Computations in living organisms modeled by marked graphs.

Abstract

The accurate copying of nucleotides in DNA replication is arguably a digital computation. So are some cognitive capacities found in all organisms. In 2005 we proved that linking quantum calculations to evidence requires guesswork subject to revision (Madjid and Myers 2005). Based on this proof, we assume computations by living organisms undergo incessant unpredictable changes in their structure. This raises a question: how can changes in computations be made while preserving the integrity of the organism? We offer an answer expressed in the mathematics of marked graphs. Computations as networks of logical operations can be represented by marked graphs with live and safe markings. We represent a sequence of changes by a sequence of marked graphs. Then "Preserving the integrity of the organism" is expressed by preserving liveness and safety throughout the sequence of marked graphs. For example, we show how a single slime-mold amoeba inserts itself into a slime-mold filament without interrupting computation spread along the filament. Because interpretations of mathematics are mathematically undetermined, a quite different interpretation of the same sequence of marked graphs is possible. An alternative interpretation of the sequence of marked graphs is to see them as a cartoon of the insertion of a fragment of thought into a chain of human thoughts.