Free Surfaces and Essences: Analogy as the Fuel and Fire of Thinking by Douglas Hofstadter, Emmanuel Sander

just seconds after the doors had been closed, and no matter what you said, they wouldn’t let you board.
    Our daily talk is filled with this kind of meeting of concrete and abstract, but we are unaware of it most of the time. Thus if a professor says, “Only a handful of students dropped in on me in my office yesterday”, we aren’t likely to envision students tumbling out of a giant hand in the sky and landing in the professor’s office. And if someone says, “There hasn’t been any snow to speak of today”, we don’t feel inclined to protest, “What do you mean? You just spoke of it!” The concreteness of the words and phrases that we constantly use to formulate our thoughts on all sorts of topics is at one and the same time a sign of the great concreteness of our way of thinking and also a sign of our extraordinary propensity to carry out abstraction, allowing us to cast a situation using words that would seem, on their surface, to refer to totally unrelated things.
    Thus a Japanese stockbroker, commenting on the unstoppable collapse of the stock market, said, “One should never try to catch a falling knife.” Most people understand this image effortlessly, as well as its relevance to the circumstances. And yet if there is a falling knife here, it’s certainly not a knife in its most ordinary sense, and the way this “knife” is falling is invisible, comparatively slow, and not spatially localized. It took a considerable act of abstraction for that individual to use that phrase in that context — but that’s nowhere close to the end of the story, for the same phrase might just as easily be applied to a politician in the throes of a corruption scandal and whose once-ardent supporters are suddenly nowhere to be seen, or to a skyscraper on fire that it would be folly to enter, or to someone so deeply depressed that even their best friends are caught up in the atmosphere of bleak pessimism, or to someone who has fallen overboard in astorm so violent that no one dares to go to their aid, or to an approaching hurricane that has destroyed a nearby town and from which everyone has been ordered to evacuate immediately, or perhaps, who knows, even to a person who was injured in their kitchen because they tried (of all things) to catch a falling knife. In short, we see that here we are dealing with a full-fledged category, rich and multifaceted.
    As soon as one starts thinking about situations to which the phrase “One should never try to catch a falling knife” could apply, they start to pop up from under nearly every stone in sight. At least for a while, one has the impression that one could paint a large fraction of the world in terms of that phrase alone, since the world is rife with huge, irrepressible forces against which one has no power and which would carry one off to one’s doom if one were so rash as to try to stop them. Thus we will find this image jumping to our mind willy-nilly, imposing itself on us whether we like it or not, and unless we can somehow stop thinking altogether, we will simply have to let this aggressive metaphor have its way with us until it has had its fill; after all, one shouldn’t try to catch a falling knife.
Synopsis of This Book
    In the chapters that follow, we don’t aim to speak about the brain at a biological level, but about cognition as a psychological phenomenon. We will not speculate about the cerebral or neural processes that underlie the psychological processes we describe, because our goal is not to explain cognition in terms of its biological substrate but to present an unconventional viewpoint concerning what thought itself is. Our discussion will thus take place at this rather abstract level, but even at that level there will be plenty of grist for the mill.
    The book’s first three chapters constitute our attempt to provide an account of what categories and analogies are. Chapter 1 focuses on categories associated with single words, and it also puts forth some