Non-Laplacian Uncertainty and Why Your Simulations Need to Tend to It Today

We are at a crossroads in our scientific appreciation of uncertainty.  The traditional view is that there is only one kind of uncertainty and that probability theory is its calculus.  This view has created several paradoxes that have befuddled decision theory about why humans prefer particular options when selecting among possible choices.  The traditional view also leads to quantitative results that are often misconstrued and demonstrably misleading.  An emerging alternative view, however, entails a richer mathematical concept of uncertainty and a broader framework for uncertainty analysis.  The concept admits a kind of uncertainty that is not handled by traditional Laplacian probability measures.  The modern approach makes practical solutions easier for several engineering and other physics-based models, and the inferences drawn from such models under this view are more reliable, and resolve several long-standing paradoxes.  We review the mathematical, decision-theoretic and even neurological reasons that suggest it is often useful to distinguish kinds of uncertainty, including what can be called non-Laplacian uncertainty.