The Recursive Mind: The Origins of Human Language, Thought, and Civilization
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The second aspect of thought is what has been called theory of mind, the ability to understand what is going on in the minds of others.
This too is recursive. I may know not only what you are thinking, but I may also know that you know what I am thinking. As we shall see, most language, at least in the form of conversation, is utterly dependent on this capacity.
No conversation is possible unless the participants share a common mind-set. Indeed, most conversation is fairly minimal, since the thread of conversation is largely assumed. I heard a student coming out of a lecture saying to her friend, That was really cool. She assumed, probably rightly, that her friend knew exactly what that was, and what she meant by cool. That, then, is the theme of the book, but there are many excursions—into such questions as whether animals have language, whether human language evolved from manual gestures, whether all languages share common principles, why fiction is adaptive.
Given the view that human thought and language evolved gradually, I sketch the likely evolution of our distinctive characteristics over the past 6 million or so years, and not, as Chomsky would have it, over the past , years. Many people have inspired my thinking scientifically and philosophically, and of course many of them, perhaps most of them, will disagree with at least some of my conclusions.
I especially thank my wife, Barbara, for putting up with the hours I spent over the computer; at least she had her golf. My sons Tim and Paul—the latter claimed to a friend that he taught me everything I know—have often corrected me on points of psychology and philosophy. Curiously, this is usually rendered in Latin, as Cogito, ergo sum , and is translated in English as I think, therefore I am.
In making this statement, Descartes was not merely thinking, he was thinking about thinking, which led him to the conclusion that he existed. Descartes himself, though, was more prone to doubt, and expanded his dictum as Je doute, donc je pense, donc je suis — I doubt, therefore I think, therefore I am.
He thus concluded that even if he doubted, someone or something must be doing the doubting, so the very fact that he doubted proved his existence. This probably came as a relief to his friends. In this book, I examine the more general role of recursion in our mental lives, and argue that it is the primary characteristic that distinguishes the human mind from that of other animals. It underlies our ability not only to reflect upon our own minds, but also to simulate the minds of others. It allows us to travel mentally in time, inserting consciousness of the past or future into present consciousness.
Recursion is also the main ingredient distinguishing human language from all other forms of animal communication. Recursion, though, is a fairly elusive concept, often used in slightly different ways. First, then, a not-too-serious dictionary definition:. Recursion n noun.
See recursion. One problem here, of course, is that this implies an infinite loop, from which you may never escape in order to read the other stuff in this book. The following variant suggests a way out:.
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This banks on the possibility that if you do get it after a round or two, you can escape and move on. The postmodern novelist John Barth concocted what is probably both the shortest and the longest story ever written, called Frame-Tale. Then twist one end once and attach it to the other end, to form a Mobius strip. As you work your way round the strip, the story goes on forever. It was a dark and stormy night, and we said to the captain, Tell us a story! Another amusing example is provided by a competition, run by The Spectator magazine, which asked readers to state what they would most like to read on opening the morning paper.
The winning entry read as follows:. To my knowledge, no story has yet attempted to write a story of a story that writes about itself. And then there is the recurring problem of fleas, as penned by the Victorian mathematician Augustus de Morgan:. This notion of inserting progressively smaller entities into larger ones ad infinitum can also give rise to interesting visual effects, as in the examples shown in figure 2. Figure 2. Two figures showing recursive insertions of circles left and triangles right.
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The Apollonian gasket derives from Apollonius, a Greek geometer from the third century BC, who studied the problem of how to draw a circle that is tangential to three circles. Starting with three circles that are tangential to one another, one can continue the process of constructing circles tangential to all triplets ad infinitum.
The resulting figure serves as a mathematical model for foam see Mackenzie for more information. The use of recursion to create infinite sequences is also exploited by mathematics. One such sequence is the set of natural i. Thus we can generate all of the positive natural numbers by the definitions. This second definition is recursive, because N appears in the condition that needs to be satisfied for N.
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You may remember, possibly from schooldays, what factorials are. As a schoolboy I found them amusing in a childish kind of way, because they were signaled with exclamation marks; thus factorial 3, usually written 3! Clearly, this can go on forever, but we can capture the entire set by using just two defining equations:.
This second equation is recursive in that a factorial is defined in terms of a factorial. We need the first equation to kick the thing off. The next example is for rabbits, and is called the Fibonacci series, defined by the following three equations:. If you are following me, you should be able to compute the series, which goes 1, 1, 2, 3, 5, 8, 13,… What the definition says, then, is that each number in the series is the sum of the two previous ones.
The Recursive Mind: The Origins of Human Language, Thought, and Civilization
Why rabbits? Fibonacci c. For a final informal example, I take you to Kyoto, Japan, where I once happened upon a sign on a gate that was written in Kanji script. I asked what it meant, and my guide told me, I hope correctly, that it meant Post no bills. There is a paradox here in that the sign was itself a bill, thereby contravening its own presence. Perhaps there needed to be another sign that said Post no Post no bills bills. There is no end to this process, so it might have been more sensible to have allowed bills on the gate in the first place.
In practice, though, limitations of time, space, or memory will prevent a recursive sequence of structure continuing forever.
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One of the characteristics of recursion, then, is that it can takes its own output as the next input, a loop that can be extended indefinitely to create sequences or structures of unbounded length or complexity. In practice, of course, we do not get caught up in infinite loops—life is simply too short for that. For the purposes of this book, then, we shall not be interested so much in the generation of infinite sequences as in a definition that might apply usefully to human thought. A definition that meets this requirement is suggested by Steven Pinker and Ray Jackendoff, who define recursion as a procedure that calls itself, or … a constituent that contains a constituent of the same kind.
The second part of this definition is important, especially in language, because it allows that recursive constructions need not involve the embedding of the same constituents, as in the example of the gate in Kyoto, but may contain constituents of the same kind —a process sometimes known as self-similar embedding. For example, noun phrases can be built from noun phrases in recursive fashion.
Tecumseh Fitch gives the example of simple noun phrases such as the dog , the cat , the tree , the lake , and one can then create new noun phrases by placing the word beside between any pair: the dog beside the tree , the cat beside the lake. These can be extended recursively to whatever level of complexity is desired. For example we could extend the noun phrase to the dog beside the tree beside the lake , or the sentence about Jane and John to Jane who flies airplanes that exceed the sound barrier loves John, who is prone to selfdoubt.
Although it is common to provide illustrations from language, the main theme of this book is that it is in thought rather than in language that recursion originates. As Pinker and Jackendoff put it, The only reason language needs to be recursive is because its function is to express recursive thoughts. If there were not any recursive thoughts, the means of expression would not need recursion either.