The Happy Days Ahead                           519

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GLOOM, WOE, AND DISASTER—There are increasing pathological trends in our culture that show us headed down the chute to self-destruction.  These trends do not require that we be conquered—wait a bit and we will fall into the lap of whichever power cares to occupy us.  I'll list some of these trends and illustrate (rather than prove) what I mean.  But it would be tediously depressing to pile up convincing proof—I'm not running for office.  I do have proof, on file right in this room.  I started clipping and filing by categories on trends as early as 1930 and my "youngest" file was started in 1945.
Span of time is important; the 3-legged stool of understanding is held up by history, languages, and mathematics.  Equipped with these three you can learn anything you want to learn.  But if you lack any one of them you are just another ignorant peasant with dung on your boots.
    A few years ago I was visited by an astronomer, young and quite brilliant.  He claimed to be a long-time reader of my fiction and his conversation proved it.  I was telling him about a time I needed a synergistic orbit from Earth to a 24-hour station; I told him what story it was in, he was familiar with the scene, mentioned having read the book in grammar school.
    This orbit is similar in appearance to cometary inter-planet transfer but is in fact a series of compromises in order to arrive in step with the space station; elapsed time is an unsmooth integral not to be found in Hudson's Manual but it can be solved bv the methods used on Siacci empiricals for atmosphere ballistics: numerical integration.
 

520                            EXPANDED UNIVERSE

    I'm married to a woman who knows more math, history, and languages than I do.  This should teach me humility (and sometimes does, for a few minutes).  Her brain is a great help to me professionally.  I was telling this young scientist bow we obtained yards of butcher paper, then each of us worked three days, independently, solved the problem and checked each other—then the answer disappeared into one line of one paragraph (SPACE CADET) but the effort had been worth-while as it controlled what I could do dramatically in that se-quence.
    Doctor Whoosis said, " But why didn't you just shove it through a computer?"
    I blinked at him.  Then said slowly, gently, "My dear boy—" (I don't usually call Ph.D.'s in hardcore sciences "My dear boy"—they impress me.  But this was a special case.)
    "My dear boy ... this was 1947."
    It took him some seconds to get it, then he blushed.
    Age is not an accomplishment and youth is no sin.  This young man was (is) brilliant, skilled in mathematics, had picked German and Russian for his doctorate.  At the time I met him he seemed to lack feeling for historical span ... but, if true, I suspect that it began to itch him and he made up that lack either formally or by reading.  Come to think of it, much of my own knowledge of history derives not from history courses but from history of astronomy, of war and military art, and of mathematics, as my formal history study stopped with Alexander and resumed with Prince Henry the Navigator.  But to understand the history of those three subjects, you must branch out into general history.

Continued…    Span of time—the Decline of Education