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This article presents an overview ofthe idea that information compression bymultiple alignment, unification and search(ICMAUS) may serve as a unifying principle incomputing (including mathematics and logic) andin such aspects of human cognition as theanalysis and production of natural language,fuzzy pattern recognition and best-matchinformation retrieval, concept hierarchies withinheritance of attributes, probabilisticreasoning, and unsupervised inductive learning.The ICMAUS concepts are described together withan outline of the SP61 software model in whichthe ICMAUS concepts are currently realised. Arange of examples is presented, illustratedwith output from the SP61 model.