To know a society is not only to know its explicit rules. One must also know how to apply them: when to use them, when to violate them, when to turn down a choice that is offered, and when we are effectively obliged to do something but have to pretend we are doing it as a free choice. Consider the paradox, for instance, of offers-meant-to-be-refused. When I am invited to a restaurant by a rich uncle, we both know he will cover the bill, but I nonetheless have to lightly insist we share it – imagine my surprise if my uncle were simply to say: "OK, then, you pay it!"

There was a similar problem during the chaotic post-Soviet years of Yeltsin's rule in Russia. Although the legal rules were known, and were largely the same as under the Soviet Union, the complex network of implicit, unwritten rules, which sustained the entire social edifice, disintegrated. In the Soviet Union, if you wanted better hospital treatment, say, or a new apartment, if you had a complaint against the authorities, were summoned to court or wanted your child to be accepted at a top school, you knew the implicit rules. You understood whom to address or bribe, and what you could or couldn't do. After the collapse of Soviet power, one of the most frustrating aspects of daily life for ordinary people was that these unwritten rules became seriously blurred. People simply did not know how to react, how to relate to explicit legal regulations, what could be ignored, and where bribery worked. (One of the functions of organised crime was to provide a kind of ersatz legality. If you owned a small business and a customer owed you money, you turned to your mafia protector, who dealt with the problem, since the state legal system was inefficient.) The stabilisation of society under the Putin reign is largely because of the newly established transparency of these unwritten rules. Now, once again, people mostly understand the complex cobweb of social interactions.

In international politics, we have not yet reached this stage. Back in the 1990s, a silent pact regulated the relationship between the great western powers and Russia. Western states treated Russia as a great power on the condition that Russia didn't act as one. But what if the person to whom the offer-to-be-rejected is made actually accepts it? What if Russia starts to act as a great power? A situation like this is properly catastrophic, threatening the entire existing fabric of relations – as happened five years ago in Georgia. Tired of only being treated as a superpower, Russia actually acted as one.

How did it come to this? The "American century" is over, and we have entered a period in which multiple centres of global capitalism have been forming. In the US, Europe, China and maybe Latin America, too, capitalist systems have developed with specific twists: the US stands for neoliberal capitalism, Europe for what remains of the welfare state, China for authoritarian capitalism, Latin America for populist capitalism. After the attempt by the US to impose itself as the sole superpower – the universal policeman – failed, there is now the need to establish the rules of interaction between these local centres as regards their conflicting interests.

This is why our times are potentially more dangerous than they may appear. During the cold war, the rules of international behaviour were clear, guaranteed by the Mad-ness – mutually assured destruction – of the superpowers. When the Soviet Union violated these unwritten rules by invading Afghanistan, it paid dearly for this infringement. The war in Afghanistan was the beginning of its end. Today, the old and new superpowers are testing each other, trying to impose their own version of global rules, experimenting with them through proxies – which are, of course, other, small nations and states.

Karl Popper once praised the scientific testing of hypotheses, saying that, in this way, we allow our hypotheses to die instead of us. In today's testing, small nations get hurt and wounded instead of the big ones – first Georgia, now Ukraine. Although the official arguments are highly moral, revolving around human rights and freedoms, the nature of the game is clear. The events in Ukraine seem something like the crisis in Georgia, part two – the next stage of a geopolitical struggle for control in a nonregulated, multicentred world.

It is definitely time to teach the superpowers, old and new, some manners, but who will do it? Obviously, only a transnational entity can manage it – more than 200 years ago, Immanuel Kant saw the need for a transnational legal order grounded in the rise of the global society. In his project for perpetual peace, he wrote: "Since the narrower or wider community of the peoples of the earth has developed so far that a violation of rights in one place is felt throughout the world, the idea of a law of world citizenship is no high-flown or exaggerated notion."

This, however, brings us to what is arguably the "principal contradiction" of the new world order (if we may use this old Maoist term): the impossibility of creating a global political order that would correspond to the global capitalist economy.

What if, for structural reasons, and not only due to empirical limitations, there cannot be a worldwide democracy or a representative world government? What if the global market economy cannot be directly organised as a global liberal democracy with worldwide elections?

Today, in our era of globalisation, we are paying the price for this "principal contradiction." In politics, age-old fixations, and particular, substantial ethnic, religious and cultural identities, have returned with a vengeance. Our predicament today is defined by this tension: the global free circulation of commodities is accompanied by growing separations in the social sphere. Since the fall of the Berlin Wall and the rise of the global market, new walls have begun emerging everywhere, separating peoples and their cultures. Perhaps the very survival of humanity depends on resolving this tension.