An Anthropology of Puzzles

The Role of Puzzles in the Origins and Evolution of Mind and Culture

Marcel Danesi

• Publisher: Routledge
• Year: 2020
• ISBN:
  9781000182323
• Edition: 1
• Topic: Sciences sociales
• Subtopic: Anthropologie

An Anthropology of Puzzles argues that the human brain is a "puzzling organ" which allows humans to literally solve their own problems of existence through puzzle format. Noting the presence of puzzles everywhere in everyday life, Marcel Danesi looks at puzzles in society since the dawn of history, showing how their presence has guided large sections of human history, from discoveries in mathematics to disquisitions in philosophy. Danesi examines the cognitive processes that are involved in puzzle making and solving, and connects them to the actual physical manifestations of classic puzzles. Building on a concept of puzzles as based on Jungian archetypes, such as the river crossing image, the path metaphor, and the journey, Danesi suggests this could be one way to understand the public fascination with puzzles. As well as drawing on underlying mental archetypes, the act of solving puzzles also provides an outlet to move beyond biological evolution, and Danesi shows that puzzles could be the product of the same basic neural mechanism that produces language and culture. Finally, Danesi explores how understanding puzzles can be a new way of understanding our human culture.

1
Puzzles in Mind and History

A good puzzle, it’s a fair thing. Nobody is lying. It’s very clear, and the problem depends just on you.

Ernö Rubik (b. 1944)

One of the oldest riddles of recorded history is the Riddle of the Sphinx. In one widely told version, the Sphinx was a mammoth creature, half human, half animal, who had enslaved the city of Thebes, stopping all those who dared enter or leave it. The Sphinx posed a riddle to all foolish visitors as a mortal challenge. Those who were incapable of answering it paid for their ineptitude with their lives at the hands of the monster. However, if someone were ever able to come up with the seemingly intractable, yet simple, answer, the Sphinx vowed to destroy itself:

What creature ambles on four at dawn, two at midday, and three at twilight?

According to legend, it was Oedipus who solved the riddle by answering “man,” who is the only creature on earth who crawls on all fours in infancy (the dawn of life), walks upright on two legs as a grown-up (the midday of life), and ends up walking on three, with the help of a walking stick, in old age (the twilight of life). Upon hearing the correct answer, the Sphinx jumped from its perch to a rock outside the city, becoming a lifeless statue. For ridding them of this terrible beast, the Thebans made Oedipus their king.

Why is this riddle so fascinating, still holding appeal millennia later? For one thing, it is an ingenious formulation of something that might otherwise escape attention—the phases of human life are like the phases of a day, implying that we cannot escape our mortal destiny in the same ineluctable way that the twilight inevitably comes. The riddle is a story within a story. The main one is the Oedipus legend, which recounts a self-fulfilling prophecy. Oedipus had been left to die on a mountain by his father Laius, who had been warned by an oracle that he would be killed by his own son. The infant Oedipus was saved by a shepherd. After growing up, and learning about his origins, the young Oedipus traveled to Thebes in search of the truth. After solving the Sphinx’s riddle, the Thebans made him the successor to their murdered king, who, unbeknownst to Oedipus, was his father. As the new king, Oedipus married Laius’s widow, Jocasta. Several years later, a plague struck the city. An oracle announced that the scourge would come to an end only after Laius’s murderer had been driven from Thebes. Oedipus investigated the murder and soon realized that Laius was the man he had killed on the road to Thebes. To his horror, he also discovered that Laius was his father and Jocasta his mother. Grief-stricken and desperate, Oedipus blinded himself, and Jocasta hanged herself. Oedipus was banished from Thebes, dying in unendurable woe at Colonus. The subtext in this legend is a significant one for the purposes of this book—riddles may be warnings about the realities of the human condition.

