If nothing else, the audacious operation in which heavily armed militants killed 16 Egyptian soldiers last Sunday, before driving a stolen armoured vehicle two kilometres into Israel, has shaken the kaleidoscope through which the Sinai peninsula is viewed across its borders with Egypt, Israel and the Gaza Strip. The subsequent show of force by the Egyptian authorities against jihadist tribesmen, the surprisingly warm praise by Israel's security establishment for the Islamist President in Cairo who authorised it, and the haste with which the Hamas leadership in Gaza denounced Sunday's attack all help to illustrate the complex – and globally important – interplay of interests threatened by an increasingly violent northern Sinai.

Whatever doubts there are about the military effectiveness of Egyptian air strikes in the area on Wednesday, it is clear that Egypt's Muslim Brotherhood President, Mohamed Morsi, is trying to persuade both world and domestic opinion of his readiness to use force to impose stability in the volatile desert region. Even close analysts of Mr Morsi's evolving presidency are uncertain how far it is either he, or the military, who are calling the shots. Whether the accompanying purge of senior intelligence and other officials was an opportunist move to rid the President of officials associated with the old guard, or part of a genuine effort to recover control of the northern Sinai, or both, is also not yet clear. But it does at least suggest that Mr Morsi understands that the killing of the Egyptian soldiers, widely mourned by their compatriots, presents him with his greatest challenge since taking office less than two months ago.

If he can summon the will, ability and essential support of the Egyptian military, the new President is, paradoxically, as well placed as anyone to try to tackle the intractable security problems of the Sinai.

In Gaza, Hamas has conducted its own, sometimes bloody, struggles with the local ultra-militant groups which Egypt and Israel are blaming for last Sunday's operations. But the Gaza government has been less eager, up to now, to detain such jihadists permanently, or to stop their infiltration into Egypt through tunnels from which it derives substantial revenues. The tunnels, which have enriched a swathe of lawless Bedouin smugglers and arms dealers in the Sinai, were a response to the blockade imposed by Israel and Egypt over the past five years. And while violence has surged in the region since the fall of Hosni Mubarak last year, the seeds of tribal anarchy and extremist global jihadism were sown by the long years of social and economic neglect by the old regime.

Nor is it only Egypt's response that suggests last Sunday's bloody attack could conceivably prove a turning point. The perfunctory – and wholly unconvincing – claim from some Hamas officials that the Israeli intelligence agency was responsible only underlines the embarrassment in the movement (itself an offshoot of the Muslim Brotherhood) that Egyptian soldiers might have been killed by militants including at least some infiltrators from Gaza. Equally, Israel's willingness to allow Egypt to increase its firepower in Sinai, despite the restrictions imposed by their 1979 treaty, suggests a softening towards a new leadership in Cairo it had been quick to brand as yet another threat to Israeli security.

In fact, Israel and Egypt – for their common security – and Hamas – in the cause of fostering relations with a potentially friendlier Egyptian neighbour – have a measure of common interest here. Borders, for example, which were more open, and therefore more regulated, would serve the interests of all three. But the Middle East is not a region where logic prevails. Whether any good can come from last Sunday's attack now rests largely on the shoulders of Mr Morsi.