Predictability, and its Discontents
We find ourselves, happily, on the cusp of scientific revolution. Recent years have seen a rapidly growing recognition, across many scientific fields, of the ubiquitous presence in application domains of deep uncertainty and complexity. We often hear the problem couched in terms of a metaphoric hedge of uncertainty and complexity phenonema that has sprung up and flowered over our familiar methods, as if complexity and uncertainty were something new, at least in measure if not in essence, and as if our growing awareness were primarily an empirical matter. Yet arguably what is new is not the presence of complexity and uncertainty phenomena in the worlds of our studies, nor the availability of the empirical evidence, but rather the expanding transdisplinary scientific basis in theory by which we look for the evidence in the first place and then comprehend its meaning.
Uncertainty manifests in defence and military circles overwhelmingly in problem contexts dominated by the potential for catastrophic failure, particularly cascading systemic failure; indeed, it is difficult to imagine a defence problem domain where unpredictability and failure are not predominant – the predominant – features. Yet traditional analysis approaches often struggle to handle multiple kinds of failure and often fail to treat deep uncertainty at all. The convenience of degenerate symmetry conditions that do not hold in messy application domains is simply unsustainable. Moreover, uncertainty also creates opportunity just as readily as it does the possibility of failure; there is more to handling failure and opportunity under uncertainty than maximising expected future utility. While defence and military matters are hardly unique in this regard, the extreme nature of the problem environments here perhaps brings manifestations of deep uncertainty through failure potential and opportunity into starkest relief.
The need for expansion of both the fundamental theory about the nature of uncertainty and how we might effectively deal with it and the application of theory to practical matters across the sciences suggests mathematics may find itself again poised in a uniquely central position. In a time when the almost ubiquitous emphasis in research resource allocation remains on demonstrating immediate application, the need and opportunity for the development of coherent new mathematical theories to support and enable the applied sciences has ironically perhaps never been greater. We find ourselves, happily, on the cusp of a mathematically enabled revolution.
Dr Darryn Reid
Principal Scientist, Joint and Operations Analysis Division, Defence Science and Technology Group
Dr Darryn J Reid is Principal Scientist in the Defence Science and Technology Group, and has been with DSTG since 1995. He has worked in distributed systems, machine learning and artificial intelligence, semantics and interoperability, formal reasoning and logics, operations research, optimisation and control, electronic warfare, intelligence analysis, missile targeting and control, command support systems, complexity, nonlinear dynamics and ergodic theory, web-based technologies, software development, functional languages, formal languages and model theory, theory of computation and algorithmic information theory, crowd modelling, economic theory and military theory. He holds the degrees of Bachelor of Science in Mathematics and Computer Science, Bachelor of Science with First Class Honours in Mathematics and Computer Science, and Doctor of Philosophy in Theoretical Computer Science from the University of Queensland. He has strong research interests in pure and applied mathematics, theoretical and applied computer science, philosophy, military theory and economics. He is also an artist. In other words, he knows just enough to understand how ignorant he is. He is currently trying to age as disgracefully as possible, with the support of his beautiful wife Julie and their son Tyler.