Intuitively, an algorithm that is computing the value of a function for a given input, is extracting an information from the input and is processing this information. During this work the information being processed 'converges to the result'. We show by examples that one can measure this information convergence. No general theory is presented, though some questions that arise on the way towards such a theory are discussed. We start with an approach based on approximations of the graph of the computed function; we call this approach semantical. It works only for algorithms that mainly calculate but do not analyze the information being processed. We extend this approach by using syntactical considerations. The principle underlying the estimations of information convergence, is that of 'maximal uncertainty' that we impose on the algorithm under analysis. The problem of information convergence brings up conceptual questions " What is information? " , " What is uncertainty? " related to similar questions more and more intensively studied in philosophy.