High-energy Large Hadron Collider results published

By Jason Palmer

Science and technology reporter, BBC News (http://news.bbc.co.uk/2/hi/8505203.stm)

The results from the highest-energy particle experiments carried out at the Large Hadron Collider (LHC) in December have begun to yield their secrets.

Scientists from the LHC's Compact Muon Solenoid (CMS) detector has now totted up all of the resulting particle interactions. They wrote in the Journal of High Energy Physics that the run created more particles than theory predicted.

However, the glut of particles should not affect results as the experiment runs to even higher energies this year.

The LHC is designed to smash together particles and atoms circling its 27km-tunnel in a bid to find evidence of further particles that underpin the field of physics as it is currently formulated.

The December announcement of particle beam energies in excess of one trillion electron volts made the LHC the world's highest-energy particle accelerator.

That makes the new results a unique look at the field of high-energy physics. The experiments, smashing protons into each other, produced a few more subatomic particles known as pions and kaons than the team was expecting.

"The level is somewhat higher than the most popular models had predicted, and it looks like it is going to increase with energy a little bit more steeply than we expected," said Gunther Roland, a CMS collaboration scientist from the Massachusetts Institute of Technology in the US.

"I think it's not going to be a problem, but it is one of the many things that we need to know as we move toward searches for the most rare particles and new physics," Professor Roland told BBC News.

He added that the "extra" particles will be more of an issue when, later in 2010, the LHC dedicates itself to collisions involving ions of the element lead, a markedly heavier pair of targets resulting in an even larger array of particles on impact.

"We'll know much more about that in two or three months when we look at the next higher energy of 7 TeV (trillion electron volts)."

Check your comprehension

~ What is the LHC designed for?

~ What are “pions” and “kaons”?

Unit 9

The Millennium Prize for resolution of the Poincaré conjecture

History and Background

In the latter part of the nineteenth century, the French mathematician Henri Poincaré was studying the problem of whether the solar system is stable. Do the planets and asteroids in the solar system continue in regular orbits for all time, or will some of them be ejected into the far reaches of the galaxy or, alternatively, crash into the sun? In this work he was led to topology, a still new kind of mathematics related to geometry, and to the study of shapes (compact manifolds) of all dimensions.

The simplest such shape was the circle, or distorted versions of it such as the ellipse or something much wilder: lay a piece of string on the table, tie one end to the other to make a loop, and then move it around at random, making sure that the string does not touch itself. The next simplest shape is the two-sphere, which we find in nature as the idealized skin of an orange, the surface of a baseball, or the surface of the earth, and which we find in Greek geometry and philosophy as the "perfect shape." Again, there are distorted versions of the shape, such as the surface of an egg, as well as still wilder objects. Both the circle and the two-sphere can be described in words or in equations as the set of points at a fixed distance from a given point (the center). Thus it makes sense to talk about the three-sphere, the four-sphere, etc. These shapes are hard to visualize, since they naturally are contained in four-dimensional space, five-dimensional space, and so on, whereas we live in three-dimensional space. Nonetheless, with mathematical training, shapes in higher-dimensional spaces can be studied just as well as shapes in dimensions two and three.

In topology, two shapes are considered the same if the points of one correspond to the points of another in a continuous way. Thus the circle, the ellipse, and the wild piece of string are considered the same. This is much like what happens in the geometry of Euclid. Suppose that one shape can be moved, without changing lengths or angles, onto another shape. Then the two shapes are considered the same (think of congruent triangles). A round, perfect two-sphere, like the surface of a ping-pong ball, is topologically the same as the surface of an egg.

In 1904 Poincaré asked whether a three-dimensional shape that satisfies the "simple connectivity test" is the same, topologically, as the ordinary round three-sphere. The round three-sphere is the set of points equidistant from a given point in four-dimensional space. His test is something that can be performed by an imaginary being who lives inside the three-dimensional shape and cannot see it from "outside." The test is that every loop in the shape can be drawn back to the point of departure without leaving the shape. This can be done for the two-sphere and the three-sphere. But it cannot be done for the surface of a doughnut, where a loop may get stuck around the hole in the doughnut.

Check your comprehension

~ What is the subject of topology?

~ Which shapes are considered the same in topology?

~ What is the ‘simple connectivity test’?

