Creating Randomness

We may intuitively think that order is good and disorder is bad, but randomness is useful, for example in preparing samples of data to train learning system.    This mathematical article touches on the issue

Mathematicians Calculate How Randomness Creeps In by Marcus Woo in Quanta Mag
The goal of a 15 puzzle is to put numbered tiles in order. Now mathematicians have solved the opposite problem — how to scramble one.

You’ve probably played a 15 puzzle. It’s that frustrating yet addictive game with 15 tiles and a single empty space in a 4-by-4 grid. The goal is to slide the tiles around and put them in numerical order or, in some versions, arrange them to form an image.

The game has become a staple of party-favor bags since it was introduced in the 1870s. It has also caught the attention of mathematicians, who’ve spent more than a century studying solutions to puzzles of different sizes and startling configurations.

Now, a new proof solves the 15 puzzle, but in reverse. The mathematicians Yang Chu and Robert Hough of Stony Brook University have identified the number of moves required to turn an ordered board into a random one.  ... "