How about http://en.wikipedia.org/wiki/Kolmogorov_complexity http://en.wikipedia.org/wiki/Kolmogorov_complexity ? The big problem with Shannon entropy is that

How about http://en.wikipedia.org/wiki/Kolmogorov_complexity http://en.wikipedia.org/wiki/Kolmogorov_complexity ? The big problem with Shannon entropy is that it's measured with respect to a probability space, so it's not an "absolute" measure of information. Kolmogorov complexity "solves" this problem by defining information content of a string as the length of the shortest program that generates the string. (You still have to pick a reference UTM, but this only affects the program lengths at worst by a constant.) [Disclaimer: Hobbyist, not expert.]