Analogies (and metaphors) as mental maps
Updated on 19 June 2023
Katharina – who initiated my blog 137 – 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 a reply 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 and for “the truth” will focus on the material world and the possibility of empirical testing. Climate change is not a good candidate to further engage with this argument. So, let’s get material, or better, let’s get physical! And what better example is there then the very material that everything else is made of – the atom and sub-atomic particles?
My starting point is that we cannot know the world as it is; we can’t look at 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 argues, the cuddly feeling that we get under our blanket of analogies and metaphors creates the illusion of knowing; the truth is shut out.
What truth? I for my part like being under my cosy blanket of metaphors. But maybe this is not so much for the cosiness but for the realisation that either there is no truth or, if there is, we don’t have direct access to it. From this position, let me try and save the good name of analogies and metaphors from the paws of Aldo’s Polynesian rat.
My answer to Aldo is that walking this “high road” road is inevitable. The trick of what we call science comes in along the way. And what’s wrong with warm and cuddly feelings along the way?
So what about the atom? If you had to imagine an atom, what would you imagine? What do you see in your mind right now? Most of us would use an image we know from school. It surely will look a bit like a solar system. The nucleus is in the middle and the electrons circle around it on elliptical trajectories. Right?
The similarity with the solar system is not an accident. At the time when the model was developed, we had much greater knowledge about the solar system. So, it seemed a useful analogy or metaphor for the atom which was just being explored at the time. What we can see here is a process of structural mapping at play. Structures, relations between objects, found in one context are transferred to a new a context. Any metaphor used in a scientific, explorative context, will have this process at its core.
And yes, I can hear you shouting right at this point, “but this model is outdated to such an extend that it is almost embarrassing that we still teach it to kids in school.” Indeed, physics has moved on. Physicists started to look at electron clouds and quantum waves. Metaphors anyone?
“Yes,” you might say, “but this only a little language game, to verbalise and illustrate what is actually going on.“
There is an argument to be made that these metaphors and images, these thought experiments, guided the mathematical models and guided empirical research. You cannot research what you can’t think. And, maybe we need to start to entertain the radical idea that there is no thought outside of language. Moreover, if we cannot research what we cannot think, than any new discovery will inevitably be bound up in an older system of thought.
What is scientific discovery then? Science is never simply looking at the “reality” and discovering “the truth”. It is also never a direct comparison between our theories and “the reality out there” to refute all those “silly” metaphors. It’s a process of working with the best possible explanation and maintaining it for as long as there is no better possible explanation around. This is how you move from the atom as a solar system, to electron clouds and quantum waves, all the way to the Higgs Boson, the god particle.
I maintain that we can’t escape the blanket of metaphors. And like children lying in their beds at night, being afraid of the dark, all we can hope for is getting a glimpse of the world out their every now then. The rest of the story inevitable unfolds in the safe hiding place under our blanket. And if it is cuddly, all the better!
To which I’ll reply wholeheartedly: Yes, Katharina, analogies and metaphors are (mental) maps.
Indeed, a geographic map is a metaphor of 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 principle point against analogies and metaphors. I’m always against principles – they are not “truths” but metaphors of reality and mental constructs.
The first paragraph of my blog 137 is effusive of compliments for analogies – as long they closely track material reality, i.e. have many “points of congruence”. Where I raise warning flags is where 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 by giving us the cuddly feel that we know and understand. A distortion of a distortion seldom yields undistorted understanding.
Ideally, mapping should allow for “one on one” congruence. A point on a map univocally identifies a point in the landscape. By optimizing 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 on one match of reality. We need to compress the information. So we leave 99% of the reality out of the map, and only include say, physical features like heights and waters. It is a convention. As long as we know – it’s fine, provided we know and remember. Just let’s not 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. In everyday parlance Europe is a continent – geographically, this is nonsense, it is a peninsula. Politically, the “Orient” began in Morocco for a while – how odd for a country to the west of Europe. The standard Mercator projection map overstates the size of certain geographical areas. Mental constructs that overlay maps make them inaccurate, nay 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, which organize reality in accordance to our political intents.
Maps finally depend on their use. The metaphor of the atom as astronomical system is useful to teach chemistry and is still valid in this context. If one wants to understand the fundamental forces of the universe, however, the canonical metaphor is that of ice skaters exchanging particles like the Higgs Boson on the go. It shows how a quantum of force moves back and forth.
I’ve given up on “the truth” long ago. The only thing that counts is 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 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 apply now 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 the essentially same message – urgency (no content is involved). It could be avalanche, nuclear explosion, whatever else comes handy. In mathematics (an analogy) we would speak of over-determination: too many variables chase 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” generic suitability betrays its high rhetorical content.
Analyzing its fit to climate change more closely, one can observe that the metaphor (a) conveys urgency which may be exaggerated; (b) suggests knowledge of the evolving event we do not have, (c) intimates solutions which, on closer inspection, may prove to be less than appropriate; (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. The (un)intended consequence is 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 gets smuggled in – as when you have a biased translator, or when the 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 tendentially shortcuts rationality. Depending on the rhetorical content an analogy can either be a hindrance or an adjuvant.
I’ll make a final analogy with catalysts. “Catalysis is the change in 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 – and not just rely on our cuddly feeling.
 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.
 Martin W. LEWIS – Karen E. WIGEN (1997): The myth of continents. A critique of metageography. California University Press, Berkeley.
 The Mercator projection portrays Greenland as larger than Australia; in actuality, Australia is more than three and a half times larger than Greenland. https://en.wikipedia.org/wiki/Mercator_projection