No one wants to learn by mistakes, but we cannot learn enough from successes to go beyond the state of the art. ... The engineer always believes he is trying something without error, but the truth of the matter is that each new structure can be a new trial. ... Such is the nature not only of science and engineering, but of all human endeavors.

A scientific hypothesis is tested by comparing its conclusions with the reality of the world as it is. Yet, no matter how many examples of agreement one may collect, they do not prove the truth of the hypothesis, for it may be argued that one has not tested it in the single case where the theory may fail to agree with reality. On the other hand, just one instance of disagreement between the hypothesis and reality is sufficient to make the hypothesis incontrovertibly false.

Thus sometimes mistakes occur. Then it is failure analysis—the discipline that seeks to reassemble the whole into something greater than the sum of its broken parts—that provides the engineer with caveats for future designs. Ironically, structural failure and not success improves the safety of later generations of a design.

Other recognized masters often express the thought that they abandon a work rather than complete it. What they mean is that they come to realize that for all their drafts and revisions, a manuscript will never be perfect, and they must simply decide when they have caught all its major flaws and when it is as close to perfect as they can make it without working beyond reasonable limits.

Even the pyramids in the land of the Sphinx, whose riddle reminds us that we all must crawl before we walk and that we will not walk forever, have been eroded by the sand and the wind. Nothing on this earth is inviolate on the scale of geological time, and nothing we create will last at full strength forever. Steel corrodes and diamonds can be split.

“Brittle fracture,” in which a large crack runs spontaneously through a structure near the speed of sound, severing steel with a report that signals the breakup of ships, the bursting of pressure vessels, or the collapse of bridges, has been a chronic problem for centuries. There is almost always a period of “gestation”—the slow lengthening and sharpening of cracks through the process of fatigue that precedes the catastrophe.