    4

    on

    the current.  The switch points representing your ten cities would

    flicker on and off for a few fractions of a second as the network sought

    an equilibrium.  Then, it would disgorge the answer to your problem.1

    In  essence,  the  neural  network  works  by  using  a  model  of  the

    terrain the salesman is planning to travel.  What's the advantage of this

    electronic model-making?  California Institute of Technology's John

    Hopfield showed that neural networks can solve the traveling

    salesman problem ten thousand times faster than a normal computer.

    Neural nets, like the human brain, can infer an invisible world

    from scraps of visible information.  Give the word "bat" to a neural

    network built by neuroscientist James Anderson at Brown University,

    and it'll respond with a list of the qualities of animals.  Give the

    machine the word diamond, and it will spit out geometric shapes.

    Give the two words together, and the machine will come up with

    baseball.2  In its limited way, the neural net has inferred a broad picture

    of a complex and, at the moment, invisible mini-world--the baseball

    stadium--from two tiny fragments of information.

    Humans do the same.  At this moment, thanks to the words bat

    and diamond, you can picture a runner stealing bases.  Look around

    you.  How many runners in baseball uniform do you see before your

    eyes?  Like the neural net, humans infer a picture of the world from

    two little words.

    The neural network technique does have its drawbacks. In the

    case of the traveling salesman problem, for example, Cal Tech's

    Hopfield points out that there is a bit of fuzziness about the net's

    answers.  They are only the one very best solution 50% of the time.  But

    they are close enough for all practical purposes.  Ninety percent of the

    time, the neural nets pick one of the two best answers.  That's one of

    the two best out of 181,440.  Normal computers, on the other hand,

    solve the traveling salesman problem with 100% accuracy.  But they do

    it too slowly to be of any earthly value.

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