History of probability and information
One of the ancient expressions of information dealing with entropy also deals with information and the number of possible outcomes in an event.
The sound eye, udjat, shows it clearly.
Here, for example, is where we find the history of African ways of combining a system of two to a system of three compartments applied by the artists in the graphic form.
Mathematical language shows these expressions, the destroyed parts of Horus' eye, to result into six compartments that exhibit exponential equations of the form: often expressed in the West with the Greek symbol : . Where c is the base and in this case equals two. This same c in other useful mathematical expressions can be 10 or more often e as an approximated value of natural logarithm. Why logarithm?
The ancient forms of udjat parts are , , , ... Because the base number 2 is raised to powers, -1, -2, -3... that we call exponents, the exponents are the logarithms and they are here with their bases resulting into fractions of unitary numerators equal to respective probabilities for equally likely outcomes of events exemplified by udjat parts.
The hieroglyph P for this particular event was initially represented in the arts by 64 squares in a grid reference where each small square had a unit area. Of all the 64 squares, the debate was centered on one. The information therefore varied inversely with probability as it does in the modern communications theory. Words such as magic and beauty were employed to mean infinity and outcome. The area study was called seked S from which the integral symbol S in calculus would be derived.
Weighted information of each class since the ancient time has always involved multiplying log (1/P) by probability Pi of the class.