The first is that the euro currency isn't necessarily a permanent commitment as it was intended to be when the euro's founders deliberately left no legal mechanism for a country to withdraw.
After the Group of 20 summit in Cannes last week, German Chancellor Angela Merkel and French President Nicolas Sarkozy said that if Greece were to have a referendum on the bailout deal on offer, the question would really be whether the Greeks would leave the euro.
Simply by raising the possibility of Greece withdrawing, Merkel and Sarkozy created a new reality. There is no legal route for a euro member to give up the common currency and no financial road map for how that might be achieved. The prospect is now real.
The second reality we have learned is that leaving the euro would also make it almost impossible for a country to remain legally a member of the European Union. Among the cast-iron requirements to be a member of the 27-nation EU are a commitment to the free market in labor and capital. To leave the euro, Greece would have to impose currency controls to prevent a flood of savings from leaving the country.
This is because Greece would have to replace the euro with a much-devalued drachma, its former currency. Faced with the prospect of their savings suddenly losing 20 or 40 percent in value, Greeks would hurriedly shift to banks in Germany or Austria. This would bankrupt Greek banks, so the government would have to impose currency controls and ban such transfers. Such measures are illegal under single market rules.
The third new reality we have learned is that the euro has become a club with much tighter rules. Greece has learned and Italy is learning that a country that doesn't follow Europe's new rules on austerity and budget discipline can expect no help, however hard on its population.
The new euro rules also mean that countries like Britain, which keep their own currency while being a full member of the EU, are going to find life in Europe to be much more difficult.
It is a great irony that the City of London, along with New York, is one of the world's two great financial centers. But the pound is an independent and sovereign currency. This has been an important advantage during the financial crisis of the past year since despite high levels of debt and budget deficits Britain was untouched by the sovereign debt crisis because it wasn't locked into the fixed currency of the euro. Unlike Greece, Britain could allow the pound sterling to fall and rise on world markets.
But Britain's special status, being in Europe and the single market but not in the euro, is coming under threat because of the way the eurozone countries are moving toward fiscal union in response to the crisis. The attempt to have a single currency with a common interest rate that was shared by 17 different national economies with 17 different economic policies was always going to be difficult.
The last decade has revealed the dangerous risks this involves, when low-productivity Greeks and Italians are able to borrow as if they were high-productivity Germans.
So the eurozone countries have had little choice but to agree a much tougher regime of controls on debts and budget deficits in the future. European bureaucrats are now installed in Athens and Rome to ensure that Greece and Italy follow orders in applying the austerity and reform policies the European partners demand.
The French and Germans, long jealous of London's special financial status, have for years sought to cut it down to size.
"London -- the center of financial services in Europe -- is under constant attack through Brussels directives," British Prime Minister David Cameron said last month. "It is a key national interest that we need to defend.
"And of course, all countries in Europe pursue their national interests. Would the French and the Germans like a larger share of financial services in Paris and Frankfurt? Of course they would. I want to make sure we keep them in London."
The latest threat is known as the Tobin tax, a proposal to impose an EU-wide tax on all financial transactions. Such a levee would hit London very much harder than anywhere else and probably drive a great deal of business out of Europe altogether.
"I think it's probably one of the biggest threats we've seen to the city in my career of 40-odd years," argues Stuart Fraser of the City of London Corp.
France's Michel Barnier, the European internal market commissioner, is urging new regulations that would keep trading in euro-denominated instruments inside countries that use the euro, excluding London. Britain is also worried about the new European markets infrastructure regulation, which deals with derivatives.
These reforms can be enacted in Europe by majority vote and Britain fears that the 17 eurozone countries have a built-in majority and could caucus together to undermine London's predominant role, whatever the other 10 members of the 27-nation EU might say.
"As the 27 we need to make sure that the single market is adequately looked after," Cameron insisted last month. "There are a lot of things the eurozone is doing together -- having more meetings alone, establishing machinery. It raises the question of could there be caucusing."
Britain holds one key card. Some of the reforms that euro needs will require changes in the EU treaties, where Britain does wield a veto. In return for allowing treaty changes, Britain could demand a special protocol that protects London's financial role. That is the British strategy, and it may backfire badly, isolating Britain even further. These new realities of Europe reflect how deeply, and how fast, the crisis is changing the world's largest economic bloc.