A General Theory of Possibility: The Abstract Art of Otherwise and the Physics of Resilience

“As always happens with contradictions, something in the assumptions has to give… Declaring something impossible leads to more things being possible.”

A General Theory of Possibility: The Abstract Art of Otherwise and the Physics of Resilience

“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. He would be a century old when he realized the unimaginable. 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.

Science is a great gift because it constantly reveals what is true. It peels away the layers of knowledge and reveals newer, deeper, and more complex substrata. 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 of or New Hypothesis about the Universe, Thomas Wright 1750. This print is also available as a stationery card, a face mask and a printed copy.

Italian physicists have discovered how to free ourselves from the need for certainty and this interplay is called “The Italian Physics”. 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. Also available in print form and as a mask for the face

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 wrote:

It has been difficult to find a better way of understanding nature than there are now. This may require us to use completely different explanations.

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 InformationOnly if it is in its current state It could have been any other.”

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 is the difference between helpful and unhelpful changes to the recipe? It’s a special kind of information, information that is Easily ableIt is capable of being kept instantiated within 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 in The Boy Whose Heart Was Filled by Stars: 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:

The truth is that there are not absolute truths. Even the best solutions to problems may contain errors. This principle can be found here Fallibilism, a pillar of Popper’s explanation of rational thinking. Progress is possible because fallibilism permits further criticism in the future even though at the moment we appear to be satisfied with our current solutions. This leaves room for new theories, stories and works of art. It also points out that mistakes are very interesting. If we want to move forward, it is important to try to find as many 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. Some viable resilient genes may not be possible to realize. This is because it would take a number of other nonresilient recipe for them to become reality.

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. Knowledge creation within the mind can stagnate or stop moving forward. These states can be dangerous for both individuals and societies. Dogmas and their immutable restrictions are particularly harmful to knowledge creation. They limit the capacity to criticize as well as to make conjecture.

Woven into Marletto’s case for counterfactuals is her love letter to science and the art of explanation:

Physics is like a spectacular firework show. It is beautiful, profound and informative. Physics is all about finding solutions to problems within our knowledge of reality and formulating explanations that can fill the gaps. Physics does not just concern the specific calculation that led to the apple falling. 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. They are the explanations that make this amazing stuff: they reveal things previously undiscovered and far from our intuitive abilities, all in the interest of solving a 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. Although none of these elements are visible in the sky, they all contribute to the explanation of why the sky looks the way it does. Explainations describe what we see in terms of generally invisible elements.

“Spectra of various light sources, solar, stellar, metallic, gaseous, electric” from Les phénomènes de la physique by Amédée Guillemin, 1882. Available as both a printed version and as an embroidered 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. These other explanations are necessary sometimes in order to understand the entire physical world.

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 wrote:

It happens as it always does with contradictions: something has to give in your assumptions.


The act of declaring something impossible makes it possible for more things to be made.

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).

Alice and Martin Provensen’s 1956 Iliad illustrations of the Minotaur and Theseus are reproduced here by Martin Provensen.

Marletto writes:

Theseus was the son of Aegeus, King of Athens. He went to Crete to fight against the Minotaur. Theseus reached an agreement with his father, stating that, if they defeated the Minotaur their crew would bring white sails to the ship. If he died, the crew would carry black sails. Theseus went off and 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 didn’t tell his crew about the sails. Aegeus thought that his son had died when the crew removed the black sails. Aegeus could also see the approaching ship from the top tower at Athens. Then he fell into the ocean and drowned. This is how the Aegean sea was named.

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. Particularly, properties that relate to what might or couldn’t be done to systems of physical nature cannot be referred to by him.

It turns out that this task is impossible. In order for the story’s meaning to make sense and convey its full meaning fully, there are two characteristics of the ship: the first, the one. It can also be used for sending 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. Copiability is a property that indicates the flag may contain information.

The myth of Theseus would lack the counterfactual properties and be devoid of any sense. It could also not produce the devastating feeling or shift in understanding that gave rise to the millennia long 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:

Counterfactuals allow entities to appear superficially as immaterial abstractions to be brought into the realm of physics. Information and knowledge, for example, have been traditionally considered as mere abstractions — as things that do not belong to the physical world. This idea is refuted when one considers the actual properties of physical systems that allow information and knowledge. The laws of Physics determine whether or not physical systems have those properties.

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 both a printed copy and as an embroidered 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. Although I believe it follows the same rules as grass and rocks, we still have to discover these laws to understand how they apply to our minds.

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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