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So, even though our stock of known theories is indeed snowballing, just as our stock of recorded facts is, that still does not necessarily make the whole structure harder to understand than it used to be. For while our specific theories are becoming more numerous and more detailed, they are continually being ‘demoted’ as the understanding they contain is taken over by deep, general theories. And those theories are becoming fewer, deeper and more general. By ‘more general’ I mean that each of them says more, about a wider range of situations, than several distinct theories did previously. By ‘deeper’ I mean that each of them explains more — embodies more understanding — than its predecessors did, combined.

Centuries ago, if you had wanted to build a large structure such as a bridge or a cathedral you would have engaged a master builder. He would have had some knowledge of what it takes to give a structure strength and stability with the least possible expense and effort. He would not have been able to express much of this knowledge in the language of mathematics and physics, as we can today. Instead, he relied mainly on a complex collection of intuitions, habits and rules of thumb, which he had learned from his apprentice-master and then perhaps amended through guesswork and long experience. Even so, these intuitions, habits and rules of thumb were in effect theories, explicit and inexplicit, and they contained real knowledge of the subjects we nowadays call engineering and architecture. It was for the knowledge in those theories that you would have hired him, pitifully inaccurate though it was compared with what we have today, and of very narrow applicability. When admiring centuries-old structures, people often forget that we see only the surviving ones. The overwhelming majority of structures built in medieval and earlier times have collapsed long ago, often soon after they were built. That was especially so for innovative structures. It was taken for granted that innovation risked catastrophe, and builders seldom deviated much from designs and techniques that had been validated by long tradition. Nowadays, in contrast, it is quite rare for any structure — even one that is unlike anything that has ever been built before — to fail because of faulty design. Anything that an ancient master builder could have built, his modern colleagues can build better and with far less human effort. They can also build structures which he could hardly have dreamt of, such as skyscrapers and space stations. They can use materials which he had never heard of, such as fibreglass or reinforced concrete, and which he could hardly have used even if he could somehow have been given them, for he had only a scanty and inaccurate understanding of how materials work.

Progress to our current state of knowledge was not achieved by accumulating more theories of the same kind as the master builder knew. Our knowledge, both explicit and inexplicit, is not only much greater than his but structurally different too. As I have said, the modern theories are fewer, more general and deeper. For each situation that the master builder faced while building something in his repertoire — say, when deciding how thick to make a load-bearing wall — he had a fairly specific intuition or rule of thumb, which, however, could give hopelessly wrong answers if applied to novel situations. Today one deduces such things from a theory that is general enough for it to be applied to walls made of any material, in all situations: on the Moon, underwater, or wherever. The reason why it is so general is that it is based on quite deep explanations of how materials and structures work. To find the proper thickness of a wall that is to be made from an unfamiliar material, one uses the same theory as for any other wall, but starts the calculation by assuming different facts — by using different numerical values for the various parameters. One has to look up those facts, such as the tensile strength and elasticity of the material, but one needs no additional understanding.

That is why, despite understanding incomparably more than an ancient master builder did, a modern architect does not require a longer or more arduous training. A typical theory in a modern student’s syllabus may be harder to understand than any of the master builder’s rules of thumb; but the modern theories are far fewer, and their explanatory power gives them other properties such as beauty, inner logic and connections with other subjects which make them easier to learn. Some of the ancient rules of thumb are now known to be erroneous, while others are known to be true, or to be good approximations to the truth, and we know why that is so. A few are still in use. But none of them is any longer the source of anyone’s understanding of what makes structures stand up.

I am not, of course, denying that specialization is occurring in many subjects in which knowledge is growing, including architecture. This is not a one-way process, for specializations often disappear too: wheels are no longer designed or made by wheelwrights, nor ploughs by ploughwrights, nor are letters written by scribes. It is nevertheless quite evident that the deepening, unifying tendency I have been describing is not the only one at work: a continual broadening is going on at the same time. That is, new ideas often do more than just supersede, simplify or unify existing ones. They also extend human understanding into areas that were previously not understood at all — or whose very existence was not guessed at. They may open up new opportunities, new problems, new specializations and even new subjects. And when that happens it may give us, at least temporarily, more to learn in order to understand it all.

The science of medicine is perhaps the most frequently cited case of increasing specialization seeming to follow inevitably from increasing knowledge, as new cures and better treatments for more diseases are discovered. But even in medicine the opposite, unifying tendency is also present, and is becoming stronger. Admittedly, many functions of the body are still poorly understood, and so are the mechanisms of many diseases. Consequently some areas of medical knowledge still consist mainly of collections of recorded facts, together with the skills and intuitions of doctors who have experience of particular diseases and particular treatments, and who pass on these skills and intuitions from one generation to the next. Much of medicine, in other words, is still in the rule-of-thumb era, and when new rules of thumb are discovered there is indeed more incentive for specialization. But as medical and biochemical research comes up with deeper explanations of disease processes (and healthy processes) in the body, understanding is also on the increase. More general concepts are replacing more specific ones as common, underlying molecular mechanisms are found for dissimilar diseases in different parts of the body. Once a disease can be understood as fitting into a general framework, the role of the specialist diminishes. Instead, physicians coming across an unfamiliar disease or a rare complication can rely increasingly on explanatory theories. They can look up such facts as are known. But then they may be able to apply a general theory to work out the required treatment, and expect it to be effective even if it has never been used before.