The Unilluminable Room of George Tokarsky

Illustration for article titled The Unilluminable Room of George Tokarsky

In the house that math built, there are many rooms. The Unilluminable Room is one of the strangest. How do you build a room that is guaranteed to have one spot of complete darkness? Here's the weird solution to this 26 year mystery.


Imagine a room where all the walls are covered in floor-to-ceiling mirrors. If someone were to light a match in this room, no matter how big or how complicated it was - with little side passages and oddly shaped foyers - you would always see it. The light would bounce off mirrors until it hit every spot in the room. Likewise, if someone were to launch an inexhaustible rubber ball at one of the walls, eventually it would bounce around until it hit you. But what if there were a room in which this wasn't possible? What would it take to create a room that had at least one spot of darkness when a candle was placed in it?

This question was posed in the sixties, and it was puzzled over for decades. As long as all the walls of the room were straight, it seemed impossible to find a mirrored room that a light couldn't illuminate fully.


Finally, George Tokarsky, a mathematician, came up with a room in 1995. Its overall description would be an 'L' shape, but there are many little triangular nooks in the room that angle light away from one critical. It has twenty-six sides, all straight, and there are two points (shown here in red) that are mutually exclusive. A light placed in one will not be seen in the other. A ball thrown from one spot will never hit the other. At the time, this could happen in no other room.

There have, since 1995, been found other rooms where light can't reach. There is a 24-sided room with straight walls that has an unilluminable point, and there are rooms with curved sides that can never fully be illuminated. But Tokarsky was the first to get it done. So to him we respectfully say, "Let there be dark!"

Via Wolfram Math World and Plus Maths.

Photograph by Stephen Clarke via Shutterstock


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My whole life is an unilluminable room. One. Big. Unilluminable. Room.