How does your mind work? Would you be a better thinker if you knew? Let’s do a simple thought experiment. Suppose you were in a new building in front of a door with its knob. Now follow your mind in slow motion. From hundreds of door knobs that you have found previously in your life, you have somehow extracted the essence of “door knobs”: you know more or less how they look and how they work. The surface characteristics of this new door knob may be different from all others previously found; however your mind instantly and unconsciously makes an analogy - a mental bridge - between the new one and others stored in your memory; instantly and equally unconsciously, assigns this new object to the category “door knobs”. The essence is then somehow retrieved, and you just rotate the thing to open the door…
Surfaces and essences, analogies and categories are what this book is all about. They are the essential mechanisms of thought, intelligence, creativity, learning and expertise… all that! It is a book on Cognitive Science, but written in a witty engaging delightful way.
The main thesis of the book can be stated in a single paragraph: making analogies and constructing categories of things in our mind are just two views of the same mechanism that pervades and forms the basis of human thought. From run-of-the-mill thinking activities such as choosing what word to say next to the highest reaches of expertise and creativity, the mind unconsciously brings in analogies and categories; further, both come with blurry boundaries and in increasing levels of abstraction.
The authors defend their thesis mainly by presenting a delicious bouquet of analogies and categories as examples. To explain these examples, they also use analogies and metaphors galore, including analogies about analogies, resulting in a delightfully recursive book.
First, Hofstadter & Sanders clear the way by explaining that an analogy is not just a rhetorical device, but that we use it all the time or, more strongly, we think through analogies. It is simply recognizing a stimulus that comes to us and comparing it (making an analogy) with previous similar stimulus stored in our memory, just as we saw with the example of the door knob. The stimulus may come through our senses or our imagination.
For a contrasting example, the last chapter is dedicated in part to the extraordinarily creative analogies made by Albert Einstein, that enabled him to make his astonishing discoveries. Furthermore, the authors make clear that this analogical thought came to Einstein’s mind before his formidable mathematical formalizations.
Between these extreme examples, the book presents a gamut of frequent situations that provoke our mind to use analogies and categories starting with single words! For example, a word-concept such as “dog” is a category that denotes thousands of these four-legged animals. But the surprise here is that non-noun words such as verbs ("to open" can be used to open doors, corpses, books, online folders…), and adverbs such as “much” and others also bring to mind categories and analogies. Phrases like "that’s much too little for him and too much for me"; "how much will that be?"; "much obliged" spring to mind when we recognize the category of a “much situation”. That’s a mental comparison between one situation and another, and of course that mental comparison is an analogy: a bridge between two mental structures.
Single words that initially denote a single entity, such as the "moon", mutate over time to become categories. Galileo spoke of “the moons of jupiter”. We now speak of the moons of other planets in or out of our galaxy.
Some trademarks equally evolve to become categories, such as Kleenex and Googling.
The boundaries of categories are always blurry and continuously expand during the development of a child. Initially “mommy” is a single person, but later the kid learns that "Fido is the mother of this puppy”, “The queen bee is the mother of the bee-hive”, and even of “Mother Nature” as the mother of all things alive... Children routinely use creative analogies: "I undressed the banana", says a little girl; "Mommy, the rain has been turned off!" and so on. Adults too constantly expand categories: The legs of a table; the spine of a book; a head of lettuce… let us go and have a coffee even if one person may order tea. All categories are then used when making an analogy between a new stimulus and members of the category.
The authors also consider compound words (dog dish), idioms that also denote a multitude of situations (To roll one’s sleeves up) as well as proverbs (The early bird catches the worm), and fables (“The Fox and the Grapes” by Aesop reduced to the category sour grapes, denoting things that one once craved deeply but failed to obtain and then disparages).
There are many examples of “invisible analogies” (or categories…) that we construct and use spontaneously, such as "items to save if ones’ house burns down", "items to pack for a picnic" and so on; and we have no trouble imagining for instance "activities typical of camping trip"s or "people whom one might have married".
Next, consider the ubiquitous “me too” situations: someone describes something that happened to him of her and we interrupt and say “A similar thing happened to me…” and on it goes our description of an analogous situation. How do we encode these experiences in memory so that later on we instantly recognize some essence of the experience and launch into explaining a similar one? Do we store that essence initially and subsequently enrich it; or the essence is actually built in real time when needed? It is a great mystery, since the same anecdote can be used as a “me too” in different contexts.
