If science has a native tongue, it is mathematics. Equations capture, precisely, the relationships among the elements of a system; they allow us to pose questions and calculate answers. Numerically, these answers are precise and unambiguous – but what happens when we want to know what our calculations mean? Well, that is when we revert to our own native tongue: metaphor.
Why metaphor? Because that is how we think, how learn, how we parse the world. Metaphor comes from the Greek metaphora, a “transfer”; literally a “carrying over”. The very act of understanding (from the Old English: to stand in the midst of) implies the existence of a “between”, a bridge between new and known. In effect, a metaphor. How could it be otherwise? How else can we assimilate a new piece of knowledge, other than by linking it to something we already know? In doing so, we weave a web. When we wonder what something means, what we’re really asking is: what will it impact? If I pull on this thread here, where will my web tighten, where might it unravel?
When we can’t find a suitable metaphor to describe our scientific reality, we run into problems. Take, for instance, quantum mechanics. Most of the devices we use every day are built upon eerily accurate calculations made using quantum theory. Operationally, the theory is wildly successful, yet no one can make complete sense of it. Even scientists who wield the equations with ease don’t claim to truly understand quantum theory; we still don’t have a metaphor that works.
Metaphors aren’t only a means of description, they can also lead to revelations. Centuries ago, Newton was able to calculate the gravitational attraction between two objects given their masses and the distance between them. But, while he could describe this interdependence precisely, Newton would “feign no hypothesis” as to why it was so. He had the equation, but he did not understand gravitation. It took Einstein to do that. In most situations, the answers that arise from Einstein’s and Newton’s equations are so close, the numerical discrepancy is practically negligible. The real difference is that, with Einstein, we finally have a metaphor. When we picture space-time as a dynamic “fabric” that responds to the mass with dips and ripples, we begin to understand what gravity means.
Not only are metaphors connective, they are also generative. The mere comparison of space-time to a fabric suggests questions that were previously inconceivable: Can space-time be torn? Can it be punctured? Can it gather in folds? While gravity remained Newtonian – a force acting instantaneously across an inert space – such lines of thought were not possible. They arise only in this new liminality. They live because of a metaphor.
New directions
So why do we still not appreciate the crucial role of metaphor? Metaphors in science may seem like a subjective, even literary insertion into what is meant to be an objective and rigorous discipline. Scientists themselves often play into this misconception by keeping metaphors out of academic discourse, reserving them for watered-down conversations with the general public. But in trading their personal metaphors, scientists can nudge each other’s thoughts in new directions, and push the boundaries of science forward.
There is more to consider. If metaphors create possibilities and encode meaning, it should come as no surprise that they also impact our perceptions, attitudes and behaviours. As is the case with any tool, we shape our metaphors – and then our metaphors turn around and shape us.
Even the limits of metaphor can take us forward. It can actually be quite instructive to push a metaphor to where it breaks, and mark the boundary. Take the now-standard comparison of a brain to a computer. Do you know that it started the other way around? The computational power of early computers made such an impression that people started likening them to human brains. The comparison was a compliment, an expression of awe for these magic machines that seemed to mimic human thought. As computers advanced, their calculational abilities surpassing ours, traffic along the bridge of metaphor changed direction. We came to think of the brain as a computer, reducing this complex organic marvel to a mere machine.
Now that we’ve hit a wall trying to understand how the mechanical brain makes a conscious mind, perhaps it’s time to consider that we have exhausted this particular metaphor. But that in itself is very useful information. One of the most important things to know about a metaphor is where it breaks down and why: if you use a spring, you should know its elastic limit.
When James Clerk Maxwell first turned his attention to electromagnetism, he visualised this unfamiliar entity as best he could, in terms of what he knew. In Maxwell’s early papers, Faraday’s magnetic lines of force are modelled by a large array of spinning gears, connected by strings of ball bearings. Given Victorian England’s fascination with machines, this vivid picture made the invisible electromagnetic field much less uncomfortable an idea. The image only goes so far (which is why we don’t think of electromagnetism in terms of gears and pulleys today) but by the time the limits of the metaphor were breached, enough scientific progress had been made that new models were suggested. The metaphor had just been a stepping stone, but it enabled us to move on.
