Digital infinity

Digital infinity is a technical term in theoretical linguistics. Alternative formulations are "discrete infinity" and "the infinite use of finite means". The idea is that all human languages follow a simple logical principle, according to which a limited set of digits—irreducible atomic sound elements—are combined to produce an infinite range of potentially meaningful expressions. Noam Chomsky cites Galileo as perhaps the first to recognise the significance of digital infinity. This principle, notes Chomsky, is "the core property of human language, and one of its most distinctive properties: the use of finite means to express an unlimited array of thoughts". In his Dialogo, Galileo describes with wonder the discovery of a means to communicate one's "most secret thoughts to any other person ... with no greater difficulty than the various collocations of twenty-four little characters upon a paper." "This is the greatest of all human inventions," Galileo continues, noting it to be "comparable to the creations of a Michelangelo". 'Digital infinity' corresponds to Noam Chomsky's 'universal grammar' mechanism, conceived as a computational module inserted somehow into Homo sapiens otherwise 'messy' (non-digital) brain. This conception of human cognition—central to the so-called 'cognitive revolution' of the 1950s and 1960s—is generally attributed to Alan Turing, who was the first scientist to argue that a man-made machine might truly be said to 'think'. But his often forgotten conclusion however was in line with previous observations that a "thinking" machine would be absurd, since we have no formal idea what "thinking" is — and indeed we still don't. Chomsky frequently pointed this out. Chomsky agreed that while a mind can be said to "compute"—as we have some idea of what computing is and some good evidence the brain is doing it on at least some level—we cannot however claim that a computer or any other machine is "thinking" because we have no coherent definition of what thinking is.