L4 BK14 Can We Trust What We See?

We trust our eyes—but what if seeing is not the same as knowing?

Inspired by the extraordinary art of M.C. Escher, Can We Trust What We See? explores how simple rules can generate complex worlds, how perspective changes what appears possible, and how our cognitive frameworks shape the reality we experience.

Moving between art, mathematics, modern science, and ancient Eastern approaches to perception, Fang Tianliang examines impossible buildings, transforming patterns, self-drawing hands, and images without a clear beginning or end. The book does not ask readers to reject what they see, but to look again—and to recognise how much may remain beyond the limits of ordinary perception.

CAN WE TRUST WHAT WE SEE?

A Journey Through Vision, Cognition, and the Boundaries of Reality

PREFACE

This is a book about “seeing.”

Its throughline is the artistic journey of the Dutch printmaker Maurits Cornelis Escher, spanning half a century, together with the major Escher retrospective held at Somerset House in London in the summer of 2026. Around this thread, the book weaves in the latest research from visual neuroscience, a series of revolutions in the history of science, and the searching questions that ancient Eastern and Western philosophy have asked about the relationship between perception and reality — all in an attempt to guide the reader through a shift in thinking, from blind faith in the senses to the deliberate construction of what this book calls a “cognitive framework.”

Throughout, the book strictly distinguishes between different levels of content: historical fact; neuroscientific phenomena that are well established; influential but still-contested contemporary theoretical hypotheses (such as the predictive-processing model or the interface theory of perception); and the resonances between Eastern and Western ancient philosophy and modern science. Where a hypothesis is contested, this book never presents it as settled fact. Where ancient philosophy offers wisdom, this book never forces the claim that it “predicted” modern science. What is truly worth treasuring is never a superficial coincidence, but the shared humility and courage with which human civilizations, across different eras and cultures, have used different methods to ask the same question again and again.

Now, follow me — beginning with an exhibition in London, just after the rain.

PROLOGUE: The Gallery After the Rain

Try to answer an almost absurdly simple question: is the world you are seeing with your own eyes, right now, the way it actually is?

Don’t rush to say yes. Give yourself three seconds.

Every morning, the instant you open your eyes, sunlight, lines, and the outlines of objects pour into your brain — without a flicker of delay, without a second’s hesitation. We tend to believe, without a moment’s thought: “I saw it, so it’s real.” This belief is so smooth, so automatic, that we almost never notice that behind every act of “seeing” lies an entire process of construction — complex, precise, and, in its own way, rather arbitrary.

In psychology and philosophy, this tendency to treat one’s own perception as a direct transcript of the world’s true appearance is deeply rooted in everyday experience. It is called “Naive Realism.” It functions like a default setting built into our perceptual system — one that makes us unconsciously certain that our eyes are a faithful high-definition camera, that whatever the outside world looks like, our retinas simply take it in whole, with no translation, no interpretation, no human editing in between.

But what if this journey — across modern art, visual neuroscience, evolutionary models, the history of science, and ancient epistemology — is about to tell you something entirely different? What if “seeing” was never a simple act of reception at all, but an unending negotiation between the brain and the world?

Summer, 2026. London. The rain has just stopped; the flagstones along the Thames still hold a damp sheen. The heavy wooden doors of Somerset House swing slowly open, and over the gallery’s speakers, an English voice quietly announces: the exhibition opens in five minutes. The crowd files in, footsteps echoing clearly on the wooden floor, murmurs and the rustle of paper guides drifting in from somewhere further off.

This journey will begin with an artist. In his lifetime, he depicted more of one thing than anything else — not people, not landscapes, but rules themselves.

CHAPTER ONE: The Awakening at the Alhambra

At the entrance to the gallery stands an enormous image: countless ordinary-looking black-and-white geometric shapes undergo an impossible, continuous metamorphosis before your eyes — fish become birds, birds become triangles, triangles become darting lizards. On the wall is a name that has shaken not only the art world, but for more than half a century has captivated mathematicians, architects, programmers, and cognitive scientists alike: M. C. Escher — Maurits Cornelis Escher.

Why, in the twenty-first century, do people still line up to see the work of a Dutch printmaker who died more than fifty years ago?

He never painted the Mona Lisa, never painted Sunflowers, and rarely depicted landscapes or portraits at all. In his work there is almost no trace of soft light and shadow, no ambiguous emotion, none of the fleeting instant that Impressionism prized. Instead, with an extraordinary geometric precision, he cut a fissure into the picture plane — he was not copying the natural world; he was dismantling the hidden rules by which the human eye and brain construct that world in the first place.

Before we go further, it’s worth pausing to meet the man himself. Maurits Cornelis Escher was born on June 17, 1898, in Leeuwarden, in the Dutch province of Friesland, the youngest son in his family. His father, George Arnold Escher, was a hydraulic engineer who had once been invited by the Meiji government to work in Japan for several years before returning home to become chief engineer of the water authority in Leeuwarden; his mother, Sara Gleichman, was his father’s second wife. Escher had an older half-brother, Berend George Escher, who would go on to become a professor of geology at Leiden University — a sibling relationship that would later, quietly, plant the seed of crystallography in his younger brother’s work.

As a boy, Escher was an unremarkable student, but his gift for drawing stood out. In 1919 he enrolled at the Haarlem School of Architecture and Decorative Arts, initially to study architecture, but switched to the graphic arts within a week. In 1924 he married Jetta Umiker, a Swiss woman he had met while travelling in Italy; together they had three sons — Giorgio, Arthur, and Jan. For the next decade or so, the family moved between Rome, Switzerland, and Belgium, before finally settling in the Netherlands in 1941. Escher died on March 27, 1972, in a hospital in Hilversum, at the age of seventy-three.

For most of his life, Escher was largely overlooked by the mainstream art world, gaining broad recognition only late in life — he did not receive a proper major retrospective until he was seventy. Yet within mathematics and science, his influence only grew. Douglas Hofstadter’s Pulitzer Prize–winning 1979 book, Gödel, Escher, Bach, takes its title from him and draws heavily on his work as a central metaphor. His imagery has also seeped into popular culture — from album covers and comic books to films like Inception and video games like Monument Valley, his impossible buildings and looping staircases are everywhere. In a strange and singular way, this quietly obscure Dutch printmaker ultimately came to be claimed, with equal seriousness, by both art history and the history of science.

To understand the starting point of this lifelong exploration, we need to turn back the clock to the autumn of 1922.

That year, the twenty-four-year-old Escher travelled to the Alhambra in Granada, Spain, for the first time. Sunlight streamed through carved archways onto walls and floors covered in Moorish mosaic tilework. In the Mexuar Hall he copied a sixteen-pointed star pattern, then moved on — this first visit was more a stop on a longer journey than a decisive turning point. For the following decade or so, Escher lived in Italy, devoted mainly to landscape prints, and largely set the memory of the Alhambra aside.

Fig. 1-1 | Court of the Lions, Alhambra, 1871. The Alhambra's geometric ornament, repetition and continuous patterns became an important source of inspiration for Escher's later exploration of tessellation.

Photograph by Juan Laurent, c. 1871. Source: Department of Image Collections, National Gallery of Art Library, Washington, DC. Rights: Public Domain / free of known copyright restrictions.

The real turning point came fourteen years later, in the spring of 1936. That year, Escher and his wife Jetta sailed along the coasts of Italy and France to Spain, where he returned once more to the Alhambra and also visited the Mezquita in Córdoba. In the centuries before this, the mainstream of Western art had been perspective — the faithful depiction of nature and human figures, the use of light and shadow to construct the illusion of three-dimensionality. Painters since the Renaissance had, almost without exception, pursued a single goal: making the flat, two-dimensional canvas look like a true slice of a three-dimensional world. But at the Alhambra, because Islamic religious tradition restrained the use of figurative human sculpture, Moorish craftsmen had carved out an entirely different path: tessellation.

One tile interlocks with the next; black polygons fit seamlessly into white ones, without a millimetre of gap, without a moment’s pause, spreading across the space in every direction as precisely as a mathematical formula — as if the wall itself were a frozen proof, one that could, in principle, extend forever. This time, Escher and Jetta stayed at the Alhambra for a full three days, standing together on the smooth stone floors, copying into their notebooks geometric patterns whose very names he could not identify. He later wrote that the Moorish craftsmen were “masters at filling a plane with similar, interlocking figures,” and called this second visit “the richest source of inspiration” of his life.

Fig. 1-2 | From a single rule, interlocking shapes define one another, unfolding into an order that appears infinite.

Original illustration.

The Alhambra brought Escher, for the first time, to a powerful realization: the shapes in a design are not simply “placed” there in isolation from one another; they interlock, they define one another. What truly determines the overall visual order is not any single, isolated shape, but the relationships between shapes — black exists precisely because white yields its boundary to it; white exists precisely because black defines its outline in return.

After returning from this second visit, Escher began an exploration that would occupy the rest of his life. Step by step, he began stripping away the visual assumptions we never think to question — first, that figure and ground are fixed; then, that up and down are absolute; and finally, even the last and most fundamental assumption of all — that the observer can stand outside the system being observed.

What the Alhambra left Escher was not a single flash of insight, but a methodological inheritance that would carry through nearly four decades of his career. Back in the Netherlands, he began systematically organizing his research into what he called the “Regular Division of the Plane,” working through the same geometric motifs again and again in pencil and watercolour in private notebooks — how a lizard’s outline needed to deform in order to interlock seamlessly with its neighbour; how a set of triangles needed to twist to preserve both symmetry and recognizable figuration. According to scholars who have studied Escher’s tessellation work, the surviving studies in these notebooks number in the hundreds, and many were never turned into finished prints at all — they were purely private exercises through which Escher sharpened this “visual grammar.”

This also explains why later works as stylistically different as Sky and Water, the Metamorphosis series, and Waterfall all share, underneath, the same underlying logic rooted in the Alhambra: shapes interlocking with no gap between them. In a sense, what the Alhambra gave Escher was not the inspiration for any single work, but an entire creative language he could call on again and again, deepening it each time — which is why, whenever this book returns later to the theme of how shapes define one another, its origin can always be traced back to those three days in Granada, under the midday sun of 1936.

CHAPTER TWO: The Geometric Awakening — When an Artist Begins to Think Like a Mathematician

Shortly after returning from the Alhambra in 1936, Escher showed his tessellation studies to his half-brother, Berend “Beer” Escher, a professor of geology at Leiden University who specialized in crystallography. Beer immediately noticed that his younger brother’s seemingly free-form patterns bore a striking resemblance to the mathematical structures of “plane symmetry groups” studied in crystallography, and sent him a short reading list — including the Hungarian mathematician George Pólya’s classic paper on the seventeen plane symmetry groups, or “wallpaper groups.” Escher devoured this material, gradually translating its underlying mathematics into the endless fish, lizards, and birds that would fill his canvases.

Historians of mathematics have since noted a striking coincidence: of the seventeen plane symmetry groups mathematically proven to exist, as many as thirteen already appear in the tile decorations of the Alhambra — meaning that centuries earlier, Moorish craftsmen, guided by pure craft intuition and geometric aesthetics, had already, without realizing it, come close to exhausting most of the plane-symmetry possibilities that mathematicians would only later prove and classify with rigour. It was under Pólya’s guidance that Escher first came to understand that the patterns he had copied by intuition at the Alhambra concealed, beneath their surface, an entire mathematical structure that could be enumerated, classified, and proven complete — which is why he later gave his lifelong tessellation research the formal name “Regular Division of the Plane,” and in his private notebooks numbered and classified each group of designs with something close to the rigour of a mathematical paper.

