  In this paper we will analyze discrete probability distributions in which
probabilities of particular outcomes of some experiment (microstates) can be
represented by the ratio of natural numbers (in other words, probabilities are
represented by digital numbers of finite representation length). We will
introduce several results that are based on recently proposed JoyStick
Probability Selector, which represents a geometrical interpretation of the
probability based on the Born rule. The terms of generic space and generic
dimension of the discrete distribution, as well as, effective dimension are
going to be introduced. It will be shown how this simple geometric
representation can lead to an optimal code length coding of the sequence of
signals. Then, we will give a new, geometrical, interpretation of the Shannon
entropy of the discrete distribution. We will suggest that the Shannon entropy
represents the logarithm of the effective dimension of the distribution.
Proposed geometrical interpretation of the Shannon entropy can be used to prove
some information inequalities in an elementary way.
