Illusion vs Reality

“Illusion, a derivative of reality, and vice versa.” – GS

For a little backstory… one day, a follower threw me a curveball: ‘What separates illusion from reality?’ I countered with a snap response: ‘What separates acceleration from speed?’

Perception in Motion: Illusion, Confusion, and Zen Insight

Many perceive the two 3D cross-like shapes as moving significantly, though they remain stationary!

The interplay of color shades (light/dark) on the edges and body of the cross-like wire frames creates the illusion of motion. The alternating shadings simulate “motion blur,” leading some researchers to attribute these illusory movements to delays in luminance processing, producing a signal that deceives the motion system and induces “kinetopsia” (motion perception)..

This brings to mind an anecdote: Two Zen monks debated a flag moved by the wind. One claimed, ‘The flag is moving…’ while the other countered, ‘The wind is moving!’ The monastery’s prior intervened, stating, ‘Not the wind, not the flag; the mind is moving…’

This short anecdote serves to explain that the concept and perception of motion is sometimes ambiguous.

Autokinetic Illusion

Immerse yourself in the mesmerizing experience as blue droplets seemingly sway gracefully, creating an illusion of gentle motion. The yellow horizontal lines contribute to a wave-like dance, enhancing the visual allure.

Hold On Tight” by Gianni A. Sarcone, crafted in 1997.

This op art piece embodies a peripheral drift illusion (PDI), wherein a sawtooth luminance grating in the visual periphery induces the illusion of movement.

Fascinatingly, studies by vision researchers reveal that the illusory motion activates brain regions akin to those triggered by actual movement.

Noteworthy accolades include a feature on Google Science Fair (@googlescifair):

Explore and acquire “Hold On Tight” as prints and posters through our online gallery.

Wandering Eye

The entire sea urchin functions as a massive compound eye because each of its spines conceals tube feet with light-sensitive cells at their bases. Essentially, a sea urchin is one large, moving, spine-covered eye. While its vision might not astonish an eye doctor, for an animal devoid of actual eyes, it’s rather impressive!

A representation of the computational model of the ‘spherical’ vision of the sea urchin.

For further details, you can read more here.

Perceptual Puzzle

Size Distortion: The length and curvature of the blue curves A and B in the diagram are highly deceptive. However, the curves are congruent! This presents an intriguing variation of the Delboeuf illusion, wherein size judgment is distorted by peripheral context.

Impossible Paper Turn-up

Let’s explore a captivating paper-folding puzzle, part of the impossible origami family. It is simple to carry out and can be done at any moment.

Cut a 10-centimeter-wide strip from a two-colored sheet (in our case, yellow and red). Make sure the paper strip is at least 24-25 cm long! By gluing the ends together, you may turn this strip into a ring, as shown below. The goal is to create a turn-up in the ring without tearing it… Impossible? Many of your friends will attempt, but the outcome will always be negative.

This is how the trick works:

Flatten the paper ring and fold the top edge by 2-3 cm (see fig. 1). Unfold only the single top layer of the fold, creating two triangular folds at each corner of the flattened ring (fig. 2). Next, fold the two outer edges along the base of the flattened triangles (fig. 3). Then, fold the outer edge upstream. This way, a folded edge is now on each face of the flattened ring.

Now, insert your fingers inside the ring, firmly holding one corner between your thumbs and index fingers. Carefully separate your hands, pulling the sheet at the corner, releasing the excess paper hidden between the folds (fig. 5a and 5b). Repeat on the other corner. Finally, rearrange the paper ring, smoothing out the visible folds. The top edge of the ring is now completely turned on itself, creating a perfect turn-up without tears. Who would have thought? Congratulations, magician!

Egguation

Solve for the perfect omelette with this eggcellent formula!

In fact, if you graph x2 + y2 = 2y, you will obtain a flawless egg shape:

However, there are also other methods to create a perfect ovoid shape using a compass and ruler, as illustrated below.

Typical Ovoids: a – Cundry & Rollet ovoid (1989); b – Classic ovoid; c – Ovoid Sqrt 327 (Dixon, 1987); d – Antonio Castilla ovoid (Cuarado, 2010).

Cat Tessellation

Explore the captivating world of tessellations! Immerse your surroundings in the charm of feline grace and geometric perfection. Available as prints and merchandise in our online gallery.

Cat Tessellation by Gianni A. Sarcone

There’s a story behind this geometric drawing; it depicts our late cat, Sylvestre. He was an Abyssinian cat with a fawn-colored coat, mirroring the illustration. Sylvestre was our daily companion in the studio for nearly 20 years.

Amazing Disentanglement Puzzle

How to transform ordinary rulers into captivating feats of magic? Equip yourself with two standard 30 cm rulers, made of wood or other materials. Attach a 20 cm string to each ruler by threading it through the hole at one end (see Fig. 1). Form a cord loop around one ruler, knotting the loose end of the cord, as depicted in figures 2 and 3. Ensure the string ring is not too tight, allowing it to glide smoothly along the ruler.

Repeat with the second ruler, threading the cord through the loop of the first ruler, as shown in figure 4.

The challenge is to separate the rulers without cutting or unraveling the cords. Despite the apparent difficulties, the solution unfolds seamlessly.

This string puzzle can also be build using two plastic pipes and two curtain rings (see figure 5).


show solution

Timeless Trigonometry: Plimpton 322’s Revolutionary Legacy in Mathematics

Plimpton 322,” a clay tablet originating from ancient Mesopotamia during the Old Babylonian period (1900-1600 BCE), precedes Hipparchus by over 1,000 years. This artifact not only provides novel avenues for contemporary mathematical research but also holds implications for mathematics education. The trigonometry revealed in “Plimpton 322” presents a more straightforward and precise approach, showcasing distinct advantages compared to our current methods.

The Plimpton 322 clay tablet, featuring numbers inscribed in cuneiform script.

Read more.