“As always happens with contradictions, something in the assumptions has to give… Declaring something impossible leads to more things being possible.”
“Everything that is possible is real,” Bach scribbled in the margins of a symphony three centuries ago, when the existence of other galaxies was unimaginable and hummingbirds were considered magic, when the fact of the atom was yet to trouble the young Emily Dickinson and the fact that it is mutable was yet to splinter the foundation of reality as we understood it.
“What will they think of my music on the star of Urania?” the young Beethoven wondered in his marginalia upon hearing of the discovery of Uranus, daring to imagine the unimaginable. In two centuries, his Fifth Symphony would sail past the seventh planet on a golden disc aboard a spacecraft launched into the unknown on the wings of laws discovered by a college student watching an apple fall on his illiterate mother’s orchard during a plague quarantine and a sickly brokenhearted mathematician defending his mother in a witchcraft trial.
The great gift of science is that it continually reveals to us what is real, unpeeling the wallpaper of our knowledge to reveal newer and newer layers of nature, deeper and deeper substrata of reality. The great peril of science — this eternal impulse of human nature — is that the human mind continually limits what is possible, erecting walls of assumption between itself and the reality of nature. And yet the entire fact of life — your individual life, and mine, and life itself as a feature of the universe — is a matter of probable impossibilities.
Plate from An Original Theory or New Hypothesis of the Universe by Thomas Wright, 1750. (Available as a print, as a face mask, and as stationery cards.)
This interplay, and how to liberate our search for truth from our craving for certainty, is what Italian physicist Chiara Marletto explores in The Science of Can and Can’t: A Physicist’s Journey through the Land of Counterfactuals (public library) — part field guide to her particular realm of study, part manifesto for the countercultural courage to keep unmasoning the walls of the imaginable and bending the mind beyond the accepted horizons of the possible. What emerges is an impassioned, scrumptiously reasoned insistence that all breakthroughs in science require “as much imagination and perceptiveness as you need to write a good story or a profound poem.”
Counterfactuals — explanations about what could or could not be caused to happen in the physical universe, as distinct from the standard scientific theories about what is bound to happen based on what has happened in the past — are one such thrilling mode of rotating in the palm of the mind the unsolved mysteries of nature in order to examine them from revelatory new perspectives, perspectives blind-spotted by our present assumptions. Counterfactuals are the science of otherwise — the physics counterpart to Jane Kenyon’s excellent poem — shimmering with new ways of understanding everything from information to time to free will.
Double rainbow from Les phénomènes de la physique, 1868. Available as a print and face mask.
In the foreword, Marletto’s collaborator David Deutsch observes that the rate of scientific discovery over the past few centuries has been increasing exponentially, but the discovery of new fundamental truths about nature has stalled and an indolence about attempting new modes of explanation has set in. He writes:
There has never been a time when there have been more blatant contradictions, gaps, and unresolved vagueness in our deepest understanding of nature, or more exciting prospects to explore them. Sometimes this will require us to adopt radically different modes of explanation.
Illustrating the validity of counterfactuals as a mode of understanding, he gives the example of a computer, which could record and process nothing new if every change to the contents of its memory were pre-set in the factory — a computer “can hold information only if its state could have been otherwise.”
Marletto places at the heart of her case for counterfactuals the notion of resilience — not resilience in the creaturely sense, to which we aspire and which trees so perfectly embody, but a deeper kind of resilience, existing on the fundamental level of information yet giving rise to all the physical reality that makes the creaturely kind possible — resilience as the dazzling, rare feature of our universe, even within the no-design fundamental laws of which a system can continue existing in an ever-changing environment. With an eye to genes — those recipes for keeping a species in existence, peppered with mutation — she writes:
What distinguishes helpful changes in the recipe from unhelpful ones? It is a particular kind of information: information that is capable of keeping itself instantiated in physical systems. It is resilient information.
[…]
“Knowledge” merely denotes a particular kind of information, which has the capacity to perpetuate itself and stay embodied in physical systems — in this case by encoding some facts about the environment… Knowledge is the key to resilience… In fact, knowledge is the most resilient stuff that can exist in our universe.