Escher himself never received any formal mathematical training; he was, in a sense, an artist who approached mathematical truth by pure intuition. And it was precisely because of this that his work would later be so warmly embraced by professional mathematicians. In 1954, the International Congress of Mathematicians was held in Amsterdam, and its organizing committee arranged a solo exhibition of Escher’s work at the Stedelijk Museum — a remarkable event in the history of art: a painter with no formal mathematical education, invited with full seriousness into the inner sanctum of the mathematical world.

At that exhibition, a twenty-three-year-old British mathematics student was profoundly struck. His name was Roger Penrose — more than half a century later, he would win the Nobel Prize in Physics for his contributions to general relativity and black hole theory. By his own account, seeing Relativity (1953) at that exhibition left him “absolutely spellbound.” Back in England, he tried designing paradoxical figures of his own and produced the “Penrose triangle.” His father, the geneticist Lionel Penrose, was inspired in turn and, building on his son’s work, designed the “Penrose stairs” — a flight of steps that appears to climb continuously upward while somehow, impossibly, always returning to where it began. Father and son published this discovery in 1958 in the British Journal of Psychology.

When Escher later learned of the Penrose stairs, he seized on the idea eagerly, transforming it into one of his most famous works — Ascending and Descending (1960). In the print, a procession of grey-robed monks walks around a rooftop cloister, one line perpetually “ascending,” another perpetually “descending” — yet the staircase joins seamlessly back on itself, forming a fully closed loop. What makes this exchange so striking is its reciprocity: Escher, inspired by Penrose’s work, created Ascending and Descending and, the following year, Waterfall — while Penrose’s original paradoxical figure had itself been sparked by Escher’s art. It was a rare instance of genuine two-way dialogue between art and mathematics.

This dialogue was more than a one-way borrowing of technique. The paper Penrose and his father published in 1958, titled “Impossible Objects: A Special Type of Visual Illusion,” appeared in a psychology journal rather than a mathematics journal — itself telling, since it shows that these “impossible figures” were, from the start, simultaneously a product of geometry and an object of study for perceptual psychology, concerned both with whether such a structure could be drawn at all and with how the visual system could be deceived by it. Escher’s pen and the Penroses’ paper were, in effect, converging on the same core question from two different professional directions. At that same 1954 exhibition, the Canadian mathematician Donald Coxeter was likewise deeply moved, and later explained the principles of hyperbolic geometry to Escher, inspiring the celebrated late-career Circle Limit series — a set of prints that compress infinite tessellation into a single finite disc. In a sense, the second half of Escher’s career was continually reshaped by this two-decade-long, two-way dialogue with the world of mathematics.

That dialogue also transformed Escher’s public role entirely. In the years that followed, this printmaker — who had never even completed formal mathematical training — was repeatedly invited onto podiums that had once belonged exclusively to professional scholars: he was invited to speak at the International Congress of Crystallography in Cambridge, explaining to professional crystallographers the tessellation principles he had spent decades working out in his notebooks; he also travelled to MIT in the United States to speak to a room of mathematicians and engineers about the geometric logic behind his work. Escher himself once admitted, in a letter, that he “always held exact science in the greatest respect” — his father and several of his brothers had backgrounds in engineering or the natural sciences, a family atmosphere that may well have quietly shaped the temperament he brought to his art: sensitive and imaginative, yet obsessed with structural precision.

What makes this print so significant is this: if you look at any single short stretch of the staircase, it obeys the rules of perspective and gravity perfectly — nowhere is there a “local error.” Yet if your eye follows the staircase all the way around, you find that you have somehow, impossibly, gained or lost an entire storey of height — something absolutely impossible in the physical world.

In cognitive science, figures like the Penrose stairs are called “impossible figures.” They work because the visual system, when interpreting an image, habitually analyzes local relationships between lines and angles and then infers an overall three-dimensional structure from them; an impossible figure exploits exactly this vulnerability in local inference — every individual local inference is valid, but when all of them are stitched together, the whole becomes logically incoherent.

This is Escher’s first great lesson: the eye does not “photograph” a scene all at once. It works like a detective, piecing together clues step by step to reach a conclusion. And anyone who understands this process well enough can design a set of clues that seem airtight and yet contradict one another — leading even the most rational mind to willingly arrive at a conclusion that cannot actually exist.

From the tiles of the Alhambra to Penrose’s paradoxical staircase, it took Escher more than twenty years to forge himself from a mere “pattern enthusiast” into something closer to a genuine “visual logician.” And what he did next would be even more radical — he was about to make the image itself begin to move.

CHAPTER THREE: Beyond the Medium — A Panorama of Escher’s Work

Before we go deeper into the secrets of the eye and the brain, let’s pause a little longer in the gallery and meet a few more old friends — several other masterpieces Escher left the world, each interrogating, in its own way, the same question: what, exactly, are we looking at?

Consider first Waterfall (1961). A water channel winds down a series of steps that appear to continually “descend,” finally plunging to drive a waterwheel — yet on closer inspection, the channel loops back on itself, and the water seems to cycle endlessly upward without any external force doing work. Waterfall is another peak achievement in Escher’s “impossible figure” series, borrowing the same paradoxical triangle structure — the Penrose triangle — devised by Penrose and his father. What makes this print especially deceptive is that Escher carefully surrounded the channel with two ordinary-looking, pagoda-style towers; the “normality” of these everyday objects dilutes and obscures the paradox at the structure’s core, making it that much harder for the eye to catch. It’s a reminder, too, that the more a paradox is wrapped in an ordinary exterior, the harder it becomes to notice, let alone question.

This print carries another layer of meaning, easy to overlook, that connects directly to the book’s central theme: if you isolate any single stretch of the channel in Waterfall and examine it on its own, it fully obeys the basic common sense of fluid dynamics — water flows from high to low, and a drop in elevation produces a waterfall; everything checks out. What produces the paradox is never a single “wrong” segment of the image; it is Escher stitching together three individually correct segments in a way that violates the overall topology. This echoes a point this book returns to again and again: the hardest errors to detect are rarely hidden in any one specific judgment — they are hidden in the way we carelessly stitch several individually reasonable judgments into a single overall account, whether in a print or in real-world reasoning.

Consider next Metamorphosis II (1939–1940), a scroll nearly four metres long. It begins on the left with the word “METAMORPHOSE” spelled out in neat lettering, which gradually becomes a checkerboard, which becomes crawling lizards, which become a honeycomb, from which black-and-white birds take flight, which slowly turn into fish, which swim off into a realistic depiction of an Italian town in the distance. The Metamorphosis series is widely regarded as the definitive statement of Escher’s entire artistic philosophy. Nowhere in this long scroll is there a sudden, jarring leap; every transformation grows organically out of the one before it.

It’s worth looking closely at the internal structure of this scroll: Escher doesn’t simply let the sequence advance along a single straight line — instead, the transformation periodically “loops back.” After text becomes pattern, partway through the scroll the pattern turns back into text again (this time spelling “EMBLEMATA”), as if to remind the viewer that “beginning” and “end,” along a sufficiently long chain of continuous change, are themselves relative and arbitrary markers, depending entirely on where we choose to start reading and where we choose to stop. And the black-and-white birds that gradually “hatch” from the honeycomb in the middle section — the outlines of their wings and bodies are, in fact, direct extensions of the black-and-white checkerboard boundaries from the section before. With remarkable restraint, Escher demonstrates that even two images as intuitively unrelated as a “hexagonal honeycomb” and a “bird in flight” can reach one another along a purely geometric, continuous path.

This offers an important lesson. In daily life, we habitually carve the world into clean categories — this is a bird, that is a fish, this is text, that is pattern — as if these categories were boundaries the world had already drawn for us in advance. Metamorphosis at least reminds us that many categories we take to be sharply distinct may, on some scale, shade continuously into one another; the classifications we treat as self-evident also carry a measure of shaping by cognition and language. The line between bird and fish, between text and pattern, may not be as natural or absolute as our intuition suggests — this is not to say every classification is arbitrary, but rather that at least some of the boundaries we take for granted are worth re-examining: do they belong to the things themselves, or to the way we observe and name them?

Finally, there is Three Worlds (1955): a still pond, its surface scattered with yellowed fallen leaves, its water reflecting the bare trees along the bank, and beneath the surface, a large fish gliding silently by. This print — the most “realistic” of the three, containing almost no geometric paradox at all — reveals a subtler visual truth of its own: within the same body of water, at the same instant, three nearly independent “worlds” are layered on top of one another. The leaves on the surface belong to the world above ground; the reflection belongs to a mirrored, inverted sky; the fish beneath belongs to an entirely different underwater dimension. All three share the same patch of paper, yet each obeys its own set of physical logic and causality.

Look closely at the composition and you’ll notice that Escher deliberately placed the leaves, the reflection, and the fish at three slightly offset visual focal points — the outline of the leaves is sharpest and catches the eye first; the reflection of the bare trees is a step softer, its edges slightly blurred; and the fish beneath the surface is submerged in the deepest, haziest layer of visual information, requiring the viewer to actively redirect their attention to “fish” it out of the water’s shadow. This carefully engineered visual hierarchy quietly anticipates a central proposition of the next chapter: when the eye takes in a single field of view, it is not passively “receiving” all the information at once, but actively shifting focus between layers according to some priority. With a landscape print containing almost no geometric trickery at all, Escher plants, in advance, a perfect visual seed for the neuroscience discussion the book is about to unfold.

With a print that employs almost no illusionistic trickery at all, Escher shows us something remarkable: even without any deliberate geometric deception, the ordinary optical phenomena of transparency and reflection are enough to let a single field of view hold several otherwise disconnected worlds at once. We tend to treat “what’s in front of us” as one unified, singular scene, forgetting how often our field of vision may actually be carrying several independent layers of reality that simply happen, at this particular moment, to overlap geometrically.

From the water that defies conservation of energy in Waterfall, to the continuous spectrum linking text and fish in Metamorphosis, to the three overlapping realities of Three Worlds — again and again, with his burin and his engraving tools, Escher demonstrates that the visual world is far more elastic, and far more deceptive, than we imagine. It can be torn apart by paradoxical logic; it can be stretched and kneaded seamlessly across categories; and it can hold, within a single image, several independent realities coexisting in harmony.

With these questions in mind, let’s move on to Escher’s three most celebrated masterpieces — Sky and Water, Belvedere, and Relativity — and see what happens when the image itself truly begins to move.

CHAPTER FOUR: The World Begins to Move

Picture Escher’s famous print Sky and Water: at the top, a black bird soars through a daylit sky; at the bottom, a white fish glides through nocturnal water. As your eyes move from top to bottom, a transformation unfolds quietly: gaps between the black bird’s wings begin to take on the outline of white fish; the sky’s white background becomes fish-shaped; in the middle row, bird and fish interlock completely, each defining the other’s boundary; and as your gaze continues downward, the bird dissolves into darkness, leaving only living white fish swimming through the water.

So: which is the subject — the bird, or the fish?

In perceptual psychology, this corresponds to the classic concept of “figure-ground organization,” first systematically proposed around 1915 by the Danish psychologist Edgar Rubin, whose iconic example is the famous “Rubin’s vase” — a black goblet that is, at the same time, two white faces turned toward one another in profile.

Human visual perception tends, at any given moment, to organize one set of shapes as the “figure” (the foreground subject) and another as the “ground” (the background); when attention shifts, the relationship between the two reverses — and this reversal is often involuntary. You can try to “decide” that you will see only the vase, and still find that the two faces reassert themselves without your consent. We assume we are taking in every detail of a scene at once, but in fact the brain, moment to moment, is constantly editing what counts as foreground and what counts as background — following rules that are not even fully under our conscious control.

