Engineering had long ago come to an end.

Engineering is possible under one condition of the equation: Total available Calories divided by Population equals Artistic-Technological Style. When the ratio Calories-to-Population is large—say, five thousand or more, five thousand daily calories for every living person—then the Artistic-Technological Style is big. People carve Mount Rushmore; they build great foundries; they manufacture enormous automobiles to carry one housewife half a mile for the purchase of one lipstick.

Life is coarse and rich where C:P is large. At the other extreme, where C:P is too small, life does not exist at all. It has starved out.

Experimentally, add little increments to C:P and it will be some time before the right-hand side of the equation becomes significant. But at last, in the 1,000 to 1,500 calorie range, Artistic-Technological Style firmly appears in self-perpetuating form. C:P in that range produces the small arts, the appreciations, the peaceful arrangements of necessities into subtle relationships of traditionally agreed-upon virtue.

Think of Japan, locked into its Shogunate prison, with a hungry population scrabbling food out of mountainsides and beauty out of arrangements of lichens. The small, inexpensive sub-sub-arts are characteristic of the 1,000 to 1,500 calorie range.

And this was the range of Earth, the world of ten billion men, when the planet was stolen by its new binary.

Some few persons inexpensively studied the study of science with pencil and renewable paper, but the last research accelerator had long since been shut down. The juice from its hydro-power dam was needed to supply meager light to a million homes and to cook the pablum for two million brand-new babies.

In those days, one dedicated Byzantine wrote the definitive encyclopedia of engineering (though he was no engineer). Its four hundred and twenty tiny volumes examined exhaustively the engineering feats of ancient Greece and Egypt, the Wall of Shih-Hwang Ti, the Gothic builders, Brunel who changed the face of England, the Roeblings of Brooklyn, Groves of the Pentagon, Duggan of the Shelter System (before C:P dropped to the point where war became vanishingly implausible), Levern of Operation Up. But the encyclopedist could not use a slide rule without thinking, faltering, jotting down his decimals.

And then ... the magnitudes grew less.

Under the tectonic and climatic battering of the great abduction of Earth from its primary, under the sine-wave advances to and retreats from the equator of the ice sheath, as the small successor Suns waxed, waned, died and were replaced, the ratio C:P remained stable. C had diminished enormously; so had P. As the calories to support life grew scarce, so the consuming mouths of mankind grew less in number.