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Alumni and Friends

Asymptopia - Centre for Mathematical Sciences Newsletter. March 1999

Common Ground:
Landscape Design at the Centre for Mathematical Sciences

Livingston Eyre Associates, Landscape Architects

Park. Court. Square. Garden. Four words that conjure up strong images of manmade spaces for most people, and especially so for landscape architects. These spaces have evolved from very disparate original functions and meanings into recognisable components of our modern civic fabric. These kinds of public space, together with the systems of interior rooms that buildings enclose, form a continuum of human interchange. Outdoor rooms and interior landscapes are indeed familiar turns of phrase which serve, on consideration, to emphasise the existence of this undervalued relationship between the inside and the outside world we build for ourselves.

It is a reasonably infrequent occurrence for a landscape architectural firm to design a single project - a single building site - that is composed of more than two or three main types of public space. Here at the Centre for Mathematical Sciences is an architectural design, born of a client brief, that sets the stage for an unusually rich matrix of exterior public space. Thomas Jefferson, at the University of Virginia, created a wonderfully subtle and elegant system of spaces - what he termed an "academical village" - which has much resonance with the architectural scheme for the Centre. It was Jefferson's genius at Virginia and it is our charge at the Centre to extend and explore the idea of a community of scholars as an urban paradigm using a kit of parts - park, court, square, garden - that supports the client's needs and affirms shard notions of good public spaces.

The buildings that form the Centre for Mathematical Sciences academic village are gathered in the centre of the site, leaving a continuous open ring of space between the face of the Pavilions and the site edges. This is the mediating space between the neighbourhood and the Centre, developed as a linear parkland that wraps around the buildings. It draws upon an existing ancient hedge of bramble and elm, reinforced and enriched by a new multiple-species fruiting hedge, as its outer defining edge, while the strong and consistent face of the Pavilions provides the inner edge. Along the length of this parkland run the main circulation paths for cycles, pedestrians, and, to the North, vehicles. The dense green outside edges of this park serve to visually soften and absorb the impact of vehicle and cycle parking.

Directly in front of the vault of the Central Core building's main entry and aligned along the main entry axis into the site from the East lies the Centre's Central Court, a serene rectilinear greensward articulated by the traditional Cambridge pattern of York stone pavements edged with cobble margins. These simple planar surfaces allow the gentle sweeping lines of the outer edges to emerge from the earth and carry the eye deep into the Central Core through the transparent entry façade. Pavilion 3 Courtyard Sketch

At the eastern end of the Central Court the Centre meets the important public pedestrian connection with the site through the spaces defined by the Physical Sciences and Technology Library, the Isaac Newton Institute, and an intervening Gatehouse. This area is the most important crossroads of the site, where the geometries of the architecture focus pedestrian routes to and from the key elements. Here will be found the greatest bustle and urbanity on the site as students, faculty, and visitors intermix in the course of the daily life of the Centre. Here, then, is developed a place with the character of a fine urban square, carefully proportioned with respect to its framing buildings; paved in the rich colours and subtly modelled surfaces of York stone flags and setts; furnished with generous lengths of low walls with copings that encourage sitting and socialising; and given focus through the incorporation of Newton's Apple tree as the central feature.

The spaces between the Pavilions are the most intimate and the most powerfully influenced in their character by the surrounding buildings. They are in an important way the most private, as they are not intended as major entries or exits from the Centre, but are rather the main field of view for a great number of overlooking faculty offices. As the gardens descend from ground level to the lower level of the Central Core building, they have been conceived as a series of fragmented terraces organised around the skewed axis of a stepped ramp that leads from the park down to the glass façade of the Core. The rich variety of the planting in these more intimate areas contrasts with the simpler grassland regime of the adjoining park. Parkland Sketch

