A math-magic article I wrote for the German magazine Zeit Wissen: with the 13 triangular and square pieces (fig. 1) it is possible to form two large squares shown in fig. 2. Though the second large square has an extra piece the dimensions of the squares seem to be the same! Can you explain why this is possible?
Convex / Concave, it all depends on your point of view!
Although the plates are the same, in the second picture, the indents of the egg plate look more like convex domes rather than concave indents.
Do the light gray triangular shapes in the diagram below have the same hue and brightness?Continue Reading
Our visual system can interpret colors and shades in surprising ways. With this 3×3 Tic-Tac-Toe grid I would like to show that our sensibility to color brightness can be easily fooled. Well, do you notice something particular in the grid below?
In the examples on your right hand, you can perceive two apples with four different zones. But what happens if we conceal the brightness boundaries of the color zones with black thick lines? You may see the apples as having a uniform color!
“Reality is merely an illusion,
albeit a very persistent one.”
— Albert Einstein
Everything you “see” depends strongly on the context and attention you give to it. The mind and the world you experience are inseparable, as it is your 3-pound brain that make the world meaningful. Seeing isn’t some kind of direct perception of reality. Actually, our bairns are cnostanlty itnerperting, correcting, and giving srtuctrue to the viusal ipnut form our eeys. If this were not the case, you would not see any colors (consider that all the beautiful colors you see don’t really exist), and you would probably see the world upside-down! Moreover, you would notice in your visual field a very large dot, called the “blind spot,” where the optical nerve enters the eye.
A Zen master said once: “If you pour water into a cup, water becomes the cup; if you fill a bottle with water, it becomes the bottle!” Likewise, the context shapes the appearance of the world surrounding you. Your brains work by comparing information and stimuli: contrasting colors, shapes, depth in a dynamic changing environment … that’s why perception is relative and not absolute. Continue Reading
I am very proud that my “Dynamic Müller-Lyer Illusion” won the third prize as best illusion of the year 2017!
As you surely know, the “BEST ILLUSION OF THE YEAR CONTEST” is a yearly competition under the patronage of Scientific American, organized by the Neural Correlate Company (New York, USA).
Müller-Lyer’s illusion proves that a segment can visually appear longer or shorter depending on the sense of the arrow heads at its ends. In what consists my variant? As shown in the animation, the red dot in the middle of the line is equidistant from the other two red dots, although the ends of the line visually appear to alternately stretch and shrink like a rubber band!
The radial version of the illusion is even more impressive:
The perceptual increasing and decreasing of the segments occurs in a very short time. Thus, I suppose it is more a physiological phenomenon, rather than a psychological bias. Our attention seems to be attracted by the receptive field WITHIN the V-shaped arrow heads, causing an illusory inward or outward shift of the ends of the line.
Inspired from the astrological tables, here is a new puzzle of my creation designed according to the ‘Golden Number Rules’, which is reflected in the proportion of each single piece of the game. Thanks to the balanced dimensions of its pieces, this puzzle acquires some intriguing magical properties!
This “math-magical” puzzle is composed of a tray in which the pieces are assembled.