Geopolitics is an inexact science, but the off-the-scale responses to the events of the past few months in the Middle East should send any sensible analyst rushing to double-check their data.
How is it that a putative nuclear deal with Iran can be welcomed as a “historic” opportunity in Washington and Tehran, but as a “historic mistake” in Jerusalem and “more dangerous than 9/11” in Riyadh, in the phrase of one leading Saudi Arabian commentator?
At the very least, the breadth of variance in those responses points to the immense stresses being placed on an old geopolitical framework, while inviting the question: is the world a safer place? And will it be safer tomorrow?
Listen to the American and British governments, and the answer to both questions is an emphatic “yes”, and there is indeed an impressive-sounding list of achievements to support that assertion.
Iran’s nuclear programme is now frozen; Syria’s chemical weapons are being destroyed; al-Qaeda leadership is decimated and on the run; Somalia and Mali are reclaimed from Islamist militants; piracy attacks have been stamped out; Europe is stable; relations with China are functional; and the US economy is in recovery.
It is true that China’s fraught relationship with Japan is a cause for concern, as is the threat of “lone wolf” terrorism and the risk of asymmetric cyber-attacks, but for the average US or European citizen, the balance of the security ledger appears to be in our favour.
“Certainly, compared with the days of the Cold War, we are safer than we have ever been,” says Michael O’Hanlon, a senior fellow at the Brookings Institution think tank and the author of books on US defence and security.
“Some people are nostalgic for the certainties of that era, but they forget that we faced the real threat of annihilation. There was the Cuban Missile Crisis, war in Vietnam and a far greater number of civil conflicts. Today, crime rates are at a decades-long low. Objectively, we are safer now than we’ve ever been.”
It is a message that, importantly for Mr Obama, also resonates with the West’s war-weary publics, who have signalled clearly that they have no appetite for engagement.
Even when the evidence proved that the Assad regime had used chemical weapons — and polls showed that a hefty majority of Americans accepted this to be true — there was no stomach for a fight.
The fact that this “good news” about peace with Iran and Syria and the defeat of al-Qaeda is what the public wants to hear, doesn’t necessarily make it true, says Mike Doran, a former Bush-administration official now at the Saban Centre for Middle East Policy.
“People like peace talks, it warms their hearts and it makes them feel the world is a better place, but all we’re actually doing with these deals with Iran and Syria is strengthening our enemies,” he says. “That certainly does not make us safer.”
“The very notion of partnership and alliance with the US has suffered a huge blow as a result of this Iran deal, which is simply a capitulation. That is the greatest source of danger. We’ve lost all sense of common purpose with anyone except Iran.”
On this view, Mr Obama’s new realpolitik in the region is not a brilliant, if brutal, re-ordering of US national interests, but a recipe for instability. It might make us in the West temporarily safer, but at what cost?
The deal with Syria might have avoided air strikes, but it also undermined Mr Obama, strengthened the hand of Vladimir Putin, Russia’s president, and propped up the Assad regime, the necessity for whose demise had been the one thing on which Mr Obama had appeared certain.
As a result of the deal lauded in London and Washington, slaughter and starvation of civilians continues unremarked upon by the outside world, while jihadi groups prosper in the dark spaces left behind.
Similarly, the deal with Iran potentially clears a decade-long nuclear headache for the West and opens the doors to opportunities for European businesses, but it, too, will very likely intensify the Sunni-Shia civil war that is already gripping the region.
“The fact that Iran doesn’t want to fight with us doesn’t mean they won’t continue fighting with our traditional allies,” adds Mr Doran. “Our fight with Iran was a proxy fight all along, and we’re basically telling our allies: 'We’re done with that.’ ” But, as conservative thinkers and pro-Israeli corners of Congress sound alarm bells in Washington, the response from the administration has been unflinching: we hear you, but we don’t really care.
“That is the provocative response. 'Who cares?’ ” says Mr O’Hanlon, a Brookings defence and security expert. “Who really cares if the Saudis and the Israelis are angry? According to some measures of American national security, the policy is not to make them happy; it’s to keep the American people and our other allies safe.
“We have to distinguish between petty complaints from some of our allies, and what they can really do about it. The Saudis and the Israelis still know that we’ve got their back at some level. But this reminds them they don’t have a blank cheque when it comes to asking Washington for favours.”
After a decade of apparently fruitless war, and budget crunches at home, opinion polls show most Americans agree with Mr Obama: upsetting old allies is a price worth paying for the chance to de-fang Iran and Syria.
