It’s been 19 years since Pixar released Monsters, Inc. with all that CGI hair. Where are my hairy icons? Ones that get all long and knotted as the notifications number goes up.
Why can’t I feel my phone? I found that paper from 2010 (when I was complaining about keyboards) about using precision electrostatics to make artificial textures on touchscreens.
I should be able to run my thumb over my phone while it’s in my pocket and feel bumps for apps that want my attention. Touching an active element should feel rough. A scrollbar should *slip. Imagine the accessibility gains. But honestly I don’t even care if it’s useful: 1.5 billion smartphone screens are manufactured every year. For that number, I expect bells. I expect whistles.
Wang tiles (Hao Wang, 1961) are a class of formal systems. They are modelled visually by square tiles with a color on each side. A set of such tiles is selected, and copies of the tiles are arranged side by side with matching colors, without rotating or reflecting them.
The basic question about a set of Wang tiles is whether it can tile the plane or not, i.e., whether an entire infinite plane can be filled this way. The next question is whether this can be done in a periodic pattern.
In 1966, Wang's student Robert Berger solved the problem in the negative. He proved that no algorithm for the problem can exist, by showing how to translate any Turing machine into a set of Wang tiles that tiles the plane if and only if the Turing machine does not halt. The undecidability of the halting problem then implies the undecidability of Wang's tiling problem.