    41

    m

    is aware of his job, its purpose, the paycheck that won't arrive until Fri-

    day, the debate he and his wife may have when he gets home.  And he

    has to make predictions.  What pile of paperwork should he dig into if

    he wants to finish the report whose deadline will come at the end of

    the day?  How much can he afford to spend on a new suit if he plans to

    take the family to Hawaii for vacation?  What should he say to his

    spouse when he steps back into the house that night to put her in a

    good mood?  What should he avoid saying if he wants to sidestep a

    battle?

    To make predictions like these, scientists construct models of the

    real world.  For example, the 19th century German Bernhard Riemann

    painstakingly worked out a mathematical picture of an imaginary

    territory.  This curved landscape was warped in an odd way.  It arched

    invisibly into a fourth dimension.

    Riemann used mathematical equations to feel out the features of

    this void like a blind man piecing together an "image" of an unfamiliar

    space by probing with his cane.66  The diligent German ended up with

    a mathematical landscape portrait of an "n-dimensional manifold,"

    better known to its friends as "curved space."

    Einstein felt he could apply this fanciful world-view to the

    universe in which you and I live--a cosmos with the three tangible

    dimensions of height, width and depth, and one extra dimension: time.

    In Einstein's view, our universe was indeed curved, forming a

    hyper-sphere that bulged outward into a dimension we cannot see.

    From Riemann's curved world picture, the frizzy-haired

    physicist was able to predict a set of hitherto unobserved phenomena.

    When those predictions proved true, scientists adopted the Riemann

    model as an accurate portrait of much of the world invisible to them.

    That fantasy picture of an invisibly curved cosmos has been enabling

    them to make predictions ever since.67

      oment by moment to survive.  As he sits in a car slowed by traffic, he

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