# 18 REASONING

Machines—with their irrefutable logic, their cold preciseness of figures, their tireless, utterly exact observation, their absolute knowledge of mathematics—they could elaborate any idea, however simple its beginning, and reach the conclusion. From any three facts they even then could have built in mind all the Universe. Machines had imagination of the ideal sort. They had the ability to construct a necessary future result from a present fact. But Man had imagination of a different kind, theirs was the illogical, brilliant imagination that sees the future result vaguely, without knowing the why, nor the how, and imagination that outstrips the machine in its preciseness. Man might reach the conclusion more swiftly, but the machine always reached the conclusion eventually, and it was always the correct conclusion. By leaps and bounds man advanced. By steady, irresistible steps the machine marched forward. —John W. Campbell, Jr.

18.1 MUST MACHINES BE LOGICAL

18.2 CHAINS OF REASONING

18.3 CHAINING

18.4 LOGICAL CHAINS

18.5 STRONG ARGUMENTS

18.6 MAGNITUDE FROM MULTITUDE

18.7 WHAT IS A NUMBER

18.8 MATHEMATICS MADE HARD

18.9 ROBUSTNESS AND RECOVERY