Planting concept
At the Centre, trees are employed in two ways: first, in copses and rows, to reinforce the green outermost boundary edge of the site, and second, in sharp wedge-shaped groups to knit the park and garden spaces together into a coherent whole. The wedge-shaped groups are generated by the geometry of the ascending terraces and reach out across the park to the boundaries. These successive layers of trees serve to animate the experience of walking along the paths and also serve to soften and articulate the rhythm of the predominantly hard architectural edge of the park formed by the Pavilions. On the North side of the Centre, the tree wedges perform another vital function. The required vehicular access road and car parks are an unavoidably strong visual element here, and an equally powerful landscape pattern is required if it is to hold its own. The wedges here have been placed, insofar as possible, in a manner that suggests that their pattern predates and dictates the location and behaviour of cars and lorries, breaking down the potentially long and unrelieved vista of roadway and parking. Shrubs are used throughout in simple blocks which serve to reinforce the building form or, in the case of evergreen ground cover, accentuate the contours of the site. Fruit and form and colour and texture have all been considered so that the planted landscape can provide a constantly changing framework for the new centre.

Ozone Holes and the Sun's Interior
By Michael McIntyre, Department of Applied Mathematics and Theoretical Physics (DAMTP)

Why, sceptics often ask, do the strongest ozone holes appear in the south, in the stratosphere over Antarctica, when the man-made chlorofluorocarbons (CFCs) said to be causing them are emitted mainly in the north? An adequate answer involves complicated chemistry and radiation - infrared, visible and ultraviolet - and complicated fluid dynamics. To understand what is going on in the stratosphere, we have to deal not only with the chemistry and radiation but also with exotic wavelike and turbulent motions in a strongly stratified, rapidly rotating fluid. Today's understanding of these motions, owing much to research done in DAMTP, tells a remarkable story of order emerging out of chaos. Some of the order can be traced to the strong chirality, or handedness, imposed by the sense of the Earth's rotation. Coriolis effects are crucial here - even though, contrary to what you might read in the newspapers, they are quite unimportant for the water in your bathtub. (I recently read in a very prominent newspaper that Ecuador, being eponymously on the equator, is the country where the bathwater doesn't know which way to turn.) More seriously, there is now an overwhelming weight of evidence (not recognized by all newspapers) that the ozone hole is, indeed, caused mainly by CFCs and other man-made chemicals.

What happens is this. CFC molecules go on epic journeys. They wander around the lower atmosphere for times of the order of a century, visiting the southern as well as the northern hemisphere again and again, before entering the stratosphere or dissolving in the ocean. The majority eventually enter the stratosphere, via the tropics. The Coriolis effects make the stratosphere into a gigantic suction pump, inexorably pulling air upwards from the tropical lower atmosphere and pushing it polewards and back downwards in higher latitudes, over tortuous pathways, in some cases all the way to the Arctic or the Antarctic. This is order out of chaos on a grand scale.

The journey through the stratosphere takes several years, and, at altitudes above about 25 km, brings the CFC molecules into the glare of hard solar ultraviolet. The photons are energetic enough to break the tight chemical bonds that give the CFCs their stability and non-toxicity at sea level. The broken molecular fragments are very reactive and enter a complicated chain of chemical events. It is they and their reaction products that bring about the destruction of ozone - most conspicuously under the extreme conditions of the Antarctic polar stratosphere, but also, to a lesser extent, in many other places including the Arctic.

And what has this to do with the Sun's interior? Our understanding of the stratospheric pumping action, plus the latest observational data, has led to what I think will be a breakthrough in solar physics. Coriolis effects are once again important. The Sun's turbulent convection zone, shown orange in the figure, pumps a circulation in the underlying 'tachocline', shown green with its thickness exaggerated for graphical clarity. Confronting the fluid-dynamical theory with the data, we are forced to a radical conclusion: the Sun not merely can, but must, have in its stably stratified interior a magnetic field (red lines) that is strong enough to reshape the circulation and differential rotation in the interior (see figure caption). This has far-reaching consequences for understanding solar spindown history and possible internal variability, and promises to solve a longstanding puzzle about the destruction not of CFCs but of lithium. It should yield otherwise unobtainable information about the Sun's deepest interior, adding value to the observational data. Space precludes further explanation here, but a first report has already appeared in Nature (20 August 1998), written by Douglas Gough and myself.

