PlanetPhysics/Computer 2

Any [[../AAT/|automaton]] $𝒞$ which is capable of either executing a set of logical instructions $𝕀$ (that is called a program , $\mathbb{P}$) or whose [[../Cod/|operation]] is defined either by an [[../RecursiveFunction/|algorithm/]] set of algorithms Failed to parse (unknown function "\A"): {\displaystyle \A} or a [[../RecursiveFunction/|recursive function]] ${ℱ}_R$ 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 [[../PreciseIdea/|concept]] of [[../AAT/|sequential machine]] or [[../CategoryOfAutomata/|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 {\mathbf 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 [[../SimilarityAndAnalogousSystemsDynamicAdjointnessAndTopologicalEquivalence/|systems]] and the human brain cannot be adequately described or represented by any computer, computer model, or [[../StableAutomaton/|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 [[../Commutativity/|commutative diagram]]. On the other hand, most organisms-- that possess [[../VariableNetwork/|variable topology]] and varying [[../StableAutomaton/|transition functions]] ${\delta }_v$ (viz. entry on automata)-- may only be encoded by the unique limit of a sequence of [[../AbelianCategory3/|non-commutative]] [[../CategoricalDiagramsDefinedByFunctors/|categorical diagrams]] which is not necessarily finite, and that cannot be recursively computed.