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Analogical Reasoning Puzzles

What they tell us about analogy as a thought process.

Key points

  • Analogical questions are miniature logic puzzles that impel us to seek connections among things.
  • Analogical questions on IQ tests are based on associative thinking.
  • They reveal in microcosm how associations are forged more broadly.
  • As open-ended puzzles, they are unlike the controlled type on IQ tests, which provide answer options.

In my view, one of the most vexing of all types of questions used on IQ tests is the one that asks us to complete an analogical formula such as the following one:

Bird is to flying as human is to...

I have always been frustrated by this type of puzzle. The answer, by the way, is walking. My frustration comes from the fact that almost anything can be used to complete the logical formula, and this is why the usual IQ test offers answer options from which to choose the one that best completes the formula. This makes the whole mental exercise a controllable one, of course, but also artificial since it does not mirror the subjective variability that characterizes how we actually associate concepts in our minds.

The thought process involves associating types of locomotion according to specific species: birds fly, and humans walk (and run, of. course, after they learn to walk). This type of problem is named analogical—a term that has various meanings in different disciplines. The common element in all uses of the term seems to be a process of arguing from similarity or contrast in known respects (as the case may be) to similarity or contrast in other respects.

Such thinking, however, is hardly moot or artificial in itself. It reflects an innate penchant to seek connections or differences among things (whether or not they exist). In other words, it involves associative reasoning, which was first studied concretely by Aristotle, who identified four strategies by which associations are forged: by similarity (an orange and a lemon), difference (hot and cold), contiguity in time (sunrise and a rooster’s crow), and contiguity in space (a cup and saucer).

In the 17th century, John Locke added perception to the theory of association, claiming that it was the underlying factor that guided the associative process; that is, we tend to perceive things that are similar (or different) in shape or function in addition to being contiguous in time or space, as connected conceptually to each other. In the 19th century, the early psychologists studied experimentally how subjects made such associations, concluding that analogical thinking impels us to seek similarities or contrasts among things–that is, we tend to perceive things as either alike or unlike, with few gradations in between.

The psychologists found that factors such as intensity, inseparability, and repetition played a role in how we learn to make associations early on in life: for example, arms are associated with bodies because they are inseparable from them; rainbows are associated with rain because of repeated observations of the two as co-occurring phenomena; and so on.

Analogical-associative thinking also plays a practical role in all spheres of human life, from problem-solving to understanding scientific theories. So, those irksome IQ problems are actually meaningful in their own way, constituting examples of analogical-associative thinking in microcosm. As such, they impel us to make connections among concepts, as encoded in words, thus activating a kind of mental navigation process within us that seeks connections among concepts as formed through experience. It is likely for this reason that they are considered to be components of a general intelligence–whether verifiable or not.

To make these puzzles a little more challenging and realistic, no multiple-choice answer options will be provided for the ones presented here (as they are on IQ tests). This means that they may produce answers other than the ones below. In my view, this makes such puzzles more reflective of what associative thinking entails, which produces similar, subjectively differentiated responses to the same conceptual patterns in real life. At the turn of the 20th century, Wilhelm Wundt, an early founder of psychology, aptly put it as follows: “There exist only changing and transient ideational processes; there are no permanent ideas that return again and disappear again.”

Analogical reasoning puzzles

  1. Laughing is to cheerfulness as crying is to…
  2. Words are to literature as images are to …
  3. Pens are to paper as computer keyboards are to …
  4. Boats are to water as airplanes are to …
  5. Love is to heart as thought is to …
  6. Morning is to evening as dawn is to …
  7. France is to Europe as India is to …
  8. Rome is to Italy as Madrid is to …
  9. Picasso is to Cubism as Dalí is to …
  10. Atoms are to molecules as prime numbers are to …

[Answers below...]

Puzzle answers

  1. Sadness/unhappiness. Laughing and crying are prompted by contrasting emotional states such as happiness/cheerfulness and sadness/unhappiness, respectively.
  2. Painting/drawing/art. Words are the expressive tools used in literature, while images are the corresponding tools in painting/drawing/art.
  3. Screens/monitors. Pens are used to write something on paper, while the computer keyboard allows us to write on a screen.
  4. Air. Boats move through the water, while airplanes move through the air.
  5. Mind/intellect. Proverbially, love is said to occur in the heart, while thoughts are said, in contrast, to occur in the mind.
  6. Twilight. Dawn and twilight are the rhetorical equivalents of morning and evening.
  7. Asia. France is on the European continent, while India is on the Asian continent.
  8. Spain. Rome and Madrid are the capital cities of Italy and Spain, respectively.
  9. Surrealism. Pablo Picasso is considered the pioneer of the art style known as Cubism, and Salvador Dalí is the prominent representative of the Surrealist art style.
  10. Composite numbers. I will admit that this is a bit of a stretch, but an analogy nonetheless. The idea is that composite numbers can be decomposed into a unique set of prime factors, corresponding to the fact that molecules are made up of atoms.
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