The question raised became known as the Poincaré conjecture. Over the years, many outstanding mathematicians tried to solve it--Poincaré himself, Whitehead, Bing, Papakirioukopolos, Stallings, and others. While their efforts frequently led to the creation of significant new mathematics, each time a flaw was found in the proof. In 1961 came astonishing news. Stephen Smale, then of the University of California at Berkeley (now at the City University of Hong Kong) proved that the analogue of the Poincaré conjecture was true for spheres of five or more dimensions. The higher-dimensional version of the conjecture required a more stringent version of Poincaré's test; it asks whether a so-called homotopy sphere is a true sphere. Smale's theorem was an achievement of extraordinary proportions. It did not, however, answer Poincaré's original question. The search for an answer became all the more alluring.

Smale's theorem suggested that the theory of spheres of dimensions three and four was unlike the theory of spheres in higher dimension. This notion was confirmed a decade later, when Michael Freedman, then at the University of California, San Diego, now of Microsoft Research Station Q, announced a proof of the Poincaré conjecture in dimension four. His work used techniques quite different from those of Smale. Freedman also gave a classification, or kind of species list, of all simply connected four-dimensional manifolds.

Both Smale (in 1966) and Freedman (in 1986) received Fields medals for their work.

There remained the original conjecture of Poincaré in dimension three. It seemed to be the most difficult of all, as the continuing series of failed efforts, both to prove and to disprove it, showed. In the meantime, however, there came three developments that would play crucial roles in Perelman's solution of the conjecture.

Check your comprehension

~ For spheres of which dimensions was the Poincaré conjecture first proved?

~ What did continuing attempts to prove or disprove the original Poincaré conjecture show?

Geometrization

The first of these developments was William Thurston's geometrization conjecture. It laid out a program for understanding all three-dimensional shapes in a coherent way, much as had been done for two-dimensional shapes in the latter half of the nineteenth century. According to Thurston, three-dimensional shapes could be broken down into pieces governed by one of eight geometries, somewhat as a molecule can be broken into its constituent, much simpler atoms. This is the origin of the name, "geometrization conjecture."

A remarkable feature of the geometrization conjecture was that it implied the Poincaré conjecture as a special case. Such a bold assertion was accordingly thought to be far, far out of reach--perhaps a subject of research for the twenty-second century. Nonetheless, in an imaginative tour the force that drew on many fields of mathematics, Thurston was able to prove the geometrization conjecture for a wide class of shapes (Haken manifolds) that have a sufficient degree of complexity. While these methods did not apply to the three-sphere, Thurston's work shed new light on the central role of Poincaré's conjecture and placed it in a far broader mathematical context.

Check your comprehension

~ What does the geometrization conjecture state?

Limits of spaces

The second current of ideas did not appear to have a connection with the Poincaré conjecture until much later. While technical in nature, the work, in which the names of Cheeger and Perelman figure prominently, has to do with how one can take limits of geometric shapes, just as we learned to take limits in beginning calculus class. Think of Zeno and his paradox: you walk half the distance from where you are standing to the wall of your living room. Then you walk half the remaining distance. And so on. With each step you get closer to the wall. The wall is your "limiting position," but you never reach it in a finite number of steps. Now imagine a shape changing with time. With each "step" it changes shape, but can nonetheless be a "nice" shape at each step-- smooth, as the mathematicians say. For the limiting shape the situation is different. It may be nice and smooth, or it may have special points that are different from all the others, that is, singular points, or "singularities." Imagine a Y-shaped piece of tubing that is collapsing: as time increases, the diameter of the tube gets smaller and smaller. Imagine further that one second after the tube begins its collapse, the diameter has gone to zero. Now the shape is different: it is a Y shape of infinitely thin wire. The point where the arms of the Y meet is different from all the others. It is the singular point of this shape. The kinds of shapes that can occur as limits are called Aleksandrov spaces, named after the Russian mathematician A. D. Aleksandrov who initiated and developed their theory.

Check your comprehension

~ What does Zeno’s paradox state?

~ What is the limiting shape for a Y-shaped piece of tubing?

~ What are limiting shapes called?

