Mathematician Marcus du Sautoy on the Unknown, the Horizons of the Knowable, and Why the Cross-Pollination of Disciplines is the Seedbed of Truth
By Maria Popova
“What we cannot know creates the space for myth, for stories, for imagination, as much as for science… Stories are crucial in providing the material for what one day might be known. Without stories, we wouldn’t have any science at all.”
In a recent MoMA talk about the lacuna between truth and meaning, I proposed that, just like there is a limit to the speed of light arising from the fundamental laws of physics that govern the universe, there might be a fundamental cognitive limit that keeps human consciousness from ever fully comprehending itself. After all, the moment a system becomes self-referential, it becomes susceptible to limitation and paradox — the logical equivalent to Audre Lorde’s memorable metaphor that “the master’s tools will never dismantle the master’s house.”
Pioneering astronomer Maria Mitchell articulated this splendidly when she wrote in her diary in 1854:
The world of learning is so broad, and the human soul is so limited in power! We reach forth and strain every nerve, but we seize only a bit of the curtain that hides the infinite from us.
The century and a half since has been strewn with myriad scientific breakthroughs that have repeatedly transmuted what we once thought to be unknowable into what is merely unknown and therefore knowable, then eventually known. Evolutionary theory and the discovery of DNA have answered age-old questions considered unanswerable for all but the last blink of our species’ history. Einstein’s relativity and the rise of quantum mechanics have radically revised our understanding of the universe and the nature of reality.
And yet the central question remains: Against the infinity of the knowable, is there a fundamental finitude to our capacity for knowing?
That’s what English mathematician Marcus du Sautoy, chair for the Public Understanding of Science at Oxford University, explores with intelligent and imaginative zest in The Great Unknown: Seven Journeys to the Frontiers of Science (public library) — an inquiry into the puzzlement and promise of seven such unknowns, which Du Sautoy terms “edges,” marking horizons of knowledge beyond which we can’t currently see.
In a sentiment that calls to mind Hannah Arendt’s assertion that our appetite for seemingly unanswerable questions is what makes us human, Du Sautoy writes:
For any scientist the real challenge is not to stay within the secure garden of the known but to venture out into the wilds of the unknown.
The knowledge of what we don’t know seems to expand faster than our catalog of breakthroughs. The known unknowns outstrip the known knowns. And it is those unknowns that drive science. A scientist is more interested in the things he or she can’t understand than in telling all the stories we already know the answers to. Science is a living, breathing subject because of all those questions we can’t answer.
Among those are questions like whether the universe is infinite or finite, what dark matter is made of, the perplexity of multiverses, and the crowning curio of devising a model of reality that explains the nature and behavior of all energy and matter — often called a “theory of everything” or a “final theory” — unifying the two presently incompatible models of Einstein’s theory of relativity, which deals with the largest scale of physics, and quantum field theory, which deals with the smallest scale.
Du Sautoy, who believes — as do I — that “we are in a golden age of science,” considers the central ambivalence behind such a final theory and the very notion of knowing everything. Echoing artist Georgia O’Keeffe’s famous advice that “making your unknown known is the important thing — and keeping the unknown always beyond you,” he writes:
Would we want to know everything? Scientists have a strangely ambivalent relationship with the unknown. On the one hand, what we don’t know is what intrigues and fascinates us, and yet the mark of success as a scientist is resolution and knowledge, to make the unknown known.
And yet, too often, our human tendency when faced with unknowns is to capitulate to their unknowability prematurely — nowhere more famously, nor more absurdly, than in the proclamation Lord Kelvin, one of the most esteemed scientists of his era, made before the British Association of Science in 1900: “There is nothing new to be discovered in physics now. All that remains is more and more precise measurement.” Elsewhere in Europe, Einstein was incubating the ideas that would precipitate humanity’s greatest leap of physics just five years later. Lord Kelvin had failed to see beyond the edge of the known.
A quarter century after James Gleick introduced the world to chaos theory, Du Sautoy selects chaos as the first if his seven “edges” and writes:
There are natural phenomena that will never be tamed and known. Chaos theory asserts that I cannot know the future of certain systems because they are too sensitive to small inaccuracies. Because we can never have complete knowledge of the present, chaos theory denies us access to the future.
That’s not to say that all futures are unknowable. Very often we are in regions that aren’t chaotic, where small fluctuations have little effect. This is why mathematics has been so powerful in helping us to predict and plan. The power of mathematical equations has allowed us to land spaceships on other planets, predict the paths of deadly typhoons on Earth, and model the effects of deadly viruses, allowing us to take action before they become a pandemic. But at other times we cannot accurately predict or control outcomes.
This, Du Sautoy notes, is representative of the common denominator between all of the “edges” he identifies — the idea, also reflected in the aforementioned problem of consciousness, that we might be fundamentally unable to grasp a system from a bird’s-eye perspective so long as we are caged inside that system. Perhaps the most pervasive manifestation of this paradox is language itself, the hallmark of our cognitive evolution — language contains and carries knowledge, but language is a system, be it the language of the written word or that of mathematics.
Du Sautoy reflects on this possible meta-limitation:
Many philosophers identify language as a problem when it comes to the question of consciousness. Understanding quantum physics is also a problem because the only language that helps us navigate its ideas is mathematics.
At the heart of this tendency is what is known as “the paradox of unknowability” — the logical proof that unless you know all there is to be known, there will always exist for you truths that are inherently unknowable. And yet truth can exist beyond logic because logic itself has fundamental limits, which the great mathematician Kurt Gödel so elegantly demonstrated in the 1930s.
So where does this leave us? With an eye to his seven “edges,” Du Sautoy writes:
Perhaps the best we can hope for is that science gives us verisimilitudinous knowledge of the universe; that is, it gives us a narrative that appears to describe reality. We believe that a theory that makes our experience of the world intelligible is one that is close to the true nature of the world, even if philosophers tell us we’ll never know. As Niels Bohr said, “It is wrong to think that the task of physics is to find out how nature is. Physics concerns what we can say about nature.”
In consonance with my foundational belief that the cross-pollination of disciplines is what catalyzes the combinatorial creativity out of which every meaningful new idea is born, Du Sautoy adds:
Science flourishes when we share the unknowable with other disciplines. If the unknowable has an impact on how we lead our lives, then it is worth having ways to probe the consequences of choosing an answer to an unknowable. Music, poetry, stories, and art are powerful tools for exploring the implications of the unknowable.
Chaos theory implies that … humans are in some ways part of the unknowable. Although we are physical systems, no amount of data will help us completely predict human behavior. The humanities are the best language we have for understanding as much as we can about what it is to be human.
Studies into consciousness suggest boundaries beyond which we cannot go. Our internal worlds are potentially unknowable to others. But isn’t that one of the reasons we write and read novels? It is the most effective way to give others access to that internal world.
What we cannot know creates the space for myth, for stories, for imagination, as much as for science. We may not know, but that doesn’t stop us from creating stories, and these stories are crucial in providing the material for what one day might be known. Without stories, we wouldn’t have any science at all.
Complement the thoroughly fascinating The Great Unknown, which examines the implications of these seven elemental unknowns for everything from consciousness to our experience of time to the future of artificial intelligence, with Nobel-winning Polish poet Wisława Szymborska on how our certitudes keep us small, astrophysicist Marcelo Gleiser on how to live with mystery in the age of knowledge, philosopher Karl Popper on truth vs. certainty, and artist Ann Hamilton on the creative power of not-knowing.
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