Curiosities

Triple Klein Bottle

Gianni Sarcone

Τριαλάβαστρον (Trialábastron), a triple Klein bottle, is an artistic exploration of Klein bottle geometry. In topology, the Klein bottle is a non-orientable surface that cannot be embedded in three-dimensional Euclidean space without self-intersection, though it can be smoothly realized in four dimensions.

A close relative is the Möbius strip, another non-orientable surface in three-dimensional space. On such surfaces, a continuous path can return to its origin with reversed orientation, revealing how geometry can twist the notion of inside and outside.

a triple Klein bottle

Here is another representation of a triple Klein bottle—UK sculptor Alan Bennett’s striking construction of three Klein bottles nested within one another. Of course, “inside” only applies in the sense of their embedding in physical space; from a topological standpoint, they remain entirely separate, non-interacting surfaces.

recursive Klein bottle

Why W Is Called “Double-U”

Gianni Sarcone

The letter W ultimately derives from the letter V, but its history is more layered than a simple invention after the Norman Conquest.

In classical Latin, inherited from the Greek and Phoenician alphabet traditions (Fig 1), the letter V served a dual function: it represented both the vowel /u/ and the consonantal sound /v/. There was no distinct symbol for /w/. In contrast, Old English (Anglo-Saxon) already had a need for this sound and used a separate rune, “wynn” (ƿ, Fig. 2), to represent it.

After the Norman Conquest of England in 1066, scribal practices shifted toward continental Latin conventions. The rune wynn gradually fell out of use, and scribes began representing the /w/ sound by writing a doubled form of U (or V, since the two were not yet fully distinguished, Figs. 3-4). This “double u” convention eventually evolved graphically: two V-shaped characters were written side by side, then gradually joined.

From this duplication comes the modern name “double U,” which preserves the historical origin even though the visual form is closer to two V’s than two U’s. The lowercase w developed directly from this doubled form, simplifying over time into a continuous script shape.

In short, W is not a direct Roman invention, but a medieval solution: a hybrid born from Latin writing habits adapting to a sound already present in Old English.

Your Brain vs. Geometry: Rooftop illusion

Gianni Sarcone

Believe it or not, the green and purple rooftops are congruent—identical in shape, size, and angles. What changes is not the geometry, but your perception of it. Perspective, orientation, and contextual cues lead your visual system to interpret the same form as two different structures.

rooftop illusion, related to shepard tables

This effect is closely related to Shepard’s tabletop illusion and earlier studies in which identical parallelograms (A and B), when rotated (and superimposed), are perceived as different shapes, as the brain prioritizes interpretation over measurement.

Since some still insist these roofs are not congruent, I’ve put together a short animation that shows otherwise.

animated rooftop illusion

Bear-ly Seal

Gianni Sarcone

People often ask where my ideas come from. There is no single answer. They tend to surface quietly, shaped by places I’ve seen and cultures I’ve crossed.

“Seal or Bear?” grew out of that kind of moment. An animal suspended in the vastness of a frozen world—emerging from an ice hole, yet refusing to settle into a single identity. Is it a polar bear? A seal? Or something that holds both readings at once?

Bear of seal?

The idea came to me while traveling through northern Canada, surrounded by the stillness of Arctic landscapes and the deep presence of Inuit traditions. That silence has a way of sharpening perception—of making ambiguity feel natural rather than puzzling.

First created in the 1990s, the illusion went on to become a reference point in visual perception studies and later found its way into textbooks.

More recently, the “Seal or Bear?” illusion will be featured by the NHK Educational Corporation as part of a 2026–2027 educational series on psychology and visual perception.

Galloping Primes

Gianni Sarcone

Every frame in this GIF is a 3,100-digit prime number:

prime gif

Together, they recreate the world’s first motion picture: Eadweard Muybridge’s iconic 1878 “Galloping Horse.”

How it works: Each frame is converted into a grid of 1s and 8s, then slightly tweaked until the math clicks and a prime number is born. Fast primality tests spot the candidates, and rigorous checks confirm them.

The result? An animated piece of history, built entirely out of pure mathematics.

☞ Source: https://www.lbatalha.com/blog/prime-motion-picture

Impossible Beach Cabin

Gianni Sarcone
impossible house sketch

With summer just around the corner, I find myself drifting back to the shores of time, to this delightfully impossible little structure perched on the beach.

A drawing concept created for a children’s coloring book on optical illusions. Over the years, I’ve explored this theme through many curious and playful variations.

impossible house
Available as fine art print from my online gallery.

Are the kids engaging in creative activities inside the cabin or outside it?

