Perception

Relative Size Illusions

Gianni Sarcone

Here are two relative size illusions I described back in 1997 and 2013.

The first, called Sarcone’s Crosses, challenges classic illusions like the Ebbinghaus illusion (Titchener Circles, 1898) and the Obonai square illusion (1954). It features a cross (the test shape) surrounded by squares of different sizes.

As shown in Fig. 1.a, 1.b, and 1.c, the three blue crosses are all the same size — yet the one on the left (Fig. 1.a) appears larger. Surprisingly, the illusion still works even when smaller squares completely cover the cross (Fig. 1.c).

So, the size of surrounding shapes doesn’t always dictate how we perceive the central one.

In the second illusion (Fig. 2.a and 2.b), due to assimilation, the red diagonal inside the larger ellipse seems longer — but the blue line is actually the longest.

Perception loves to play tricks on us.

sarcone's relative sizze illusions

You can explore more of my illusions and visual inventions on my official site: giannisarcone.com

Illusive Pietà

Gianni Sarcone

Uncovering the subtle visual tricks Michelangelo wove into his masterpiece.

We’re not very good at judging the true size and positioning of objects just by looking. Take Michelangelo’s Pietà—it hides some subtle, conceptual “illusions”:

  • If they were standing, the Virgin Mary would actually be much taller than Christ, which may be surprising.
  • Her knees are slightly off-center, forming a kind of base or pedestal that supports Christ’s body.
  • And while logically the Virgin should look older, her face is almost childlike, creating a striking contrast with the mature, somber face of her son.

Michelangelo himself explained this choice:
“The mother had to be young—young enough to appear forever a virgin. Meanwhile, her son, who took on our human nature, must, in the stripping away of death, be a man like any other.”

Art is full of illusions designed to meet the visual expectations of viewers—and sometimes to correct what might seem off or unnatural to the eye. Because reality, at times, doesn’t always feel quite real or right to those who look at it.

And one last curious detail: Pietà is the only work Michelangelo ever signed. Stung by whispers that another sculptor had made it, he returned one night and boldly carved his name across Mary’s sash— “MICHAELA[N]GELVS BONAROTVS FLORENT[INVS] FACIEBAT” (Michelangelo Buonarroti, the Florentine, made this). A rare flash of pride from an artist who usually let his work speak for itself.)

Pietà by Michelangelo

A Hidden Time Machine

Gianni Sarcone

We all carry within us a time machine—hidden in plain sight, right in the middle of our face. It may sound unlikely, but the NOSE is the only sensory organ capable of transporting us into the past without our even realizing it.

Our sense of smell activates memories like no other. A single scent can unlock a precise moment from childhood or early adulthood: the fragrance of oranges at Christmastime, melting snow during your first school field trip in winter, the scent of your sweetheart’s sweater the day you met, your grandmother’s simmering tomato sauce during Sunday lunches, the waxed floor of your grandparents’ house, school glue in primary class, the sunscreen of beachside summers, old book ink in the town library, the leather of your first satchel, or the aroma of fresh coffee at dawn when everyone else was still asleep…

The nose is a powerful trigger for nostalgia because the olfactory bulb, where smells are processed, is directly connected to the limbic system—the brain’s emotional and memory center. This close link allows smells to summon vivid memories, often with startling clarity, and sometimes, with them, an unexpected flood of emotions.

Each smell opens a door to a suspended instant—fragile, vivid. It’s an inward journey to a hidden past, a place buried deep, that suddenly bursts forth like a firework of nostalgia.

Each of us holds a palette of scents capable of bringing us back—suddenly, vividly—to a time that’s gone. Mine carries rustic, earthy tones: my maternal grandparents were farmers, and I spent much of my early childhood with them in the mountains of Irpinia.

I remember the sticky perfume of freshly harvested tobacco leaves, the white film of yeast clinging to wine grapes, the wild asparagus gathered by riverbanks, the unmistakable sweet scent of the ceuze—what we called mulberries in dialect—and the zenzifero, a local mint that gave ricotta ravioli its delicate fragrance…

I doubt I’ll ever stumble across those long-lost smells again—or perhaps they’re just dormant, waiting. But if they do return, that would be the most beautiful time travel I could ever hope for.

