Reality Map… or a Carefully (Un)folded Illusion We Mistake for the Real?

Gianni Sarcone

The diagram offers just one interpretation among many: a visual way to suggest that every element in a hierarchy contains its own mini-hierarchy, and so on—an endless, anastomosed structure of nested systems. The names may shift, but the core idea stays the same. It’s our knowledge that draws the lines and defines the extent of this vast, branching tree.

Today, we think we’ve mapped the boundaries where the infinitely large and the infinitely small end. Yet with each scientific advance, those borders are pushed ever further.

But some philosophical questions arise: is our reality fractal in nature? Not necessarily. It may be that each entity, each element within this hierarchical branching structure, is fundamentally different from the others. And more than that—borrowing and reworking an idea from Aristotle—the whole is not merely the sum of its parts; it is something else entirely… and, in a way, the reverse is also true.

Yes, the branches may indeed extend infinitely, forming a structure that resembles a bridge stretching endlessly, anchored to no shore—a true paradox. Strange, perhaps. Stranger still: although our reality may not be fractal in the strict sense, we might consider it holographic in nature. From any single, distinct element, it is possible to reconstruct a part—or even the whole—of what surrounds it.

This phenomenon has a name in Latin: pars pro toto—a part that reflects the whole. In this sense, everything is contained within each of us, even in our differences.

I’ll end with a thought: if we perceive an ordered world amid the chaos of complexity, it is likely due to our remarkable ability to intuit patterns and to organize what we call reality according to the logics we ourselves invent. That, perhaps, is the most beautiful illusion of all.

reality map

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.

Unveiling the Ancient Unicursal Labyrinth

Gianni Sarcone

Ancient labyrinths, known as unicursal, were also referred to as “Cretan” labyrinths, drawing from their roots in Greek mythology. In Great Britain, similar turf mazes based on the same pattern are called ‘caerdroia‘—a Welsh term meaning “City of Troy.” These mazes can still be found in a few remote villages and rural hamlets.

They were typically built around a central core—often shaped like a cross resembling a ‘gammadion’. With the help of the diagrams below, you’ll find it quite straightforward to construct one yourself.

(There are two main historical variations of the Cretan labyrinth, as you can see in Figures. A and B.)

The image is taken from my article “Parcours et détours,” originally published in the French journal MathÉcole.

You can read the full piece here (in French).

The Word: From Incantation to Influence

Gianni Sarcone

In the beginning, whether real or invented, certain words—many from a distant past—formed a bridge between humans and the great Mystery. One such word that survived the ages, still cloaked in a strange aura of power, is Abracadabra. Even today, magicians use it to conjure effect, echoing its ancient weight.

Originally, Abracadabra wasn’t just theatrical. It was an apotropaic charm—spoken or inscribed to ward off harm. The earliest record, from the 2nd century CE in a medical treatise by Serenus Sammonicus, describes it as a remedy for fever. Written in a tapering triangle, the word visually dissolved with each line, symbolizing the illness retreating. Its origins are uncertain. Some link it to Aramaic or Hebrew—“I create as I speak” (אברא כדברא). Others see it as a coded sequence from the Greek alphabet (ΑΒΓΔ), or a variant of another potent name: Abraxas.

An incantation born of another—what a journey through a world woven in magic.

Abraxas (Greek: ἀβραξάς), central to the Gnostic teachings of Basilides, named a powerful being ruling over 365 heavens. Engraved on amulets, Abraxas was thought to hold innate power. These stones, often cited in magical texts, show a belief system where sound and symbol merged—where the right word could invoke protection, healing, or cosmic order. Its earlier spelling, Abrasax, likely morphed through transliteration. With seven letters, the name was also tied to the seven classical planets, deepening its cosmic charge. Whatever its true roots, one idea persists: properly arranged, words carry force.

Across time, this belief shifted but never vanished. Ancient incantations gave way to new forms of verbal power.

Antiphon of Athens (5th century BCE) stripped speech of ritual but kept its essence. Considered a forerunner of psychotherapy, he used dialogue to ease emotional suffering. His method wasn’t mystical—it was precise, rooted in rhetoric and clarity. Where once words summoned the divine, now they served insight and balance.

Language, even without the trappings of magic, remains transformative. In the 20th century, thinkers like Paul Watzlawick showed how communication doesn’t just reflect our world—it shapes it. A change in phrasing can shift perception. A word can open or close a mind.

From Abraxas to Abracadabra, from spell to speech, the thread continues: words influence, connect, heal. What began as incantation lives on as conversation—still crafting reality, still carrying power.

The Interrogation Mark: From Greek Semicolons to Spanish Twists

Gianni Sarcone

In ancient Greek, questions were marked by a semicolon (Ερωτηματικό) rather than a question mark. This practice faded over time, and no special punctuation indicated questions in antiquity. The modern question mark emerged in the Middle Ages when scribes used “qo” (from Latin quaestio). To avoid confusion, they stacked the letters, turning the Q into a curl and the O into a dot, creating the question mark (“?”). In Spanish, the question mark was placed only at the end until 1754, when the Ortografía de la Real Academia introduced the inverted opening question mark (¿), as in: ¿Qué edad tienes? (How old are you?).

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.

Read more

The Illusion of Color in Astrophysics

Gianni Sarcone

Study on Colors in Astrophysics – Ongoing Research

Under specific atmospheric conditions and with the technological tools employed, stars or planets may appear to emit green or blue light to some observers. However, as illustrated in the accompanying diagram, this is often nothing more than an optical illusion. The blue region seen in the diagram is actually a medium gray, entirely desaturated. You can verify this by using Photoshop’s color picker tool (or an analogous method) to check the true color values.

This phenomenon raises interesting questions about how color perception in astrophysics can be influenced by both atmospheric effects and the limitations of observational tools. How much of what we “see” in the cosmos is truly the color of the objects themselves, and how much is a product of the interaction between light, our atmosphere, and the instruments we use to detect it?