The Turing Machine is the paradigmatic case of computing machines, but there are others, such as Artificial Neural Networks, Table Computing, Relational-Indeterminate computing and diverse forms of analogical computing, each of which based on a particular underlying intuition of the phenomenon of computing. This variety can be captured in terms of system levels, re-interpreting and generalizing Newell's hierarchy, which includes the knowledge level at the top and the symbol level immediately below it. In this re-interpretation the knowledge level consists of human knowledge and the symbol level is generalized into a new level that here is called The Mode of Computing. Each computing paradigm uses a particular mode, and a central question for Cognition is what is the mode of natural computing. The mode of computing provides a novel perspective on the phenomena of computing, the representational and non-representational views of cognition, and consciousness.