This phenomenon, in which perception flips spontaneously between two interpretations without ever settling stably on both at once, is known in perceptual psychology as “bistable perception.” Rubin’s vase and another classic example — the Necker cube, a wire-frame outline of a transparent cube that can be seen from two different viewing angles — both belong to this category. When neuroscientists use brain imaging to study bistable perception, they find that even though the retinal image presented to both eyes never changes at all, when a subject reports their subjective perception flipping from one interpretation to the other, activity patterns in several higher-order cortical regions responsible for integrating visual information shift markedly as well. This finding is highly suggestive: it means that what determines “what we see” is not the external stimulus alone — some higher-level interpretive framework inside the brain is participating in, and even driving, this cognitive process in real time. This is also why the same image of Rubin’s vase can produce strikingly different subjective experiences across different viewers, or even in the same viewer at different moments.

In cognitive science, this class of phenomena — in which a single sensory input can support two mutually exclusive but equally stable interpretations — is collectively known as “multistable perception.” Rubin’s vase is the best-known example; another classic case is the Necker cube: an outline of a transparent cube built from just twelve line segments, whose orientation the brain involuntarily flips between two equally valid three-dimensional readings, never managing to “see” both at once. Researchers have found that this switching is not entirely random, but is linked to a process of “competitive inhibition” that plays out continuously among local neural circuits — multiple conflicting interpretations briefly suppress one another at the neural level, until one temporarily “wins” and becomes the version we consciously register in that moment, before gradually being suppressed and overtaken again by the other. This is a reminder that even facing the same, entirely unchanging sensory information, the brain does not necessarily have only one “correct” way of organizing it — often, what’s actually present is not a single stable answer, but two or more possible interpretations locked in continuous, alternating contention.

If Sky and Water demonstrates the reversal of figure and ground, Belvedere displays an even subtler visual paradox: every local detail is correct, yet the whole is in complete contradiction. The columns on the lower level of the belvedere stand in front; the columns on the upper level stand behind. Looked at in isolation, the upper level’s joinery and stonework obey geometry perfectly; so does the lower level, on its own. But by crossing and displacing the columns, Escher forces the front and back of the structure to interweave impossibly — and in the lower-left corner, a boy sits on a bench holding an impossible cube, as if hinting that the entire building has grown out of this small illusion-toy. The mind keeps trying to revise between two conflicting spatial interpretations, never able to find a single stable account that can hold both at once.

At the very bottom of Belvedere, there is also a figure confined in what looks like a dungeon-like cell, holding the very same drawing of the impossible cube — as if imprisoned for having “grasped” this impossible figure. This detail is often overlooked by viewers, yet it carries real weight: it hints that once someone truly sees through the paradoxical structure behind a particular visual logic, what follows is not necessarily an easy epiphany — it may instead be a kind of exclusion, a status as an outsider. This forms a distant but clear echo with the fate of the prisoner who leaves and then returns to Plato’s cave, which we will discuss later in this book.

And in the masterwork Relativity, Escher goes further still, removing one of the most basic physical assumptions we take for granted: gravity. The print shows a building laced with an intricate network of staircases, with figures climbing up and others walking down — yet, on closer inspection, they are all walking on different sides of the very same staircase. Within this space, three mutually perpendicular directions of gravity coexist at once. For someone standing on one face, a surface is flat ground; for someone on another face, that same surface is a sheer wall. Everyone walks with perfect composure, because each figure is faithfully obeying the gravity of their own particular orientation. When two figures pass each other at one of the building’s intersections, they come remarkably close — and yet they inhabit entirely different axes: for one, it’s a gentle downward slope; for the other, a wall to be climbed.

Look closely at how this print is constructed, and you’ll notice that Escher never lets the three systems of gravity “fight” one another — quite the opposite: within each local region, the figures, furniture, doors, and windows all strictly obey the single system of gravity that applies there, arranged neatly, without a single flaw. What actually produces the sense of paradox is not any local error at all, but the fact that these three self-consistent, mutually incompatible logical systems have all been placed inside the same building, on the same sheet of paper. This is a reminder that the hardest cognitive biases to detect rarely occur where “some specific judgment went wrong” — they occur where we never realize that the entire standard of judgment we rely on may itself be only one of many equally self-consistent, mutually contradictory systems.

Here we arrive at the single most important concept in this entire book: what I will call, from this point on, the cognitive framework.

Fig. 4-1 | We may be looking at the same world, yet experience, knowledge, culture, values and needs influence what we notice and how we organise and interpret what we see. A cognitive framework is not reality itself, but it helps shape how we understand reality.

Original illustration.

(A note on terms: this book uses “cognitive framework” to describe the default structure a person gradually forms, through upbringing, education, culture, and experience, for making sense of the world. It bears some resemblance to what ancient Eastern thought called “views” or “notions,” though the two are not fully equivalent.)

Isn’t this how we live in the real world — walking through this same building from Relativity? Each of us stands on a cognitive framework built from our own upbringing, education, and values. The “common sense” beneath our own feet may, in someone else’s framework, be an impassable wall. We believe we are debating the same objective reality, when in fact we are each simply walking forward along our own axis of gravity — until, at some moment of collision, we suddenly discover that what was “obvious” to us is entirely incommensurable with what was “obvious” to someone else.

In the later part of his career, Escher’s work turned toward ultimate recursion and self-reference. In Drawing Hands, a left hand holds a pencil, sketching the cuff of a right hand — while that same right hand’s pencil is, in turn, sketching the wrist of the left. Outside the frame is Escher’s own, real hand, which drew both of these fictional hands, each creating the other. Which hand created which? Or was it, in fact, that unseen third hand outside the frame that created them both?

What makes this print so haunting is that it takes a puzzle that would otherwise belong purely to logic and linguistics — the “self-referential paradox” — and renders it in the most direct, visual form imaginable. Much as the sentence “this sentence is false” resists any simple judgment of true or false, the “creator status” of each hand in the image sits inside a loop that can never be independently confirmed: each hand is, at once, both creator and created. Using nothing more than plain pencil drawing, Escher touches one of the thorniest problems in twentieth-century logic — and in doing so, he anticipates a core difficulty this book will return to later: when we try to use the brain to understand how the brain itself works, the very “tool of understanding” we are using is exactly the object we are trying to understand. Observer and observed have already, quietly, begun to overlap.

And in Print Gallery, a young man stands in a gallery looking at a print; the print depicts a seaside town, and the buildings within it curl outward until they wrap around and enclose the very gallery in which the young man is standing! At the very centre of the composition — the point where this spiral structure should logically converge — Escher never actually drew anything at all: he left a small blank space there. Nearly half a century later, that blank was finally filled in by mathematicians using computation (a story this book will tell in full in its final chapter).

The spiral structure of Print Gallery is, in fact, built on a mathematical self-similar scaling pattern sometimes called the “Escher spiral” (a variant of the Droste effect): the image begins in the real space where the young man is standing, and expands and distorts clockwise, eventually returning, mysteriously, to that same space — as if the boundary between reality and the painting within the painting were itself a single, seamless Möbius strip. Mathematical analysis has since shown that the distortion Escher completed by hand, purely by intuition, aligns remarkably closely with the theoretical model later derived rigorously by computer — further proof that although Escher never received formal mathematical training, decades of visual intuition had already brought him to the edge of an extraordinarily precise geometric law.

The observer, in the end, becomes part of the system itself. The one looking at the print discovers that he is standing inside it; the eye that tries to observe reality discovers that it is, itself, part of that reality.

Across half a century of artistic life, Escher posed a profound question: if our eyes can so easily be led astray by local logic, if the brain habitually fills in a scene according to its own fixed rules — then who, really, is doing the “seeing” here? The eye, or the brain?

CHAPTER FIVE: Who Is Really Seeing? — A Journey Inside the Dark Chamber of the Skull

To answer the question Escher raised, we have to leave the gallery and enter the laboratories of modern visual neuroscience.

Conventional intuition holds that the eye works like a high-precision camera: light strikes the retina, and the optic nerve transmits the image, unaltered, to the brain, which simply “plays back” the recording. But decades of research in visual neuroscience show this to be, in almost every respect, a misconception.

To begin with the physiology: your eye is not a full-frame, high-resolution camera. Only a narrow region at the very centre of the retina, the fovea, offers high resolution and clear colour and detail discrimination — and its field of view is only about two degrees, roughly the width of your thumbnail held at arm’s length. Beyond this, in the peripheral visual field, the density of photoreceptor cells drops sharply and rod cells (which are more sensitive to light and dark than to colour or fine detail) predominate, so spatial resolution and the ability to discriminate detail and colour both decline markedly.

Fig. 5-1 | Human vision is not like a uniformly high-resolution camera. ① Central vision (fovea): high acuity, ~1–2°. ② Peripheral vision: moderate to low acuity, ~2°–60°. ③ Far peripheral vision: low acuity, beyond 60° up to ~200°.

Original illustration.

This design — sharp at the centre, blurred at the periphery — is, from an evolutionary standpoint, an extremely shrewd allocation of resources: densely packing high-resolution photoreceptors across the entire retina would carry an enormous cost, and if the whole retina matched the density of the fovea, the resulting volume of neural data would far exceed what the brain could process. Evolution chose a more economical path instead — investing high resolution only in the small central region that most needs fine discrimination, and leaving the vast peripheral region to rod cells, which sacrifice detail resolution in exchange for greater sensitivity to motion and changes in light. This is precisely why the eye relies on rapid eye movements called “saccades,” continually redirecting the fovea to different points in the visual field, so that, over time, the brain can stitch these scattered, high-resolution “snapshots” into what feels like a single, seamless, continuous image — the subjective sense that “the entire visual field is equally sharp” is, on the leading account, substantially a product of this ongoing process of integration rather than a direct readout of the retina.

What’s more intriguing still: during each saccade, the eye sweeps across a stretch of the visual field at extremely high speed — if this rapidly moving image were transmitted to the brain unaltered, we ought to see a violent, dizzying blur, the visual equivalent of filming video while shaking a phone wildly. Yet in practice, we never notice any such blur at all. One well-supported explanation is that visual sensitivity is reduced around the moments of each saccade — a phenomenon known as “saccadic suppression” — so that much of the chaotic visual information that would otherwise appear during each rapid eye movement is, in effect, screened out, leaving us instead with a sequence of seemingly continuous, stable still images. As you read this very sentence, your eyes are jumping rapidly from point to point again and again — and yet you feel no blur, no gap at all. Saccadic suppression is one of the mechanisms thought to be quietly at work behind that seamlessness, right now.

What’s more, every human retina has a blind spot — a point where the optic nerve passes through the retina, leaving no photoreceptors at all. You can try a simple experiment: close one eye, fix your gaze on a point, and slowly move a pen through your peripheral field of view; at a certain position, the tip of the pen will briefly “vanish” — that’s the moment its image falls exactly on the blind spot.

Fig. 5-2 | Every human retina has a blind spot with no photoreceptors at all — the brain simply fills it in without you ever noticing.

Original illustration.

So why, in everyday life, do you never notice your peripheral vision going blurry, and never see a black hole hovering in the middle of your visual field?

One influential explanation in contemporary cognitive science holds that the brain is not a passive receiver of visual signals at all, but is constantly using prior experience and context to predict, complete, and correct its input. This is called the “predictive processing” model, one of the most influential theoretical frameworks in neuroscience and cognitive science over the past two decades, associated with researchers such as Karl Friston and Anil Seth.

In this model, the brain sits sealed inside the skull, with no direct access to the physical world outside — like a windowless chamber. All it receives is a stream of electrical pulses carried by the optic nerve — signals that, in themselves, have no colour and no shape; they are simply variations in the firing rate of neurons. To make sense of its environment efficiently, the brain draws on past experience and its current cognitive framework to construct, in real time, a prediction of what the world “ought to look like,” and then uses the incoming sensory signal to test and correct that prediction.

