But the notion that Mr Putin has notched up a brilliant victory is misleading. In reality, he has gambled dangerously – and he is likely to lose his bet on the use of force. The annexation of Crimea is risky enough. But an invasion of eastern Ukraine would spell disaster for Russia.

Mr Putin’s decision to grab Crimea was a desperate response to a Ukrainian revolution that the Kremlin could neither stop nor control. Rather than go down in history as a weakling who was watching ice dancing in Sochi as Russia “l(fā)ost” Ukraine, Mr Putin decided to move on Crimea. It worked. Within days, he was enjoying standing ovations in Moscow and soaring opinion poll ratings.

But by grabbing Crimea, Russia has ensured that it will eventually lose Ukraine. If Ukraine is allowed to proceed with elections in May, an anti-Moscow majority is all but assured since the Russian speakers of Crimea will no longer be voting, and the remaining electorate is likely to be radicalised by the Russian threat. The interim Ukrainian government has just signed an accord with the EU – the very development that Russia was striving to prevent in the first place. Despite the carefully engineered display of pro-Russian euphoria in Crimea, the territory’s disgruntled minorities – particularly the Tatars – may well resist incorporation into Russia.

A military move into eastern Ukraine would greatly increase the dangers of a political, military and economic blowback sufficiently powerful to threaten the leadership in the Kremlin. Western military analysts have no doubt that, in the first instance, the Russian army would swiftly overwhelm Ukrainian forces. But recent history suggests that, when the world’s leading powers resort to military intervention against a hostile local population, they almost always suffer a long-term strategic defeat. The swift conventional military victory feels great at the time – but is followed by long-term agony.

Mr Putin, who has lamented that the collapse of the Soviet Union was the greatest “geopolitical disaster of the 20th century”, should know that “disaster” was greatly accelerated by the draining effects of the Soviet war in Afghanistan. Even the mighty US – with the largest economy and the most advanced military machine in the world – was unable to win in either Iraq or Afghanistan.

The cautious, professorial leader in the White House has apparently learnt the lessons of these failed wars far better than his swaggering bare-chested rival in the Kremlin. Of course, the Russian (and American) public get a certain retro thrill from a macho leader who is willing to send in the tanks. But, in time, they end up lamenting his folly.

Why is it that military force has become so much less effective in achieving political goals? Jeremy Shapiro of the Brookings Institution, who until recently worked for the policy-planning staff at the US state department, suggests that changes in military and social technology have made it much harder for invading armies to secure a lasting victory.

Unless the population of the area that has been invaded is tiny – or almost entirely welcoming – an insurgency is likely to develop. Modern-day insurgents usually have weaponry, such as roadside bombs or rocket-propelled grenades, that can inflict steady casualties on an occupying army.

They now also have social media and mobile communications technology that make it much easier to get organised. If the insurgency also has powerful external supporters – as in Afghanistan, Syria and Iraq – it can be almost impossible to subdue.

The Russians have one “advantage” that they could deploy in trying to suppress an insurgency in Ukraine: the willingness to act with extreme brutality that was displayed during the Chechen wars. But the population of Chechnya is only a little more than 1m and the territory lies within the borders of the Russian state. Deploying “Grozny tactics” after an invasion of a sovereign nation of 45m people, on the borders of the EU, would be an entirely different matter.

For that reason, Mr Putin may prefer – for now – to use his military to nibble away at smaller targets, such as Moldova. His tactics in Ukraine could initially be restricted to economic pressure, using the leverage of Russian energy, as well as political destabilisation and bribery. Yet trying to turn its large, western neighbour into a basket case is also not a great long-term option for Russia. Even if Mr Putin is not yet set on an invasion of eastern Ukraine, economic and political warfare could unleash a series of events that would eventually lead to armed conflict.

If Russian troops do go into Ukraine, you can expect initial triumphalism in Moscow – and hand-wringing in the west. But a “show of strength” in Ukraine would ultimately gravely weaken the Russian state.