And you? What scents carry you away to other times, other worlds?

smell memory, nose

Smelling the Color 9: When Numbers Take Shape and Color

Gianni Sarcone

In English, the expression to smell the color 9 describes something completely impossible…

And yet, some people have the unusual ability to mentally visualize colors or spatial patterns when thinking about units of time—or more broadly, numbers. This phenomenon, known as synesthesia (from the Greek syn, “together”, and aisthēsis, “sensation”), occurs when stimulation of one sense involuntarily triggers sensations in another. It’s not a figure of speech—these perceptions feel very real to those who experience them.

The first documented case in medical literature appeared in 1710. Dr. John Thomas Woolhouse (1650–1734), an ophthalmologist to King James II of England, reported a blind young man who claimed he could perceive colors induced by sounds.

Neuroscientist Vilayanur S. Ramachandran and his team at the University of California, San Diego, observed that the most common form of synesthesia links “graphemes“—letters or numbers—to specific colors. Since my work bridges art and mathematics, I’ll focus here on number-based synesthesia.

People who experience synesthesia in its pure form are relatively few. However, many report strikingly similar associations between numbers and colors or spatial layouts, suggesting these perceptions aren’t just products of imagination or attention-seeking. For example, number–form synesthesia may result from cross-activation between brain regions in the parietal lobe that handle numerical and spatial processing. In contrast, number–color synesthesia likely stems from an overabundance of connections between adjacent areas that interfere with each other when triggered (see fig. 1 below).

brain synesthesia

Figures 2 and 3 illustrate common synesthetic patterns—either as color associations (fig. 2) or spatial arrangements (fig. 3, based on observations by Sir Francis Galton). Statistically, people often associate the digits 0 or 1—and sometimes 8 or 9—with black or white. Yellow, red, and blue are typically linked to smaller digits like 2, 3, or 4, while brown, purple, and gray tend to be tied to larger ones like 6, 7, or 8. Curiously, it’s not the idea of the number but the visual form of the digit that seems to trigger the sensation. For instance, when the number 5 is shown as the Roman numeral V, many synesthetes report no color at all.

color number synesthesia

And you—do you see numbers in color or arranged in space? Feel free to share your synesthetic experiences with me.

Misdirection → Illusion → Aha! Moment…

Gianni Sarcone

How misdirection, illusion, and wonder shape my creative process.

The path from misdirection to revelation is at the heart of how illusion and wonder spark insight. Misdirection steers our attention—often subtly—away from what truly matters. It disrupts our expectations, creating a gap between what we see and what is. Within that gap lies the illusion: a crafted discrepancy, a visual or cognitive sleight-of-hand that unsettles our perception.

But the magic doesn’t end there. When the illusion is cracked—when the mind shifts, recalibrates, and sees—the famous Aha! moment erupts. That flash of understanding isn’t just delightful; it’s deeply educational. It rewires how we interpret the world.

This sequence—misdirection, illusion, revelation—mirrors the creative process itself. It shows how confusion, when carefully designed, can be a gateway to clarity. In the right hands, illusion is not deception—it’s a tool to awaken curiosity, stretch perception, and provoke insight. Wonder, in this sense, becomes a powerful cognitive catalyst.

That’s why my art and, I believe, my writing, revolve around this sense of wonder—arguably the most direct and playful route to that pleasurable, often conflicting moment of insight: the sudden discovery of something previously unknown.

Hands-On Wonders: A Mathemagical Collection

Gianni Sarcone

Ever wondered what happens when math puts on a magician’s hat? These books are the distilled magic of my hands-on math workshops across Europe — from Paris to Palermo, Geneva to Ghent — where paper folded, minds twisted, and logic sparkled in English, French, and Italian!

Impossible Folding Puzzles

1) “Impossible Folding Puzzles and Other Mathematical Paradoxes” — a playful dive into mind-bending problems where nothing is quite what it seems. Can a puzzle have no solution… or too many? Dare to fold your brain.

Still available on Amazon.

2) “Pliages, découpages et magie : Manuel de prestidi-géométrie” — where math meets illusion to spark curiosity and creativity.
Perfect for teachers, students, and curious minds: touch, fold, cut… and let the magic unfold!
Available on Amazon.

2) “Pliages, découpages et magie : Manuel de prestidi-géométrie” — un livre où maths et illusion se rencontrent pour éveiller curiosité et créativité.
Pour enseignants, élèves et esprits joueurs : touchez, pliez, découpez… la magie opère!
Dispo sur Amazon.