Differential equations

The third development concerns differential equations. These equations involve rates of change in the unknown quantities of the equation, e.g., the rate of change of the position of an apple as it falls from a tree towards the earth's center. Differential equations are expressed in the language of calculus, which Isaac Newton invented in the 1680s in order to explain how material bodies (apples, the moon, and so on) move under the influence of an external force. Nowadays physicists use differential equations to study a great range of phenomena: the motion of galaxies and the stars within them, the flow of air and water, the propagation of sound and light, the conduction of heat, and even the creation, interaction, and annihilation of elementary particles such as electrons, protons, and quarks.

In our story, conduction of heat and change of temperature play a special role. This kind of physics was first treated mathematically by Joseph Fourier in his 1822 book, Théorie Analytique de la Chaleur. The differential equation that governs change of temperature is called the heat equation. It has the remarkable property that as time increases, irregularities in the distribution of temperature decrease.

Differential equations apply to geometric and topological problems as well as to physical ones. But one studies not the rate at which temperature changes, but rather the rate of change in some geometric quantity as it relates to other quantities such as curvature. A piece of paper lying on the table has curvature zero. A sphere has positive curvature. The curvature is a large number for a small sphere, but is a small number for a large sphere such as the surface of the earth. Indeed, the curvature of the earth is so small that its surface has sometimes mistakenly been thought to be flat. For an example of negative curvature, think of a point on the bell of a trumpet. In some directions the metal bends away from your eye; in others it bends towards it.

Check your comprehension

~Which problems dodifferential equations apply to?

~ Is the earth surface flat? Why was it thought to be flat?

Ricci flow

The differential equation that was to play a key role in solving the Poincaré conjecture is the Ricci flow equation. It was discovered two times, independently. In physics, by Friedan, 1985 and in mathematics by Richard Hamilton in his 1982 paper. The physicists were working on the renormalization group of quantum field theory, while Hamilton was interested in geometric applications of the Ricci flow equation itself.

On the left-hand side of the Ricci flow equation is a quantity that expresses how the geometry changes with time--the derivative of the metric tensor, as the mathematicians like to say. On the right-hand side is the Ricci tensor, a measure of the extent to which the shape is curved. The Ricci tensor, based on Riemann's theory of geometry (1854), also appears in Einstein's equations for general relativity (1915). Those equations govern the interaction of matter, energy, curvature of space, and the motion of material bodies.

The Ricci flow equation is the analogue, in the geometric context, of Fourier's heat equation. The idea, grosso modo, for its application to geometry is that, just as Fourier's heat equation disperses temperature, the Ricci flow equation disperses curvature. Thus, even if a shape was irregular and distorted, Ricci flow would gradually remove these anomalies, resulting in a very regular shape whose topological nature was evident. Indeed, in 1982 Hamilton showed that for positively curved, simply connected shapes of dimension three (compact three-manifolds) the Ricci flow transforms the shape into one that is ever more like the round three-sphere. In the long run, it becomes almost indistinguishable from this perfect, ideal shape. When the curvature is not strictly positive, however, solutions of the Ricci flow equation behave in a much more complicated way. This is because the equation is nonlinear. While parts of the shape may evolve towards a smoother, more regular state, other parts might develop singularities. This richer behavior posed serious difficulties. But it also held promise: it was conceivable that the formation of singularities could reveal Thurston's decomposition of a shape into its constituent geometric atoms.

Check your comprehension

~ How does Ricci flow transform irregular shapes?

~Do all parts of a shape evolve alike?

Richard Hamilton

Hamilton was the driving force in developing the theory of Ricci flow in mathematics, both conceptually and technically. Hamilton had established the Ricci flow equation as a tool with the potential to resolve both conjectures as well as other geometric problems. Nevertheless, serious obstacles barred the way to a proof of the Poincaré conjecture. Notable among these obstacles was lack of an adequate understanding of the formation of singularities in Ricci flow, akin to the formation of black holes in the evolution of the cosmos. Indeed, it was not at all clear how or if formation of singularities could be understood. Despite the new front opened by Hamilton, and despite continued work by others using traditional topological tools for either a proof or a disproof, progress on the conjectures came to a standstill.

Such was the state of affairs in 2000, when John Milnor wrote an article describing the Poincaré conjecture and the many attempts to solve it. At that writing, it was not clear whether the conjecture was true or false, and it was not clear which method might decide the issue. Analytic methods (differential equations) were mentioned in a later version (2004).

