Thinking About Analogy

Douglas Hofsatdter’s first book, Godel, Escher, Bach, had a profound influence on me while I was at university. First published in 1979, I don’t remember when I first read the book. but have since re-read more than once (and it’s not a short book!).

In the book, Hofstadter explores common themes in the lives and works of Kurt Godel (logician), M.C.Escher (artist) and Johann Sebastian Bach (musician), drawing out concepts fundamental to mathematics, symmetry, intelligence and philosophy of mind. Specifically, Hofstadter discusses how self-reference and formal rules allow systems to develop meanings which ’emerge’ from the system however meaningless the individual elements of that system. That is, the book describes how thinking emerges from the mechanics of neurons firing, creating a unified sense of self, in the same way that a colony of ants self-organises to produce social behaviours which ’emerge’ from the acts of individual ants.

More recently, in I Am A Strange Loop, Douglas Hofstadter explored reflexivity and feedback loops in the brain, describing consciousness as “the dance of symbols in the brain”. He elaborates on the analogy of the brain and mind working at different levels and, importantly, the dance is composed of symbols (not neuronal activity) although neuronal activity is ultimately responsible for the dance (at another level of description).

Analogy is a mental process of transferring information or meaning from one domain (the source) to another domain (the target). Analogy is also used to describe the relation between the source and the target (ie a similarity). Many (if not most) early cultures make an analogy between the Sun and God. Similarly, many scientists use analogy to build conceptual models, as when Niels Bohr used an analogy with the solar system to describe his model of the atom.

In his most recent book, Surfaces and Essences written with Emmanuel Sander, Douglas Hofstadter returns to some of the same themes to write perhaps his magnum opus on the role of analogy in thinking. The authors argue that analogy has a central role in all our thought, and is the key to human intelligence. They demonstrate that none of us can think for more than an instant without using a wide range of analogies, from everyday conversation through to the most important scientific discoveries.

Most importantly of all, the central thread of the book is that analogy and categories (concepts) are universal and key to understanding thinking. This is because analogy and categorisation are the same fundamental process – deciding how and why things are similar or different.

Language allows us to draw distinctions between meanings, and every language does this in its own unique way. The result of this is that the conceptual distinctions of one language, may be considered artificial, pointless, bizarre, stupid or incomprehensible in another language. For example, the verb “to play” is a common word in English, with a variety of uses, so that it makes perfect sense to say, “Edmond plays basketball and soccer” (a natural sentence in English, despite the differences between throwing a ball into a hoop and kicking a ball into a net.

However, another example which also makes sense in English, might be, “Sylvia plays tennis, Monopoly and violin”. The sentence makes perfect sense in English, but makes no sense in many other languages as the activities of making music, buying imaginary houses and hitting a ball are very different. Therefore an Italian would say, “Sylvia gioca al tennis a Monopoly, e suona il violino”. For them, it would be unthinkable to play a musical instrument (it might be interpreted as playing catch with a Stradivarius). English and French speakers naturally categorise violin-playing with soccer-playing and basketball-playing, while Italian speakers would consider this to be very strange. Chinese speakers would consider it equally strange, and would also want to use a number of different verbs for playing musical instruments, depending on whether the instrument is pulled, blown, plucked, pushed or banged.

Each language is rich in labels of categories that help us to ‘carve up’ the world into useful chunks. From our own point of view, the way we carve up the world seems natural and sensible, but the ‘right’ way to see the world is contingent on how where we grew up and which language we speak.

Consider another example, this time of the difference between English and Indonesian (Bahasa). The English words “brother” and “sister” seem to describe family relationships in a sensible and useful way (to an Englishman). In Indonesia, the words “kakak” and “adik” describe the same family relations, but they divide siblings up by age rather than gender. “Kakak” means elder sibling and “adik” means younger sibling, which seems the natural way to divide up the world to Indonesians. Indonesians don’t feel the need to say “sister” in a single word, just as the English don’t feel the need to say “older sibling” in a single word (we can say older brother or sister which is effectively the same thing). So in order to describe an older sister or a female older sibling, English and Indonesian speakers need a phrase rather a single word.[The French have words for both ways of slicing the world, although “frère” and “soeur” are the more common.]

Proverbs show how we like to use language to make analogies across different situations. In English, we say “Once bitten, twice shy”, while Romanians say, “Someone who gets burned by eating will blow even on yoghurt”, Afghans, “Someone bitten by a snake fears even a rope”, and Chinese “Bitten by a snake, frightened by tiny lizards”. I’m sure you can spot the analogy between all the phrases …

Thus analogy is central to all our thought and each mental category comes from a long series of analogies that help us to link objects, actions and situations, even when they are distant from each other. Thinking this way (in analogies and stories) helps us to make sense of new situations through a rich set of categories that we continuously develop and extend. However, the word “analogy” is rarely used in conversation, giving the misleading impression that they are relatively uncommon when in reality they occur every moment of every day.

Moreover, categories are highly flexible. For example, is the retired Concorde plane sitting on a pedestal at the Charles de Gaulle airport in the category of airplane, Concorde, statue, ex-Concorde, symbol, work of art or all of these categories? While we all desire to have everything fit a single true identity, but in reality identity is a moving target depending on what perspective we see things from (ie it changes with context). If we think of a sandwich as A-B-A or as bread-meat-bread, then jelly and peanut butter are members of the category “meat” (as is “jelly and peanut butter” sometimes)., and three people can also make a “sandwich”.

