It is believed that the Romans learned by the method of trial and error, which is just another way of saying try and fail. By means of observing and analyzing unintended failures, they deduced rules of thumb.
For multiple arch bridges, one rule was to have the dimension of the spans be no more than an order of magnitude greater than the dimension of the piers between them. Although there do not appear to be any records explaining the architectural or technical purpose of the stepped rings surrounding the base of the dome of the Roman Pantheon, there should be little doubt that they were introduced to contain the concrete dome and thus prevent cracks from opening up in it.
And, as Vitruvius so explicitly explained, the Greeks learned that a stone lintel spanning more than about three column diameters was prone to crack and fall. In his book, he advised that when longer spans were desired, timber lintels should be employed.
Such stories of success and failure in ancient engineering are instructive not because we still use rules of thumb to design masonry arch bridges or stone temples. The stories are relevant to modern engineering design because they reveal in their simple contexts the way engineers accumulate knowledge and engineering advances.
Experience, both good and bad, guides us in extending the state of the art toward new limits. Those limits are seldom well defined in advance. It is the essence and adventure of engineering for us to be the pathfinders who push against and through the frontiers of knowledge and bring back news of what lay beyond and how to reach it.
As the ancients did, we find ourselves now and then designing things that do not work as intended. But the overwhelming number of engineered things large and small do work, and do so safely and reliably in service to society, advancing civilization. Engineers today may not be designing ancient monuments, but they are working in the grand tradition of those ancient engineers who did.
As seemingly distant in time, technology, and scale from those ancient structures as the integrated circuit and digital computer and other modern electronic devices may seem, they and all engineering marvels are our contemporary masterpieces of engineering design and execution. They have their origins in the same conceptualizing and synthesizing processes that the ancient engineers employed. Like our professional ancestors, todayís engineers are essential to civilization.