Some Lesson About the Law From Self-Referential Problems in Mathematics

We first describe briefly mathematician Kurt Gödel\u27s brilliant Incompleteness Theorem of 1931, and explore some of its general implications. We then attempt to draw a parallel between axiomatic systems of number theory (or of logic in general) and systems of law, and defend the analogy against anticipated objections. Finally, we reach two types of conclusions. First, failure to distinguish between language and metalanguage in mathematical self-referential problems leads to fallacies that are highly analogous to certain legal fallacies. Second, and perhaps more significantly, Gödel\u27s theorem strongly suggests that it is impossible to create a legal system that is complete in the sense that there is a derivable rule for every fact situation. It follows that criticisms of constitutional systems for failure to determine every answer are unfair: they demand more than any legal system can give. At best they are antilegal in the sense that rejection of such constitutional systems on such a ground would require the rejection of all constitutional systems

The impact of spatial wind variations on freshwater transport by the Alaska Coastal Current

The Alaska Coastal Current (ACC) is located in a region with prevailing downwelling-favorable winds, flows over a long stretch of coastline (over 2000 km), and is driven by multiple sources of freshwater discharge totaling 24000 m3 s–1 along its length. Using the Regional Ocean Modeling System (ROMS) we attempt to determine how spatially variable winds affect the downstream transport of freshwater along a long coastline with nearly continuous sources of freshwater. The model domain represents a fraction of the ACC region and periodic boundary conditions are applied to allow propagation of the buoyant flow from upstream. The model is forced by multiple freshwater sources in the central part of the domain and by both constant and spatially-varying, predominantly downwelling-favorable, winds. Freshwater flux gain in the coastal current (as opposed to spreading offshore) is calculated by taking a 30-day averaged difference between freshwater fluxes at the downstream and upstream edges of the buoyancy forcing region. Model runs are split into two categories: relatively high gains (50 – 60% of total discharge) were observed under moderate wind stress (∼0.05 Pa) or no wind conditions while lower gains (35– 45%) were observed under light average wind stresses (∼0.025 Pa), especially when wind varied alongshore. The offshore freshwater transport is eddy-driven and is enhanced in the areas of converging wind forcing. Eddy generation is associated with the wind-induced deepening of the buoyant layer near the coast. When the surface boundary layer is thin under light wind conditions, this deepening translates into enhanced vertical shear of the alongshore current through the thermal wind balance. Reversal of alongshore wind to upwelling-favorable wind effectively blocks the downstream freshwater transport and spreads the buoyant layer offshore