To translate one language into another, find the linear transformation that maps one to the other. Simple, say a team of Google engineers.
The new trick is to represent an entire language using the relationship between its words. The set of all the relationships, the so-called “language space”, can be thought of as a set of vectors that each point from one word to another. And in recent years, linguists have discovered that it is possible to handle these vectors mathematically. For example, the operation ‘king’ – ‘man’ + ‘woman’ results in a vector that is similar to ‘queen’.