There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

The planetary boundaries framework defines a safe operating space for humanity based on the intrinsic biophysical processes that regulate the stability of the Earth system. Here, we revise and update the planetary boundary framework, with a focus on the underpinning biophysical science, based on targeted input from expert research communities and on more general scientific advances over the past 5 years. Several of the boundaries now have a two-tier approach, reflecting the importance of cross-scale interactions and the regional-level heterogeneity of the processes that underpin the boundaries. Two core boundaries—climate change and biosphere integrity—have been identified, each of which has the potential on its own to drive the Earth system into a new state should they be substantially and persistently transgressed.

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Planetary boundaries: Guiding human development on a changing planet

THE major active ingredient of marijuana, Δ9-tetrahydrocannabi-nol (Δ9-THC), has been used as a psychoactive agent for thousands of years. Marijuana, and Δ9-THC, also exert a wide range of other effects including analgesia, anti-inflammation, immunosuppression, anticonvulsion, alleviation of intraocular pressure in glaucoma, and attenuation of vomiting1. The clinical application of cannabinoids has, however, been limited by their psychoactive effects, and this has led to interest in the biochemical bases of their action. Progress stemmed initially from the synthesis of potent derivatives of δ9-THC4,5, and more recently from the cloning of a gene encoding a G-protein-coupled receptor for cannabinoids6. This receptor is expressed in the brain but not in the periphery, except for a low level in testes. It has been proposed that the non-psychoactive effects of cannabinoids are either mediated centrally or through direct interaction with other, non-receptor proteins1,7,8. Here we report the cloning of a receptor for cannabinoids that is not expressed in the brain but rather in macrophages in the marginal zone of spleen.

Molecular characterization of a peripheral receptor for cannabinoids

This paper contrasts the natural and anthropogenic controls on the conversion of unreactive N2 to more reactive forms of nitrogen (Nr). A variety of data sets are used to construct global N budgets for 1860 and the early 1990s and to make projections for the global N budget in 2050. Regional N budgets for Asia, North America, and other major regions for the early 1990s, as well as the marine N budget, are presented to highlight the dominant fluxes of nitrogen in each region. Important findings are that human activities increasingly dominate the N budget at the global and at most regional scales, the terrestrial and open ocean N budgets are essentially dis- connected, and the fixed forms of N are accumulating in most environmental reservoirs. The largest uncertainties in our understanding of the N budget at most scales are the rates of natural biological nitrogen fixation, the amount of Nr storage in most environmental reservoirs, and the production rates of N2 by denitrification.

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Nitrogen cycles: past, present, and future

Relationships between wind speed and gas transfer, combined with knowledge of the partial pressure difference of CO2 across the air-sea interface are frequently used to determine the CO2 flux between the ocean and the atmosphere. Little attention has been paid to the influence of variability in wind speed on the calculated gas transfer velocities and the possibility of chemical enhancement of CO2 exchange at low wind speeds over the ocean. The effect of these parameters is illustrated using a quadratic dependence of gas exchange on wind speed which is fit through gas transfer velocities over the ocean determined by the natural-14C disequilibrium and the bomb-14C inventory methods. Some of the variability between different data sets can be accounted for by the suggested mechanisms, but much of the variation appears due to other causes. Possible causes for the large difference between two frequently used relationships between gas transfer and wind speed are discussed. To determine fluxes of gases other than CO2 across the air-water interface, the relevant expressions for gas transfer, and the temperature and salinity dependence of the Schmidt number and solubility of several gases of environmental interest are included in an appendix.

Relationship between wind speed and gas exchange over the ocean

Introduction Phytoplankton in order to survive in the upper ocean carry out photosynthesis absorbing the solar radiation penetrating in the ocean Thereby they also absorb heat High biomass during the spring bloom is thought to substantially affect the penetration of light and in turn heat in the upper ocean The biological effect of this process has been extensively investigated and is described as the Self Shading effect However the possible physical effects on the thermal structure and therefore on stratification of the water column are still poorly understood Here we study the impact of marine biomass on ocean stratification and sea surface temperature (SST) using an Ocean General Circulation Model (OPA; Madec and Imbard, 1996; Madec et al, 1999) coupled to a Dynamic Green Ocean Model (Buitenhuis et al, this meeting; Aumont et al, 2003) Results

Early steps towards modelling the phytoplankton-heat feedback

For the first time the tandem isomerization and nucleophilic aromatic substitution of allylic fluoro-substituted benzylic alcohols is described.

Ruthenium‐Catalyzed Remote Electronic Activation of Aromatic C—F Bonds.

The propagation of non-uniformly modulated, evolutionary random waves in viscoelastic, transversely isotropic, stratified materials is investigated. The theory is developed in the context of a multi-layered soil medium overlying bedrock, where the material properties of the bedrock are considered to be much stiffer than those of the soil and the power spectral density of the random excitation is assumed to be known at the bedrock. The governing differential equations are first derived in the frequency/wave-number domain so that the displacement response of the ground may be computed. The eigen-solution expansion method is then used to solve for the responses of the layers. This utilizes the precise integration method, in combination with the extended Wittrick-Williams algorithm, to obtain all the eigen-solutions of the ordinary differential equation. The recently developed pseudo-excitation method for structural random vibration is then used to determine the solution of the layered soil responses.

Andrew J. Watson

Papers

Early steps towards modelling the phytoplankton-heat feedback

Ruthenium‐Catalyzed Remote Electronic Activation of Aromatic C—F Bonds.

Propagation of non-uniformly modulated evolutionary random waves in a stratified viscoelastic solid

Expression and localization of NRF2/Keap1 signalling pathway genes in mouse preimplantation embryos exposed to free fatty acids.

Overturning Pathways Control AMOC Weakening in CMIP6 Models