672 ON METHODOLOGY $19.3 A colleague with whom I used to attend software engineering conferences once swore that he would walk out the next time he heard an automotive comparison("if programs were like cars...").Had he kept the pledge,he would not have attended many talks. Are metaphors good or bad?They can be very good,or very bad,depending on the purposes for which they are used. Scientists use metaphors to guide their research;many have reported how they rely [Hadamard 1945] on concrete,visual images to explore the most abstract concepts.The great mathematician Hadamard,for example,describes the vivid images-clouds,red balls colliding,"a kind of ribbon,which is thicker or darker at the place corresponding to the possibly important terms"of a mathematical series-to which he and his peers have resorted to solve difficult problems in the most abstract realms of analysis and algebra. Metaphors can be excellent teaching tools.The great scientist-expositors-the Einsteins,Feynmans,Sagans-are peerless in conveying difficult ideas by appealing to analogies with concepts from everyday's experience.This is the best. But the worst also exists.If we start taking metaphors at their face value,and deducing properties of the domain under study from properties of the metaphor,we are in serious trouble.A pseudo-syllogism ("Proof by analogy")of the form A resembles B B has property p Ergo:A has property p is usually fallacious because the conclusion(4 has property p)is precise whereas the first Swifi,Gulliver's premise resembles B)is not.What matters is how exactly 4 is like B,and,even more, Travels,Part.3,“A how 4 is unlike B;clearly some properties of B must be different from those of Voyage to Laputa, etc.",chapter 5. otherwise 4 and B would be the same thing (as in those stories by Borges or Perec in which a novel or painting is about itself,or in the language that the academicians of Laputa in Gulliver's Travels devised from the observation that "since words are only names for things,it would be more convenient for all men to carry about them such things as were necessary to express the particular business they are to discourse on").A metaphor is defined by what differs as much as by what is common.But then to justify the conclusion we have to check that p only involves the common part.Once Hadamard had intuited his result,he knew he had to prove it step by step using the austere rites of mathematics,and many a student of a Feynman or Laurent Schwartz has realized,when faced with the week's homework,that brilliant images are only the beginning of the process. The more alluring the metaphor,the greater the danger of falling into twisted reasoning of the above form.Think for example of the analogy so commonly used in the reusability literature,this book included,between software components and the"chips"of our hardware colleagues,through such terms as "software IC"(coined and trademarked by Brad Cox).Up to where do we use the metaphor to help us gain insights,and where do we start confusing the real thing 4 with the metaphor B? Bachelard's fascinating book on the Formation ofthe Scientific Mind,which shows [Bachelard 1960] some of the best minds of the eighteenth century struggling with the transition from magical modes of reasoning to the scientific method,tells a story that anyone who is ever tempted to use a metaphor in scientific discourse should keep in mind.In trying to672 ON METHODOLOGY §19.3 A colleague with whom I used to attend software engineering conferences once swore that he would walk out the next time he heard an automotive comparison (“if programs were like cars…”). Had he kept the pledge, he would not have attended many talks. Are metaphors good or bad? They can be very good, or very bad, depending on the purposes for which they are used. Scientists use metaphors to guide their research; many have reported how they rely on concrete, visual images to explore the most abstract concepts. The great mathematician Hadamard, for example, describes the vivid images — clouds, red balls colliding, “a kind of ribbon, which is thicker or darker at the place corresponding to the possibly important terms” of a mathematical series — to which he and his peers have resorted to solve difficult problems in the most abstract realms of analysis and algebra. Metaphors can be excellent teaching tools. The great scientist-expositors — the Einsteins, Feynmans, Sagans — are peerless in conveying difficult ideas by appealing to analogies with concepts from everyday’s experience. This is the best. But the worst also exists. If we start taking metaphors at their face value, and deducing properties of the domain under study from properties of the metaphor, we are in serious trouble. A pseudo-syllogism (“Proof by analogy”) of the form A resembles B B has property p Ergo: A has property p is usually fallacious because the conclusion (A has property p) is precise whereas the first premise (A resembles B) is not. What matters is how exactly A is like B, and, even more, how A is unlike B; clearly some properties of B must be different from those of A, otherwise A and B would be the same thing (as in those stories by Borges or Pérec in which a novel or painting is about itself, or in the language that the academicians of Laputa in Gulliver’s Travels devised from the observation that “since words are only names for things, it would be more convenient for all men to carry about them such things as were necessary to express the particular business they are to discourse on”). A metaphor is defined by what differs as much as by what is common. But then to justify the conclusion we have to check that p only involves the common part. Once Hadamard had intuited his result, he knew he had to prove it step by step using the austere rites of mathematics; and many a student of a Feynman or Laurent Schwartz has realized, when faced with the week’s homework, that brilliant images are only the beginning of the process. The more alluring the metaphor, the greater the danger of falling into twisted reasoning of the above form. Think for example of the analogy so commonly used in the reusability literature, this book included, between software components and the “chips” of our hardware colleagues, through such terms as “software IC” (coined and trademarked by Brad Cox). Up to where do we use the metaphor to help us gain insights, and where do we start confusing the real thing A with the metaphor B? Bachelard’s fascinating book on the Formation of the Scientific Mind, which shows some of the best minds of the eighteenth century struggling with the transition from magical modes of reasoning to the scientific method, tells a story that anyone who is ever tempted to use a metaphor in scientific discourse should keep in mind. In trying to [Hadamard 1945]. Swift, Gulliver’s Travels, Part 3, “A Voyage to Laputa, etc.”, chapter 5. [Bachelard 1960]