To the philosopher Max Black, metaphor not only describes, but can in some instances create the similarity between two terms. Any idea you hold up is like a source of light shining from a particular angle – each illuminates or casts into shadow different parts of the object you are studying. Both light and shadow carry information.
Vacuum cleaners of the cosmos
Metaphors are perhaps most useful in situations when we understand the least. Over the past century we have employed many different metaphors for black holes – which science still does not completely understand. Looking back, these metaphors trace our changing attitudes to these perplexing astronomical objects.
Black holes announced themselves in the humblest way possible: as a tiny equation appended to a letter, encased in a wrinkled, dog-eared envelope. The letter, written in the trenches of the First World War by the physicist, astronomer and German lieutenant Karl Schwarzschild, was addressed to Albert Einstein. It contained the first ever solution of his new theory. General relativity was an absolute triumph, but its equations were so difficult to solve that Einstein had doubted the task would be accomplished in his lifetime. Yet barely a month after his theory was published, here came a perfect solution – a mathematical dream drifting out from the nightmare of war. You would think he would have been overjoyed. You would be wrong.
Schwarzchild’s equation was simple, concise and elegant, but the implications it carried were, at the time, unthinkable. According to the solution, a black hole contains at its centre what is now known as a singularity: a point where the smooth rubber sheet of Einstein’s space-time is punctured, and physics as we know it breaks down. In the words of the physicist John Wheeler, “The black hole teaches us that space can be crumpled like a piece of paper into an infinitesimal dot, that time can be extinguished like a blown-out flame, and that the laws of physics that we regard as ‘sacred,’ as immutable, are anything but.”
Fortunately this dreaded singularity, which tears space-time to shreds, is sheathed within an “event horizon”. Outside it, we are safe. One foot on the edge, and we are doomed. Encoded in Schwarzschild’s equation, there is a radius that marks this sphere of no return. Some called it “the barrier” (stay out!); others, the “sphere catastrophique”. Black holes show no mercy. In the words of the physicist Steven Gubser, they “hijack the future of every object that falls into them”. Nothing can escape, not even the most fleet-footed thing in the Universe – not even light. They were framed as demons, greedy gluttons that gobble up everything. The Bermuda triangles of space. The vacuum cleaners of the cosmos. But perhaps most sinister is the association carried by the name that eventually stuck. The “black hole of Calcutta” was a tiny, cramped cell in which over 60 prisoners of war were incarcerated in 1756, more than half of whom suffocated in the heat.
Over time, attitudes to black holes became less severe. Where once the emphasis was on their “grotesque deformities and grim instabilities”, writes physicist Janna Levin, we now think of them more often as anchors that provide “a centre for our own galactic pinwheel and possibly every other island of stars”. We tend, instead, to describe the “throat” of a black hole as the “lip of a waterfall, beyond which space-time cascades ineluctably downward”, or the neck of “a glass bottle in the hands of a skilful Murano glassblower”.
Wondering what occasioned the change in tone? The simplicity of the equations eventually won us over. It turns out that astrophysical objects are extremely difficult to model. Stars, with their nuclear reactions, internal pressure and fluid dynamics are a particular challenge. A black hole, by comparison, is wonderfully simple. In short, we discovered the mathematical uses of black holes, and our association with them changed. We “tamed” them, until they became objects of fascination, safe even for elementary school children to handle.
Mathematical metaphors
There is yet another way that metaphors can lead to scientific discovery, and that is within the field of mathematics itself. Mathematical equations are schematic representations of the relationships between various aspects of a system. Equations describe how these quantities are tied together, how they tug or push at each other, what sort of web they weave. Regardless of the circumstances that inspire them, once written down, symbols in equations are like words in a poem: multi-layered, saturated with meaning. Occasionally, when we are very lucky, we come across a pair of systems that bear no apparent physical similarity, but are described by the same equation. Insights gleaned in one system carry over into the other. Every symbol now has two meanings – one per system – giving us a map between two seemingly unrelated entities; we have, in short, a mathematical metaphor.
