Termination of global warmth at the Palaeocene/Eocene boundary through productivity feedback

The onset of the Palaeocene/Eocene thermal maximum (about 55 Myr ago) was marked by global surface temperatures warming by 5-7 degrees C over approximately 30,000 yr (ref. 1), probably because of enhanced mantle outgassing and the pulsed release of approximately 1,500 gigatonnes of methane carbon from decomposing gas-hydrate reservoirs. The aftermath of this rapid, intense and global warming event may be the best example in the geological record of the response of the Earth to high atmospheric carbon dioxide concentrations and high temperatures. This response has been suggested to include an intensified flux of organic carbon from the ocean surface to the deep ocean and its subsequent burial through biogeochemical feedback mechanisms. Here we present firm evidence for this view from two ocean drilling cores, which record the largest accumulation rates of biogenic barium--indicative of export palaeoproductivity--at times of maximum global temperatures and peak excursion values of delta13C. The unusually rapid return of delta13C to values similar to those before the methane release and the apparent coupling of the accumulation rates of biogenic barium to temperature, suggests that the enhanced deposition of organic matter to the deep sea may have efficiently cooled this greenhouse climate by the rapid removal of excess carbon dioxide from the atmosphere.     

Understanding the infinite II: Coalgebra

In this paper we give an account of the rise and development of coalgebraic thinking in mathematics and computer science as an illustration of the way mathematical frameworks may be transformed. Originating in a foundational dispute as to the correct way to characterise sets, logicians and computer scientists came to see maximizing and minimizing extremal axiomatisations as a dual pair, each necessary to represent entities of interest. In particular, many important infinitely large entities can be characterised in terms of such axiomatisations. We consider reasons for the delay in arriving at the coalgebraic framework, despite many unrecognised manifestations occurring years earlier, and discuss an apparent asymmetry in the relationship between algebra and coalgebra.