Talk:PlanetPhysics/Computer 2

Original TeX Content from PlanetPhysics Archive

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\begin{document}

 \begin{definition}
Any \htmladdnormallink{automaton}{http://planetphysics.us/encyclopedia/AAT.html} $\mathcal{C}$ which is capable of either executing a set of logical instructions $\mathbb{I}$ (that is called a {\em program}, $\mathbb{P}$) or whose \htmladdnormallink{operation}{http://planetphysics.us/encyclopedia/Cod.html} is defined either by an \htmladdnormallink{algorithm/}{http://planetphysics.us/encyclopedia/RecursiveFunction.html} set of algorithms $\A$ or a \htmladdnormallink{recursive function}{http://planetphysics.us/encyclopedia/RecursiveFunction.html} $\mathcal{F}_R$ is called a \emph{computer}.
\end{definition}

\subsection{Remarks}

Occasionally, and incompletely, a \htmladdnormallink{computer}{http://upload.wikimedia.org/wikipedia/commons/1/1f/Columbia_Supercomputer_-_NASA_Advanced_Supercomputing_Facility.jpg} is simply being defined as
``{\em a machine that manipulates data according to a list of instructions.}''. First of all, implicit in the latter description is the \htmladdnormallink{concept}{http://planetphysics.us/encyclopedia/PreciseIdea.html} of \emph{\htmladdnormallink{sequential machine}{http://planetphysics.us/encyclopedia/AAT.html}} or \htmladdnormallink{automaton}{http://planetphysics.us/encyclopedia/CategoryOfAutomata.html} 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 {\bf 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 \htmladdnormallink{systems}{http://planetphysics.us/encyclopedia/SimilarityAndAnalogousSystemsDynamicAdjointnessAndTopologicalEquivalence.html} and the human brain cannot be adequately described or represented by any computer, computer model, or \htmladdnormallink{classical automaton}{http://planetphysics.us/encyclopedia/StableAutomaton.html}; 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 \htmladdnormallink{commutative diagram}{http://planetphysics.us/encyclopedia/Commutativity.html}. On the other hand, most organisms-- that possess \htmladdnormallink{variable topology}{http://planetphysics.us/encyclopedia/VariableNetwork.html} and varying \htmladdnormallink{transition functions}{http://planetphysics.us/encyclopedia/StableAutomaton.html} $\delta_v$ (viz. entry on automata)-- may only be encoded by the unique limit of a sequence of \htmladdnormallink{non-commutative}{http://planetphysics.us/encyclopedia/AbelianCategory3.html} \htmladdnormallink{categorical diagrams}{http://planetphysics.us/encyclopedia/CategoricalDiagramsDefinedByFunctors.html} which is not necessarily finite, and that cannot be {\em recursively} computed.

\begin{thebibliography}{9}
\bibitem{NASAspc}
A \htmladdnormallink{JPG Image of NASA's Columbia Supercomputer Advanced Facility}{http://upload.wikimedia.org/wikipedia/commons/1/1f/Columbia_Supercomputer_-_NASA_Advanced_Supercomputing_Facility.jpg}

\end{thebibliography} 

\end{document}