Why are Euro-zone markets so jittery — up today, crashing tomorrow? One answer of course is the European economy is weak and uncertain  – just like its political institutions.

But there is a another answer that relies upon simple mathematics.

The financial key for countries like Greece and Italy is not to repay their large sovereign debts — no one really expects that — they must simply be able to outgrow them. If the economy grows faster than the compounding debt, the burden of the debt (as measured by debt to gdp) will slowly decline and tensions ease.

Suppose, for example, that country A has current debt equal to 100% of its gdp and has to pay 3% interest on its debt. They it can slowly escape the debt burden only if its nominal growth rate is higher than 3%. I stress the nominal part because the growth can be either real production increases or inflation. There is a big difference between real and inflationary growth for the economy, of course, but in terms of debt math it doesn’t make any difference. Anything that increases the debt/gdp denominator will do.

Eurozone countries cannot influence their individual inflation rates because the European Central Bank controls the monetary levers and does not seem interested in risking higher inflation, so real growth is the only answer for them (unlike the British and Americans).

So this creates a three-factor problem: interest rates, debt levels and real growth. A country like Greece, which has a debt level more than 150% of its income according to this chart from the Economist website, must have real growth of 150+% of its sovereign debt interest rate — which is functionally impossible at today’s interest levels. Writing down the debt is the only realistic option.

Germany, on the other hand, has debt equal to 82% of gdp and faces low interest rates. Growing its way out of debt is a realistic proposition (so long as Germany doesn’t somehow inherit Greece’s debt). But if growth slows down or interest rates rise dramatically, even Germany could have a problem. This is the concern with France, which has a slightly higher debt burden but much softer growth prospects.

So where do the jitters come from? Well, there are so many possible sources of good and bad news that the markets are whip-lashed. Today’s good news on budget reforms (bringing the debt ratio down a bit) is followed by tomorrow’s bad news on growth prospects, which in turn pushes up interest rates, which makes the bad news worse.

Fasten your seat belts. We are in for a bumpy ride.