An algorithmic activity is a procedure for carrying out a task. The real and abstract worlds are constantly setting forth tasks to be done; their variety appears endless. Similarly, the procedures for carrying them out appear to be in very large supply; in fact, these procedures appear to encompass all human activity, discouraging systematic study. Fortunately, we may focus our attention on a subset of these tasks, namely, transformations of sequences of symbols.…Many believe that this subset of tasks is really a “basis”; i.e., in terms of these transformations on symbols, all real and abstract tasks can be specified. The word “believe” is appropriate, since no mathematical proof of such an assertion has been given. We may take this statement as being akin to a theory for which evidence continues to accumulate.