The same item may belong to thousands of categories depending on context or point of view. The authors make this as clear as clear water (an analogy…) by presenting the story of “a drinking glass”: it is born as a product, and goes on to become an item for sale, a discounted item, a sold item, a water-container, an insect-holder, occasionally a wine-holder, a broken item, a recyclable object and dozens other categories… Our mind easily and transparently re-assigns categories; extends the boundaries of categories ("desk" has evolved to become also virtual desk; a "wave" once upon a time could only be found in liquids and now we have electromagnetic and even gravitational waves); and makes increasingly abstract categories, such as going from a particular four-legged entity that barks next door to the categories bulldog, dog, mammal, animal, live-being and so on.
Analogies firmly entrenched into memory also act as filters of reality, distorting it. They come to mind uninvited, spontaneously, and sometimes manipulate our mind without us realizing it. Some of them are quite innocent, such as inevitably thinking of September 11 when hearing the news about the small plane crashing against a building on October 11, 2006. There are other more serious, when an analogy comes to mind that misleads us or takes us in the wrong direction. Take for instance calling one's life partner with the name of one's lover because of some hidden similarity... Actually, people are more convinced by their previous concepts, analogies and categories than from barrages of scientific facts, such as can be seen by the recent diatribes against climate science or the theory of evolution.
We are thus "prisoners of the known", yet "only the known can free us from the unknown", and can therefore also be conscious of, extend, change and invent analogies. Sometimes we spontaneously create metaphors just for fun or to make a point or to explain something to ourselves or others. The authors call these "caricature analogies". But analogies are also made for more serious purposes - for instance when going to a job interview, we inevitably make analogies to previous work interviews and our experiences in them; or when going out with a new date, our experiences with previous persons may color our perception. And analogies are the bread and butter of sophisticated human translators, who are thoroughly familiar with the concepts, idioms, turns of phrase and analogies usually used in two cultures.
An analogy may start its life as a naive analogy. A certain pain may be assigned to the category stomach ache, which is not wrong but too general for accurate diagnosis. Hofstadter and Sanders show that the arithmetic operation of division usually associated at school with the concept of sharing (say ten marbles to be shared among five kids and many other instances of the category...) gets children into trouble when the result of the division is greater than the quotient, as it happens when dividing by a number smaller than one. Division as sharing thus is an example of a naive category that does not help, but rather hinders further comprehension; the kids then need to acquire another way of looking at the category, Division as using the dividend to measure the divisor.
So as that example shows, are analogies also at the root of the most formal of sciences, e.g. Mathematics? Indeed they are! The authors show that analogies are also at the origin of more complex math concepts such as groups, rings, fields... These are other examples showing that sometimes we are the bosses, and analogies the slaves of our creativity.
The authors also reflect on the nature of intelligence, expertise, learning and creativity. They say that the essence of intelligence is the ability to instantly find precise, interesting, creative analogies. This is what makes "homo sapiens, sapiens". Analogies help us understand our own experiences and others’.
An expert is “simply” a person that has a vast store of carefully organized and detailed categories at multiple levels of abstraction. Making an analogy to previous situations encountered enables the expert to pinpoint problems and find solutions to them.
Creativity is often stated as synonymous to "thinking out of the box", which is a useless advice if one doesn't know the limits of one's boxes. An example presented in the book is the creative act of pushing a wine bottle's cork in rather than taking it out when there is no corkscrew on sight. This depends on abstracting the category "ways of taking a cork out" to "ways of accessing the wine".
Hofstadter & Sanders criticize school systems and curricula for not taking seriously the role of analogy in learning. Children learn through making analogies to previous mental structures built in and out of school. Nothing can be learnt in abstract form independently of everything else. Initial naive analogies persist in memory even after mathematical formalizations have been taught.
The last chapter is dedicated to creative analogies that have been used in math and physics. Particularly fascinating is a trip through Einstein's mind, showing the incredible ability that the famous scientist had for pinpointing the right analogy from which he then derived his world-famous discoveries. Even more than a math and physics genius, he was an analogizer extraordinaire, in the words of the authors.
You’ll have great fun with Hofstadter & Sanders’ writing style as they defend their thesis that analogies and categories, surfaces and essences are at the root of the way our mind works. Enjoy the examples of everyday and scientific situations as you watch the workings of your mind in slow-motion. This experience will make you a better thinker!