Linearly Inseparable and Higher Dimensions

Interpretation of the Idea

A lot of diagrams show higher dimensions starting from 3D and picturing that lower space could be transferred to higher space in such way that it could be sliced with a flat plane. Beyond 3D it is difficult to imagine planes and hyperplanes as flat surfaces which can divide the space they are in in to two. In the diagram below you can imagine the space just as collection of different directions. In 2D there is x and y, up down, left right, in 3D there is one more direction, but lets not focus on the directions we imagine, but even then, we live in 4D where fourth dimension is time. Just another direction/ dimension to describe space. So to transfer variables to higher dimension could simply mean introducing some new direction, new formula which makes it easier to manage firstly seemingly inseparable classes. In higher/ different dimensions the distances could be different and therefore allow easier separation.

Figure 2. Higher dimension separation (Source: Ubaby, 2016)