Schematic slice through the Sun. The tachocline (green) has strong shear or differential rotation. It is much thinner than shown, about 2% of the Sun's radius. The circulation pumped by the overlying convection zone (orange) tends to burrow inexorably downward into the Sun's interior, which is stably stratified like the Earth's stratosphere. If nothing else were happening then the tachocline would be too deep, today, for consistency with the data. Something must be stopping the circulation from burrowing downward. The only possibility is an interior magnetic field such as that shown by the red field lines. The circulation skims off magnetic flux like a fruit peeler, gradually feeding it into the convection zone. The dynamics could be chaotic and could have unexpected effects on the seeding of the solar dynamo, with implications for sunspot activity and possibly for climate variability, as in the so called Maunder Minimum of the 'Little Ice Age'.

The Millennium Mathematics Project
John Barrow

From July 1999, Professor John D. Barrow will join DAMTP as a Research Professor of Mathematical Sciences and Director of the Millennium Mathematics Project. This exciting new project aims to improve the understanding and appreciation of mathematics amongst young people and the public at large. Stimulated by the challenge of reversing falling levels of numeracy amongst young people, it will build on the successes of NRICH and PASSMath, our existing web-based programmes for schools, but seek to promote mathematics in new ways and in new places.

The challenge of stimulating interest in mathematics amongst school students and maintaining that interest in gifted pupils is one that should be of concern throughout the UK business and industrial communities. The new millennium will present us with a world of growing technical complexity where an ability to appreciate the patterns, programs, risks, and complexities of the world will require familiarity and expertise in mathematics. The Millennium Mathematics Project aims to help ensure that our educators and young people are introduced to the appeal and central importance of mathematics in ways that display its relevance to the commercial, scientific, and cultural worlds. We recognise also that just as there are many who can appreciate and value music or painting without being musicians or painters so we must encourage an appreciation for mathematics and the insights that it can give into the patterns in the world around us.

John Barrow is well suited to lead this Project. Besides being known for his work in cosmology and mathematical physics, he is a prolific author and lecturer committed to the public understanding of science. He has written ten books about a wide spectrum of subjects that expound what is happening in science and mathematics and which highlight their connections with other human interests, in art, music, history, and the great questions of existence. Previously, he held positions at the Universities of Oxford, the University of California at Berkeley, and Sussex where he is currently Professor of Astronomy, Director of the Astronomy Centre and PPARC Senior Fellow. He is a frequent contributor to the print and broadcast media in the UK and abroad. He gave the 1989 Gifford Lectures, and many other public presentations to audiences from a wide range of backgrounds. He also has the unique distinction of having delivered invited lectures on mathematics and science at 10 Downing Street, Windsor Castle, and the Vatican Palace.

Cambridge Mathematicians win Fields Medals

At the International Congress of Mathematicians in Berlin in August, Cambridge University mathematicians won two out of the four highly prestigious Fields Medals, the highest accolade for mathematics, awarded every four years, and equivalent to the Nobel Prizes. Richard Borcherds, a Royal Society Research Professor, and Tim Gowers, the Rouse Ball Professor of Mathematics, both work in the Department of Pure Mathematics and Mathematical Statistics and completed the Mathematical Tripos and their doctoral studies at Cambridge. Richard Borcherds won his award for initiating a whole new field of study in algebra, called "Vertex Algebras". This new mathematical concept has profound connections with other well-established areas of pure mathematics and with some of the latest developments in theoretical physics.

Borcherds' vertex algebras are closely connected with, and were in part motivated by, a theory developed by physicists called string theory. String theory is aimed at providing a unified understanding of all the basic forces and fundamental particles of nature. Borcherds uses theorems from string theory in his work and a new sort of algebra he has introduced, called "generalised Kac-Moody algebras", seems, in turn, to be playing a role in the latest developments in string theory.

Tim Gowers' award is for his spectacular applications of new combinatorial methods to solve problems in probabilistic number theory and Banach spaces, invented by Polish mathematician Stefan Banach in the 1920s, which provide a unifying framework for many mathematical results and phenomena.

His most recent work, which is said to have captured the enthusiasm of the Fields' committee, involves a new proof of a theorem of a Hungarian mathematician called Endre Szemerédi. This theorem proved a conjecture of Erdös and Turan, two famous mathematicians from Hungary, that a sufficiently dense set of integers must contain arithmetic progressions of all lengths. "It might not sound that interesting to reprove an existing theorem," says Gowers, "but my proof gave far more information and introduced techniques that will almost certainly be useful for many other problems."