A quote from Ludwig Wittgenstein is relevant to the present panel: "To convince someone of the truth, it is not enough to state it, but rather one must find the
path from error to truth." In our present context, this path goes through a model, and can therefore be resolved according to the mathematical structure relevant to that model.
The errors that we can describe can be managed through investment of resources. A good path towards convincing predictions is to profile such an investment and quantify its impact on the credibility of decisions and perhaps even on their consequences. Such profiling requires us to resolve, in a commensurate fashion, the impact of various portions of that investment on the error and their respective contribution to credibility. For that, we must first recognize the known contributors to the error which are typically pursued through investments in, 1) experimental resources to learn system-level constraints, 2) experimental resources to learn fundamental behavior , 3) first principles, upscaling, and governing equations, 4) computational resources and 5) insurance against failure. Typically, each of these errors is pursues within its own calculus in a manner that is not conducive for an integrated assessment. What is needed is a unified mathematical treatment that allows the error management task to be treated as a well-posed optimization problem over suitable objectives, constraints, and controls.
The errors that we cannot describe can be gleaned from failures. Indeed one key value of prediction is to extract knowledge from failure. This task, however, requires well-adapted mathematical representations for characterizing independence.
While sensitivity analysis has been pursued to tackle these errors independently, it is not well-adapted to complexities presented by interacting systems or by sensitivities of the extreme events to evolving knowledge. The mathematical framework required for a unified characterization and management of all these uncertainties in a constructive fashion must be broad enough to encompass experimental physics, partial differential equations, computational science, data analytics, probability and statistics, and risk assessment.
