Definition 0.1   Any automaton which is capable of either executing a set of logical instructions (that is called a program, ) or whose operation is defined either by an algorithm/ set of algorithms or a Recursive Function is called a computer.

Remarks

Occasionally, and incompletely, a computer is simply being defined as “a machine that manipulates data according to a list of instructions.”. First of all, implicit in the latter description is the concept of sequential machine or automaton that has a precise mathematical definition, and is not simply just any `machine'. Secondly, the vague term of “list of instructions” needs actually be replaced by a “set of logical instructions”, which is precisely defined, for example by algorithms or recursive functions as in the top definition of the computer term.

Notably, and contrary to widespread misconceptions in old-age philosophy ( e.g. Descartes, John von Neumann, etc.), AI and the computer community, complex, living systems and the human brain cannot be adequately described or represented by any computer, computer model, or classical automaton; this is, in essence, because the latter cannot be adequately modelled by any recursive function, finitary algorithm or (computer) program. Furthermore, any computer can be encoded with a categorical commutative diagram. On the other hand, most organisms– that possess variable topology and varying transition functions (viz. entry on automata)– may only be encoded by the unique limit of a sequence of non-commutative categorical diagrams which is not necessarily finite, and that cannot be recursively computed.

Bibliography

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A JPG Image of NASA's Columbia Supercomputer Advanced Facility