This mechanism is often compared, mathematically, to a process of Bayesian inference: the brain holds a “prior probability” grounded in past experience (for example, that tablecloths are usually continuous and unbroken), and when new sensory signals arrive, it combines that prior with the incoming evidence to compute a “posterior probability” — the most plausible interpretation of the current scene — which then immediately becomes the new “prior” for the next instant, in an ongoing loop. The neuroscientist Anil Seth has vividly described this process as a form of “controlled hallucination” — the world we “see” is, fundamentally, the brain’s best guess, generated through probabilistic inference; and that guess happens to be so accurate that it aligns closely with the world outside, which is exactly why we almost never notice that it is a guess at all. It’s worth being precise here about the term “controlled hallucination” as well: this is an explanatory metaphor used by researchers such as Seth to describe a general theoretical account of perception — it does not mean that ordinary, everyday seeing is a hallucination in the clinical sense; rather, it highlights that the visual experience we take to be a passive “recording” is, in fact, an actively constructed process.

If the brain’s predictive model expects a continuous stretch of wall or tablecloth pattern at a given point, then even where the blind spot receives no light signal at all, the brain will automatically draw on surrounding context to “fill in” the image, seamlessly, without a trace. This is precisely why Escher’s impossible buildings work so reliably — Escher was, in effect, precisely steering the brain’s own predictive machinery. Local cues trigger a global prediction, and as the eye moves across the image, new sensory signals collide with that earlier prediction, and the brain, caught in a loop of trying to resolve the error, experiences that dizzying visual instability.

The predictive processing model is not the only line of evidence here. In the late twentieth century, the cognitive psychologists Daniel Simons and Christopher Chabris designed a now-famous experiment: “The Invisible Gorilla.” Participants watched a video of six people passing two basketballs back and forth, and were told to silently count how many times the players wearing white shirts passed the ball. Partway through the video, a person in a black gorilla suit walks casually into the middle of the frame, thumps its chest, and walks off again — remaining on screen for a full nine seconds. In the original study, roughly half of the participants, when later asked whether they had noticed anything unusual, insisted they had seen nothing at all.

This is known as “inattentional blindness”: when our attention is heavily concentrated on a given task, even a large, seemingly conspicuous object can go entirely unnoticed if it falls outside the spotlight of our attention. A related phenomenon, “change blindness,” shows something similar: researchers present the same scene twice, with a brief blank flicker in between, and in the second image, some prominent object has changed colour, moved, or vanished entirely — yet many viewers take a surprisingly long time to notice, because the brain, between the two frames, simply carries forward the “scene model” it has already constructed, rather than re-checking every detail frame by frame. Together, these two experiments show that “seeing” depends not only on whether light falls on the retina, but on whether the brain allocates enough attentional resources to actually register and process that signal.

The significance of these two categories of experiment reaches well beyond the laboratory. In the real world, inattentional blindness and change blindness bear directly on issues such as the reliability of eyewitness testimony and the allocation of attention while driving — researchers have found that even experienced drivers, absorbed in operating a navigation system or talking with a passenger, can genuinely fail to notice a pedestrian or vehicle of considerable size in their field of view, and the underlying mechanism is no different from that overlooked gorilla in the lab. This is also why modern traffic-safety education increasingly emphasizes “scanning” and “actively allocating attention,” rather than simply “keeping your eyes wide open” — because the latter, as both experiments make clear, is a naive assumption that is nowhere near sufficient to guarantee safety.

From the standpoint of predictive processing, “attention” itself can be reconceived: it is not a searchlight roaming freely across the visual field, but something closer to a “confidence weighting” the brain assigns to different sensory signals — signals arriving from a heavily attended region are given greater weight, more powerfully correcting the brain’s existing prediction; while signals arriving from outside the spotlight of attention, even when they conflict sharply with the prediction (such as a gorilla sauntering conspicuously through the frame), are assigned much lower weight, and may not be enough to overturn the “scene model” the brain is currently maintaining. In other words, “failing to see” is not a matter of light never reaching the eye — it is the brain deciding that a given signal does not merit priority inclusion in the prediction and interpretation currently running.

Further research reveals that even something as seemingly fixed as “colour” is not, in fact, an intrinsic property of an object. In 2015, an image of a striped dress ignited a global argument on the internet: some people were absolutely certain they saw white and gold; others were equally certain they saw blue and black — and neither side could understand how the other could possibly be seeing something so different. Subsequent research in vision science points to “colour constancy” as the key mechanism at work: when the brain judges an object’s “true” colour, it unconsciously makes an assumption about the lighting conditions under which the image was captured (was this photographed under warm indoor lighting, or cool natural daylight?), and adjusts the raw colour signal from the retina accordingly. Because different brains made slightly different assumptions about the lighting in this particular photograph, the resulting perceived colours diverged into two starkly opposite versions — all from a single photograph, with identical pixels.

Colour constancy itself is, at bottom, a highly practical compensation system that the brain evolved to cope with the enormous variability of natural lighting: midday sun leans toward a cool white, dusk light leans toward a warm orange, and yet across every lighting condition we still tend to perceive a leaf as “green” — the brain is, in effect, automatically subtracting the colour bias introduced by the light source, trying to recover what the object’s colour “ought to be.” This system runs seamlessly in the vast majority of everyday situations, and it is only in edge cases like “The Dress,” where the lighting information itself is genuinely ambiguous or even contradictory, that the “computation” quietly running underneath is exposed. This case demonstrates vividly that colour is never simply “attached” to the surface of an object, waiting passively to be picked up by the eye; it is something the brain actively computes, in the context of assumed lighting.

If the visual examples above are not yet enough to unsettle your intuitions, the ways different senses interfere with one another push the point further still. In 1976, the psychologists Harry McGurk and John MacDonald discovered a peculiar cross-modal illusion, later named the “McGurk effect”: when a video shows someone’s mouth clearly forming the syllable “ga,” while the audio track actually plays “ba,” most viewers “hear” a third sound, somewhere between the two — showing that hearing itself is not an isolated process, but can be hijacked and reshaped in real time by visual information.

Then there is the “rubber hand illusion” — the discovery that overturns something even more unsettling: our confidence in the boundaries of our own body. First systematically reported in 1998 by Matthew Botvinick and Jonathan Cohen, the experiment hides one of a participant’s arms behind a screen, out of sight, while a lifelike rubber hand is placed on the table in front of them, in the same position the real hand would occupy. An experimenter then strokes both the hidden real hand and the visible rubber hand with a small brush, in perfect synchrony. After about a minute or two of this synchronized stimulation, most participants report a strange but utterly convincing sensation: they begin to “feel” that the rubber hand on the table has, in some sense, become part of their own body — so much so that if the experimenter suddenly raises a hammer as if to strike the rubber hand, participants will often flinch and pull back involuntarily, and measurable physiological stress responses (such as changes in skin conductance) can be detected, even though the participants know perfectly well that it is only a piece of rubber. This experiment shows persuasively that even something we take to be absolutely certain — where my body is, where its boundary lies — is not a fixed, objective fact, but rather the brain’s dynamically computed “best guess,” built from the mutual corroboration of vision, touch, and other sensory signals. This echoes, in spirit, Escher’s Drawing Hands: just as those two hands create one another within the frame, the “adopted” rubber hand in the laboratory reminds us, in its own way, that the line between “self” and “other” is far softer than we tend to assume.

The rubber hand illusion matters so much because it touches on “proprioception,” a frequently overlooked sixth sense: the brain relies not only on vision and hearing to judge the external world, but must also continuously track the position of its own limbs in space. This tracking system, too, does not run off some fixed, unchanging “internal map” — it must integrate visual, tactile, and musculo-skeletal signals in real time to dynamically compute “where my hand ought to be right now.” This also explains why, in a small number of post-surgical or nerve-injury cases, patients experience “phantom limb” phenomena — even after a limb no longer exists, the brain may continue generating a “prediction” about that limb’s position and presence, leaving the patient genuinely feeling that the missing arm or leg is still attached, sometimes even registering pain from it. The rubber hand illusion and phantom limb phenomena, approaching from two opposite directions, converge on the same lesson: the body’s boundary is never a fixed fact written into bone and skin — it is an ongoing dynamic computation the brain performs on the basis of multiple sensory signals.

In recent years, as virtual reality (VR) technology has spread, researchers have extended the logic of the rubber hand illusion into experiments on the “full body illusion”: simply by letting a head-mounted-display wearer see, from a first-person perspective, a virtual body that moves in perfect synchrony with their own — even when that virtual body differs entirely from the participant’s actual gender, build, or skin tone — the brain will, before long, begin treating that virtual body as part of its own. These experiments further confirm a theme this book returns to repeatedly: the boundary of the “self” is nowhere near a fixed, innately given setting; it is a soft boundary the brain continually renegotiates based on whatever sensory evidence is currently available — and this is precisely the neuroscientific basis for why virtual reality and immersive technology can so profoundly shape a user’s subjective experience.

Beyond these, perception research holds a few other equally fascinating phenomena: synesthesia, the inborn tendency in some people for one sense to automatically trigger another (seeing a particular colour when looking at a number, for instance); and blindsight, in which patients who have lost conscious visual awareness due to damage to the primary visual cortex can still “guess” the location or motion of objects in their visual field with accuracy well above chance — each, from a different angle, reinforcing just how layered and complex perception really is. Curious readers can find a brief note on each in the appendix.

From the physical limits of the retina, to the predictive processing model’s account of “controlled hallucination,” to inattentional blindness, change blindness, colour constancy, and cross-modal integration — modern neuroscience, from many independent directions, keeps arriving at the same conclusion: what we consciously perceive is not a raw copy of sensory input, but the result of extensive neural processing shaped by sensory signals, prior experience, and attention.

It’s worth pausing here to distinguish three separate levels, so as not to conflate them: what this chapter has discussed is the mechanism by which the brain processes sensory signals at the physiological and neural level; the “cognitive framework” introduced earlier in this book refers to the psychological structure a person gradually builds, through upbringing, education, and culture, for making sense of the world; and the information environment we will discuss later belongs to a social and cultural level entirely. Neural-level perceptual processing, the psychological-level cognitive framework, and the social-level information environment can influence one another, and can form illuminating analogies with one another — but they are not the same concept, and should not be casually strung together into a single causal chain that has, in fact, been scientifically demonstrated. As this book moves forward, it will try to make clear which level it is speaking about at any given moment.

Escher, following his own intuition, touched on a question — who, exactly, is doing the seeing? — that has now found, in the instruments and data of the laboratory, a rigorous echo from an entirely different dimension.

CHAPTER SIX: The Long Disenchantment of Science — From Geocentrism to the Interface of Evolution

If visual science reveals how the brain processes sensory signals, then every great leap in the history of science has been, in its own way, another instance of humanity overturning its own intuitive biases.

Before Copernicus, humans had observed the sky with their own eyes for thousands of years: the sun rises in the east and sets in the west, day after day; the ground beneath our feet feels solid and unmoving. This was the most intuitive conclusion, the one that best matched everyday visual experience — and it was also the “common sense” that the authoritative systems of Aristotle and Ptolemy had, through remarkably precise mathematical models, kept in place for over a thousand years. The great historical significance of Nicolaus Copernicus’s heliocentric model lies in this: it was the first time in the history of science that anyone had systematically demonstrated that even our most stable, most unquestioned visual experience might not be an accurate description of the physical world. The sun appears to move — but what is actually moving is the ground beneath our feet, the very thing we had assumed was still.

