Thursday, March 22, 2012

We're Just Getting Started: A Glimpse at the History of Uncertainty

We've had our cerebral cortex for several tens of thousands of years. We've lived in more or less sedentary settlements and produced excess food for 7 or 8 thousand years. We've written down our thoughts for roughly 5 thousand years. And Science? The ancient Greeks had some, but science and its systematic application are overwhelmingly a European invention of the past 500 years. We can be proud of our accomplishments (quantum theory, polio vaccine, powered machines), and we should worry about our destructive capabilities (atomic, biological and chemical weapons). But it is quite plausible, as Koestler suggests, that we've only just begun to discover our cerebral capabilities. It is more than just plausible that the mysteries of the universe are still largely hidden from us. As evidence, consider the fact that the main theories of physics - general relativity, quantum mechanics, statistical mechanics, thermodynamics - are still not unified. And it goes without say that the consilient unity of science is still far from us.

What holds for science in general, holds also for the study of uncertainty. The ancient Greeks invented the axiomatic method and used it in the study of mathematics. Some medieval thinkers explored the mathematics of uncertainty, but it wasn't until around 1600 that serious thought was directed to the systematic study of uncertainty, and statistics as a separate and mature discipline emerged only in the 19th century. The 20th century saw a florescence of uncertainty models. Lukaczewicz discovered 3-valued logic in 1917, and in 1965 Zadeh introduced his work on fuzzy logic. In between, Wald formulated a modern version of min-max in 1945. A plethora of other theories, including P-boxes, lower previsions, Dempster-Shafer theory, generalized information theory and info-gap theory all suggest that the study of uncertainty will continue to grow and diversify.

In short, we have learned many facts and begun to understand our world and its uncertainties, but the disputes and open questions are still rampant and the yet-unformulated questions are endless. This means that innovations, discoveries, inventions, surprises, errors, and misunderstandings are to be expected in the study or management of uncertainty. We are just getting started.