Check your comprehension

~ Could mathematicians understand and explain the formation of singularities in Ricci flow?

~ Was progress on the Poincaré conjecture noticeable at the turn of the 20-21 centuries?

Perelman announces a solution of the Poincaré conjecture

It was thus a huge surprise when Grigoriy Perelman announced, in a series of preprints posted on ArXiv.org in 2002 and 2003, a solution not only of the Poincaré conjecture, but also of Thurston's geometrization conjecture.

The core of Perelman's method of proof is the theory of Ricci flow. To its applications in topology he brought not only great technical virtuosity, but also new ideas. One was to combine collapsing theory in Riemannian geometry with Ricci flow to give an understanding of the parts of the shape that were collapsing onto a lower-dimensional space. Another was the introduction of a new quantity, the entropy, which instead of measuring disorder at the atomic level, as in the classical theory of heat exchange, measures disorder in the global geometry of the space. Perelman's entropy, like the thermodynamic entropy, is increasing in time: there is no turning back. Using his entropy function and a related local version (the L-length functional), Perelman was able to understand the nature of the singularities that formed under Ricci flow. There were just a few kinds, and one could write down simple models of their formation. This was a breakthrough of first importance.

Once the simple models of singularities were understood, it was clear how to cut out the parts of the shape near them as to continue the Ricci flow past the times at which they would otherwise form. With these results in hand, Perelman showed that the formation times of the singularities could not run into Zeno's wall: imagine a singularity that occurs after one second, then after half a second more, then after a quarter of a second more, and so on. If this were to occur, the "wall," which one would reach two seconds after departure, would correspond to a time at which the mathematics of Ricci flow would cease to hold. The proof would be unattainable. But with this new mathematics in hand, attainable it was.

The posting of Perelman's preprints and his subsequent talks at MIT, SUNY-Stony Brook, Princeton, and the University of Pennsylvania set off a worldwide effort to understand and verify his groundbreaking work. In the US, Bruce Kleiner and John Lott wrote a set of detailed notes on Perelman's work. These were posted online as the verification effort proceeded. A final version was posted to ArXiv.org in May 2006, and the refereed article appeared in Geometry and Topology in 2008. This was the first time that work on a problem of such importance was facilitated via a public website. John Morgan and Gang Tian wrote a book-long exposition of Perelman's proof, posted on ArXiv.org in July of 2006, and published by the American Mathematical Society in CMI's monograph series (August 2007). These expositions, those by other teams, and, importantly, the multi-year scrutiny of the mathematical community, provided the needed verification. Perelman had solved the Poincaré conjecture. After a century's wait, it was settled!

Among other articles that appeared following Perelman's work is a paper in the Asian Journal of Mathematics, posted on ArXiv.org in June of 2006 by the American-Chinese team, Huai-Dong Cao (Lehigh University) and Xi-Ping Zhu (Zhongshan University). Another is a paper by the European group of Bessieres, Besson, Boileau, Maillot, and Porti, posted on ArXiv.org in June of 2007. It was accepted for publication by Inventiones Mathematicae in October of 2009. It gives an alternative approach to the last step in Perelman's proof of the geometrization conjecture.

Perelman's proof of the Poincaré and geometrization conjectures is a major mathematical advance. His ideas and methods have already found new applications in analysis and geometry; surely the future will bring many more.

Check your comprehension

~ Which new ideas did Perelman bring to the theory of Ricci flow?

~ Where did Perelman publish his outstanding results?

~ What was the aim of a number of publications following Perelman announcement of finding a solution not only of the Poincaré conjecture, but also of Thurston's geometrization conjecture?

References:

Perelman's articles on arXiv.org

11/11/2002. The Entropy Formula for the Ricci Flow and its Geometric Applications

3/10/2003. Ricci Flow with Surgery on Three-Manifolds

7/17/2003. Finite Extinction Time for the Solutions to the Ricci Flow on Certain Three-Manifolds

Unit 10

Meeting with scientists

Dmitry Medvedev discussed developing Russian science’s technological base, grants, and social support measures with young scientists.

The meeting’s participants included the 2010 laureates of prizes for science and innovation, President of the Russian Academy of Sciences Yury Osipov, and Education Minister Andrei Fursenko.

The meeting took place at the Polytechnic Museum, where the First Russian National Science Festival began today. Dmitry Medvedev addressed brief welcoming remarks to the event’s participants.

