Egyptians marked the fortieth anniversary of their army's putative triumph over Israel by bloodying one another in Tahrir Square. Syrians, too, commemorated the date with internecine violence. Only in Israel were chests, rather than heads, beaten in collective remembrance. The contrast illustrated the curious ways history can be marshaled, forgotten, and mourned. Memory indeed serves, but ever-changing masters.

The Yom Kippur War—Arabs prefer the Ramadan War, as though it was a battle between fasts—erupted on the afternoon of October 6, 1973, when Egyptian and Syrian forces surprised and overran Israeli positions. The following three weeks of fighting was brutal, the scale monumental. Rarely in the post–World War II period have the actions of both senior and junior commanders, the mass movement of armored and artillery formations, and the maneuvering of entire armies determined the course of a conflict and its outcome. Never again—thankfully—did the Cold War combine with nuclear brinkmanship and OPEC blackmail to produce a global, nearly apocalyptic crisis. And an historical debate that rages to this day. Indeed, the moment the war concluded, the fight over its legacy commenced.

In Egypt, for example, legions of schoolchildren daily ascend to Cairo's Citadel to tour the National Military Museum and its immense 1973 pavilion. Inside a nineteenth century-style panorama, through pieces of destroyed Israeli armor and aircraft and a curious iron engine labelled "Egypt's Secret Weapon" (actually, an hydraulic pump used to dissolve Israel's defensive sand dunes), Egyptian kids learn how their country's forces erected bridges across the Suez Canal and subdued enemy bunkers along the Bar Lev Line. With flags unfurling and bayonets fixed, they banished the occupiers, erased the stain of the 1967 debacle, and reclaimed sacred Sinai for Egypt.

The rendition, if purplish, is true—but only to that point. Nowhere in the exhibit is it noted that the offensive was eventually blunted and beaten back to an enclave surrounded by Israeli forces that had spanned the Canal into Egypt. No mention is made that some 80,000 Egyptian soldiers nearly surrendered for lack of water or that Cairo came within Israel's striking range. And, of course, there's no hint that those soldiers and that city were saved by a last-minute application of American might and statecraft. Emerging from this arcade of glory, any child could rightly ask why, if Egypt had won such an unmitigated victory, did it succumb to such a humiliating peace?

The Egyptian exhibition also fails to note that at that same hour, two o'clock in the afternoon of October 6, tens of thousands of Syrian troops, spearheaded by divisions of Soviet-made tanks, punched through Israeli defenses on the Golan Heights. The reason for the omission is obvious: Egypt's need to claim that it defeated Israel's juggernaut alone. But the official Syrian version of the war similarly obscures Egypt's role just as it ignores all but the war's earliest stage. Though Syrian units swiftly succeeded in recapturing much of the Golan, they were almost as quickly stopped by numerically inferior Israeli forces and compelled to fall back on Damascus. The Syrian capital was also threatened by IDF guns which were ultimately silenced not by Arab arms but by Soviet threats and American pressure.

Perhaps because, in contrast Egypt's foothold in Sinai, no part of the Golan remained in Syrian hands at the war's end, perhaps because of the army's failure to exploit the extraordinary advantages it initially gained, celebrations of "The War of Independence," as Damascus dubbed it, were relatively muted. Still, the annual parades of long-range missiles and other offensive hardware served to highlight the Syrians' steadfastness against the Zionist entity and to perpetuate the myth of their valor.

This was the view of the war in Egypt and Syria until its recent clouding by turmoil. The Egyptian victory belonged to the military dictatorship of Anwar Sadat, predecessor of Husni Mubarak and, now, General Abdel Fattah al-Sisi. The success of an ostensibly secular nationalist regime could not fully be shared by the Muslim Brotherhood. The peace with Israel, though long reduced to mere non-belligerency, was not only injurious to Egyptian pride but theologically abhorrent to Islamists. The Syrian "independence" was claimed by Hafez al-Assad, the homicidal father of the even more murderous Bashar, both Baathists, both repugnant to the rebels. Little wonder that in both Egypt and Syria this year, October 6 was occasioned not by celebrating past battles against an external enemy but rather by the civil struggles for Egypt and Syria's future.

