pursued simultaneously.

The sensible way forward would be for the Obama administration to condition its support for the YPG on the latter’s willingness to rein in its territorial ambitions; the quid pro quo could be a promise of US support for Kurdish rights in Syria during a political transition and beyond. At the same time, the administration would need to nudge Erdoğan to return to peace talks with the PKK in exchange for US support of Turkish interests in northern Syria, including prevention of a unified PYD/YPG-run Kurdish region and an end to the YPG’s provision of weapons and other assistance to the PKK in southeastern Turkey.

Such a deal, a tall order by any reckoning, is further complicated by two issues. One is Erdoğan’s increasing authoritarianism, including, in recent months, the intimidation, censorship, and detention of journalists and other critics, and the use of the fight against the PKK to try to push through constitutional amendments in Turkey to create a presidential system. The Turkish head of state may prove difficult to dissuade from the effort to erode his country’s democratic institutions, unless either military failure in the southeast or a popular uprising against his rule provides the necessary counter-pressure. The other issue is the Turkish perception that the PKK’s resurgence is part of a larger regional competition involving Iran. According to this view, Iran has stoked Kurdish irredentist nationalism in Turkey, Iraq, and Syria (but not at home) against those Kurds who are supported by Turkey and who are willing to work within the existing state system. The area in which this struggle has unfolded most dramatically is northern Iraq.

“We are in a chess game in which we are the pieces, not the players,” observed Shaho Saeed, a philosophy teacher at the University of Sulaimani, in northern Iraq. In the past, the Kurds’ four hosts—Turkey, Iran, Iraq and Syria—used the Kurds’ geographic and ideological divisions to limit their aspirations in their own territory. Now, with Damascus preoccupied with greater threats and the government in Baghdad effectively neutralized, the Kurds have two enemies fewer to cope with, more time, and more terrain in which to lay the foundations of a future unified state. Their two other hosts, Turkey and Iran, remain strong, however, and despite their quarrel over who should rule Syria, both seek to prevent the emergence of an independent Kurdish state.

Turkey’s proven method of influencing Iraq’s Kurds is economic: it uses its weight as an economic powerhouse to offer favorable trade, investment, and business contracts to northern Iraq. In return for their pliancy, Iraqi Kurds gain an export channel for their oil through Turkey, which secures what has become their principal revenue stream. This arrangement, in place since 2008, has worked well for both sides and has survived regional upheavals, at least until now. But neither Turkey nor Iraq’s Kurdish leadership has much to offer Syria’s own Kurds, at least as long the PYD remains in charge and subordinate to the PKK.

Iran’s method is to rule by dividing: to support one Kurd against another, and Baghdad against the Kurds. The main dividing line in northern Iraq lies between pro-Barzani Kurds near the Turkish border, who speak the Kurmanji dialect, and Surani-speaking pro-Talabani Kurds in areas closer to Iran. Notwithstanding the two parties’ strategic partnership and common enmity toward the Islamic State, Iran has handily exploited the historic competition between them, and has tried to bring its own favored Kurds—the PKK in Turkey, the PYD/YPG in Syria, and Talabani’s PUK in Iraq—into a broad alliance against Barzani’s KDP. For its part, the PUK is torn between its ideological predisposition and its economic interests: “Its heart belongs to the PKK but its pocket to the KDP,” as Shaho Saeed put it memorably.

In short, the Kurdish political landscape is no less fractured than the region around it. Iraqi Kurdistan may have ended its economic dependence on Baghdad but any notion it harbors of breaking away from Iraq can never amount to more than quasi-independence—shibeh istiqlaal in Arabic—as an opposition leader put it, as long as the region, floating on a sea of corruption and adrift in economic misery, lacks the economic resources, military power, and international recognition it would need. Were Barzani to press ahead with formal statehood, the Kurds, who would be a late addition to the family of nation-states, would be living in a newly independent failed state on the model of South Sudan. Heavily indebted to the oil companies that came in search of its riches, the new entity would be choked off economically by Turkey and wracked by internal conflicts stoked by Iran.

Having been denied a state for the last one hundred years, and now facing a collapse of the old post-Ottoman states in Baghdad and Damascus, many Kurds may dream of destroying the modern borders of the Middle East to finally create one. Yet they first have to contend with ISIS, which wants not just to erase the borders but to bring down the entire Middle East as we know it. Nor have the Kurds been very effective at changing any of the borders that obstruct them. What comes next may be determined less by Kurdish dreams and schemes than by what remains of Syria once Daesh leaves, and what protections for Kurds might be wrung from that. Paradoxically, to guarantee their autonomy—and their survival—the Kurds may end up needing Sykes-Picot just as much as their old overlords did.