When Gov. Jerry Brown relaxes and talks politics the ideas whirl and burst around his head like pinwheels in a fireworks display, but when he faces the TV cameras he speaks in headlines in the style of any other politician. It must be like trying to run and walk at the same time.

For the new chairman of the Democratic Governors Association, this tension between thinking and performing styles may increase. Brown's job, by his own definition, is to focus sharply on a Democratic alternative to the Reagan economic plan and to give the governors a stronger voice in the party's verbal battle with the White House.

He is supposed to be quick, direct and hard-hitting, but his intellectual style tends to contradict such a sure-fire sniper's approach. His mind fires on all cylinders at once, and in all directions.

Floating around the National Governors Association meeting in Atlantic City this week, Brown seemed in one sense an outsider, a position he would not find strange. He was not in the back-slapping, glad-handing ranks around the bars but moved in his own sphere, encircled constantly by a flotilla of enthusiastic aides.

Yet, when the Democratic governors, that disparate group of liberals, conservatives, old-fashioned loyalists and Reagan sympathizers, made their choice, who was it who emerged? Step forward, Edmund G. Brown Jr.

At his subsequent press conference, Brown announced that one of the first decisions of the group was to demand a stronger voice in official party responses to presidential announcements and TV spectaculars, in which the chairman would doubtless play a leading role.

He then denounced the Reagan economic program in a series of brief, routine aphorisms. A specter would come to haunt the Republicans; Reagan was the successor to Coolidge, Hoover, Eisenhower and Nixon; the president was playing a shell game.

The message sounded familiar and simple enough, though perhaps uncomfortable for some governors who have given broad support to the Reagan budget strategy, but Brown's thinking is much more complicated, and probably even less palatable to his colleagues.

He begins with the assumption that history moves in cycles, that it has brought Reagan just as it brought FDR, to correct the excesses of previous administrations. He does not accept that there is a "Reagan idea" which has enough energy, enough momentum, to carry it through the next decade. The Democrats' challenge is to adapt to the changing expectations of the population -- on the reduction of "big" government, for example --but not to abandon their central beliefs about the role of government itself.

If that is enough to turn some of Brown's colleagues slightly pale, the mental whirling which accompanies it would make them dizzy.

He starts with the proposition that the government is indispensable to the creation of wealth; if wealth is knowledge, the government should be putting more cash into universities; the problem with the Reagan plan is that it will hamper wealth-creation. All this is linked, in a flash, to the growing manufacturing power of the Third World, the interventionist economic policies of leading European countries, the number of electronics engineers in Japanese universities, and a host of other factors all jostling for position in Brown's mind.

He makes connections with bewildering speed, seemingly impatient with the tedious process of building up links step by step. Sitting down to relax with him soon becomes an exhausting business, as he switches -- in a curiously humorless and abrupt way foreign to most politicians -- from theory to theory. Eventually the substance begins to emerge, and it is surpris-ingly familiar:

Government has an important role in the economic life of the nation and there are certain props -- support for public works, investment in education and training -- which cannot be removed without disastrous consequences.

It is the old Democratic politics after all.

What is different about Brown, and what has landed him with his screwball image and his failures in national campaigns, is his method. He starts, unashamedly, with abstract ideas and plays with them incessantly. There are so many flying around that it seems he could find a rationalization for almost any political act. Such a philosophical approach is -- maybe rightly -- an alarm bell to most political pros.

So the Democratic governors have taken a risk with Brown. They may have made their decision at least partly because he promised some lucrative fundraising in California, but they now find themselves under the leadership of perhaps the most unpredictable and erratic of their number. He has been called a "spacey mystic" and "Governor Moonbeam" among other things, and many regular politicians do not yet take him very seriously.

Now he has to juggle his ideas in the most cunning way of all: into a coherent policy -- particularly on economic affairs -- that can begin to unite the governors, win him a Senate seat from California next year and promise him something better nationally in 1984 than he has found in his previous presidential outings.

Uncomfortable as it might be, he has to find a way of nudging himself into the national mainstream, ideas and all.