Berkeley mathematician Raphael Robinson discovered this remarkable set of aperiodic tiles in 1978. The six shapes will neatly tile a plane, as shown below, and though the pattern cannot be regular, it reliably produces a hierarchical design: Each small orange square sits at the corner of a larger orange square, which sits at the corner of a still larger one, and so on ad infinitum. This is because subgroups of tiles form “supertiles” with similar properties — see here.
(Thanks, Jacob.)
In 1913 J.N. Muncey of Jessup, Iowa, showed that the first 144 odd prime numbers (counting 1 as prime) can be arranged into a magic square.
Each row, column, and long diagonal totals 4514.
Speakers of the Kuuk Thaayorre language, spoken by the Thaayorre people in Queensland’s Pormpuraaw settlement, use absolute cardinal directions (north, south, east, west) rather than relative spatial terms (left, right), even at small scales. So, for example, they would say, “The cup is southeast of the plate” or “The boy standing to the south of Mary is my brother.”
In 2010, University of California psychologists Lera Boroditsky and Alice Gaby gave Kuuk Thaayorre speakers sets of cards depicting temporal progressions — a man aging, a crocodile growing, a banana being eaten — and asked them to arrange the shuffled cards on the ground to indicate the correct temporal order.
English speakers arrange the cards from left to right, Hebrew speakers from right to left. But the Kuuk Thaayorre arranged them from east to west, regardless of the direction the subjects themselves were facing.
Among other things, this means that the Kuuk Thaayorre must be constantly aware of their orientation in the world. “We never told anyone which direction they were facing,” Boroditsky wrote later. “The Kuuk Thaayorre knew that already and spontaneously used this spatial orientation to construct their representations of time.”
(Lera Boroditsky, “How Language Shapes Thought,” Scientific American 304:2 [February 2011], 62-65.)
Give a hundred people a picture of the earth, identify the North Pole for them, and a hundred will hold the photo with the North Pole toward their head and the South Pole toward their feet. Of course, what they are really doing, if they are standing up, is pointing the South Pole at the center of the earth and, if they are standing at the equator, pointing the North Pole at some spot in the sky, which, as the earth turns, traces a circle intersecting the plane of the ecliptic at 23 1/2 degrees. Now why people persist in this foolishness I don’t know. In my living room I have a small framed photograph showing a thin crescent against a black background. Even though the colors are wrong, people always say, ‘Oh, the moon!’; but it is the earth. The earth isn’t ever supposed to be a crescent, I suppose.
— Astronaut Michael Collins, Carrying the Fire, 1975
On Sept. 21, 1849, naturalist and explorer Philip Henry Gosse wrote in his diary:
E. delivered of a son. Received green swallow from Jamaica.
The son grew up to be poet, author, and critic Edmund Gosse, who wrote:
“This entry has caused amusement, as showing that he was as much interested in the bird as in the boy. But this does not follow; what the wording exemplifies is my Father’s extreme punctilio.
“The green swallow arrived later in the day than the son, and the earlier visitor was therefore recorded first; my Father was scrupulous in every species of arrangement.”
The esoteric programming language DOGO “heralds a new era of computer-literate pets.” Commands include:
SIT — If the value of the current memory cell is 0, jump to STAY.
STAY — If the value of the current memory cell is not 0, jump to SIT.
ROLL-OVER — Select the next operation in the operation list.
HEEL — Execute the currently selected operation.
This program prints the words HELLO WORLD:
roll-over roll-over heel roll-over roll-over roll-over roll-over heel heel heel heel heel heel heel heel heel sit roll-over roll-over roll-over heel roll-over roll-over roll-over heel heel heel heel heel heel heel heel roll-over roll-over heel roll-over roll-over roll-over roll-over roll-over heel roll-over roll-over roll-over roll-over roll-over stay roll-over roll-over roll-over heel roll-over roll-over heel roll-over roll-over roll-over heel roll-over roll-over roll-over roll-over heel heel heel heel heel heel heel sit roll-over roll-over roll-over heel roll-over roll-over roll-over heel heel heel heel roll-over roll-over heel roll-over roll-over roll-over roll-over roll-over heel roll-over roll-over roll-over roll-over roll-over stay roll-over roll-over roll-over heel roll-over roll-over roll-over heel roll-over roll-over roll-over roll-over roll-over heel roll-over heel heel heel heel heel heel heel roll-over roll-over roll-over roll-over roll-over heel heel roll-over heel heel heel roll-over roll-over roll-over roll-over roll-over heel roll-over roll-over roll-over heel heel heel roll-over roll-over roll-over roll-over heel heel heel heel heel heel heel heel sit roll-over roll-over roll-over heel roll-over roll-over roll-over heel heel heel heel roll-over roll-over heel roll-over roll-over roll-over roll-over roll-over heel roll-over roll-over roll-over roll-over roll-over stay roll-over roll-over roll-over heel roll-over roll-over heel roll-over roll-over roll-over heel heel heel roll-over roll-over roll-over roll-over heel heel heel heel heel heel heel heel