May 8, 2026—Mathematicians create an impossible shape that can’t exist in real life, construction begins on the DUNE neutrino project, and a famed naturalist celebrates a milestone birthday. Happy Friday!

—Andrea Gawrylewski
Chief Newsletter Editor

TOP NEWS

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TOP STORY

Impossible Objects

An impossible object is something that looks realistic when drawn but can’t exist in real life. Dutch artist M. C. Escher is famous for depicting such objects, for instance: staircases and waterfalls that are impossible to build in three dimensions. Many of Escher’s works are based on constructions by British mathematicians Roger and Lionel Penrose, such as the Penrose triangle and Penrose stairs, which they published in the 1950s.

Three impossible figures are shown. The first two are variations on what is generally known as a Penrose triangle: a three‑sided geometric shape made of rectangular beams that appear to connect in a continuous loop. The third is a Penrose staircase: a drawing of a continuous loop of steps that appear to ascend or descend forever.

Robert Ghrist

Two mathematicians, Robert Ghrist of the University of Pennsylvania and Zoe Cooperband of the U.S. Naval Research Laboratory, invented an impossible object that breaks reality in novel ways. It starts with a variant of the Penrose staircase. A bug walking around the blue path in the graphic, for instance, will feel like it is traveling a level course, but if it takes the ladder connecting two opposite sides, it will feel as if it has climbed to a new height. Both courses are locally consistent but globally inconsistent.

A rectangular blue path is created by a series of blue cubes, placed as if they were stepping stones, and settled into apparent three-dimensional space. A tower of pink cubes connects two of the rectangle's sides. This figure is labeled “Penrose staircase variant.”

Robert Ghrist

The researchers then imagined rearranging this rectangular path into a line and pasting it onto a cylinder so that the left-hand side connected to the right-hand side. In that case, a bug that walked to the right from its starting point would find itself exactly back where it started. The scientists further imagined winding the path like a Möbius strip—a form one can make by twisting a strip of paper and attaching the two ends. A bug that traveled to the right from its starting point would find that after it completed the loop, what it once considered right side up had changed. This path forms the basis of the new impossible shape, which is a continuous multilevel staircase. Click through to see detailed depictions of how this shape works.

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First question of today's science quiz: What 1845 effort to find the Northwest Passage ended in tragedy after the crews of two ships got trapped in Arctic ice?

How well did you keep up with science news this week? Put yourself to the test with today's science quiz. Also, check out today's Spellements puzzle. If you spot any missing science terms from the puzzle, email them to games@sciam.com.

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Though Escher didn’t have a formal background in mathematics, the field inspired much of his art. Some of my favorite works of his are his tessellations–the interconnected and repeating patterns he devised (and which inspired some of my own rudimentary attempts in college visual design classes). You can see some of his so-called symmetry work at the official website of the M.C. Escher Foundation. I love too many to pick a favorite, but I'm especially fond of his use of birds and other shapes from nature. Research into repeating units of pattern is very much alive and mathematicians recently proved the existence of the einstein tile—a hat-shaped tile that can cover an infinite plane and never repeat.

You can reach out to me anytime: newsletters@sciam.com. Have a great weekend!

—Andrea Gawrylewski
Chief Newsletter Editor

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