Fig. 6-1 | Nicolaus Copernicus (1473–1543). His heliocentric model became a powerful reminder that even our most stable everyday experience need not provide the most accurate description of the physical world.

Portrait, c. 1580, artist unknown. Collection: Regional Museum in Toruń, Poland. Rights: Public Domain / Public Domain Mark 1.0.

Half a century or so later, Galileo Galilei pointed a modified telescope at Jupiter and discovered four moons orbiting it — powerful evidence for the claim that not every celestial body must revolve around the Earth. For this he was put on trial by the Roman Inquisition and forced to publicly renounce the heliocentric view. But what history ultimately remembers is not who won that trial; it is the pair of eyes behind that telescope lens — the first to refuse to trust sight alone, and to place their trust instead in instruments and reasoning.

This transcendence of everyday intuition found a profoundly moving echo nearly four centuries later. On December 24, 1968, the command module of Apollo 8 drifted behind the far side of the Moon. Houston’s radio signal was blocked by the Moon’s bulk; the cabin fell silent. The astronaut William Anders pressed himself to the window; before him lay only the black death of space and the ashen grey of the lunar surface. And then, at the edge of that grey horizon, a fragile band of vivid blue began to rise. Anders grabbed a Hasselblad camera, quickly loaded colour film, and pressed the shutter, capturing the photograph that would become famous around the world: Earthrise — the blue Earth, suspended above the dead, grey horizon of the Moon.

Fig. 6-2 | Earthrise, taken by Apollo 8, December 24, 1968. Humanity travelled to the Moon only to discover the deepest reward was seeing Earth itself for the first time.

Photograph by astronaut William Anders, Apollo 8 mission, frame AS08-14-2383. Rights: U.S. Government work, not subject to copyright protection under 17 U.S.C. § 105; in the public domain. Credited to NASA by convention.

Anders later described, on more than one occasion, the feeling that stayed with him: that humanity had travelled an enormous distance to explore the Moon, only to discover that the deepest reward of the journey was seeing, for the first time, the Earth it called home. This intense psychological shock — of looking back at the Earth from space — was later given a name by the writer Frank White: the “overview effect.” Many astronauts, describing this experience, have spoken of a profound cognitive shift: seen from orbit or from the Moon, national borders disappear, conflict and strife seem impossibly small, and in their place comes an almost instinctive sense of belonging to a single, shared human community.

While we remain within the Earth, confined to our everyday senses, we cannot see ourselves whole; only by stepping entirely outside our usual frame of reference, and looking back from some far horizon, do we truly come to see ourselves.

This disenchantment did not stop at astronomical scales. In the early twentieth century, physics repeatedly overturned our intuitive picture of the “objective world” at scales both vanishingly small and impossibly fast. Einstein’s theory of relativity, for instance, tells us that “simultaneity” is not an absolute, universal concept — two events that appear simultaneous to one observer may occur in sequence for another observer moving at a different velocity. Escher’s print Relativity borrows its title only in a poetic sense; the coexistence of three directions of gravity within the frame has nothing to do with the rigorous physics of spacetime curvature in Einstein’s general relativity, and the two should never be confused. The former is a game played in geometry and psychology; the latter is a physical theory built on precise mathematical derivation and experimental confirmation.

In quantum mechanics, meanwhile, the relationship between “observation” and the “system being observed” has fuelled nearly a century of debate among physicists over interpretation — a highly specialized field, with several competing schools of thought, that is easily misunderstood in popular accounts, and one we won’t attempt to unpack here. We raise it only to make a single point: even within the most “precise” branch of modern physics, the relationship between observer and observed world turns out to be far more complicated than naive intuition would suggest.

If relativity and quantum mechanics challenge intuition at the scale of physics, then in the field of evolutionary cognition, the scholar Donald Hoffman has proposed a theory from an altogether different angle — one that is genuinely controversial, yet strikingly thought-provoking: the “interface theory of perception.” Hoffman and his collaborators use mathematical models drawn from evolutionary game theory to ask a specific question: over the long course of natural selection, which strategy would fare better in evolutionary competition — a species that perceives the world’s true structure as accurately as possible, or one that perceives only simplified signals directly tied to survival and reproduction? Their models suggest, under the specific assumptions they construct, a counterintuitive finding: strategies that attend only to “fitness payoff,” rather than to the world’s actual structure, tend to outcompete strategies aimed at accurate perception — and may, in some cases, drive the latter to extinction entirely.

Hoffman offers a vivid analogy from computing: the blue “folder” icon on your screen does not mean there is a literal plastic folder inside your computer’s chip; it is a radically simplified interface that hides the underlying complexity of binary code, circuit voltages, and disk storage. The icon’s purpose is not to “faithfully display” everything happening inside the machine, but to let the user operate the computer efficiently — click, drag, delete — without ever needing to understand the physical implementation underneath. Hoffman goes on to speculate boldly that the colours, shapes, and even our sense of space and time, may likewise be a radically simplified “biological interface,” shaped by evolution to let us survive and reproduce efficiently, without necessarily reflecting the true underlying structure of the objective world at all.

It’s important to state clearly: Hoffman’s interface theory of perception is a genuinely thought-provoking hypothesis that remains widely contested within academia. Its mathematical model rests on specific assumptions drawn from evolutionary game theory; it is not a consensus view accepted broadly across the scientific community, and it has drawn no small amount of criticism and pushback from other evolutionary biologists and philosophers. We present it here not as settled fact, but as an invitation — a thought experiment rich with imaginative possibility — to consider a more open-ended question: to what extent is the world we see a “practical, simplified version,” shaped for the sake of survival?

From Copernicus to Galileo, from the window of Apollo 8 to the ongoing debate over the interpretation of quantum mechanics, to the bold interface hypothesis in evolutionary cognition — the history of science, through repeated revision, keeps returning us to the same caution: what appears self-evident to human perception should not automatically be mistaken for the deepest structure of reality.

CHAPTER SEVEN: A Dialogue with Ancient Eastern Epistemology

As modern science, following the path of experiment and logic, gradually presses up against the limits of human understanding — if we turn instead to the classical texts of ancient Eastern civilization, we find that its thinkers, using an entirely different language and vantage point, once raised strikingly similar epistemological questions.

This is not to say the ancients somehow predicted modern science. Ancient philosophy and modern quantitative science belong to fundamentally different paradigms — the former relies on speculative reasoning, direct insight, and contemplative practice; the latter on repeatable experiment and mathematical modelling. Their methods, standards of verification, and epistemic status are all quite different. But on the deep philosophical question of how the senses relate to reality, the two carry on a conversation across more than two thousand years.

In the Warring States period, Zhuangzi and Huizi stood together on a bridge over the Hao River. Zhuangzi said: “Look how freely the fish swim about — that is the happiness of fish.” Huizi replied: “You are not a fish — how could you know the happiness of fish?” Zhuangzi said: “You are not me — how do you know that I don’t know the happiness of fish?”

Fig. 7-1 | Traditional portrait of Zhuangzi (Zhuang Zhou), from the Album of Full-Length Portraits of Sages and Worthies, artist unknown — a later traditional depiction rather than a contemporary likeness. The ancient Chinese thinker explored the boundaries between perception, experience and reality through enduring episodes such as the Butterfly Dream and the Debate on the Hao River.

Source: Wikimedia Commons / National Palace Museum category. Rights: Public Domain / Public Domain Mark 1.0.

This famous “debate on the bridge over the Hao” touches on the limits of what can be known: Huizi, a philosopher of the School of Names, asserts the impossibility of crossing between the perception and experience of different subjects — you are not a fish, so how could you know what a fish feels? Zhuangzi, meanwhile, displays a keen sensitivity to different forms of life and a kind of poetic empathy. In modern terms, one might say Zhuangzi gestures, loosely, toward the idea that different species may inhabit different perceptual worlds — but this is only a contemporary reading; it does not mean Zhuangzi himself proposed anything as systematic as the modern biological concept of an Umwelt. At its core, the debate is still about a broader question: can one person ever truly understand another’s happiness?

And in the “Discussion on Making All Things Equal” chapter of the Zhuangzi comes the famous story of Zhuangzi’s dream of the butterfly: “Once Zhuang Zhou dreamed he was a butterfly, fluttering about happily... he did not know whether it was Zhou dreaming he was a butterfly, or the butterfly dreaming it was Zhou.” Within a dream, perception feels entirely real — its logic holds together on its own terms — and only upon waking does one realize it was only a dream. Zhuangzi uses this to raise a careful doubt about “absolute certainty”: how can we be sure that our present, waking experience is not itself nested within some larger, unrecognized framework?

The same chapter contains another often-quoted line that deepens this thought further: “In the very moment of life there is death; in the very moment of death there is life. In the very moment something is permissible, it is impermissible; in the very moment it is impermissible, it is permissible.” Zhuangzi is not preaching a thoroughgoing relativism — the claim that no standard means anything at all — but rather reminding us that many of the standards we take for granted, and treat as mutually opposed, hold true only from within a particular stance or framework; step outside that framework, and the opposition itself may simply dissolve.

This insight — that categories we take to be sharply opposed are in fact built on a continuous underlying process — forms a striking echo, across more than two thousand years, with Escher’s Metamorphosis series, discussed in Chapter Three. Escher demonstrates with his pen that “text” and “pattern,” “honeycomb” and “bird,” can reach one another along a continuously graded path, and that the boundaries between the categories we take for granted are, to a great extent, markers imposed after the fact by the observer; Zhuangzi, in turn, argues in philosophical language that seemingly stark oppositions like “life” and “death,” “permissible” and “impermissible,” may likewise be nothing more than different segments artificially carved out of a single continuous process. Working from radically different traditions and purposes — one using a geometric pen, the other using speculative language — both invite us to question whether some categories that appear rigid and absolute are, in fact, more dependent on perspective, language, or processes of change than we normally assume.

In the Tang dynasty, at Faxing Temple in Guangzhou, there is a well-known Chan Buddhist story recorded in the Platform Sutra: two monks were watching a temple banner flutter in the wind. One said, “The banner is moving.” The other objected: “No — the wind is moving.” Neither would concede the point — until the Sixth Patriarch, Huineng, happened to pass by and offered the line that has echoed down through the centuries since: “It is neither the banner moving, nor the wind moving — it is your mind that moves.”

This exchange is often reduced to a simple idealist claim — as if to say the external world doesn’t exist at all, and everything is merely a projection of the mind. We won’t attempt any definitive interpretation of the underlying Chan doctrine here; we only want to borrow it as an analogy. If we temporarily lend it a modern cognitive-science reading, we might say that the two monks were arguing not because one of them had seen wrongly, but because each had locked his attention onto a different part of the same continuous event — one focused on the “banner,” a passive physical object; the other on the “wind,” an active physical cause. This analogy resonates in an interesting way with two ideas we’ve already discussed — figure-ground organization (which part is figure, which is ground) and cognitive framework: very often, when people argue fiercely, it looks as though they are fighting over the single “correct answer” to some objective fact, when in reality, both sides are simply fighting over which locally selected slice of a single continuous phenomenon they happen to be focused on.

The Diamond Sutra contains a well-known verse: “All phenomenal appearances are illusory. When one sees that all appearances are not, in themselves, appearances, one sees the Tathagata.” In the language of modern epistemology, this can be understood as a caution against equating the appearances that present themselves to our consciousness with ultimate reality itself. Everything our eyes see has already passed through the physical filtering of our sensory organs and the layered shaping and interpretation of our conscious framework — like layers of filters stacked over the original signal.

