Being able to determine if something is “truly” random is not just an investigation carried out by forensic accountants, sociologists, and law enforcement. Rather it is an interesting and complicated mathematical problem. Consider the two plots above. You may look at the on the left and see the clumps, the spacing, and think “That can’t be the random plot.” And yet it is. The plot on the left has been randomly generated, while the plot on the left is a scatter plot of glowworm positions on a ceiling.
So here, the clumps actually help indicate randomness. Try thinking of it in another way: imagine you have two students who were asked to flip a coin 100 times for homework. The first student was diligent and flipped accordingly:
Now while it might seem strange that the first student has long runs, it fits closer to what one would expect if the flip is random. On the other hand, in the second student’s data, there is less than a 0.1% chance that they wouldn’t get a single run longer than four in a row!
The images and coin flip data was found at this article. It takes a closer look at some of these topics and provides some pretty neat historical background.
(…) is a work that was published by Archimedes in two volumes c. 225 BC. It most notably details how to find the surface area of a sphere and the volume of the contained ball and the analogous values for a cylinder, and was the first to do so.