Analogies and metaphors as mental maps

In her blog post, Katharina Höne, who initiated my blog post ‘Don’t Blame Man, Blame the Polynesian Rat‘, replied to it in this way:

In a very thoughtful piece titled ‘Don’t blame man, blame the Polynesian rat’, Aldo Matteucci warned about the dangers of analogies (and metaphors, for that matter). He did so in response to one of my blog posts, in which I praised the usefulness of metaphors to make sense of complex and intangible entities or phenomena, such as climate change.

As you would expect, an argument against analogy and metaphor, in favour of ‘the truth’, will focus on the material world and the possibility of empirical testing. Climate change is not an ideal candidate for further engaging with this argument. So, let’s get material – or better, let’s get physical! And what better example is there than the very material that everything else is made of: the atom and subatomic particles?

My starting point is that we cannot know the world as it is; we can’t observe it directly. We can’t discover things in themselves. For the process of discovery and understanding, metaphors and analogies are inevitable. This is where Aldo offers a warning. He argues that ‘analogies are the high road to “self-affirmation” – they invariably give us the warm feeling that we “know”, or that the explanation is “plausible”. We’ll never let truth stand in the way of such a cuddly feeling.’ Ultimately, he contends, the cosy feeling we get under our blanket of analogies and metaphors creates the illusion of knowing, while the truth is shut out.

What truth? For my part, I like being under my cosy blanket of metaphors. But perhaps this is not so much for the cosiness as for the realisation that either there is no truth or, if there is, we don’t have direct access to it. From this perspective, let me try to rescue the good name of analogies and metaphors from the paws of Aldo’s Polynesian rat.

My response to Aldo is that walking this ‘high road’ is inevitable. The trick of what we call science comes along the way. And what’s wrong with warm and cuddly feelings on the journey?

So, what about the atom? If you had to imagine an atom, what would you picture? What do you see in your mind right now? Most of us would use an image we remember from school. It would likely resemble a solar system. The nucleus is in the centre, and the electrons circle around it on elliptical trajectories. Right?

The similarity with the solar system is not accidental. At the time when the model was developed, we had much greater knowledge of the solar system. So, it seemed a useful analogy or metaphor for the atom, which was just beginning to be explored. What we see here is a process of structural mapping at play. Structures – relationships between objects found in one context – are transferred to a new context. Any metaphor used in a scientific, exploratory context will have this process at its core.

And yes, I can hear you shouting at this point, ‘But this model is so outdated that it’s almost embarrassing we still teach it to children in school!’ Indeed, physics has moved on. Physicists began looking at electron clouds and quantum waves. Metaphors, anyone?

‘Yes,’ you might say, ‘but that’s only a little language game to verbalise and illustrate what’s really going on.’

There is an argument that these metaphors and images, these thought experiments, guided the mathematical models and empirical research. You cannot research what you can’t think. And perhaps we need to start entertaining the radical idea that there is no thought outside of language. Moreover, if we cannot research what we cannot think, then any new discovery will inevitably be entangled in an older system of thought.

What, then, is scientific discovery? Science is never simply observing ‘reality’ and discovering ‘the truth’. Nor is it a direct comparison between our theories and ‘the reality out there’, dismissing all those ‘silly’ metaphors. It’s a process of working with the best possible explanation and maintaining it until a better one comes along. This is how we move from the atom as a solar system, to electron clouds and quantum waves, and eventually to the Higgs boson, the ‘God particle’.

I maintain that we can’t escape the blanket of metaphors. And like children lying in bed at night, afraid of the dark, all we can hope for is to glimpse the world out there every now and then. The rest of the story inevitably unfolds in the safe hiding place under our blanket. And if it’s cosy, all the better!

To which I’ll reply wholeheartedly: Yes, Katharina, analogies and metaphors are (mental) maps. Indeed, a geographic map is a metaphor for the underlying physical reality. I like your metaphor for metaphors, and I’ll use it in my reply. But first, a clarifying point. I never made a principled argument against analogies and metaphors. I’m always against principles as they are not ‘truths’, but metaphors for reality and mental constructs.

The first paragraph of my blog ‘Don’t Blame Man, Blame the Polynesian Rat’ is full of compliments for analogies, as long as they closely track material reality, i.e. have many ‘points of congruence’. Where I raise warning flags is when the maps track mental maps rather than ‘geography’. If the mental map is flawed, the metaphor will be as well. Metaphors are bundle packets of ‘pre-compressed knowledge’ from a different context: it’s an ‘all or nothing’ proposition. By smuggling in spurious elements, metaphors can seriously mislead us, giving the cuddly feeling that we know and understand. A distortion of a distortion seldom yields undistorted understanding.

