If international crisis management were run according to the laws of logic, it would be easy to see how the US and Russia could put their heads together and work out a plan to prevent civil war in Syria. Or at least it would have been easy at an earlier stage in the crisis, before Syria tipped into sectarian conflict.
Ignoring the politics - the re-election of Vladimir Putin as president of Russia and Barack Obama's focus on his election in November - it is clear that Washington and Moscow have a greater interest in working together than in falling out.
For the US, Syria is a country where it has no vital interests, beyond the need to prevent a civil war that could inflame the whole region. Its key interests at the moment are in Iran, where the focus is preventing the Islamic Republic from acquiring nuclear weapons potential, and in a smooth retreat from Afghanistan after more than a decade of war. In both these theatres, Russia is needed as an ally.
To take Afghanistan first, the southern supply route through Pakistan into this landlocked country is blocked by worsening relations with Islamabad. The only rail route through which the Americans can bring home $60 billion (Dh220billion) worth of military equipment goes through Russia. Russia is not, at the moment, going to play the role of spoiler in Afghanistan - it needs peace there as much as the US - but if there is ever going to be regional settlement it must involve the Americans and the Russians working hand in glove together.
As for Iran, it is the closest thing Russia has to a stable ally in the Middle East, after Washington and other western powers knocked out Saddam Hussein in Iraq and Muammar Qaddafi in Libya. But Russia has no interest in a nuclear-armed Iran, either, nor the regional arms race that would ensue from that development. Logically, Russia should put its weight behind efforts to bring the Iranian nuclear programme within legal norms.
Diplomacy, however, is not chess. This past week has seen a shouting match between Hillary Clinton, the US secretary of state, and Sergei Lavrov, the Russian foreign minister, after Mrs Clinton accused Russia of selling Damascus attack helicopters to massacre the Syrian people. The Russians counter that they have not sold any attack helicopters to Syria since the 1990s, and if there are any on their way to Syria, they are old machines being returned after maintenance.
The bare facts of the helicopter sale are beside the point. The key is that Russia's ally is attacking its own people from the air, which is never going to win Moscow popularity in the Middle East.
In the US, the tone of commentary has reached a fever pitch of anger and disappointment at Russia. John Bolton, the Republican firebrand who served briefly as US ambassador to the United Nations, seems keen to restart the Cold War. He is proposing to ditch the latest nuclear arms control agreement with Moscow and unleash an arms race in space to prove to Russia and China that America is not in decline.
Emotions are also high in the Kremlin, where Mr Putin has just returned after a timeout as prime minister. There is no question that one of the issues which is driving Russia is the feeling of being duped by the Americans into allowing Nato to remove Qaddafi on the basis of a humanitarian resolution at the UN Security Council. This time, Mr Putin wants a guarantee of respect.
For the Russians, Syria is a question of principle, that their wishes should never be trampled so lightly again. In Washington, by contrast, it is hard to see what the issue is. Electoral expediency - the requirement to avoid a new military entanglement - means that policy is confused. The key issue is that the voters should not get fired up about Syria, and if they do, their attention should be distracted by Russia-bashing.
It is worth exploring what Mr Putin wants. Sergei Pushkov, chairman of the international affairs committee of the State Duma, the Russian parliament, says Mr Putin has decided that Russia should be an "independent centre of power".
After 20 years of debate about Russia's role in the world, Mr Pushkov says, Russia is not going to be part of Nato, nor part of the European Union, nor will it have a military alliance with China.
"It should be a pole of attraction by itself. Russia has the clout and the economic might to be a centre of attraction for adjacent republics and quite a few other countries."
Many analysts would dismiss such ambitions: with a declining population, and the best brains in the country going abroad to Europe, Silicon Valley or Israel, Russia needs to focus on domestic concerns, and not cling on to a naval base in Syria whose purpose, beyond prestige, is uncertain.
Unless Moscow has something positive to offer, the countries that will cleave to Russia are likely to be a bunch of pariahs.
Leaving these criticisms aside, it is clear which way the wind is blowing in Moscow. While the US just seems to want the Syria crisis to go away, Mr Putin is using it as a marker for his new term.
The president may be angry, but he is not a fool. For all the talk of issues of principle, he will be looking for the right offer from Washington, one which secures for Russia its toehold in the Levant. The problem is that it is hard to see such an offer emerging from a White House hog-tied by an election campaign.
Much will depend on the meeting early next week when Mr Obama meets the Russian leader for the first time since his re-election, on the sidelines of the G20 summit in Mexico. Given the bitter war of words, it is difficult to see anything of substance emerging from this.
This meeting will be an obstacle to overcome before the logic of the relations between these two countries eventually imposes itself, though that could be a long way down the road.
On Twitter: @aphilps
