Beirut: Things don't gel. Walk past a TV anywhere in the world these days and chances are there's an image of missiles exploding in Kobane, on the Syria-Turkey border. You'd be forgiven for thinking US President Barack Obama is up there, teaching those jihadis the meaning of military superiority.

But a comment by Anthony Cordesman, of the Centre for Strategic and International Studies, when we discussed a different aspect of this war last week, stuck in my mind.

"The sortie numbers are very small – this is almost token levels of force," he said from his  Washington base.

It turns out that the doctor is right. Compare sorties flown in the 2003 invasion of Iraq and today's war on the so-called Islamic State in Syria and Iraq, and the current crisis might be destined to be a footnote in military history – save for its enormous humanitarian cost; its damage to American credibility in the region; and its still uncalibrated potential to ignite a full-blown regional war.

The US-led Operation Iraqi Freedom lasted for 26 days, during which more than 41,000 sorties were flown.

Wisely, perhaps, this campaign has not been given such a name.

But already it is bigger and bolder – lasting almost three times as long and forecasted to have years more to run; and is being conducted in two countries.

However the sortie numbers are pitiable by comparison – "over 1700" to date, the Pentagon says, which computes to less that 5 per cent of the 2003 invasion effort; or a bit more than 1 per cent if spread over the extra time in the current conflict.

Military types will offer reasons for why the two operations are different. But in one glaring aspect they are the same – that is, as projections of American power. And on this count the operation has failed; revealing instead, the limits of American power.

The first air strikes on IS targets in or near Kobane were on September 27. And analysis of the Pentagon's daily reports for the period in which the battle for the city, as opposed to the surrounding districts, has been fought, October 1 to October 12, reveals all of 39 attacks.

That's an average of just three hits a day as a story of unbearable tragedy and heroic resistance unfolded on the ground – mass torture, rape, mutilation; hundreds of villages captured; 200,000-plus refugees on the move; more than 500 dead; and under-armed  and under-resourced Kurdish fighters struggling to hold out against impossible odds, as one of the United Nations' more revered crisis manager, Staffan de Mistura, who now serves as the UN's Syria envoy, told reporters: "You remember Srebrenica?"

Alluding to the 1995 slaughter of thousands of Muslims by Bosnian Serb forces, he went on: "We do. We never forgot. And probably we never forgive ourselves for that."

Kobane's proximity to the Turkish border means the TV cameras of the world are recording it all, at which point we have a train wreck as the humanitarian dimension of the Kobane story collides with the medalled and braided  sensibilities of military planners and their civilian masters, who find themselves so hog-tied by the constraints of conflicting coalition agendas that it all revives the wondrous claim by the American officer in Vietnam: "It became necessary to destroy the town to save it."

And as the cameras pan to take in dozens of Turkish tanks, positioned on the border to stop Turkish Kurds lunging over the frontier to go to the aid of the Kurds in Kobane, there's good reason to figure that some viewers are gagging on the cynicism of it all.

Given the aura of American and allied technological advantage, the detail of the strikes in and around Kobane become quite pedestrian. Given reports on Islamic State's massive looting of Iraqi and Syrian military stores - and those in Iraq were chock-full of US-supplied armaments and vehicles - the tally at Kobane puts only a slight dent in the jihadis' inventory.

Likewise, there's no body count, but even if counted in the hundreds, it would leave IS with as many as 30,000 fighters and, reportedly, with recruitment surging.

The Pentagon reports detail about 60 targets and the outcome of the strikes – but the language is confusing. In most cases the unambiguous "destroyed" is used; but in more that a dozen cases, the non-specific "struck" or "damaged" are used. Words like "large" and "small" are used – but not defined.

Here's the detail: 

• Artillery positions – 3 destroyed
• Fighting positions – 3 destroyed; 1 struck
• Large IS units – 1 destroyed; 2 struck
• Small IS units – 1 destroyed; 5 struck

Buildings

• Command/control centres – 1 destroyed; 1 damaged
• Occupied barracks – 8 destroyed; 1 damages
• Training facilities – 2 destroyed
• Unspecified buildings – 2 destroyed
• Staging areas – 2 destroyed
• Supply depots – 2 destroyed
• Checkpoints – 1 destroyed

Vehicles

• Tanks – 2 damaged
• Trucks – 3 destroyed
• Unspecified vehicles – 7 destroyed; 1 damaged
• Armed vehicles – 10 destroyed

So there seems to be a calculation at the Pentagon – they have virtually written off Kobane, but they can't be seen to be doing nothing. Unanswered, is why have they written it off?

Their operational planning can't have predicted precisely this element of the crisis. But surely there was an understanding that the conflict would take surprise turns, requiring a change of gears and performance lest the whole gang – Obama, Tony Abbott, Julie Bishop et al – be seen to be callous … and maybe out of their depth.

Pentagon spokesman Rear Admiral John Kirby was upfront, telling reporters last Wednesday: "Air strikes alone are not going to do this; they're not going to fix this – they're not going to save the town of Kobane.

"We've been saying that over and over again. And yet we continue to get questions of, well, 'why aren't you doing more?' and 'how come they're not more effective?'"

On Sunday, his boss and Chairman of the Joint Chiefs of Staff, Army General Martin Dempsey, pretty well pushed Kobane into the grave – "I am fearful that Kobane will fall", throwing in that "no doubt" IS would inflict horrific atrocities on the thousands still in Kobane.

All this, according to a Pentagon news report on what Dempsey had to say on one of the Sunday TV talk shows, would happen despite those three air strikes a day – which the Pentagon news report describes as "continuous".

Dempsey got to talking about security at the US Embassy and at the international airport in Baghdad, adding: "This is a case where you're not going to wait till they're climbing over the walls."

So why did they wait at Kobane, and why are they still waiting?

Lest the Turks or the Pentagon be seen to carry the burden of lamely explaining why nothing was happening, US Secretary of State John Kerry joined in: "As horrific as it is to watch in real time what is happening in Kobane, you have to stand back and understand the strategic objective –notwithstanding the crisis in Kobane, the original targets of our efforts have been [Islamic State's] command and control centres, the infrastructure ..."

If IS gets away with the capture of Kobane after such a pitiable display of military power by the US and its allies, there will be grave implications on two fronts.

First, IS will have been given a textbook lesson in how to humiliate the West and to undermine all that Obama's coalition says it stands for, by launching a similar assault on another hapless Syrian town – and again to have the world watch the slaughter as the  Turks, or some other member of the alliance, sit on their hands, watching through binoculars; and the Pentagon sends a few aircraft which will do little to curb IS.

Second, the Sunni communities of Syria and Iraq will watch all of this and shake their heads in wonder, reluctantly conceding that IS will have its way, so why oppose the jihadists? Why fight for the ones who say they are the good guys, when their performance is not all that good?