# A Sense of Space

My first encounter with Virtual Reality was in the 1980s, when text adventures became popular on the new affordable desktop computers.
We spent countless hours trying to figure out what to do with the pocket fluff in the text adventure version of Douglas Adams’ The Hitchhiker’s Guide to the Galaxy, made by Infocom.

Many of these games shamelessly exploited the limitations of their virtual realities: Because all interactions are verbal, there is always the possibility that what reads like a visual description of a place can in no way represent a real place. This gives plenty of opportunity for devious puzzles and mazes. A few years ago, I came up with my own little nightmarish maze, called the Un-Maze. You can play it here in a web browser. It is very bare bones, but it will tell you when you have found the exit.

The rest of this post will explain this puzzle, so don’t read on yet of you like a challenge. Let’s make it simple, let’s imagine a maze where every room has only two exits, called left and right. We might think of this maze as an infinite sequence of rooms. If it happens so that all the rooms look alike, and we have no means of altering the appearance of a room, we could also be just in a single room whose right exit leads through a twisting passage to the right exit.

My Un-Maze up above lets you decorate the rooms a little bit, because you can pick up and drop three different pebbles, and when you type “look”, the game will tell you whether there is a pebble in your current room. A basic unjustified assumption we make about such mazes is that when we exit a room to the right, we should be able to get back to that room by exiting the next room to the left. Many mazes in text adventures warn you about this, by telling you that you are entering a long winding passage.

The simple idea behind the Un-Maze is that your location in space is solely determined by your previous actions. For instance, if you decided to walk left-right-right, then you are in the room left-right-right.

This is yet another model of a strange universe where in every room we can only move left or right. This infinite tree assumes that we have unlimited memory. What happens if we can only remember our previous three actions? Our universe would look like this:

We change the name of a room by forgetting its first letter and appending the first letter of the action we took to get there (Left or Right) to its end.

If, for instance, you knew that the exit to the maze was at room LLL, you could reach the exit from any room my going three times left. This is still a maze were all rooms look exactly the same. To change this, we can remove some exits. In the following maze, we have removed the possibility to turn right from some rooms, and now it takes five turns to get from LLL to RRR:

The text adventure maze features four directions and the rooms are given by the memory of the last two turns. You found the exit if you manage to first go east and then north. Good luck.