There’s an old mathematicians’ joke: an astronomer, a physicist and a mathematician are in a train going from London to Edinburgh. As they pass the border, the astronomer looks out the window and sees a solitary black sheep in a field. “Oh look,” he says, “all the sheep in Scotland are black.” “You can’t say that”, counters the physicist, “all you can say is that some sheep in Scotland are black”. “Well, to be precise,” the mathematician says, polishing his spectacles, “all you can really say is that one half of one sheep is black”.

As we have travelled around Russia, and as we write this article, we sometimes feel like that astronomer: forming our understanding of this country without the luxury of a breadth of experience. So we are consciously careful of rushing to conclusions. We have also been very fortunate to have met many fascinating people here, and much of what we recount are anecdotes and opinions given by them to us.

With the provisos out of the way, let’s begin...

The most striking image of Moscow is not the towers of St Basil’s Cathedral, or the queues around Red Square waiting to see Lenin’s Tomb; rather it is the sight of a city - and a society - moving in two divergent directions.

Moscow has seemingly every signifier of Western luxury, from high couture to fast food. They are all very well attended, but by a very small proportion of the population. The overriding impression is one of flaunted wealth, particularly by that modern Russian phenomenon, oligarchs’ wives. Dripping with jewellery, poured into Dior, they parade around the centre, taking advantage of the various exclusive restaurants and cafes available to them.

Needless to say, much of this is out of reach of not only Russia’s poor, but also of those we could describe vaguely as ‘young professionals’. With the emergence of various “cost recovery” programmes, people are having to give more of their salaries to pay for basic health care, further education and previously subsidised electricity and centralised hot water.

We were also surprised, in a wonderfully arrogant, anglophone way, at how few people spoke English. This was possibly even more true in the capital than in other, provincial cities. A few statistics seem to provide a fairly lucid answer to this: the starting salary for a teacher is around 5000 roubles (£100) per month, just over half of the average salary in Russia (9000 roubles - £180). For perspective, the rent for a small flat in Ulan Ude, one of Russia’s cheaper cities, is 4000R (£80). As our Moscow hosts pointed out, good written and spoken English is a valuable skill for many Russian businesses, with salaries to match. So those who choose to become English teachers are either extremely dedicated, or not very good at English! Away from Moscow, in Irkutsk and Ulan Ude for example, there are far fewer business opportunities and the standard of English teaching and, therefore, spoken English is noticeably better.

(Incidentally, pity the poor university lecturer who receives considerably less than this: around 2000 roubles per month - around £40. And, with most universities no longer being funded from the federal budget, but by the regional authorities, there’s a chance that many of these in rural areas will be downgraded to technical colleges.)

Elderly people are having a difficult time too, with their free public transport having been withdrawn and inflation having wiped out much of their savings. A friend of ours’ grandmother, in an entirely unchecked anecdote, had savings that would have bought her a small car; after inflation this was reduced to little more than the cost of two loaves of bread.

Perhaps this is why, as we stood in front of St Basil’s Cathedral, we saw a communist demonstration amassing in Red Square: eight or nine elderly ladies standing firm in front of Lenin’s Tomb, hammer and sickle in hand. This caused much amusement among our Muscovite hosts and most other young Russians watching. Those eight or nine ladies, though, are not alone among the older generation - there are many more people who would only dare whisper it. There are, of course, far more people - of all ages - who feel consternation and occasional dread at a certain Soviet nostalgia - highlighted by the construction of a statue of KGB founder Felix Dzerzhinsky in a small town outside Moscow - and familiar authoritarianism creeping back in.

Even the oligarchs are within the bounds of this fear: for every Abramovich, who not only runs Chelsea, but also the State of Chukor in Siberia (he’s the governor), there is a Khodorsky: the one time richest man in Russia, with an estimated $9 billion fortune. Having acquired a newspaper, Moscovskiye Novosti, and filled it with anti-Putin journalists, he found himself convicted of fraud and tax evasion - a verdict fairly universally accepted as political rather than fiscal. He’s now serving time - cutely, a year for every billion dollars accrued - in a Siberian labour camp, sewing prison uniforms for 23 roubles a day.

It could be said the oligarchs brought it upon themselves, having groomed Putin for office, only for him to return to his KGB (and later FSB) roots. The rest of the population are affected daily by the doublespeak of his “managed democracy”.

This was certainly the ‘side’ of Russia that most surprised us. So many small freedoms, granted within the lifetime of every adult here, are now being revoked. A Russian national who visits another city has to register with the police within 3 days of their arrival. If not they can, at the very least, be fined heavily, should they be found out. The chances of this are apparently much higher than one would think, particularly if you are of either a mediterranean (possible Chechyn) or asian (possible illegal immigrant) complexion.

Nearly everyone we met seemed to have a story about this, from the swarthy Frenchman detained for hours in a police cell for taking photos around Moscow,to the Buryat girl who has to walk next to a (white) Russian to avoid being stopped by every policeman in town. And then, of course there’s the media - all of the majority TV channels are government controlled, which makes things very easy for incumbent leaders.

Hopefully these things are blips on a slightly upwards trajectory. There are certainly success stories; they just aren’t as frequent as the other ones. One such story, which has the familiar gloss of the American Dream, is the story of our last meal in Ulan Ude.

In the suburb where our host, S, lives, we went for a traditional Buryat meal, buza. Buza are small, minced-meat balls (a mixture of pork and beef here, mutton further south in Mongolia), wrapped in dim-sum-like pastry and gently steamed. To eat them, you bite a small hole in the bottom and suck the liquor out of them, before wolfing them down, mopping up each last drop of sauce with a piece of bread. I’m not sure either of the last two parts are traditional, but they were so delicious, gluttony overrode courtesy.

Five years ago, the owner of the cafe was selling his homemade buza on a railway platform. Within two years, he had saved enough money from this to buy a small cafe, serving mainly bus drivers and other regular diners. Now he has a large cafe, nearly always full, and a successful restaurant upstairs. Even this though is a story of one man’s ingenuity - he didn’t receive any state backing, nor could he get any form of loan from a bank. But still, it shows that opportunities to prosper do exist; they are just hard to find.

As we move to leave Russia, I hope that this doesn’t sound negative, or convey the impression that we haven’t enjoyed our time here. Quite the opposite: it’s been a fascinating, puzzling, occasionally frustrating few weeks in a country that has constantly surprised us and confounded every expectation. This article is really just an attempt to give you a flavour of what we experienced, what we witnessed, and the partial bewilderment of a country in so many ways similar to ours and yet so different. One thing we can say categorically, the people we have met here have been extraordinary and certainly the most generous I have ever known. We can only hope that one day they get a government that does them justice.

Until then it seems, they are destined - like Gatsby - to beat on, boats against the current, borne ceaselessly back to the past.