ABSTRACT
In the twentieth century, science had to face up in earnest to the problematic relationship between the local and the global.
In mathematics this surfaced in various guises. At the turn of the century there was the foundational crisis coming out of unregulated self-reference — most famously via Russell’s Paradox in the newly developing set theory. By the 1930s Hilbert’s formalism set the stage for self-reference on a more secure but limited basis — using Go¨del numberings and variants of that technique — with no less startling results. In the physical sciences quantum theory threw up the Einstein-Rosen-Podolsky thought experiment, radically challenging people’s preconceptions about causal locality. While by the second half of the century, chaos theory was telling us how the most everyday phenomena — even a dripping tap — could present us with practical incomputability, framed by strangely emergent patterns of events.