PRESIDENT OF RUSSIA DMITRY MEDVEDEV: Friends, I congratulate the laureates once again, and everyone here, on Russian Science Day. It is a pleasure to talk with you in an informal setting this time, not in the Kremlin, but at the Polytechnic Museum, which as we have seen, is about to be reborn. We all wish this work success, because this museum is a great support for everyone interested in science and technology. We need to ensure that it retains all of its former qualities, while at the same time moving forward and becoming a technologically advanced centre of interest to today’s youth.

Now to the issues before us, namely, the question of attracting talented young people into science and innovation. In December 2009, we discussed this subject in depth with the heads of the Russian Academy of Sciences. I hope that we will come back to it during our discussions today. Here, I am addressing Mr Osipov [Yury Osipov, President of the Russian Academy of Sciences]. Why, because I think that our decisions must be implemented. As far as I know, there is progress, including on the biggest problems, and the biggest problems, even in science, are the issues of everyday life. We said that we must start by resolving young scientists’ housing problems. I took the Government to task over this later. I think that did have some effect, and it seems that some apartments are ready now. How many, Mr Osipov?

PRESIDENT OF THE RUSSIAN ACADEMY OF SCIENCES YURY OSIPOV:We have received 150 apartments so far. This was done over January alone. Now it is still February, and the Government is holding constant meetings on the issue.

DMITRY MEDVEDEV:So I don’t need to scold anyone anymore? I can take a softer line now?

YURY OSIPOV:Sometimes it can be useful to get a scolding from you, Mr President.

DMITRY MEDVEDEV:Well, I will do so then, what choice do I have?

YURY OSIPOV:But things are moving now.

DMITRY MEDVEDEV:It’s good that things are moving, because I remember the bored looks on the faces of some of my colleagues when this was all being discussed, and I had to really make use of my power then. Let’s keep up the pace then and get this work finished.

YURY OSIPOV:Thank you.

DMITRY MEDVEDEV:Another matter is that the Russian Academy of Sciences’ Youth Commission made available an additional 1,000 salaried positions at the end of last year. I was briefed on this today by the minister. I think this is very good. We are talking about almost half of the Russian Academy of Sciences’ existing 400 research centres, am I right?

YURY OSIPOV:Yes, the money has been distributed, and we have kept 70 positions in reserve with the idea that particularly interesting people could emerge, while the rest have been distributed between the different institutes on a tender basis. It is interesting to note that there is competition for these positions, more than two institutes for each position. This is good to see. The money has now been distributed, and the institutes are now organising tenders to select the people to whom it will go to.

Thank you very much for this, Mr President.

DMITRY MEDVEDEV:Good, so things are moving in this area too?

YURY OSIPOV:Yes, things are moving full steam ahead.

DMITRY MEDVEDEV:Good, I remind you that the size of the presidential grants for young Ph.D. and D.Sc. holders was increased substantially and now comes to 600,000 rubles for Ph.D. degree holders, and 1 million rubles for D.Sc. degree holders.

EDUCATION AND SCIENCE MINISTER ANDREI FURSENKO: For a year.

DMITRY MEDVEDEV:For a year, of course.

But this is not all, of course, and we can keep discussing this. I think that the state authorities need to do more to put in place all of the best possible conditions. Of course, this will never be anything completely exceptional, but the authorities in the broad sense – the federal, regional, and even municipal authorities - do need to ensure the minimum essential conditions.

The global world and the world of science know no borders, and we understand this. We therefore invite not only our own scientists to take part in these projects, but foreigners too. I think this is the right approach, because this is what scientific competition is all about, all the more so as our scientists go abroad and also participate – on a competitive basis – in projects abroad. This is just the kind of full-blooded environment that will help us to resolve the more difficult tasks ahead.

We have young people here today, and I want them to take part too in discussing the various issues involved in developing science, and developing education in general in our country and improving the way science is managed. The Youth Coordination Council has already made a shortlist of projects competing for the presidential grants and prizes for young scientists. In the views of senior colleagues, these projects are of high quality, and we shall see what comes of them. It is important to develop the network of regional councils of young scientists and specialists that have been established now in 81 different regions, practically throughout the entire country.