Pliage decoupages

3) “MateMagica” —  They say there’s enough carbon in the human body to make 900 pencils… but just one is all you need for these clever puzzles!
Fun, surprising, and thought-provoking — because, as Martin Gardner put it, “Mathematics is just the solution of a puzzle.”
Now on Amazon.

3) “MateMagica” —  Si dice che nel corpo umano ci sia abbastanza carbonio per 900 matite… ma per questi rompicapi ne basta una!
Sorprendenti, divertenti e stimolanti — perché, come diceva Martin Gardner, “la matematica è nient’altro che la soluzione di un rompicapo.”
Disponibile su Amazon.

I write and illustrate my own books in five languages: English, French, Italian, German, and Spanish.
If you’re a publisher or literary agent seeking original, high-quality educational content that blends creativity with clarity, I’d be pleased to explore potential collaborations.

B.U.T. – Bridging Unlikely Thoughts

Gianni Sarcone

Ah, the infamous “BUT“! The semiologist in me would have a field day with this little word. It’s like the ultimate plot twist in a sentence—an entire world of contradiction wrapped in just three letters. It’s the “Dr. Jekyll and Mr. Hyde” of conjunctions: on one hand, it tries to introduce a new idea, and on the other, it erases everything said before, as if it were all just a warm-up.
As a historian, I’d argue it’s the “philosopher’s stone” of language. A single “BUT” has the power to change history—like when someone says, “I’m not sexist, BUT women just aren’t good at math.” And then—BAM!—history is rewritten in a very particular shade of awkward.
The comedy gold lies in the absurdity of it all. It’s a linguistic loophole, designed to create just enough space for a “disclaimer” while conveniently ignoring any of its consequences. Call it the punctuation equivalent of “I have a friend who…” or “No offense, but…”—it sets you up for everything that follows, no matter how absurd!

The Many Flavors of Absence

Gianni Sarcone

A guy walks into a bar and asks for a coffee without cream. The bartender replies, “Sorry, we’re out of cream—how about a coffee without milk instead?” 

It’s a simple joke, but it highlights something curious: absence has weight. Psychologically, a coffee without cream doesn’t feel quite the same as a coffee without milk. 

Now, let’s take it a step further. Is the absence of a loved one the same as the absence of a random stranger? Of course not. Absence isn’t just a void—it carries the shape of what’s missing. 

The ancient Greeks had a word for this: steresis (στερήσις), the idea that everything is defined by both what is present and what is absent. Zen philosophy explores a similar concept with mu (無), suggesting that sometimes, absence is a kind of presence in itself. 

So next time you order a coffee without cream, pause for a second—what is it you really don’t want to be in there?

The Silent Orbit of Thought

Gianni Sarcone

The circle, a timeless symbol of wholeness, is found at the core of human thought. In the West, it evokes the Pythagorean harmony of the cosmos, the eternal return of Nietzsche, the indivisible unity of Being. A form without beginning or end, it embodies the perfect balance between presence and absence, the finite and the infinite.
In Eastern traditions, the ensō (円相)—literally “circular form”—is a distilled gesture of perception, a visual echo of clarity. Not merely a shape, but an experience, it is drawn in a single stroke, capturing the ephemeral moment where thought and movement dissolve into pure expression. It is said that the earliest Zen painting was an ensō, traced to offer a student something tangible yet elusive, a paradox to ponder.
A circle can be brushed on paper, traced in sand, drawn on a misted window, or merely imagined. It lacks nothing, needs nothing, yet contains all things. In its quiet completeness, it is not an answer, but an opening—an invitation to see beyond the limits of form.

Umbrella Illusion

Gianni Sarcone

One of my illusions from the late ’90s. Take a look at the colorful umbrellas in Figures A and B of the table below—are they the same or different? About 80% of people will say that Umbrella A has jagged, zigzag edges, while Umbrella B has a smooth, wavy outline. But here’s the trick—you’ve been fooled by the brightness contrast of the rays inside the umbrellas. In reality, both umbrellas are identical in shape, perfectly congruent.

This illusion works even when only the lines of the shapes are emphasized. As demonstrated in the table below, the outline of Umbrella A appears jagged and zigzagged, while Umbrella B seems to have, once again, a smooth, wavy outline.

This illusion shows a phenomenon called curvature blindness, which was rediscovered in 2017 by Japanese psychologist Kohske Takahashi. He created a powerful variant and studied its impact on how we perceive shapes.

© Kohske Takahashi – The wavy lines appear different depending on the background and how the repetitive dark color is applied to them.

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