More paradoxically, perhaps, was the manner with which Israelis observed the forty years' mark. To be sure, each Yom Kippur yields an outpouring of public grief over the battlefield deaths of more than 2,500 Israeli soldiers—the equivalent, in current per capita terms, of 230,000 Americans—and the maiming of vastly more. The nation remained traumatized by the instantaneous transformation of the IDF from invincible machine to semi-functional family and all in a single day, Judaism's holiest. The iconic image of the Israeli paratroopers gazing dreamily before the Western Wall in 1967 collided with those of Israeli POWs in Syria and Egypt and of Prime Minister Golda Meir weeping before that same Wall.

In response to that shock, a great many Israelis either turned toward or away from religion, pivoted right to the settler movement or leftward to Peace Now. Whether perceived as the result of the failure of Israeli leaders to launch a preemptive strike or their hubristic rejection of Egypt's peace offers, Israelis uniformly view the war as a type of punishment—in the term coined by former general and president Chaim Herzog, a War of Atonement.

This year, especially, Yom Kippur was a day of national paroxysm. The "generation of Sinai," recalling the biblical Children of Israel who roamed the desert for forty years cleansing themselves of the taint of slavery, still colors modern Israeli politics and intellectual life. The media and public discourse dealt with little else than the catastrophe of 1973, with the enduring torment, self-criticism, and loss.

Yet here lies the paradox. Unlike Americans, who take pride in wars that began with surprise attacks such as those on Fort Sumter or Pearl Harbor but which concluded with brilliant victories, Israelis cannot celebrate what was arguably their most remarkable military feat. Indeed, cadets at the U.S. service academies study not the lightening success of the Six-Day War but Israel's astonishing ability to alter tactics overnight to meet new challenges—to put paratroopers in front of, rather than behind, armored units to neutralize advanced anti-tank missiles, to improvise the game-changing pincer movement across the Canal. Israelis seem unaware that the Six-Day War was also an intelligence failure—the IDF predicted that war was unlikely before 1970—and less than impressed that their soldiers' sacrifice, though agonizing, saved countless Israeli lives.

Indeed, Israel's enemies also derived lessons from the war. They saw how, while enjoying total surprise and overwhelming advantages in men and materiel, Arab armies still could not prevail, could not even avert defeat. Despairing of destroying Israel by conventional means, its adversaries turned to terror and delegitimization, which have similarly failed. Egyptian and Syrian rulers meanwhile opted for quiet, if not peaceful, borders which facilitated the beating of a great many Israeli swords into ploughshares. This, in turn, helped the Jewish State to absorb a million refuges and modernize its economy.

The memories of the Yom Kippur epic have also impacted its other protagonists. Remembering the hours-long gas lines precipitated by the Arab oil boycott, Americans have ever since striven for energy independence from the Middle East. The U.S.-Israel strategic alliance, founded in 1967 but galvanized in 1973, has remained a multi-faceted mainstay of American foreign policy. But fewer Americans are willing to pursue the type of gunboat diplomacy that proved so decisive in 1973, to preserve the Persian Gulf primacy considered precious during the Kissingerian age, or to maintain the bonds forged with Egypt's military rulers—one of America's proudest achievements of the war.

The Russians, on the other hand, are yearning to return to their role as Cold War players, as owners of a Mediterranean fleet capable of going eyeball-to-eyeball with America's. Though it signaled the end of the Soviets' Middle Eastern empire, 1973 remains the high watermark which Moscow still aspires to regain.

The ghosts of the Yom Kippur War will no doubt continue to alter their shape and meaning according to shifts in international and Middle Eastern affairs. Unchanging, though, will be the debates they spur—that and their power to haunt us.