Various versions of the Sphinx’s riddle exist. The one above is paraphrased from the play Oedipus Rex by Sophocles. Whatever its version, it is evidence that, since the dawn of history, people have devised riddles to understand themselves and the world around them. These might therefore reveal how sentient reflective thought emerged in our species, constituting miniature models of how we grasp things. This chapter provides an overview of the origin, history, and connection of puzzles to human thought and culture. The purpose is to argue in an initial way that puzzles arise from a deep-seated need to ask questions about existence. They do so in their own miniature way, constituting small-scale versions of the larger-scale questions of philosophy and science.

Riddles, puzzles, and games

There is no historical era or culture without riddles. They constitute a universal speech art that cuts across all languages. This is perhaps why riddles lose almost nothing in translation, tapping into common themes of human concern, from mortality to the meanings of things. The topic of riddles will be explored in more detail in the next chapter. Suffice it to say here that we continue to cherish and appreciate them, no matter who created them or when they were devised. Like works of visual art, they never lose their aura, being passed on from generation to generation intact.

The English word puzzle, as used today, encompasses everything from riddles and crosswords to Sudoku, optical illusions, and brainteasers in logic and mathematics. The word was coined near the end of the sixteenth century, and applied a little later to describe the jigsaw puzzle. As a generic categorical term, puzzle is a convenient one for classifying diverse enigmatological artifacts as singular psychological and anthropological phenomena.

Labeling some ancient riddle or puzzle, therefore, is a retrospective form of reference. The concept of problem came out of ancient geometry, where it was used to refer to a proposition in which some shape or figure had to be constructed. From this, the word was extended to cover any mathematical question that required a specific kind of answer and a strategy to do so. Many of the ancient mathematical problems were actually puzzles, as we would name them today. The main difference is that the intent of a problem is to produce a specific and recognizable answer; the intent of a puzzle, on the other hand, is to hide the answer, presenting information that appears to be incomplete in some way. Both problems and puzzles are Q & A (Question and Answer) structures. So, the difference between the two can be shown diagrammatically as follows:

• Problem
• Q → A (the question leads directly to an answer)

• Puzzle
• Q → (A) (the answer to the question is not immediately obvious)

Riddles have the same structure and it is for this reason that they can be called puzzles, even though there are some key differences between riddles and other puzzle inventions (as will be discussed in the next chapter). As the Oedipus story indicates, riddles were often connected to ominous destiny, unlike problems in geometry. But riddles also had a recreational social function. The Biblical kings Solomon and Hiram, for example, organized riddle contests simply for the pleasure of outwitting each other. The Greeks included riddles at banquets, as we might do today at social gatherings, for entertainment reasons. The Romans made riddles a central feature of the Saturnalia, a feast that they celebrated over the winter solstice. So, riddles were conceived both as part of portentous myth, used by the Greek oracles to cast fortunes, and as part of recreation. This dual function extended throughout the medieval and Renaissance periods. Only by the eighteenth century, did they lose their divinatory value, becoming mainly forms of mind-play, included as regular features by newspapers and periodicals. It was then that famous personages started creating riddles as part of an ever-expanding leisure culture and as part of a new literary genre. Benjamin Franklin, for example, composed riddles under the pen name of Richard Saunders for inclusion in his Poor Richard’s Almanack (first published in 1732). The puzzle section was a factor in the almanac’s unexpected success. In France, no less a literary figure than the satirist Voltaire would regularly compose riddles for pure enjoyment and to challenge or taunt his friends and enemies.