heel heel sit roll-over roll-over roll-over heel roll-over roll-over roll-over heel heel heel heel heel heel heel heel heel roll-over roll-over heel roll-over roll-over roll-over roll-over roll-over heel roll-over roll-over roll-over roll-over roll-over stay roll-over roll-over roll-over heel roll-over roll-over roll-over roll-over heel heel heel roll-over roll-over roll-over roll-over heel roll-over roll-over roll-over roll-over heel heel heel heel roll-over roll-over heel roll-over heel heel heel roll-over roll-over roll-over roll-over roll-over heel roll-over roll-over heel heel heel heel heel heel roll-over roll-over roll-over roll-over heel roll-over roll-over heel heel heel heel heel heel heel heel roll-over roll-over roll-over roll-over heel roll-over roll-over roll-over heel heel roll-over roll-over roll-over roll-over heel roll-over roll-over roll-over roll-over roll-over heel
Here’s a similar program in Blub, which is designed to be readable by fish:
blub. blub? blub. blub. blub. blub. blub. blub. blub. blub. blub. blub. blub. blub. blub. blub. blub. blub. blub. blub. blub! blub? blub? blub. blub. blub. blub. blub. blub. blub. blub. blub. blub. blub. blub. blub. blub. blub. blub. blub. blub. blub? blub! blub! blub? blub! blub? blub. blub! blub. blub. blub? blub. blub. blub. blub. blub. blub. blub. blub. blub. blub. blub. blub. blub. blub. blub! blub? blub? blub. blub. blub. blub. blub. blub. blub. blub. blub. blub. blub? blub! blub! blub? blub! blub? blub. blub. blub. blub! blub. blub. blub. blub. blub. blub. blub. blub. blub. blub. blub. blub. blub. blub. blub. blub! blub. blub! blub. blub. blub. blub. blub. blub. blub. blub! blub. blub. blub? blub. blub? blub. blub? blub. blub. blub. blub. blub. blub. blub. blub. blub. blub. blub. blub. blub. blub. blub. blub. blub! blub? blub? blub. blub. blub. blub. blub. blub. blub. blub. blub. blub. blub? blub! blub! blub? blub! blub? blub. blub! blub. blub. blub? blub. blub? blub. blub? blub. blub. blub. blub. blub. blub. blub. blub. blub. blub. blub. blub. blub. blub. blub. blub. blub. blub. blub. blub. blub! blub? blub? blub. blub. blub. blub. blub. blub. blub. blub. blub. blub. blub. blub. blub. blub. blub. blub. blub. blub. blub. blub. blub? blub! blub! blub? blub! blub? blub. blub! blub! blub! blub! blub! blub! blub! blub. blub? blub. blub? blub. blub? blub. blub? blub. blub! blub. blub. blub. blub. blub. blub. blub. blub! blub. blub! blub! blub! blub! blub! blub! blub! blub! blub! blub! blub! blub! blub! blub. blub! blub! blub! blub! blub! blub! blub! blub! blub! blub! blub! blub! blub! blub! blub! blub! blub! blub. blub. blub? blub. blub? blub. blub. blub! blub.
See User Friendly.
Venus flytraps can “count.” When an insect contacts one of the triggering hairs between its hinged leaves, the trap prepares to close, but it won’t do so unless a second contact occurs within about 20 seconds. This spares the plant from wasting energy shutting on raindrops and other nonliving stimuli.
The plant will release a cocktail of prey-decomposing acidic enzymes after five stimuli, enough to “convince” it that it’s caught a creature worth consuming.
(Jennifer Böhm et al., “The Venus Flytrap Dionaea muscipula Counts Prey-Induced Action Potentials to Induce Sodium Uptake,” Current Biology 26:3 [Feb. 8, 2016], 286–295.)
Iranian artist Hamid Naderi Yeganeh makes art from math. The image above shows all circles of the form 
When architect Jørn Utzon submitted his plan for the Sydney Opera House, the shapes of the roof vaults were not defined geometrically. Without this information, engineers couldn’t calculate the complex forces and strains involved and make a plan for construction.
The team spent three years and hundreds of thousands of working hours trying to define the shapes as paraboloids and ellipsoids. Finally, in 1961, they realized that all the half-shells could be cut from the surface of a common sphere (below). This would lend a visual harmony to the whole complex and, since a sphere’s curvature is the same in all directions, it would permit the materials to be mass-produced.
“Each half-shell is now a spherical triangle,” explains University of Sydney mathematician Joe Hammer. “One side of the triangle is the ridge that is part of a small circle of the sphere. The other two vertices of the triangle are on the ridge. Each side shell is also a spherical triangle, the boundaries of which are small circles of the common sphere.”
In awarding Utzon the Pritzker Prize in 2003, Frank Gehry said, “Utzon made a building well ahead of its time, far ahead of available technology, and he persevered … to build a building that changed the image of an entire country.”
(Joe Hammer, “Mathematical Tour Through the Sydney Opera House,” Mathematical Intelligencer 26:4 [September 2004], 48-52.)
For his keynote address at the 1998 ACM OOPSLA conference, Sun Microsystems computer scientist Guy Steele illustrated the value of growing a computer language by growing the language of his talk itself, starting with words of one syllable and using these to build new definitions that permit increasing sophistication.
“For this talk, I chose to take as my primitives all the words of one syllable, and no more, from the language I use for most of my speech each day, which is called English. My firm rule for this talk is that if I need to use a word of two or more syllables, I must first define it.”
(Via MetaFilter.)