The roof insists we’re looking at the exterior, while the floor pulls us firmly indoors. Both readings feel correct, yet they cancel each other out. So, there’s no clean resolution here—just a quiet visual paradox.

Curious to see more of my optical illusion book concepts, impossible worlds, and mind-bending creations? Take a stroll through my author page.

impossible house poster

The idea itself is far from new and has inspired countless artists, architects, and photographers. It even exists in three dimensions. A notable example is Roy Lichtenstein‘s House I (1996), an ingenious sculpture that appears to be a solid house but is actually a concave construction made of angled steel planes. As viewers move around it, the structure seems to rotate and reshape itself, turning perception into part of the artwork.

Born into Iki

Gianni Sarcone

I am iki from birth.

But what is iki (粋)?

Edo, under the Tokugawa shogunate. Merchants wealthy enough to unsettle the hierarchy, yet still ranked below the samurai. Power without status—watched closely, dressed carefully.

Sumptuary laws did the rest: no gold, no loud silk, no bright declarations. Only browns, greys, indigo. A forced muting of visibility.

Constraint rarely suppresses imagination. It concentrates it.

From this narrow register emerged a refined spectrum known as Shijuhattcha Hyakunezumi (四十八茶百鼠)—“48 browns, 100 greys.” Not literal numbers, but a cultural way of naming excess within restraint: an almost infinite sensitivity to difference inside what first appears uniform.

Fashion became a coded language. Subtle shifts in tone, legible only to trained eyes. Outside, discipline. Inside, excess held in reserve. A lining of rare fabric. A color hidden against the skin. A private flash revealed only when a sleeve turns in the wind.

This is iki: elegance that refuses emphasis. Presence without display. A form of refinement that collapses the moment it is named.

Its opposite is yabo (野暮): excess, insistence, the compulsion to be seen. Not morality—measure. Or the lack of it.

Today, the direction has inverted. Visibility has become currency. Those who do not perform disappear; those who do not declare are not counted. What was once failure has become strategy.

And yet the counter-move remains simple.

Lower the volume. Leave gaps. Let meaning breathe in what is not shown.

And become something worth looking at twice.

Life Within Life

Gianni Sarcone

Inside plants and living beings, there are remnants of ancient independent beings that once lived on their own, long before becoming part of the cellular world we know today. Known in biology as “organelles,” these are the living proof of ‘endosymbiotic theory’. They survive not as ghosts, but as symbiotic, working structures—still active, still essential, still carrying their own ancient logic.

From the host cell, these once-independent bacteria receive what any free organism would constantly struggle to secure: a stable, protected environment. No predators. No sudden shifts in conditions. A controlled internal world with steady access to water, nutrients, and chemical balance. In short, they are sheltered inside a living system that maintains their continuity.

Chloroplasts are the light catchers. You can think of them as tiny green alchemists, turning sunlight and water into stored energy, like weaving daylight into sugar. They belong to plants and algae, quietly building the foundation of almost every food chain on Earth.

Mitochondria are the fire keepers. They don’t create energy from light, but unlock it from what we consume, breaking down fuel to release usable power for the cell. Without them, nothing in the body moves, thinks, or repairs itself.

There is also a quieter detail: mitochondria are inherited almost exclusively from the mother. They pass from mother to child through the egg, like an intimate biological thread, while paternal mitochondria are usually removed after fertilization. Every cell therefore carries a subtle maternal imprint within its energy system.

In simplified terms, chloroplasts harness sunlight and water to generate sugars, storing energy in chemical form, while mitochondria release that stored energy for the cell by breaking down those molecules. One captures energy from light; the other unlocks it from organic matter—together sustaining the energetic cycle of complex life.

Algae in my eyes

Gianni Sarcone

Deep in the retina, an ancient memory persists. Our visual cells rely on “opsins“—light-sensitive molecules inherited from unicellular organisms that existed long before animals. For over a billion years, life has refined this simple act: catching light.
In the sea, the same logic still plays out. Some oysters host algae on their mantle; they feed them, and in return these light-sensitive cells signal the presence of light. A quiet watch system—almost an eye, spread across a surface.
In certain algae, like Chlamydomonas reinhardtii, a tiny eyespot—the stigma—is enough to steer the organism toward light. Not an eye, but already a direction, a choice.
Our rods and cones extend that first invention: a long lineage of light detectors, slowly shaped over time, linking our vision today to the faint glimmers of the earliest oceans.

In the tiny alga Volvox, a newly found light sensor glows green, showing where it sits around the cell’s center. (Image: Eva Laura von der Heyde / University of Bielefeld)

→ Further reading.