  The Turing Machine has two implicit properties that depend on its underlying
notion of computing: the format is fully determinate and computations are
information preserving. Distributed representations lack these properties and
cannot be fully captured by Turing's standard model. To address this limitation
a distributed extension of the Turing Machine is introduced in this paper. In
the extended machine, functions and abstractions are expressed extensionally
and computations are entropic. The machine is applied to the definition of an
associative memory, with its corresponding memory register, recognition and
retrieval operations. The memory is tested with an experiment for storing and
recognizing hand written digits with satisfactory results. The experiment can
be seen as a proof of concept that information can be stored and processed
effectively in a highly distributed fashion using a symbolic but not fully
determinate format. The new machine augments the symbolic mode of computing
with consequences on the way Church Thesis is understood. The paper is
concluded with a discussion of some implications of the extended machine for
Artificial Intelligence and Cognition.