Art by Deborah Marcero from The Boy Whose Head Was Filled with Stars: A Life of Edwin Hubble by Isabelle Marinov.
Leaning on Karl Popper’s famous pillar of sensemaking — “Knowledge consists in the search for truth… It is not the search for certainty.” — she adds:
There are no absolute sources of certain truth: any good solution to a problem may also contain some errors. This principle is based on fallibilism, a pillar of Popper’s explanation of rational thinking. Fallibilism makes progress feasible because it allows for further criticism to occur in the future, even when at present we seem to be content with whatever solution we have found. It leaves space for creating ever-improving theories, stories, works of art, and music; it also tells us that errors are extremely interesting things to look for. Whenever we try to make progress, we should hope to find more of them, as fast as possible.
She turns to the two ways in which nature and human nature generate new knowledge, the generative process we call creativity — “by conjecture and criticism, in the mind; by variation and natural selection, in the wild” — and considers the crucial difference between the two:
Natural selection, unlike conjecture and criticism, cannot perform jumps: each of the recipes that leads to a new resilient recipe must itself be resilient — i.e., it must code for a successful variant of a trait of the particular animal in question that permits the animal’s survival for long enough to allow replication of that recipe, via reproduction. But there may be viable, resilient recipes coding for useful traits that can never be realised because they would require a sequence of nonresilient recipes to be realised first, which is impossible, as those recipes produce animals that cannot survive and cannot pass on their genes.
The thinking process, in contrast, can perform jumps… The sequence of ideas leading to a good idea need not consist entirely of good, viable ideas. Nonetheless, knowledge creation in the mind, too, can enter stagnation and stop progressing. We must be wary of not entering such states both as individuals and as societies. Particularly detrimental to knowledge creation are the immutable limitations imposed by dogmas, as they restrain the ability to conjecture and criticise.
Woven into Marletto’s case for counterfactuals is her love letter to science and the art of explanation:
Physics is a dazzling firework display; it is profound, beautiful, and illuminating; a source of never-ending delight. Physics is about solving problems in our understanding of reality by formulating explanations that fill gaps in our previous understanding. The point of physics is not the particular calculation about the fall of an apple. It is the explanation behind it, which unifies all motions—that of the apple with that of a planet in the solar system, and beyond. The dazzling stuff consists of explanations: for they surprise us by revealing things that were previously unknown and very distant from our intuition, with the aim of solving a particular problem.
[…]
The appearance of the dark sky at night… can be explained in terms of unexpected underlying phenomena involving things like photons, the remarkable fact that the universe is expanding, and so on. None of those elements is apparent in the sky itself, but they are all part of the explanation for why it looks as it does, in terms of what is really out there. Explanations are accounts of what is seen in terms of mostly unseen elements.
“Spectra of various light sources, solar, stellar, metallic, gaseous, electric” from Les phénomènes de la physique by Amédée Guillemin, 1882. (Available as a print and as a face mask.)
“What we see, we see / and seeing is changing,” Adrienne Rich wrote in her ode to astrophysics. It is changing, however, only when we change the way we look, change our tools for looking, be they physical instruments — the microscope and the telescope, revealing unseen layers of reality — or the instrument of the mind, which devises the microscope and the telescope and the theory. I hear Thoreau bellowing his admonition down the hallway of time as he puzzled over what it takes to see reality unblinded by our preconceptions: “We hear and apprehend only what we already half know.” Marletto writes:
The traditional conception of physics cannot possibly capture counterfactual properties, because it insists on expressing everything in terms of predictions about what happens in the universe given the initial conditions and the laws of motion only — in terms of trajectories of apples or electrons, forgetting the other levels of explanation. But these other levels of explanation are essential sometimes to grasp the whole of physical reality.
Drawing on the example of Neptune and the neutrino — both discovered not by direct observation of the previously unseen planet or particle but by observing curious contradictions in the surrounding system and deducing from them that something in the set of assumptions about what the system is and how it works must be revised. She writes:
As always happens with contradictions, something in the assumptions has to give.
