  Ill-posed inverse problems of the form y = X p where y is J-dimensional
vector of a data, p is m-dimensional probability vector which cannot be
measured directly and matrix X of observable variables is a known J,m matrix, J
< m, are frequently solved by Shannon's entropy maximization (MaxEnt). Several
axiomatizations were proposed to justify the MaxEnt method (also) in this
context. The main aim of the presented work is two-fold: 1) to view the concept
of complementarity of MaxEnt and Maximum Likelihood (ML) tasks from a geometric
perspective, and consequently 2) to provide an intuitive and non-axiomatic
answer to the 'Why MaxEnt?' question.
