Algorithmic randomness

Imagine you have a jar filled with red and blue candies, but you don't know how many of each color there are. You want to guess the proportion of red to blue candies, but you don't have any way of opening the jar or looking inside. The only thing you can do is shake the jar and listen to the sound of the candies moving around.

Algorithmic randomness is like trying to guess the proportion of red to blue candies based on the sound they make when you shake the jar.

Now imagine you have a computer program that generates random numbers. You know that these numbers are not truly random, but rather they are generated by an algorithm or formula. However, the output of the algorithm can still seem random to a human observer.

Algorithmic randomness is the study of how random these computer-generated numbers really are. Mathematicians and computer scientists use certain tests to determine whether a sequence of numbers is truly random or merely the output of a repeating pattern.

In summary, algorithmic randomness is the study of how random computer-generated numbers really are, and how to tell if they are truly random or just the output of a repeating pattern.