Our senses play a huge role in the way that we understand and interpret the world, the analogies we make and the language we use, and most obviously vision with the analogy between understanding and seeing an everyday occurrence – phrases such as crystal clear, enlightening, brilliant, luminous, blindly, perspective, shadow, look at, viewpoint, insight. appear, blurry, glance, clear, murky, opaque and more come directly from our experience of vision. Our language is always colourful.

But our other senses often clarify our understanding too:

  • touched by a gesture, struck by a beautiful picture, hurt by a jabbing remark
  • taste the joy of victory, find a behaviour tasteless. be in a sour mood, make a bitter remark
  • hear from a friend, think something sounds crazy, wear a loud shirt, find someone a crashing bore
  • see things in a new light, watch the trends, feel that things look ominous
  • smell a rat, think a plan stinks, dislike someone sniffing around your partner

Our physiological senses are embodiments of out psychological senses (and vice versa) and the idea of embodiment is increasingly important in cognitive psychology and neuroscience – that is the idea that our concepts and thinking depend on our bodies. The interaction between our bodies and our environment is the basis of all our thought. All our thinking is anchored in past experience, through analogy, and in our current experience, through our body. We think through the medium of mental concepts, built up, stored and retrieved through a lifetime of experience and the manipulation of those experiences through analogy.

The frame blends, conceptual blends and hybrid mental structures discussed in other works of linguistic philosophy and, embodied cognition and cognitive psychology are all at heart analogies of one kind or another, or mental manipulations based on analogies. Hofstadter and Sander also argue that mental arithmetic and number manipulations are also based on analogies (of sharing or measuring) where the same calculation can be made more difficult or easy by using one analogy rather than another. Arithmetic problems are easier to solve when we can mentally simulate the solution, rather than resorting to more formal arithmetical calculation (and that this holds both before and after children have learnt the formal mathematical operations). This leads to surprising results, with many division problems easier to solve than subtraction problems (which are learnt earlier and should be easier) purely because they are easy to make an analogy to a real world situation.

Finally, they discuss why analogies are generally consider very different from categories, which is based on a simple analogy (surprise, surprise), one they call naive, that categories are “boxes” and to categorise is to place things into discrete boxes, a task considered very different to that of analogy. This implies that categorisation is much more mechanical and rule based, whereas analogy making is somewhat more creative, even speculative, and much less rule-bound. But this is wrong, as categorisation is just as subjective as analogy making, and can be uncertain, blurry or even downright wrong. Categories can be just as abstract, implicit and context-dependent as analogies.

This is demonstrated by the stories behind many of the great scientific discoveries. Albert Einsten famously said that “Imagination is more important than knowledge” and the stories behind some of his greatest discoveries, especially in his miraculous year of five ground breaking papers in 1905, demonstrate how much he relied on thinking in analogies (such as riding on a beam of light) in order to “imagine” the mathematics behind the way world looks and behaves. The Special Theory of Relativity is really nothing more than a reframing of a category (extending an existing theory into a new domain, by analogy, and then imagining what the implications might be).

Friedrich Nietzsche defined intelligence as “a moving army of metaphors” and similarly Henri Poincare described mathematics as “the art of giving the same name to different things”. Both of them knew that creativity is all about discovering new ways of categorising the same things. Originality is all about finding categorisations that are unexpected, new or surprising. If I say “mathematics is a cult” or “mathematics is a language” or “mathematics is a tool” or “mathematics is a mess” or “mathematics is a game” or “mathematics is a passion” or “mathematics is an art” or …. well any of an infinite number of possibilities, then I am finding new (some newer than others) and interesting ways to categorise the world.

To go back to one of my first examples, an atom is most definitely not a universe (nor is the solar system an atom), yet the comparison helps create new understanding, helping us to build richer conceptualisations of the world around us.

Whenever we decide to make an analogy of one thing with another thing we are creating a new way to see the world and frame our understanding. Likewise, whenever we find a way to put an idea into a new “box” (category) we are also finding a new way to see the world and (re)frame our vast range of life experiences into a broader and stronger mental model of the world around us. Despite the differences in the thinking of Eastern and Western cultures, seeing categories and distinctions (the emphasis in the West) is ultimately the same as seeing relationships (analogies) between different things.

Analogy and category are the fundamental structure of thought.


Louder Than Words by Benjamin Bergen

The Way We Think by Fauconnier & Turner

Godel, Escher, Bach: An Eternal Golden Braid by Douglas Hofstadter

I Am A Strange Loop by Douglas Hofstadter

Surfaces and Essences: Analogy as the Fuel and Fire of Thinking by Hofstadter & Sander

Metaphors We Live By by Lakoff & Johnson

Philosophy in the Flesh by Lakoff & Johnson

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4 thoughts on “Thinking About Analogy

  1. Patrick McGee

    Thank you. You have, from your thinking and writing, given me a verification of a concept I use in my training program, a good smack in the head to think more about analogy, and just a good read.

  2. Holger E. Metzger

    Good and well-researched article, Neil! Hofstadter’s I am in a strange loop is a great read. You may also want to add Lakoff’s “Don’t think of an Elephant” to the list (a less academic version of his metaphor frame debate in political – and marketing – spheres…:)). In our work, metaphor and analogy are key to understanding consumers and then talking back to them in creative communication – to re-activate the “dance” of patterns and symbols in the mind…

    1. Neil Gains


      Thanks – I enjoyed reading “Don’t think of an elephant” too. I can recommend “Surfaces and Essences” which is long and detailed, although written in a non-academic style and packed full of examples. You just need to read small chunks at a time, but it is very digestible.


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