BEYOND ALL THOSE dazzling dollar figures in Mayor Barry's budget proposal is a story not so much of precise mathematics as of what a new city administration thinks it can do for -- or to -- its constituents starting 12 months from now. Given the insanely complex labyrinth through which these numbers must go before any of them becomes real, their significance at this point has to do with policies and politics. As Mr. Barry noted, "This budget strikes a balance between what I want and what some people in Congress want." Somewhere in between, presumably, is what residents want -- which now becomes a determination for members of the council.

For political pizazz, the mayor has chosen to name his budget "New Directions," and not all of them are forward. Proposals to shut down clinics, close schools, cut trash collections and eliminate jobs on the police force may not strike taxpayers, employee unions, council members or congressional overseers as progress. And even though Mayor Barry is not requesting any increases in general tax rates, there will be higher real estate tax bills -- resulting from reassessments -- that won't be greeted with cheers.

Still, when citizens back away from their specific desires for city services, they should appreciate efforts to reduce the total number of desks and people at city hall, for this number isn't automatically correlated to the quality of services rendered anyway. So if nearly 1,400 regular jobs can be dropped from the city's charts by attrition (many of these positions are vacant already), why not try?

In terms of emphasis, the administration's financial focus on housing is sound: a commitment of more money to help renters buy homes and for the city to purchase and rehabilitate other housing to be rented to low-to-middle-income people. Important, too, is the effort to direct more money into finding employment opportunities for young adults, both for those who are in school and those who have dropped out; the proposal would reduce the city's role in the summer-job programs, however, which is disturbing.

How a city government's programs and policies are perceived generally still has more to do with efficiency, courtesy and assistance to citizens than with dollars. But these improvements, like the approvals of District budgets, continue to materialize much too slowly.