One of the most fundamental and perplexing discoveries about black holes came about in exactly this manner. It started with the simple observation that just as entropy (a measure of the disorder of a system) can never decrease in classical thermodynamics, neither can the area of a black hole. Moreover, the equations that describe how these quantities grow have exactly the same form. It’s almost as if the area of a black hole is a measure of its entropy.
This seemed preposterous. Because of their celebrated mathematical simplicity, black holes were assumed to have minimal, if not zero entropy. The resemblance was put down to mere coincidence until Jacob Bekenstein, one of John Wheeler’s students, decided to take the equation at its word. In order for the metaphor to hold, one of the symbols in the equation had to correspond to “temperature”. Some radiation (something we could register as heat) would need to be emitted from the black hole – the very same black hole that notoriously swallowed even light. It was an audacious suggestion, dismissed by many experts in the field including, at first, Stephen Hawking. But the theory of Bekenstein-Hawking radiation is now a standard topic in any conversation about black holes.
Metaphors can also be visual. An idea can be linked to a picture as easily as to a word, and it is quite instructive to explore which aspects of the idea are illustrated and which are left out. Images mine depths words cannot, so when a concept is new to us, images are some of our most effective tools.
Stephen Hawking’s deep discoveries about black hole mechanics came after he lost the use of his hands: he reached his famous conclusions through manipulating visual images in his head. “The happiest thought” of Einstein’s life – the insight that led to a complete reconceptualisation of space and time – was the result of comparison between a window washer suspended outside his building, and a man falling in a gravitational field. How do you link one to the other? By rethinking gravity.
Anchoring ideas
New concepts have a tendency to fly away. Unanchored, they billow out, expanding through space – expanding space – in mysterious, unnerving ways reminiscent of dark energy. We can lose sight entirely unless we reel them in, anchor them to other ideas, and hold them in place by the weight of their connections. Whether these metaphors are structural, mathematical, verbal or visual is immaterial. Each is a strand in the net with which we draw knowledge in.
Physicist-philosopher Carlo Rovelli says the success of science depends partly on “the creative liberty taken with conceptual structure, and this grows through analogy and recombination ... It is not easy to change the order of things, but this, at its very best, is what science does.”
In his recent book, The Warped Side of Our Universe – a collaboration with artist Lia Halloran – the physicist Kip Thorne used poetry to talk about black holes, gravitational waves and other topics he has previously addressed in prose. When asked about the experience, he said he found poetry harder to craft than prose, “but the surprise to me was that I could use it to get much more deep into the essence of the science.”
Should that really be surprising? Within the lines of poetry, words are released from their literal, everyday associations; they exist as symbols, ripe for metaphor. Freed from the constraints of a linear narrative, words conjoin in wild, unexpected ways. They may defy the rules of grammar, they may not make prosaic sense, but these flagrant juxtapositions give rise to new images – impressionistic flashes from the lush world of the mind.
One argument against the use of metaphor is that a single metaphor can seldom encompass the whole truth of a physical theory. But that’s exactly why we need more of them. We’ve learned this lesson already, with coordinate systems in geometry. (Think of how shapes can be plotted out in three dimensions, on diagrams with x, y and z axes.) Only the simplest, flattest space can be covered by a single coordinate system. For more interesting, curved spaces – like the ones around black holes – we need to patch together many overlapping coordinate systems. Each expands into places the other can’t reach.
Taking a similar approach with metaphors would be infinitely rewarding. Through both comparison and contrast, each new metaphor adds a layer of richness to our understanding, each is a foil for argument, a source of insight and a path to generating new questions.
The frontiers of science – cosmic or subatomic – are far beyond the reach of direct experience. If we are to comprehend what we encounter there, we have to find a way to link it to that which we already know. Metaphors can make meaning from the new information we uncover. It’s time we acknowledge their crucial role, and give metaphors in science the attention they deserve.
This article is from New Humanist's spring 2024 issue. Subscribe now.
