Let’s start with something trivial: sorting numbers. Regardless of the algorithm you’ll use, real numbers are *naturally* ordered. Mathematically speaking, they have a total order, in the sense that you can always decide if a number is greater than another one. There is no ambiguity in this, meaning you can actually sort them, and (excluding duplicates) this sort is unique. There are other fields which are not that lucky: colour, for instance, are very unlucky. Supposing you’re representing colours with their RGB values, there is no standard way to order triples in a line, since they are naturally not organised in a line fashion. The problem is even more complicated since colours have a meaning in the real world. How can we sort colours so that they look as continuous as possible? Which parameters affects the sorting order? Is azure closer to blue (similar hue) or to cyan (similar luminosity)? I can stop you all here and say that there is no solution to this problem. You can sort colours, but the overall result depends on what you are trying to achieve. This post will explore how colours can be sorted, and how this can lead to very different results.

# hilbert

There is one post tagged **hilbert**.