Alongside this, within Buddhist epistemology, there is another, more elaborate and systematic tradition of consciousness theory: the Yogācāra, or “Consciousness-Only,” school, which holds that all phenomena we experience must first pass through the transformation and construction of consciousness before they can be perceived at all — a position often summarized as “the ten thousand things are consciousness alone.” Its body of theory, while belonging to the same broad current of Buddhist epistemology as the Prajñā-class scripture to which the Diamond Sutra belongs, does not derive from the same textual lineage; we offer it here simply as a further point of reference.

If we temporarily borrow the language of modern cognitive science, the core claim of Yogācāra — that “the ten thousand things are consciousness alone” — bears a striking structural resemblance to the predictive processing model introduced in Chapter Five: both describe a picture in which experience does not come directly from the external world, but must first pass through some internal process of construction. Here too, however, we must draw the boundary with great care: Yogācāra’s concept of “consciousness” belongs to a complete Buddhist system that includes theories of practice, liberation, and karmic causality, ultimately oriented toward spiritual cultivation and transcendence; the predictive processing model, by contrast, is a scientific hypothesis grounded in neuronal activity and probabilistic computation, partially testable through experiment, aimed at explaining the concrete mechanics of how the brain works. This structural similarity is better understood as two separate knowledge traditions independently arriving at the same deep intuition — that experience is constructed — rather than as one anticipating or confirming the other.

Laozi, in the Dao De Jing, writes: “What cannot be seen is called subtle; what cannot be heard is called faint; what cannot be grasped is called minute... this is called the shape without shape, the image without substance.” And, in a later, more widely known line: “The greatest square has no corners; the greatest vessel is never finished; the greatest sound is nearly silent; the greatest image has no form. The Dao conceals itself, and is without name.” The Dao described here is a kind of ultimate reality that lies beyond the direct reach of human perception — unseen, unheard, untouched, and yet not simply an empty void; it is something more fundamental, one that remains forever “hidden.”

Interestingly, modern physics can offer this ancient line an imperfect but suggestive parallel: the visible light our eyes can directly perceive occupies only a narrow slice of the entire electromagnetic spectrum. Radio waves, infrared, ultraviolet, and X-rays fill the space around us just as truly as visible light does, yet our naked eyes cannot perceive them at all; we need dedicated instruments to translate these otherwise “unseeable” phenomena into signals we can understand. To be clear, this is not a claim that Laozi somehow “predicted” the electromagnetic spectrum — that would be an anachronistic overreach. The Dao Laozi describes is a philosophical category spanning cosmology, ethics, and the wisdom of living, far deeper than any single physical fact. What we want to point out is only a resonance of method: ancient Eastern philosophy, quite early on, adopted a stance of humility, reminding us that the range of our senses falls dramatically short of the vastness of the world itself.

Ancient Eastern philosophy and modern science differ in method, language, and standards of verification — and yet, viewed from a certain historical height, they form a distant but genuine echo of one another. Each, in its own way, points humbly to the limits of human sensory capacity, and warns us not to mistake the boundary of our own perception for the boundary of the world itself.

CHAPTER EIGHT: The Cave and the Thing-in-Itself — Another Line of Inquiry in Western Philosophy

While Eastern thinkers, through the butterfly dream and the “your mind that moves” of Chan Buddhism, were interrogating the gap between perception and reality, philosophers on the other side of the Mediterranean, in roughly the same historical era, were pursuing an equally profound inquiry, in an entirely different language.

In the fourth century BCE, the Greek philosopher Plato, in Book VII of his Republic, told a story that has endured for more than two thousand years — the Allegory of the Cave. Imagine a deep, dark underground cave, in which a group of prisoners have been chained since birth, their necks and limbs restrained so they can only face the wall in front of them and never turn around. Behind them burns a fire, and its light throws the shadows of puppets and carved figures — carried back and forth between the prisoners and the world outside — onto the wall the prisoners face. Having seen only these shifting shadows since birth, and never having seen the real objects beyond the cave, the prisoners naturally take the shadows to be the whole of reality; they even argue over which shadow moves faster than another, and hold in high esteem whichever prisoner is best at predicting how the shadows will move.

Plato imagines that if one of these prisoners were forcibly unchained and dragged out of the cave, confronting for the first time the real sunlight and the real world outside, he would at first feel disoriented and in pain — his eyes, long accustomed to the cave’s faint, flickering firelight, would suddenly be overwhelmed by the intensity of real daylight, and he might even suspect, at first, that this too-vivid, too-solid world was the illusion. Only once his eyes had adjusted would he finally be able to see clearly the trees and rivers in the sunlight, and the true sun itself — the very thing whose light had, all along, been casting those shadows on the wall.

And when this newly awakened prisoner returns to the cave and tries to tell his still-chained companions about the real world outside, what he receives is rarely gratitude — more often, mockery, even hostility. Because within his companions’ cognitive framework, the shadows on the wall are the whole world, beyond question.

Fig. 8-1 | Plato's Allegory of the Cave: from prisoners who have only ever faced the wall, to one who breaks free toward the sunlight outside, to his return — where the truth he brings back is met not with gratitude, but with suspicion.

Original illustration.

Plato’s cave allegory resonates sharply with several of the themes we’ve already explored: Escher’s staircases, correct in every local detail yet contradictory as a whole; the brain’s automatic filling-in of the retinal blind spot; the “interface” that simplifies reality into a shadow, or a folder icon. All of them remind us that the sense of “reality” we take as self-evident in everyday experience may, itself, be nothing more than a shadow cast on the inner wall of our own consciousness.

There is, however, an important difference worth noting: Plato still believed that behind the shifting appearances of the senses lies a more stable, more truly real level — one that can, through philosophy and reason, be gradually approached: what he called the world of Forms. As long as the prisoner is brave enough to leave the cave, reason will, in the end, be able to lead him ever closer to this more genuine level of reality. Compared with certain later Eastern traditions of thought, and with strands of modern epistemology that place greater emphasis on the limits and uncertainties of knowledge, this represents a different philosophical orientation on the question of whether reason can ultimately arrive at a final, certain truth.

More than two thousand years later, the German philosopher Immanuel Kant, in his 1781 masterwork Critique of Pure Reason, took this inquiry into the relationship between perception and reality to a new theoretical height, through an extraordinarily rigorous chain of philosophical argument.

Kant drew a crucial distinction between two concepts: the “phenomenon” and the “noumenon,” or “thing-in-itself.” In Kant’s view, all human cognitive activity must first pass through two innate forms of sensory intuition — space and time — which shape and organize raw experience, before being further structured by the categories of understanding (such as causality, quantity, and substance) into the coherent, orderly world of phenomena that we ultimately “experience.”

In other words, for Kant, we can never directly know what a thing is “in itself” — what its true, unmediated nature might be; everything we are capable of knowing has already been filtered and shaped by the two inborn lenses of space and time. The true face of the thing-in-itself remains forever hidden beyond the reach of human cognition — a domain that is, in principle, unknowable.

Kant’s claim — that human beings can never step outside their own cognitive structure to examine that structure from without — bears a striking structural resemblance to the idea raised in Chapter Four’s discussion of Print Gallery, that “the observer ultimately becomes part of the system itself.” The young man Escher depicts standing in the gallery, who ultimately discovers he has been drawn into the spiral of the very painting he was looking at, is, in a sense, a visual embodiment of Kant’s epistemological dilemma: we can never truly “step outside” our own cognitive framework to inspect, from some neutral external vantage point, whether that framework accurately reflects the world. The most we can do, as Kant did, is use rigorous reasoning to describe the boundaries and structure of that framework as precisely as possible — without ever actually managing to step beyond it.

This forms an intriguing echo, across two centuries, with the predictive processing model discussed earlier — even though the two arrive at their conclusions through entirely different methods: Kant relies on pure philosophical reasoning and transcendental argument, while predictive processing relies on experimentally testable neuroscientific hypotheses. And yet both point toward a similar structural insight: the world we “experience” is never a raw copy of external reality itself, but is always the product of some prior structure — whether Kant’s “a priori categories,” or what modern neuroscience calls the brain’s “predictive model” — doing its work of processing and organizing.

One clarification: Kant’s agnosticism about the thing-in-itself and Hoffman’s interface theory of perception, discussed earlier, may feel intuitively related, but they belong to entirely different domains of knowledge — the former is an eighteenth-century transcendental philosophical argument; the latter, a still-contested contemporary scientific hypothesis grounded in evolutionary game theory. The two should never be simply equated or treated as mutual confirmation. We place them side by side here only so that readers can sense something larger: whether in the East or the West, whether through philosophical speculation or modern science, some of the deepest minds in human history have, quite independently, cast the same wary glance at the naive belief that “seeing is believing.”

From the prisoner breaking free of his chains in Plato’s cave, to the pair of lenses — space and time — that Kant showed we can never remove: Western philosophy, following a path entirely its own, has arrived at a junction strikingly similar to the one reached by Eastern wisdom and modern neuroscience.

Before closing this comparison between Eastern and Western epistemology, it’s worth drawing together a few threads scattered across the previous two chapters for a brief, deliberately restrained comparison — restrained, because we never mean to suggest some hidden lineage or act of “prophecy” linking traditions separated by millennia and continents; and deliberate, because the different paths these traditions take in addressing the same core question are, in themselves, genuinely illuminating.

Zhuangzi’s butterfly dream and Plato’s cave allegory both address the question of how we can know we are not trapped within some larger illusion — yet the two point toward entirely different ways out. Plato imagines an outward, upward path: breaking free of the chains, leaving the cave, ultimately arriving at a more real, more stable world of Forms. Zhuangzi, by contrast, leans toward an inward posture of suspended judgment — “I do not know whether it was Zhou dreaming he was a butterfly, or the butterfly dreaming it was Zhou” — Zhuangzi is in no hurry to find an exit from the dream; instead, he lets that very uncertainty become the epistemological endpoint. Huineng’s koan of “your mind that moves” and Kant’s distinction between phenomenon and thing-in-itself likewise diverge in orientation: Huineng’s emphasis falls on how the “mind” organizes and focuses on a continuous phenomenon, closer to an immediate, practical form of observation; Kant’s emphasis falls on constructing a systematic, transcendental structure to explain the boundaries and limits of human cognition itself, closer to a theoretical, systematized argument. The Diamond Sutra’s “all phenomenal appearances are illusory” and Laozi’s “the greatest image has no form” likewise both warn against equating appearance with underlying reality — yet Buddhist thought points more toward practice and liberation, while Laozi points more toward cosmology and the wisdom of living. Even when both are, in a sense, discussing “the limits of the senses,” the ultimate questions each tradition cares about are not quite the same.

It is precisely because these real differences exist that we should be all the more cautious about oversimplified claims like “Eastern philosophy already knew all this.” What’s truly worth remembering is perhaps not some literal resemblance between an ancient maxim and a modern theory, but the fact that these traditions of thought, each using an entirely independent language and method, returned again and again to the same simple starting point: human senses and cognition have never been a transparent window onto the world — they are a medium that must be continually examined and tested.

This, perhaps, is exactly what it means: the question of whether what we see can be trusted as reality does not belong to any single culture or any single era. It is a shared, universal puzzle, rooted in the very condition of possessing consciousness and trying to make sense of the world.

CHAPTER NINE: Echoes Across the World of Illusion Art — Escher Was Not Alone

Escher used geometry and paradox to interrogate the nature of seeing, but he was not the only artist to walk this path. In the same twentieth century he lived through, several other artists, working in strikingly different styles, arrived at similar destinations from their own directions.

