The surprisingly simple tile is the first single, connected tile that can fill the entire plane in a pattern that never repeats — and can’t be made to fill it in a repeating way. On March 20, Smith and Kaplan, together with two more researchers, announced that the hat tile was something mathematicians have been seeking for more than five decades: a single tile whose copies can fill the entire plane, but only in patterns that don’t consist of a repeating block of tiles. Mathematicians call such a tile, or set of tiles, “aperiodic,” in contrast to shapes like squares or hexagons that can cover the plane in a repeating (or periodic) fashion.
I love stories like this. A plucky amateur makes a breakthrough everyone missed. It was all over the news lately and Jimmy Kimmel even tried to make a joke about it. It didn’t get much of a laugh since it was too obscure for the audience. Another more simple explanation of it.
Socolar, as a physicist, has begun exploring the tilings’ material properties. The diffraction pattern that emerges if you shine a light through one of these tilings, he has found, has the same kind of sharp peaks researchers have observed in quasicrystals.
While math may seem esoteric if often has real world uses. Many a discovery has solved a physics related problem. I suspected this one may too.
But this is far from the first time a hobbyist has made a serious breakthrough in tiling geometry. Robert Ammann, who worked as a mail sorter, discovered one set of Penrose’s tiles independently in the 1970s. Marjorie Rice, a California housewife, found a new family of pentagonal tilings in 1975. And then there was Joan Taylor’s discovery of the Socolar-Taylor tile. Perhaps hobbyists, unlike mathematicians, are “not burdened with knowing how hard this is,” Senechal said.
Also, who knew there was a community of amateurs working on tiles. I shouldn’t be surprised because shapes and geometry are buried deep in the mind. Many become obsessed with them.
I have been reading this lately.
Graham Bruce Hancock (born 2 August 1950) is a British writer who promotes pseudoscientific[2][3] theories involving many ancient civilizations and lost lands.[4] Hancock speculates that an advanced ice age civilization was destroyed in a cataclysm, but that its survivors passed on their knowledge to hunter-gatherers, giving rise to the earliest known civilizations of ancient Egypt, Mesopotamia, and Mesoamerica.[5][6]
It is by this Graham Hancock guy who has a reputation as a con man. He has made a career out of spinning bullshit about the above and he has been quite successful at it. The problem is he uses the literature and twists to make it plausible to the public. There is so little known about prehistory that a talented bullshitter can come up with lots of crap. Ancient Aliens, etc.
In it he talks about all the squares and circles carved on the surface of ancient settlements in the Amazon and worldwide. He ties that to Ayahuasca drug ceremonies where those geometric shapes and other figures show up prominently. I don’t know a lot about that but it is intriguing that our brains may be tuned to geometry in a very deep way.