[…]
Declaring something impossible leads to more things being possible.
In one of the book’s many charming touches defying the segregation of science from its sensemaking twin — art — she gives an exquisite example of counterfactuals at work in one of humanity’s most abiding masterworks of storytelling and sensemaking: the Ancient Greek myth of Theseus (which also inspired the greatest thought experiment about the nature of the self and what makes you you).
Theseus and the Minotaur by Alice and Martin Provensen from their lovely 1956 illustrations for the Iliad and the Odyssey.
Marletto writes:
Theseus, son of Aegeus, king of Athens, went to Crete to kill the Minotaur. Theseus made an agreement with his aged father that if he defeated the Minotaur, on their return his crew would raise white sails on the ship; if he perished, they would raise black sails. So off went Theseus, and he defeated the Minotaur. But on his way back, distracted by all sorts of things (including, possibly, the presence of his fiancée, Ariadne, on the ship!), he forgot to tell the crew about the sails. The crew left the black sails on, and Aegeus, who from the highest tower of Athens could see the ship approaching, thought his son was dead. So he threw himself into the sea and drowned. This tragic story is why the sea is now called the Aegean.
Now suppose we asked our master storyteller to tell that story with the constraint that he can formulate statements only about what happens — that is, he must report the full story without ever referring to counterfactual properties. In particular, he cannot refer to properties that have to do with what could or could not be done to physical systems.
This task turns out to be impossible: for the story to make sense, and to convey fully its meaning, two attributes of the ship are essential: one, that it can be used to send a signal, by assuming one of two states — white sail showing or black sail showing; the other, that the state of having black or white sails can be copied onto other physical systems — such as Aegeus’s eyes and brain. The copiability property tells us that the flag contains information.
Without these two counterfactual properties, the myth would be robbed of sense and could not possibly produce in the mind of the reader the tragic feeling, the shift in understanding, that gives rise to its millennia-wide moral. The myth of Theseus — a sensical story of tangible things like continents and oceans, a story of profoundly human things like ships and sons — helps grasp the analogous counterfactuals at work in more abstract things. A bit — that unit of information powering our digital universe — may seem like an abstract thing, but it is essentially a Thesian ship’s sail: there are the two binary states that can switch from one to the other, there is the ability to be copied. Any system endowed with these two counterfactual properties is an information medium — a conduit of knowledge.
Marletto reflects:
Adopting counterfactuals brings entities that look superficially like immaterial abstractions into the domain of physics. Information and knowledge, for example, have been traditionally considered as mere abstractions — as things that do not belong to the physical world. However, by considering the counterfactual properties of physical systems that enable information and knowledge, one refutes this idea: because whether or not a physical system has those properties is set precisely by the laws of physics.
Art from Thomas Wright’s An Original Theory or New Hypothesis of the Universe, 1750 — the first book to describe the spiral shape of the Milky Way. (Available as a print and as a face mask.)
The ultimate promise of counterfactuals as portals to possibility comes most vibrantly abloom in one of the several short genre-bending vignettes Marletto composes to illustrate the scientific concepts — a story-upon-story set in the crucible of materialism, Ancient Greece. She imagines the childhood of the legendary conqueror Alexander the Great — who by his death at thirty-two would have created one of the vastest empires in the history of our species — and his time as an uncommonly broad-minded pupil of Aristotle: a boy asking the vastest unasked questions, hungry to fathom his own mind. In one of their conversations, Alexander wonders what it is in him that endows him with the capacity for wonder — with the ability to savor poetry and philosophy and the abstract art of mathematics — if he is made of the same material as concrete things like rocks and grass. Marletto’s Aristotle answers:
What’s clear is that the mind has characteristic properties that make it capable of relating to things that are abstract. I suspect that it obeys the same laws as rocks and grass, though we have yet to find these laws and understand how to apply them to the mind.
Complement The Science of Can and Can’t with physicist Alan Lightman’s poetic meditation on what makes our improbable lives worth living between the bookends of possibility, then revisit the story of Alan Turing, the world’s first digital music, and the poetry of the possible.
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