René Magritte’s famous painting The Treachery of Images (1929) shows, at its centre, a pipe rendered with almost photographic realism — and beneath it, in careful French script, the artist has written: Ceci n’est pas une pipe (“This is not a pipe”). At first glance, this looks like a piece of wilful mystification — the painting clearly depicts a pipe, so why insist that “this is not a pipe”? But what Magritte is pointing to is a simple fact we too easily overlook: the “pipe” on the canvas is, in the end, only pigment arranged on a two-dimensional surface — an image, a sign. You cannot fill it with tobacco, nor light it and smoke it. It is the image of a pipe, not the pipe itself.

This forms a striking echo with several themes already raised in this book: our brains habitually conflate a sign with the thing the sign refers to, mistaking the map for the territory. With this single painting, Magritte lays bare, in the starkest terms, a gap we habitually cross without ever noticing that it was never truly closed.

Salvador Dalí’s The Persistence of Memory (1931), with its limp, melting clocks, touches on a related theme — but his target is really the way dream and the unconscious distort our sense of time, a poetic and psychological metaphor rather than a direct exploration of how vision itself works, so we won’t dwell on it here.

Bridget Riley’s Op Art works, such as her Fall series, are made up entirely of black-and-white wavy stripes, and yet they produce, in the viewer, a powerful sense of trembling, distortion, and motion. Unlike Escher’s narrative, paradoxical architecture, Riley’s generation of Op artists took a purer, more direct path: with no representational content or narrative at all, carefully designed geometric patterns alone are enough to powerfully stimulate the visual cortex, producing dizzying illusions of motion and depth. This demonstrates, from another angle, that our visual system carries something close to a “hard-wired,” highly sensitive physiological response to particular frequencies and arrangements of line and pattern — the same neuroscientific soil from which Escher’s own intuitively developed “visual grammar” grew.

From Magritte’s exposure of the gap between image and object to Riley’s pure geometric stripes striking directly at the physiology of the visual cortex, the artists of the twentieth century, it seems, were all conducting, without any laboratory at all, a set of visual thought experiments of their own.

What sets Escher apart is that he took none of these paths directly — not Magritte’s paradoxes of language and sign, and not Riley’s wholesale abandonment of representation and narrative. He chose instead the most “rational,” most “mathematical” road of all: using rigorous geometric logic itself, step by careful step, to lead his viewers, by their own hand, into a world that is logically impossible. It is precisely because of this that Escher’s work lends itself so naturally to such a close and searching dialogue with neuroscience and cognitive psychology.

Looking back over the path this book has traced through its first eight chapters — from the tiles of the Alhambra to Penrose’s paradoxical staircase; from the quietly filled-in blind spot on the retina to the redrawn body-boundaries of the rubber hand illusion; from Zhuangzi’s creature who could no longer tell whether it was Zhuang Zhou or a butterfly, to the flickering firelight deep within Plato’s cave — Escher is able to serve as the thread connecting all of it, perhaps not simply because his prints are strange enough, but because the path he chose, one of pure geometry and pure reason, strips away, to the greatest possible extent, the interference of emotion, narrative, and cultural background, presenting the question of how perception is constructed in a form nearly as clean as a laboratory’s controlled conditions. When we turn, in the next chapter, back to our phone screens and the algorithms that curate them, we do so carrying that same almost geometric clarity we learned from Escher.

CHAPTER TEN: When the Screen Becomes Our World — Cognitive Frameworks in the Age of Algorithms

Before we bring this journey across art, science, and philosophy to a close, let’s turn our attention from the gallery and the laboratory back to a scene each of us encounters countless times, every single day: the screen of our phone.

Today, the recommendation algorithms behind almost every social media platform and news app track our past clicks, dwell time, and engagement, and use them to continuously push content that matches our existing preferences. In communication studies and sociology, this is vividly described as the “information cocoon” or the “echo chamber effect” — concepts first systematically articulated by scholars such as Cass Sunstein in discussions of the internet-age information environment.

Here we need to keep several distinct layers straight, rather than conflating concepts drawn from different disciplines. Predictive processing describes how the brain, at a physiological level, uses prior experience to predict and complete sensory signals. “Confirmation bias,” a long-established concept in psychology, describes how people tend to notice and credit evidence that confirms what they already believe, while overlooking evidence that contradicts it. The information cocoon operates at the level of communication studies, describing how algorithms serve content matching a user’s existing preferences. These three belong to different disciplines and levels; there is no scientifically established causal chain linking them — one cannot simply say the brain’s predictive machinery “causes” confirmation bias, which in turn “causes” the effects of algorithmic recommendation.

A more careful way to put it: the human mind is, by nature, selective and predictive, a tendency predictive processing and confirmation-bias research both reveal at the psychological and neural level. Recommendation algorithms, meanwhile, further narrow the range of content we encounter, at the level of the information environment. When the two combine, they may make a person’s existing cognitive framework harder for outside information to challenge — a real and worrying picture, but more precisely a possible outcome of cognition and information environment interacting, rather than the direct consequence of any single mechanism.

If Escher’s travellers in Relativity, each walking along their own axis of gravity, symbolize people standing on the footing of their own cognitive framework, then today’s information environment is, in a sense, projecting that once purely fictional building into everyday life — and even the chance to pass close by one another, as those figures do, may be growing rarer: algorithms may guide people living along different axes of gravity into separate information corridors, less and less likely ever to meet.

Understanding this is not meant to induce technological pessimism — the belief that the individual is powerless before such a system. Quite the opposite: it is precisely because we understand this mechanism that we gain, for the first time, the possibility of consciously stepping outside it, and seeking out that “other staircase” — the perspective that differs from our own.

This may be the most practically valuable gift this journey has to offer: the next time you scroll through your phone, or argue with someone who sees things differently, remember the unfinished debate on the bridge over the Hao River, the flickering firelight in Plato’s cave, and Escher’s two travellers passing each other on entirely different axes of gravity — and pause to ask yourself:

Is this “fact” I am so certain of the one and only truth of this world — or simply the local scenery presented to me by the particular direction of gravity on which I happen to be standing?

CHAPTER ELEVEN: Returning to Escher

Let us return, once more, to the 2026 Escher retrospective at Somerset House in London. This major exhibition — titled M.C. Escher: The Exhibition — was jointly produced by the Italian company Arthemisia and the culture-tech platform Fever, curated by Federico Giudiceandrea, and brought together more than 150 original works. Running from June 5 to September 6, 2026, it marked the first time an exhibition of this scale devoted to Escher’s work had been held in London.

The exhibition included several immersive, interactive spaces: visitors could stand on a checkerboard floor between two enormous reflective spheres, beneath Escher’s giant Eye — its pupil holding a reflected skull — and feel the eerie sensation of being watched by the print itself; they could walk into a mirrored room and watch the birds from Escher’s prints multiply into infinite flocks across the reflections; and, drawing perhaps the most attention of all, there was the Relativity Room — where two people, standing in different positions within the same space, remain entirely unchanged, and the room itself does not change either, and yet, viewed from a particular angle, one figure appears to become a giant, the other to shrink into a child. This kind of carefully engineered forced perspective, designed to distort a viewer’s judgment of distance and scale, follows the same principle as the “Ames room” illusion, designed in the mid-twentieth century by the psychologist Adelbert Ames Jr. — cleverly distorting the geometry of a room itself to deceive the brain’s default assumptions about distance and perspective. But wrapped in Escher’s particular aesthetic, the experience becomes something more than a simple intellectual puzzle; it becomes a direct, embodied realization that even the relative size of “me” and “another person” is not absolute at all, but depends entirely on the geometric rules governing the space the two of us happen to be standing in together.

At this point, Escher is no longer merely showing us an illusion to look at. He is making us, ourselves, part of the illusion.

Another installation that drew visitors to linger was a digital interactive display built around Print Gallery (1956). This print carries a little-known story of its own: at the very centre of the composition — the point where the spiral structure of the image should logically converge — Escher never actually completed the drawing. He left a small blank space there, unable to render what was, in theory, a point that could not be continued any further. Nearly half a century later, the Dutch mathematicians Hendrik Lenstra and Bart de Smit used mathematical analysis and computer graphics to finally “complete” that blank space, revealing the full structure of the image’s ever-shrinking, spiraling core. The interactive display in the exhibition lets visitors drag and zoom into the image themselves, travelling all the way into this spiral centre that mathematicians only completed long after Escher’s death.

The blank space Escher left behind, and the answer mathematicians took nearly fifty years to complete, together form a fitting emblem of what this entire book has tried to convey: some truths do not fully reveal themselves the moment we first see them. They require time, tools, and a whole set of methods quite different from intuition, before they can be pieced together, verified, and finally brought fully into view.

In the exhibition’s final gallery, a section titled “Eschermania” traces, across an entire wall of material, how Escher unexpectedly became one of the most persistent visual icons of popular culture in the decades after his death. In the 1960s, the counterculture movement all but adopted Escher of its own accord — his tessellations and impossible buildings ended up printed on blacklight posters and pasted across countless college dorm walls, a development Escher himself reportedly found rather bewildering. The Rolling Stones’ Mick Jagger personally invited Escher to design the cover of Let It Bleed; Escher declined. He did, however, allow Pink Floyd to use one of his prints in connection with the track “On the Run,” from the band’s 1973 album The Dark Side of the Moon. In the decades since, both The Simpsons and Futurama have parodied his impossible staircases in animated form; the dizzying, endless stairway in the film Labyrinth pays near-direct tribute to Relativity; and the self-folding Parisian streetscape Christopher Nolan built in Inception can, visually, be traced right back to Escher’s prints. Even today, from neckties and T-shirts to home décor rugs, Escher-patterned merchandise continues to circulate around the world — much of it unofficial, unlicensed — which is, in its own way, further proof that a visual language born in a mid-twentieth-century print workshop has long since seeped into a daily life far broader than any museum.

This echoes precisely a judgment offered in Chapter Nine of this book: the reason Escher’s work has been able to cross so many domains — mathematics, psychology, pop music, film, fashion — is not because he deliberately set out to please any one particular audience, but because the themes he was obsessed with — infinity, paradox, the gap between “what we see” and “what actually exists” — are, in themselves, a universal puzzle that no one, in any culture, can ever truly avoid.

Stepping out of Somerset House, the London rain has stopped; the Thames glows with the gold of the setting sun, and the cries of gulls drift in from a distance. Red double-decker buses still weave through the streets; the buildings, the pedestrians — everything looks exactly as it did before we walked into the gallery.

And yet something, at some deeper level, has quietly changed.

You now know that colour is something the visual cortex computes, in the context of assumed lighting; you know that everything you see is filled, at every point, with the brain’s probabilistic predictions and completions; and you know, more than anything, that every person lives within their own particular cognitive framework, shaped jointly by experience and culture — like the prisoners in Plato’s cave, gazing at the stone wall before them; like the pair of lenses in Kant’s philosophy — space and time — that can never be removed; and like the winged creature in Zhuangzi’s story, who could no longer be sure whether it was Zhuang Zhou, or a butterfly.

You can no longer walk through the world, as you once did before entering this gallery, in unreserved trust of your own eyes.

This is not a reason for pessimism or doubt. It is a great cognitive awakening.

Fig. 11-1 | From the external world, through sensory input and neural processing, to a cognitive framework shaped by experience, knowledge, culture, values and goals — together giving rise to the world we come to "experience," which in turn shapes what we notice next time.

Original illustration.

A truly mature civilization has never been mature because it believed it had seen everything, or grasped the ultimate truth. From Copernicus to Apollo 8, from the tiles of the Alhambra to Penrose’s paradoxical staircase, from the quietly filled-in blind spot on the retina, to the unfinished debate on the bridge over the Hao River about the happiness of fish, to the flickering firelight deep within Plato’s cave — the truly proud moments of human civilization have, again and again, arrived precisely when we found the courage to admit that what we once believed without question might have been only a shadow.