The risks of blowback from a newly fractious Middle East are seen as containable. The civil war in Syria and a resurgent Iran might foment the kind of lone-wolf attacks seen in London and Boston this year, but these are not existential threats.
The butchering of a soldier and the bombing of a marathon are horrific acts, but as Mr Obama argued in a major speech declaring an end to the “War on Terror” last May, they are something we just have to learn to live with.
While Israel and Saudi Arabia rage at being abandoned by America, the US by its presence in the Gulf continues to backstop Saudi and Israeli security, belying claims of a US withdrawal from the region.
In Afghanistan, the threats to US security are also being contained, with drone strikes and the kind of money and expertise that was critically absent after the Soviet withdrawal. The political brouhaha with Karzai aside, the Afghan national army showed last fighting season that it can increasingly hold its own against the Taliban.
Mr Obama is not always as determined to take a back seat as his detractors suggest. Supporters point to his sending a pair of B-52 bombers into China’s self-declared “air identification zone” last week as proof of a president that will be counted when it matters.
So, while the world focuses on the Middle East, it may turn out that the outbreak of an accidental shooting war between China and Japan — something Western diplomats in Beijing estimate to be a serious risk — is actually a far greater threat to world peace.
But the question remains whether a world where America sends out such mixed signals about its leadership will be safer in the longer term.
Those who would cast Mr Obama’s deal with Syria as a triumph for diplomacy should not forget the public muddle from which it was born — with John Kerry, the secretary of state, beating the drums of war on a Friday afternoon, and Mr Obama announcing he had changed his mind (without consulting Mr Kerry) by Saturday lunchtime.
In a perfect illustration of his confusion, Mr Obama lurched between speeches promoting American exceptionalism and the heavy responsibilities that come with being the world’s only great power, as he punted the decision to Congress to avoid meeting them.
Such was his indecision that, if the White House was a listed business, and Mr Obama its CEO, shareholders would have been justified in calling for his head.
And this was not an isolated incident. It was preceded by two years of grinding indecision over Syria, impotence in the face of Egypt’s military rulers and drift in Libya that had called into question the true value of America’s stock.
It is a commonplace of Washington conversation that George W Bush was “all leadership and no analysis” and Mr Obama “all analysis, and no leadership”. What US allies, including the British, have been advocating is something in between.
Those who want to see greater US engagement argue not for a return to Bush-era adventurism, but for a more judicious backing of “coalitions of the willing” by the US, of the kind proposed in the early days of the Syrian conflict but rejected by Mr Obama.
Ian Bremmer, the head of the Eurasia Group, one of the world’s leading risk consultancies, is among those who look at the US’s relative withdrawal from the world and does not feel reassured.
The US and Britain may be safer, but for citizens of Middle Eastern countries, or those now living in the shadow of China, the world is less safe.
“The deals in Iran and Syria might not affect Americans directly, given the strength of the American economy, but it absolutely does matter for US influence abroad,” adds Mr Bremmer. “Mr Obama speaks like an exceptionalist, but there has been little willingness from the Obama administration to say: 'The buck stops here.’ ”
The result is what Mr Bremmer calls a “G-Zero” world, where every nation must fend for itself and rely less on America — a world that, as Israel and Saudi Arabia have discovered, has been abruptly fast-forwarded by accommodations with Iran and Syria.
Economically, the globe was torn apart by the 2008 financial crisis, but it is now on the road to recovery, says Mr Bremmer, with a stabilised eurozone and the US back on a growth track. However, order is breaking down geopolitically, with consequences that are difficult to predict.
Suddenly old allies are questioning relationships that had been taken for granted — whether between Britain and Germany and the US; the US with Israel and Saudi, or smaller, south-east Asian countries such as the Philippines, Vietnam, Singapore or Malaysia, which look at Mr Obama’s treatment of his Middle Eastern allies and wonder where they might stand if US strategic priorities should change.
“In place [of the Cold War] we face a much greater risk of more significant second- and third-order conflagrations,” argues Mr Bremmer.
“It is a riskier world in which the US will do comparatively well simply because of its size. But if you’re an investor or a corporation and you ask me which world you want to invest in, a US-led world or G-Zero, the answer is clear: it’s a US-led world.”
The new American pragmatism may make us feel safer today, but it is not yet clear that it will yield a more stable and prosperous tomorrow.
Peter Foster is the Telegraph's US Editor based in Washington DC.