The Greeks saw riddles as manifestations of mythos—a form of thinking based on beliefs rather than on logical argumentation. They used the term lógos to describe the latter. Socrates believed that lógos was innate in all human beings, teaching that everyone had full knowledge of truth within them, and that this a priori knowledge could be accessed through conscious reflection. In the Meno, a Socratic dialogue written by Plato (2006, originally c. 380 BCE), Socrates leads an untutored slave to grasp a complicated geometrical problem by getting him to reflect upon the truths hidden within him through a series of questions designed to elicit specific answers. From this Q & A mode of dialogue, the concept of dialectic investigation crystallized, as the art of investigating and discussing the truth of ideas. The notion of mythos can be rephrased as “imagination” and lógos as “reasoning.” As will be argued throughout this book, puzzles involve both modes of thought, to different and varying degrees. If we are given the circumference of a circle and asked to determine its radius, it is easy to figure it out if we know the formula C (circumference) = πr² (with r = radius). This is a simple problem based on using previous knowledge applied directly to a given situation—the solver can thus take a shortcut to lógos. Now, by contrast, consider the following, which at first glance would seem to suggest a similar kind of problem that can be solved just as directly. It was devised by Martin Gardner (1994: 14) and is shown in Figure 1.1.

Figure 1.1 Gardner’s diagonal puzzle.

Given the dimensions of the radius OD (6 + 4 = 10), can you calculate the length of the diagonal AB in rectangle AOBC?

As it turns out, it is impossible to solve it in an analogously straightforward fashion. So, let’s consider what is known about circles and rectangles from a different perspective. As a hunch, let’s use the information that the diagonals of a rectangle are equal to each other in length. This suggests drawing the other diagonal (OC) of the rectangle AOBC (Figure 1.2).

Figure 1.2 Solution to Gardner’s diagonal puzzle.

By doing this, we can now see that diagonal OC is also a radius of the circle. We know that radii are equal from an established theorem. Line OBD is a radius and is equal to 10 (6 + 4), as shown. Since line OC is also a radius it is thus equal to 10. From this we conclude that the other diagonal, AB, is also equal to 10. The solution now appears almost magically, rather than routinely—hence the use of the expression “Aha” to characterize the effect a solution such as this one might have on us. The solution thus starts out as imaginative thinking (playing a hunch) and then ends with reasoning (carrying through on this hunch). It shows, in other words, a flow from mythos to lógos, not a separation of the two.

Most puzzles, are characterized by this flow, to varying degrees, of course. It is relevant to note here that imaginative thinking of this kind originates in the right hemisphere of the brain (the dreaming hemisphere)—a fact that is especially useful in contemplating the possible relation of puzzles to human consciousness. Solving a puzzle is very much like a dream where the parts cohere spontaneously into wholes by themselves. There is some archeological evidence that the difference between waking (consciousness) and dreaming (unconsciousness) states in antiquity was often blurred (Jaynes 1976). Ideas were believed to come in dreams (the unconscious mind), and they likely still do, as well-known episodes from mathematics strongly suggest. The famous Indian mathematician, Srinivasa Ramanujan, claimed that his family goddess would come to him in his dreams and present him with complex mathematical equations, providing crucial insights that allowed him to complete his efforts. Similarly, Henri Poincaré (1902) observed that, typically, it was only after a period of sleep marked by dreaming that his imagination developed the relevant insights into the intractable mathematical conundrums that he tried to crack. As these anecdotes suggest, indirectly, consciousness is to reasoning what unconsciousness is to imagination. The solution to Gardner’s puzzle involved a blend of the two. Through a hunch, we were able to envision a solution that lay “hidden behind the curtain,” to use a phrase employed by Poincaré. At that point, reasoning took over, allowing us to complete the solution.

As another case-in-point, consider the well-known Nine-Dot Puzzle in Figure 1.3.

Figure 1.3 The Nine-Dot Puzzle.

Without your pencil leaving the paper, can you draw four straight lines through the following nine dots?

Those unfamiliar with this puzzle tend to tackle it by joining up the dots as if they were located on the perimeter (boundary) of an imaginary square or flattened box (Figure 1.4).

Figure 1.4 An incorrect solution to the Nine-Dot Puzzle.

But this reading of the puzzle does not yield a solution, no matter how many times one tries to draw four straight lines without lifting the pencil. A dot is always “left over.” At this point, a...