Ideally, mapping should allow for ‘one-to-one’ congruence. A point on a map should univocally identify a point in the landscape. By optimising this process over time, we get to a situation where there is ONE map for ONE landscape. If we have MANY maps for one landscape, or if ONE map describes MANY landscapes, we know something is wrong. Expect frantic, frowning warnings from me.

A map, in any case, is never a one-to-one match with reality. We need to compress the information. So we leave 99% of reality out of the map, and only include, say, physical features like heights and waters. It is a convention. As long as we know this, it’s fine, provided we remember. Just don’t use a surface map to identify oil deposits or wind directions.

Maps not only convey facts on the ground; inevitably, they also include mental constructs we have about the underlying reality. The ‘myth of continents’ is a good example (Martin W. Lewis and Karen E. Wigen (1997): The Myth of Continents: A Critique of Metageography). In everyday parlance, Europe is a continent – geographically, this is nonsense; it is a peninsula. Politically, the ‘Orient’ began in Morocco for a time – how odd for a country west of Europe. The standard Mercator projection map overstates the size of certain geographical areas. Mental constructs that overlay maps make them inaccurate, even misleading. These hidden deletions and interpretations are seldom innocent. At best, they are part of ‘silent knowledge’ we share. More critically, maps are ideological statements that organise reality in accordance with our political intents.

Maps finally depend on their use. The metaphor of the atom as an astronomical system is useful for teaching chemistry and is still valid in this context. However, if one wants to understand the fundamental forces of the universe, the canonical metaphor is that of ice skaters exchanging particles, such as the Higgs boson, on the go. It shows how a quantum of force moves back and forth.

I gave up on ‘the truth’ long ago. The only thing that matters is the usefulness of our ignorance in the immediate context – consequentialism is the philosophical term. All maps are ideological statements – this is inevitable, given the structure of our brains. The question is, how much ideology do we tolerate? This requires that we turn a metaphor inside out and ask ourselves: What does it say, and what does it hide? Worse, what does it suggest silently? And what are the likely (and unexpected) consequences?

Let’s now apply what I’ve said to your ‘house on fire’ metaphor. The first thing one notes is that it is a generic description. It is but one of numerous metaphors one could use to convey essentially the same message: urgency (no specific content is involved). It could be an avalanche, a nuclear explosion, or whatever else comes to mind. In mathematics (an analogy), we would speak of overdetermination: too many variables chasing too few equations – the result is vagueness. One could use other metaphors equally well or use the same metaphor in other situations – for instance, in the current Middle East context or to describe Iran’s alleged quest for nuclear capability. The ‘house on fire’ metaphor’s generic suitability betrays its high rhetorical content.

Analysing its fit with climate change more closely, one can observe that the metaphor (a) conveys urgency, which may be exaggerated; (b) suggests knowledge of the evolving event that we do not have; (c) intimates solutions which, on closer inspection, may prove less appropriate; and (d) evokes the precautionary principle that we should act rather than think or adapt, hoping for the best. It has ‘true and present danger’ written all over it. The (un)intended consequence is a rush ‘to do something, anything’. We did. The policy choice turned out to be another analogy – scaling up from the Montreal Protocol. It was the frog trying to be a bull (this analogy is apt; it is cautionary rather than persuasive). The outcome, foreseeable, was stagnation.

Robert Frost said, ‘Poetry is what gets lost in translation’. Analogies are translations. Analogies compress the infinite reality into information packages we can use to survive for a while (not to master reality – that’s hubris). Most of the information is lost, and extraneous elements are smuggled in – as happens when you have a biased translator, or when a word’s aura differs from the original.

Our brain has at least two ‘layers’ – the emotional and the rational. Emotions are fast; rationality is slow and entails hard thinking. Rhetoric appeals to emotions and tends to shortcut rationality. Depending on the rhetorical content, an analogy can either be a hindrance or an aid.

I’ll make a final analogy with catalysts: ‘Catalysis is the change in the rate of a chemical reaction due to the participation of a substance called a catalyst. Unlike other reagents that participate in the chemical reaction, a catalyst is not consumed by the reaction itself.’ If an analogy accelerates the thinking process, it is acceptable. If it distorts it, it is unacceptable. We need to verify, not just rely on our cuddly feelings.

1. The metaphor here is: ‘If it walks like a duck and quacks like a duck, it is a duck’ – which is an unwarranted inference. A single point of incongruence may destroy the analogy, so it behoves us to verify that we don’t think like a duck.

2. The Mercator projection portrays Greenland as larger than Australia; in actuality, Australia is more than three and a half times larger than Greenland.

The post was first published on DeepDip.