Fresh, hopeful look at urban design - emphasizing proven solutions; The Granite Garden: Urban Nature and Human Design, by Anne Whiston Spirn. New York: Basic Books. 300 pp. $25.95.

JUST as Rachel Carson wrote about the pollution of natural systems, so Anne Whiston Spirn writes about the pollution of our cities, and what we can and should do to correct it.

She uses the elements identified by Hippocrates - air, water, earth, and living things - to organize and present systematically the current scientific analysis of pollution data.In this way she substantiates the magnitude of the problems facing today's cities.

Spirn also outlines the kinds of action needed for solutions. She cautions that, while specific solutions are adaptable, they may not be appropriate to every region and climate.

Case studies she has gathered then show how cities experiencing problems have come up with solutions. Among them:

* How Boston's ''Emerald Necklace'' of green areas and urban wilds acts to supplement a flood-control and aquifer-recharge plan.

* How rooftop gardens and pocket parks, like New York's Paley Park, provide relief to the ''urban heat island,'' a city's most dense core of tall buildings and busy streets.

* How in Stuttgart, West Germany, problems of temperature inversions and stagnant air were corrected by tree-lined fresh-air corridors and strategically placed parks.

''The Granite Garden'' is essentially a manual for mending urban environments - a how-to guide for the present and a hope for the future. It is thoughtful, logical, statistically staggering, and, unfortunately, occasionally redundant.

It is also intentionally alarming in its description of the challenges facing cities. Yet no problem area is discussed without a proposal for a solution.

And it is poetic. Spirn describes the modern city as ''. . . an infernal machine that consumes and squanders enormous quantities of energy and materials, produces mountains of garbage, and puffs and spews out poisons.''

This can't help recalling (ironically) Sandburg's ''Chicago'' with its lines:

. . . sweating, proud to be Hog Butcher, Tool Maker,

Stacker of Wheat, Player with Railroads and Freight

Handler to the Nation.

Spirn's historical compass is impressive. She presents a synthesis of a multitude of previous writings and design applications, reaching back to Mesopotamia, Athens, and the ancient Assyrian capital of Nineveh.

Some reference tables require study and rereading of the accompanying text, but overall the graphics strengthen the book's central message.

The extensive note section provides a chapter-by-chapter list of reference materials, and the alphabetical bibliography corresponds to the subject breakdowns. This reference section is a veritable ''garden'' in itself.

''The Granite Garden: Urban Nature and Human Design'' optimistically brings home what historians and naturalists have told us before:

The choice is ours. This is a book for those who choose to help.

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