To see something is not yet to know it as it truly is.

And when a civilization — or a single person — begins to recognize the limits of both perception and cognition, perhaps that is when it — when we — finally learn to approach reality with greater humility and clarity, one step at a time, toward something far vaster, and far more fascinating, than we had ever imagined.

THE END

APPENDIX: Brief Notes on Terms and Sources

1. Naive Realism: A widely used descriptive concept in psychology and philosophy, referring to the everyday tendency to assume that one’s own perception directly reflects the true state of the external world.

2. Figure-Ground Organization: A core concept in Gestalt psychology, first systematically proposed by the Danish psychologist Edgar Rubin in the early twentieth century.

3. Predictive Processing / Controlled Hallucination: An influential theoretical framework in contemporary cognitive neuroscience, associated with researchers such as Karl Friston and Anil Seth. This book presents it as an “influential hypothesis,” not as an established, fully proven conclusion.

4. Inattentional blindness and “The Invisible Gorilla” experiment: A classic psychological study published by Daniel Simons and Christopher Chabris in 1999, widely replicated and cited.

5. Change blindness: A well-established phenomenon in cognitive psychology, repeatedly verified experimentally.

6. The McGurk effect: A cross-modal perceptual phenomenon published by Harry McGurk and John MacDonald in Nature in 1976 — when a person’s mouth forms the syllable “ga” while the audio plays “ba,” most viewers “hear” a third sound somewhere between the two; this is a widely replicated, well-established phenomenon showing that hearing can be “hijacked” and reshaped by vision in real time.

7. Synesthesia: An inborn form of unusual neural connectivity in some people, in which one sensory stimulus automatically triggers an experience in another sensory channel — for instance, seeing a particular colour upon viewing a given number. This is a well-established phenomenon, widely documented in clinical and experimental psychology.

8. Blindsight: Some patients who have lost conscious visual experience due to damage to the primary visual cortex (clinically termed “cortical blindness”) nonetheless show above-chance accuracy when asked to “guess” the location or motion of an object in their visual field — suggesting that visual processing may involve more than one neural pathway. The precise underlying mechanism remains an active area of research.

9. The rubber hand illusion: A classic experiment first systematically reported by Matthew Botvinick and Jonathan Cohen in 1998, widely replicated since.

10. “The Dress” colour controversy: A real internet phenomenon from 2015; subsequent research has largely explained it through the mechanism of “colour constancy,” though the precise sources of individual variation remain an active area of discussion.

11. The interface theory of perception: An evolutionary-cognitive hypothesis proposed by Donald Hoffman. This book explicitly labels it a “contested, not widely accepted theory,” and does not present it as settled fact.

12. The overview effect: A concept coined by the writer Frank White to describe the subjective psychological experience astronauts report when looking back at Earth from space — a descriptive concept, not a strict, empirically established law of psychology.

13. Zhuangzi’s “debate on the bridge over the Hao” and “the butterfly dream”: Drawn from the “Autumn Floods” and “Discussion on Making All Things Equal” chapters of the Zhuangzi, classical texts of ancient Chinese philosophy.

14. The “your mind that moves” story from the Platform Sutra: A classical text of Chan Buddhism.

15. The Diamond Sutra quotation and the Yogācāra school: The Diamond Sutra belongs to the Prajñā class of scriptures; Yogācāra is a separate, independent tradition of consciousness theory within Buddhist epistemology. Although both belong to the broader current of Buddhist epistemology, they differ in textual lineage; this book treats them in separate paragraphs to avoid conflating them.

16. Quotations from Laozi’s Dao De Jing: A classical text of ancient Chinese philosophy. The analogy drawn here to the electromagnetic spectrum is a modern, illustrative reading, not a claim that the ancients foresaw modern physics.

17. Plato’s “Allegory of the Cave”: From Book VII of the Republic, a foundational text in the history of Western philosophy.

18. Kant’s “phenomenon and thing-in-itself”: From the Critique of Pure Reason, a foundational work of German classical philosophy.

19. Magritte’s The Treachery of Images, Dalí’s The Persistence of Memory, and Bridget Riley’s Op Art works: All are well-documented, canonical works in the history of modern Western art.

20. Escher’s biography: Escher first visited the Alhambra in 1922, and returned with his wife Jetta for a second, three-day visit in 1936 — the latter being the key turning point in his turn toward tessellation-based work. His half-brother Berend Escher, a professor of geology at Leiden University, introduced him to crystallography and to Pólya’s work on the seventeen plane symmetry groups. These details draw on the official timeline published by the Museum Escher in Het Paleis in the Netherlands, along with several art-historical accounts.

21. Roger Penrose and the “Penrose stairs”: Penrose first encountered Escher’s work at the solo exhibition held during the 1954 International Congress of Mathematicians in Amsterdam (at the Stedelijk Museum), and, deeply struck, went on to design the “Penrose triangle”; his father, Lionel Penrose, built on this to design the “Penrose stairs,” and the two published their findings in 1958. Escher was subsequently inspired to create Ascending and Descending (1960) and Waterfall (1961). At the same exhibition, the mathematician Donald Coxeter also connected with Escher and inspired his later Circle Limit series; late in life, Escher was invited to lecture at the International Congress of Crystallography in Cambridge and at MIT — all verifiable historical facts.

22. The Ames room: A forced-perspective illusion device designed by the American ophthalmologist Adelbert Ames Jr. in 1946, belonging to twentieth-century psychology.

23. The mathematical completion of the blank centre of Print Gallery: Carried out by the Dutch mathematicians Hendrik Lenstra and Bart de Smit through mathematical analysis — a genuine, verifiable academic achievement.

24. The 2026 London Somerset House exhibition, M.C. Escher: The Exhibition: Jointly produced by Arthemisia and Fever, curated by Federico Giudiceandrea, running from June 5 to September 6, 2026, featuring more than 150 original works and immersive spaces including reflective spheres, a mirrored room, the Relativity Room, an interactive version of Print Gallery, and a section on Escher’s pop-culture legacy titled “Eschermania.”

25. Escher and popular culture: Mick Jagger’s invitation to Escher to design the cover of Let It Bleed, which Escher declined; Pink Floyd’s use of one of his prints in connection with “On the Run,” from the 1973 album The Dark Side of the Moon; parodies in The Simpsons and Futurama; and visual tributes in the films Labyrinth and Inception are all verifiable, publicly reported facts. As of this book’s writing, no official licensing partnership could be verified between the Escher brand and IKEA or any other major fashion retailer; a significant portion of Escher-patterned clothing, rugs, and home goods currently on the market are unofficial third-party reproductions.

26. Information cocoons, the echo chamber effect, and confirmation bias: Well-established concepts in communication studies and psychology; Cass Sunstein and others have written systematically on the information cocoon phenomenon. Chapter Ten of this book explicitly clarifies that these concepts relate to predictive processing and algorithmic recommendation systems only through analogy across different levels, not through any established, single causal chain.

27. Bayesian inference: A classical framework for probabilistic reasoning in statistics, widely borrowed as an analogy for describing the mathematical structure of the predictive processing model. This book presents it as an illustrative comparison, not as a claim that the brain literally performs rigorous Bayesian computation.

28. Multistable perception and the Necker cube: Well-established phenomena in perceptual psychology; Rubin’s vase and the Necker cube are both textbook-standard examples, and the underlying neural competitive-inhibition mechanisms remain an active area of research in visual neuroscience.

29. Saccades and saccadic suppression: Well-established phenomena in the physiology of eye movement and visual neuroscience. Saccades are the rapid, jumping movements the eye makes to continually redirect the fovea to different points in the visual field; saccadic suppression refers to the reduced sensitivity to rapid visual change that occurs around the moment of each saccade.

30. Proprioception and phantom limb phenomena: Both well-established phenomena in neuroscience and clinical medicine; phantom limb phenomena are extensively documented in the clinical literature on amputee patients.

31. The full body illusion: An experimental paradigm in cognitive neuroscience and virtual-reality research, extending the rubber hand illusion to the scale of the whole body, and verified in multiple peer-reviewed studies.

SELECTED REFERENCES

Botvinick, Matthew, and Jonathan Cohen. 1998. “Rubber Hands ‘Feel’ Touch That Eyes See.” Nature.

Chabris, Christopher, and Daniel Simons. 2010. The Invisible Gorilla: How Our Intuitions Deceive Us. Crown.

Coxeter, H. S. M. 1979. “The Non-Euclidean Symmetry of Escher’s Picture ‘Circle Limit III.’” Leonardo.

Ernst, Bruno. 1976. The Magic Mirror of M. C. Escher. Ballantine Books.

Friston, Karl. 2010. “The Free-Energy Principle: A Unified Brain Theory?” Nature Reviews Neuroscience.

Hoffman, Donald D. 2019. The Case Against Reality: Why Evolution Hid the Truth from Our Eyes. W. W. Norton.

Hofstadter, Douglas R. 1979. Gödel, Escher, Bach: An Eternal Golden Braid. Basic Books.

Kant, Immanuel. (1781) 1998. Critique of Pure Reason. Translated by Paul Guyer and Allen W. Wood. Cambridge University Press.

Laozi. Dao De Jing. Various editions; translations consulted include D. C. Lau (Penguin Classics) and Roger T. Ames and David L. Hall (Ballantine Books).

Lenstra, Hendrik W., and Bart de Smit. 2003. “Artful Mathematics: The Heritage of M. C. Escher.” Notices of the American Mathematical Society.

Locher, J. L., ed. 2000. The Magic of M. C. Escher. Harry N. Abrams.

McGurk, Harry, and John MacDonald. 1976. “Hearing Lips and Seeing Voices.” Nature.

NASA/Apollo 8 Mission Photography. 1968. Earthrise, frame AS08-14-2383. Johnson Space Center, NASA.

Penrose, L. S., and Roger Penrose. 1958. “Impossible Objects: A Special Type of Visual Illusion.” British Journal of Psychology.

Plato. The Republic, Book VII. Various editions; translation consulted includes G. M. A. Grube, revised by C. D. C. Reeve (Hackett Publishing).

Rubin, Edgar. 1915. Synsoplevede Figurer [Visual Figures]. Gyldendalske Boghandel.

Schattschneider, Doris. 1990. M. C. Escher: Visions of Symmetry. W. H. Freeman and Company.

Seth, Anil K. 2021. Being You: A New Science of Consciousness. Faber & Faber.

Seth, Anil K., and Karl J. Friston. 2016. “Active Interoceptive Inference and the Emotional Brain.” Philosophical Transactions of the Royal Society B.

Simons, Daniel J., and Christopher F. Chabris. 1999. “Gorillas in Our Midst: Sustained Inattentional Blindness for Dynamic Events.” Perception.

Simons, Daniel J., and Daniel T. Levin. 1997. “Change Blindness.” Trends in Cognitive Sciences.

Sunstein, Cass R. 2001. Republic.com. Princeton University Press.

Sunstein, Cass R. 2017. #Republic: Divided Democracy in the Age of Social Media. Princeton University Press.

The Diamond Sutra. Various editions; translation consulted includes Red Pine (Counterpoint Press).

The Platform Sutra of the Sixth Patriarch. Various editions; translation consulted includes Philip B. Yampolsky (Columbia University Press).

Wade, Nicholas J. 2005. Perception and Illusion: Historical Perspectives. Springer.

White, Frank. 1987. The Overview Effect: Space Exploration and Human Evolution. Houghton Mifflin.

Zhuangzi. Zhuangzi. Various editions; translation consulted includes Burton Watson, The Complete Works of Zhuangzi (Columbia University Press).

END