Plus, a shape that shouldn't exist in real life ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏
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
|
|
In this archival image you can see the lunar surface as viewed from the landing site of Apollo 12, the sixth crewed flight for the U.S. Apollo Program and the second to land on the moon on November 19, 1969. The UAP can be seen in the highlighted area slightly to the left of the vertical axis of the frame, above the horizon. NASA
|
|
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.
|
|
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.
|
|
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.
|
|
|
|
|
|
MOST POPULAR STORIES OF THE WEEK
|
|
- Why some mathematicians think we should abandon pi | 4 min read
- A SpaceX rocket booster is on track to hit the moon at several times the speed of sound | 3 min read
- A dangerous experiment is playing out on a cruise ship with hantavirus | 4 min read
|
|
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.
|
|
—Andrea Gawrylewski
Chief Newsletter Editor
|
|
|
|
|
Subscribe to this and all of our newsletters here.
|
|
|
|
|
