Shannon information

Shannon information is the amount of information as measured by how improbable the data is. Improbability is related to an explicit or hidden order in the data. Without an implicit order, there is no information to the data: it's called noise. But in most cases, the universe is highly ordered -- even if you don't know what that order is. It might be related to butterflies flapping their wings in Ontario years ago, but yet it is ordered.

This is a tricky concept, because if everything can be found in the digits of pi, then there is no information in the digits of pi.

But if you find a doll in the sea of infinity, because of the amount of order necessary to create that thing, you can't say it's improbable without knowing the scope of infinity, which let us say is.... infinite.

But if you find two such dolls in the sea of infinity, have you not found something much more improbable? For if the space was infinite, then is not the probability of finding something again nearly zero? So one can say with some certainty that the probability of the universe and it`s consistency is nearly zero.

I = - p_test log₂ p_test