By Bridget Kendall
Diplomatic correspondent, BBC News
What does Russia want from this crisis? And how far is it prepared to go?
Cast an eye over many headlines in Europe and America and you get one answer. But look at what the mainstream Russian media is saying and it is quite a different picture.
It is not surprising. Russian statements and actions can be interpreted in various ways.
Immediately following the Georgian attack on South Ossetia's capital overnight on Thursday, it seemed Moscow felt it was occupying the moral high ground, confident it could make a legal and humanitarian argument for its incursion into what is, strictly speaking, Georgian territory.
Both Prime Minister Putin and President Medvedev insisted that Russia had the legal right to move in to protect Russian peacekeepers who had come under fire and suffered casualties
Mr Putin spoke of Russia's "historical role" to act as a "guarantor of security" in the Caucasus, which he said no-one should dispute.
And both he and Mr Medvedev repeatedly stressed that the Russian constitution required the government to protect the safety and dignity of Russian citizens, regardless of where they were situated.
All of which probably sounded reassuring if you were a South Ossetian refugee, or a Tskhinvali resident, still cowering in a cellar.
Aid agencies say there are thousands of refugees
And may also have sounded reasonable and right if you were a Russian citizen watching television at home, appalled at the scenes of carnage and destruction that showed considerable violence had been used in South Ossetia, including against civilians.
But if you were Georgian, worried about neo-colonialist Russian ambitions to undermine Georgian independence and bring it back under Russia's thumb, Moscow claiming the right to guarantee security in the Caucasus must have been downright scary.
And if you lived in other former Soviet republics with sizeable Russian populations or disputed territories - the simmering row between Ukraine and Russia over the Crimea comes to mind - then talk of troops being constitutionally obliged to cross borders to help out Russian citizens in trouble would also have sent a shiver down your spine.
But perhaps that, in part, is what the Kremlin intended.
As the days have gone on, Russia's reach has widened.
The language has shifted. The Russians are now talking about "peace enforcement".
First there were air strikes on targets elsewhere in Georgia. The Kremlin said this was an attempt to limit Georgia's ability to move reinforcements into the conflict zone.
Then there were additional Russian ground troops - thousands of them - sent not just to South Ossetia, but also into the second breakaway region of Abkhazia. Even part of the Black Sea Fleet was mobilized and a Georgian ship sunk, according to the Russians.
Again, Moscow argued that this was a preventative measure, to reassure the local Abkhaz leadership and make sure the scenario in South Ossetia could not be repeated.
But news that Russian troops had moved deep inside Georgia, well away from either enclave, made it harder for Moscow to sustain its claim that the pouring of troops and tanks across the border into Georgia against its wishes was part of a humanitarian response.
Not surprisingly, the language has shifted. The Russians are now talking about "peace enforcement".
Their brief occupation on Monday of a Georgian military base in the town of Senaki, 40km (25 miles) down the coast from Abkhazia, was explained as "eliminating the threat" of a new attack on South Ossetia.
Incursions that penetrate deep into their territory look like the start of a Russian invasion
According to Georgians, their military base there was wholly or partially demolished.
Reports of Russian attacks on the Georgian sea port of Poti and other targets may turn out to be following a similar pattern. All part of a Russian plan, according to Moscow's explanation, to disable Georgia's military ability to stage any further attacks.
But for Georgians, who have still recent and bitter memories of what it felt like to be under Russia's rule, Moscow's comments are hard to take at face value.
Incursions that penetrate deep into their territory, way beyond the disputed enclaves, look like the start of a Russian invasion - a move, if not to occupy the whole country, then maybe to split it in half and take over its main highways, or at the very least, to position a permanent Russian military presence in the two breakaway enclaves, turning into hard fact the soft annexation many observers have raised concerns about for so long.
And that opens up the question of whether Russia's humanitarian justifications were always only a pretext.
Mr Putin has said Russia is obliged to protect its citizens
Or was this operation part of a much more ambitious plan to reassert Russian control over a region Moscow has for centuries claimed as its rightful sphere of influence, and which it feared was about to be turned - by the Americans - into a Nato outpost in the Caucasus?
There has been a hint of this in some things Mr Putin has said.
There was his claim that Georgia was using its aspiration to join Nato to draw other nations into the dispute. There was his angry outburst at the Americans and others for taking sides by providing Georgian troops passage back from Iraq - in essence aiding their return to a war zone.
And there was his biting critique of what he called Western cynicism and hypocrisy, that when Saddam Hussein in Iraq carried out atrocities it was alright to invade to stop him, but if Russia intervened to stop bloodshed in the Caucasus, then it was cast as the villain.
Mr Putin, of course, is well aware that he is citing back at the West its own arguments.
In recent years the ground has shifted away from the idea that national boundaries should be respected at all costs.
Humanitarian intervention was the justification given for the Nato attack on Yugoslavia in 1999. It lay in part behind the United States and Britain's 2003 invasion of Iraq. It lies at the root of that decision which so angered Russia to grant Kosovo independent status from Serbia - against Serbia's wishes.
No-one wants a return to the dangerous tensions of the Cold War days
And only this summer a debate raged internationally about whether the outside world should overrule Burma's government and move in to help the flood victims - also an invasion on humanitarian grounds.
Mr Putin may well think that when it comes to so called humanitarian interventions, the West has now been hoisted by its own petard.
But scoring diplomatic points with such high stakes cannot come without a cost.
Russia's failure so far to contemplate a ceasefire, its insistence on pursuing further military goals and its stubborn refusal to even talk about pulling any of its troops out of the "conflict zone", has worried and infuriated both Europe and the United States, and raised the stakes in this "great game".
George W Bush may be a lame duck president with low approval ratings in a country distracted by an election campaign, but his brief statement from the Rose Garden on Monday was extraordinary, both in content and in tone.
By alleging outright that an effort might be under way to depose the Georgian president and stating bluntly that Russia had invaded a sovereign state and threatened a democratic government, he was putting the US government fair and squarely in the Georgian camp, and putting Moscow on notice that if it does not pull back, there will be consequences it might regret.
Of course, his harsh rhetoric was partly to back up European peace efforts.
Both the French president and his foreign minister are beating a path to Moscow to try to get the Russian leadership to change its mind. The OSCE is doing what it can to help. New efforts are underway at the UN to produce a ceasefire resolution that will not be blown away by a Russian veto.
And it is quite clear to everyone, including Moscow, that the West is highly unlikely to agree to use force to try to coerce Russia into new behaviour.
No-one wants a return to the dangerous tensions of the Cold War days. There are too many other security problems to tackle round the globe - in Iraq, in Afghanistan, in North Korea and Iran.
But Mr Bush roundly warned Russia that if it does not take steps to end the conflict, its relations with the US and Europe would be damaged.
This could mark a turning point in East-West relations, a moment when the beacon of post Cold War global collaboration flickered and disappeared
And possibly this might give Moscow pause for thought. How many times, after all, have Russian officials complained over recent months that their country is the victim of misunderstanding, seen through a prism of Cold war typecasting that does not recognise Russia has changed?
So possibly the Russian government might decide its escapade in Georgia has gone far enough and the time has come to bring this conflict to a close.
But there is another worrying possibility: the danger that this crisis has unfolded too far to rewind, and those in charge in Moscow may have decided that when it comes to what the United States and Europe think, they no longer care.