Arguing by analogy is like eating soup with a fork -- messy and unnourishing. Witness the observations occasioned by the visit of Prime Minister Margaret Thatcher about the meaning of Britian's economic experience for the America of Ronald Reagan.

In fact, serious comparison between the two countries reveals mainly the enormity of the differences -- in politics, economics, place in the world and national character. Except for professional hawkers of doctrine, Britian offers no model to the United States.

Thatcher and reagan, to be sure, both come from the right wing of conservative parties. Both speak the same philosophical Jargon. Both reveal in rhetoric about tight money, smaller government, tax cuts and free enterprise. So, much as shoe salesmen talk of shoes, those in the business of selling conservative ideology talk of the thatcher-reagan connection.

But recent British experience can be arranged to teach any lesson. Thatcher has enjoyed a certain success in curbing inflation. She has brought down the annual rise in consumer prices from over 20 percent when she took office in 1979 to under 10 percent today.

The cost of that achievement, however, has been high. With a year of negative growth in 1980 and another shaping up for 1981, Britian has the most stagnant economy among the industrialized countries. Unemployment has climbed in the past year from 5.5 percent to 9.3 percent -- the highest in the developed world. Business and labor are both screaming bloody murder.

The big political difference asserts itself at that point. Thatcher governs through a disciplined Tory party that enjoys a majority in the Parliament. She is safely in office until 1984. She can afford an economic slump in the hope that a turnaround will see her past the voters on Election Day.

President Reagan commands neither a disciplined party nor a majority in Congress. Despite a landslide victory in the election last November, he will have a hard time pushing through the greater part of his economic program. Give him a jobless rate of around 10 percent plus two years of negative growth, and he would be so dead with labor and business and in Congress that he would lose control of economic policy. He would be virtually out of power.

Differences in economic structure suggest the United States will probably not have to take such stiff medicine to cure the disease of inflation. A large part of Britian's economic plant, including the nationalized steel, coal and auto industries, is grossly inefficient. A highly politicized trade-union leadership (some of it Communist) works against a Conservative government on principle. A complete social service system, including housing benefits based on local councils, keeps workers immobile in even such heavy unemployment pockets as Scotland and Wales.

The American population, as the last census shows, remains mobile beyond all expectations. American labor leaders are keen to participate in economic recovery. Despite areas of weakness (particularly in autos and steel), the American economy is basically buoyant. Indeed, it is hard to get a good recession going.

Because of that buoyancy, the American economy remains by far the largest in the world. If it has pockets (around the Great Lakes) that resemble Wales, it also has pockets (around Boston and Dallas and San Francisco) that out-Japan. In one way or another -- as a market for goods; or as a storehouse for wealth; or as a purveyor of high technology, including defense; or as a source of capital -- the rest of the world depends upon the American lefiathan. If Reagan did to the U.S. economy what Thatcher did to the British economy, he would inflict upon the other industrialized countries a synchronized recession.

Last, there is a matter easer to feel than describe -- national character. The betrothal of the Prince of Wales reminds us that Britian is a place where royals count, and lords and ladies. Homas gets paid to fortune and talent as well as to birth. Britian enjoys what Sir Lewis namier called a "democracy of respect." Civility there, the will to play by the rules, is proof againt even the invidious poisons of inflation.

A populist streak distinguishes American democracy. Rivalrous striving to get ahead fuels a ceaseless chopping and changing. We regularly eat elites for breakfast and traditions for lunch. Americans are not to maintain political civility through years of high inflation. We'll do something -- anything.

No doubt the United States has something to learn from Britian. And from Japan and Germany, France and Sinapore and other countries. But when it comes to finding solutions to basic problems, America, in the future as in the past, will have to find its own ways.