A segment of an image tends to seem larger when it’s filled with visual elements. This is true whether the elements are discrete or continuous.
Above, the right part of the top figure and the left part of the bottom figure each seems to fill more than half of its tier, though plainly these impressions can’t both be valid.
The illusion was first studied by German physicists Johann Joseph Oppel and August Kundt in the 1860s.
Born with an orthopedic condition that caused her knees to bend backward, Ella Harper made a virtue of necessity and joined W.H. Harris’s Nickel Plate Circus, where she took up a starring role and earned $200 a week ($7,200 today). Her pitch card reads:
I am called the camel girl because my knees turn backward. I can walk best on my hands and feet as you see me in the picture. I have traveled considerably in the show business for the past four years and now, this is 1886 and I intend to quit the show business and go to school and fit myself for another occupation.
She married a schoolteacher in 1905 and died in 1921 at 51.
The Vermin only teaze and pinch
Their Foes superior by an Inch.
So, Nat’ralists observe, a Flea
Hath smaller Fleas that on him prey,
And these have smaller yet to bite ’em,
And so proceed ad infinitum.
— Jonathan Swift
Great fleas have little fleas upon their backs to bite ’em,
And little fleas have lesser fleas, and so ad infinitum.
And the great fleas themselves, in turn, have greater fleas to go on;
While these again have greater still, and greater still, and so on.
— Augustus De Morgan
In all three of these figures, the gray ring’s color is uniform. But in the second and third figures the upper half appears distinctly darker, showing that the brain exaggerates differences in brightness between adjacent surfaces. German psychologist Kurt Koffka first reported the effect in 1935.
The peculiar architecture of Echo Bridge, in Newton, Massachusetts, will re-echo a human voice 18 times and a pistol shot (reportedly) 25 times.
In 1889 author Moses King wrote, “The favorite word to hurl at the arch is JULY, and the serious charge of lie — lie — lie is thrown back as vigorously and almost as frequently as if the bridge were a political newspaper in campaign time.”
In Riddles in Mathematics (1961), Eugene Northrop proposes that two men can simultaneously be each other’s uncle and nephew:
Mr. and Mrs. Allen … had a son Tom, and Mr. and Mrs. Black … had a son Dick. Mr. Allen and Mr. Black both died. And Tom and Dick, after they were grown men, each married the other’s mother. Dick and Mrs. Allen then had a son Harry, and Tom and Mrs. Black a son George. Now consider the relationship between Harry and George. Since Harry is the brother of Tom, George’s father, Harry must be George’s uncle. On the other hand George is the brother of Harry’s father, Dick, so Harry must be George’s nephew. In exactly the same way George is Harry’s uncle and nephew.
In Fun for the Family (1939), Jerome S. Meyer observes that if you father a son with the mother of your father’s second wife, and if your stepmother also has a son, then you can dine alone and still enjoy the company of your stepbrother’s nephew’s father, your father’s mother-in-law’s husband, and your stepmother’s father-in-law. Lewis Carroll considered a similar dinner.
A certified poet from Slough,
Whose methods of rhyming were rough,
Retorted, “I see
That the letters agree
And if that’s not sufficient I’m through.”
— Clifford Witting
In the Saturday Review in 1946, architect Gerald Lynton Kaufman proposed nine “poetry forms in mathematics”:
These yellow rings are not superimposed on an existing photograph — they’re actually painted on the landscape. Swiss artist Felice Varini created Three Ellipses for Three Locks in 2014 by painting segments on roads, walls, and nearly 100 buildings in the historic center of Hasselt, Belgium. The effect was visible only to a viewer in one particular vantage point.
Here’s another project by the same artist.
04/12/2026 CORRECTION: The installation pictured above was created in 2007 by Varini at Cardiff Bay Barrage in South Wales. He created a second installation with the same title seven years later in Hasselt. My mistake. (Thanks, Christian.)
Robert Heinlein’s 1959 short story “–All You Zombies–“ accomplishes a kind of narrative hat trick: All the major characters turn out to be the same person, who takes on different roles through time travel and sex reassignment. The main character is his own partner, mother, father, and child.
Though it contains a number of paradoxes, Princeton philosopher David Lewis judged it to be a “perfectly consistent” time travel story. Ironically, Heinlein had written it in a single day.
