Kokichi Sugihara specializes in the impossible. He creates mind-bending physical objects that look and behave in incredible ways when seen from the right angle, such as marbles that roll uphill or circular pipes that look rectangular in a mirror.
Unlike traditional optical illusions, which short-circuit our brain’s visual processing system, Sugihara’s objects involve no visual trickery other than perspective.
“Historically, optical illusion has been a research topic in psychology. I introduced a mathematical approach to this topic, and thus can create new types of 3D optical illusions,” he explained in an email interview.
The arrow is always right
Sugihara, a mathematical engineer at Meiji University in Japan, has published several studies based off his creations and he’s also twice won the award for Best Illusion of the Year.
Perhaps the most astonishing of his impossible objects is a simple white arrow pointing to the right. Bewilderingly, even when spun around 180 degrees, the arrow still points to the right.
“Dr. Sugihara’s ambiguous objects are a mathematical work of art that uses the physics of optics to show us how our senses and perceptions can be fooled, and yet we can fully understand how the phenomena works,” said in an email Ray Hall, a professor of physics at California State University, who made the video above using a Japanese toy set which includes objects derived from Sugihara’s studies.
The secret is in the shape of the object, which is only revealed fully when the viewing angle is modified. Sugihara calls it an “anomalous mirror symmetry” in a 2016 scientific paper.
“This illusion has it all, physics that seems like magic, a reminder that we need science to transcend the limits of our perceptions, all within an elegant mathematical framework,” said Hall.
Circle or square?
Sugihara creates his objects as part of his academic research. “My background is in mathematical engineering, where we use mathematics as a tool for understanding various phenomena, and I’m now concentrating on the phenomenon of human depth perception,” he said.
His 2016 illusion “Ambiguous cylinder” has the professor moving a series of objects, which he has 3D printed, in front of a mirror. But the objects appear to be square and round at the same time.
How is that possible? The shape is affected by the viewing angle. Seen from above, the object looks like a hybrid between a square and a circle, or a square with very rounded corners. Most of the illusion comes from the edges: two arch upwards and two dip down, which forces the brain into “completing” the shape of a square and a circle alternatively when the object is rotated. (The full video shows more shapes, and this video analyzes the objects in detail.)
Some of Sugihara’s illusions are meant to be seen in motion. In a 2014 scientific paper he writes, “I coined the term ‘impossible motion’ to label a new type of optical illusion in which viewers perceive objects that appear to move in physically impossible patterns.”
One such example, a winner of Best Illusion of the Year, is called “Magnet-like slopes.”
The marbles roll uphill! The explanation lies, once again, in the perspective: the slopes actually form a valley, but the carefully constructed structure looks like a peak. Only when it is rotated the eye correctly interprets the size of the central pillar, which is shorter than it seems.
Optical illusions that offer an impossible motion eventually tend to nudge the brain into correcting the visual interpretation of the object, and once that happens the illusion is lost. But not with this one, Sugihara notes: “Suppose that a viewer changes the viewpoint, to understand the true shape of the solid, and goes back to the initial viewpoint again. Then, the impossible motion illusion still occurs. In this sense, this illusion is strong and robust,” he said.
Real or CGI?
These objects may be mind-boggling, but they are not difficult to craft. Some can even be built at home with just a printer, paper and glue. Others can be downloaded from the Internet, but require a 3D printer.
Kokichi Sugihara's illusions
Yet the illusions are so powerful that some have questioned their authenticity: Snopes.com, a fact-checking website that debunks myths and news stories, had to confirm that the video of the arrow always pointing right was real after a number of readers asked if it involved CGI.
This type of incredulous reaction leaves Sugihara amused rather than frustrated.
“It is my great joy and fun,” he said. “I feel like a magician. I also feel that mathematics has the power to create what has never existed.”