Image: Lucy Reading-Ikkanda/Quanta Magazine.

Spherical Encoding of Information Between Earth and Mars

Quanta Magazine reported on the use of a sphere to be able to communicate with Mars. It is difficult to send messages to and from Mars.

There is the rover on Mars called Curiosity, or the Curiosity rover. When it finds something of interest to astro people, it sends a message to NASA. There’s a catch. The binary message beamed to Earth has to do just that.

“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.”

It has to travel to Earth. The trip from Mars to Earth, or vice versa, is not easy. It is far. It can scramble the transmission. So the communication clarity can take time and the message can be worse by the time it gets from the source – on Earth – to the receiver – on Mars.

Once it comes to Earth, “…it’s a game of telephone, as NASA engineers make their best guess about what Curiosity was trying to tell them. In each case, the receiver has to estimate what the sender meant to say.”

The question arises about the feasibility of other means of communication. The Quanta Magazine article author posits a solution: “spherical code.”

Information, rather than in binary, is encoded in a high-dimensional sphere. Spheres are not by necessity 3-dimensional. They have volume and 3-dimensionality in regular conceptualisations. Everyone went through school using area and its inherent 2-dimensionality to learn about spheres and their properties.

Spheres can exist, as with many higher-dimensional mathematical objects, in a large number of possible valuations while keeping basic formulations or axioms of their existence consistent. So spheres “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.”

Each letter, of course, corresponding to the linear countable numbers of those letters – a as 1, b as 2, o as 15, t as 20, and so on. Akin to 3-dimensionality with left-right, up-down, forward-backward, each has coordinates on the x, y, and z axes to provide indications as to the information about various points in the volume or on the surface of the sphere.

“The key, however, is to use only a limited number of points for encoding messages. As long as those points are spaced far enough apart, it’s unlikely that one point will end up being mistaken for another.”

So the received point will be more akin to the intended point which corresponds to the correct message. Communication becomes easier. Spherical higher-numeric dimensional encoding provides a means for improve communication methodologies between Earth and Mars, and vice versa.

About Scott Jacobsen

Scott is the founder of In-Sight: Independent Interview-Based Journal and In-Sight Publishing

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