It’s hard to send a message from Mars.

When the Curiosity rover, currently active on the surface of the red planet, has something to tell NASA back on Earth, it formulates its communication in binary code and beams it our way. Noise inevitably creeps in during the long transmission, so that the message received by NASA is different from the one the rover sent. At that point it’s a game of telephone, as NASA engineers make their best guess about what Curiosity was trying to tell them.

The situation from Mars is an exaggerated version of what happens whenever a message is communicated through any noisy channel — be it from a flash drive to your computer or an air traffic control tower to an airplane. In each case, the receiver has to estimate what the sender meant to say. One way to ensure that the message gets through is to use a geometric way of packaging information called a “spherical code.”

A spherical code is a way of translating a message written in one form, like binary code, into a point on a high-dimensional sphere. (We think of spheres as three-dimensional objects, but in math, a sphere can exist in any number of dimensions.) Imagine, for example, that you’d like to transmit the word “Mars.” To do this, you’d need to find some way of relating each letter to a coordinate on the sphere. While the mathematics behind spherical codes is more complicated than this, you could imagine, for example, that the word “Mars” maps to the point (13, 1, 18, 19) on a sphere in four-dimensional space. Here, the coordinates are like values of latitude and longitude that direct you to a single point on a globe. The first letter in the word is represented by the coordinate value in the first dimension, the second letter is represented by the coordinate value in the second dimension, and so on, with the specific value of the coordinate determined by the letter’s position in the alphabet (so “a” has coordinate value 1 since it’s the first letter in the alphabet).

Of course, the same problem that applied to the original message still applies to the translated one: Curiosity sends one point on the sphere, but NASA receives another.