Kolmogorov complexity gives a high value to strings of symbols that are essentially random. But isn't randomness essentially meaningless? Should a measure of information assign a low value to it? The concept of sophistication addresses this question.
There are many ways of saying the same thing — you can use many words, or few. Perhaps information should be measured in terms of the shortest way of expressing it? In the 1960s this idea led to a measure of information called Kolmogorov complexity.
On the face of it the Universe is a fairly complex place. But could mathematics ultimately lead to a simple description of it? In fact, should simplicity be a defining feature of a "theory of everything"? We ponder the answers.