I want you to tell me, of course, about how you see the future of Russian science, what, in your view, are our strong points and weak points. Of course, we all have a fair idea of where our weak points lie at the moment, and in which areas we need to give new impetus.

But in any case, I can say that the situation has started to change of late. It has not changed radically, but things are improving. This is true of education and of science too. As someone who worked for quite a long time in the university system, I will not hide that I am very pleased to see these changes, because everyone who remembers the 1990s, remembers that they were very difficult years and the mood was very pessimistic back then. It was difficult to be optimistic. But this is all changing now.

There are problems. I have been discussing these problems not just here, not just with our young people working in science, but abroad too, with people working there. The last time was in Silicon Valley. That was an interesting discussion. There are very successful people working there, some of them left quite a long time ago, and some only recently. Some of them see their future in America, and others do not. But the conversation was very illustrative.

We should probably look at some additional incentives too. I think these could include the introduction of presidential scholarships for young people, who show promise in terms of developing priority modernisation areas. We will discuss the size of these scholarships, but they should provide decent sums of money for the chosen young people.

So, if you have similar ideas, I am willing to support them, though within reasonable limits. Let’s discuss all of this now.

Check your comprehension

~ Where did this meeting take place?

~ What is the size of presidential grants for young Ph.D. and D.Sc. holders?

http://eng.special.kremlin.ru/news/1742

Unit 11

Climate changes

Global warming has become perhaps the most complicated issue facing world leaders. On the one hand, warnings from the scientific community are becoming louder, as an increasing body of science points to rising dangers from the ongoing buildup of human-related greenhouse gases — produced mainly by the burning of fossil fuels and forests. On the other, the technological, economic and political issues that have to be resolved before a concerted worldwide effort to reduce emissions can begin have gotten no simpler, particularly in the face of a global economic slowdown.

Global talks on climate change opened in Cancún, Mexico, in late 2010 with the toughest issues unresolved, and the conference produced modest agreements. But while the measures adopted in Cancún are likely to have scant near-term impact on the warming of the planet, the international process for dealing with the issue got a significant vote of confidence.

The agreement fell well short of the broad changes scientists say are needed to avoid dangerous climate change in coming decades. But it laid the groundwork for stronger measures in the future, if nations are able to overcome the emotional arguments that have crippled climate change negotiations in recent years. The package, known as the Cancún Agreements, gives the more than 190 countries participating in the conference another year to decide whether to extend the frayed Kyoto Protocol, the 1997 agreement that requires most wealthy nations to trim their emissions while providing assistance to developing countries to pursue a cleaner energy future.

At the heart of the international debate is a momentous tussle between rich and poor countries over who steps up first and who pays most for changed energy menus.

In the United States, on Jan. 2, 2011, the Environmental Protection Agency imposed its first regulations related to greenhouse gas emissions. The immediate effect on utilities, refiners and major manufacturers will be small, with the new rules applying only to those planning to build large new facilities or make major modifications to existing plants. Over the next decade, however, the agency plans to regulate virtually all sources of greenhouse gases, imposing efficiency and emissions requirements on nearly every industry and every region.

President Obama vowed as a candidate that he would put the United States on a path to addressing climate change by reducing emissions of carbon dioxide and other greenhouse gas pollutants. He offered Congress wide latitude to pass climate change legislation, but held in reserve the threat of E.P.A. regulation if it failed to act. The deeply polarized Senate’s refusal to enact climate change legislation essentially called his bluff.

Scientists learned long ago that the earth's climate has powerfully shaped the history of the human species — biologically, culturally and geographically. But only in the last few decades has research revealed that humans can be a powerful influence on the climate as well.

A growing body of scientific evidence indicates that since 1950, the world's climate has been warming, primarily as a result of emissions from unfettered burning of fossil fuels and the razing of tropical forests. Such activity adds to the atmosphere's invisible blanket of carbon dioxide and other heat-trapping "greenhouse" gases. Recent research has shown that methane, which flows from landfills, livestock and oil and gas facilities, is a close second to carbon dioxide in impact on the atmosphere.

That conclusion has emerged through a broad body of analysis in fields as disparate as glaciology, the study of glacial formations, and palynology, the study of the distribution of pollen grains in lake mud. It is based on a host of assessments by the world's leading organizations of climate and earth scientists.

In the last several years, the scientific case that the rising human influence on climate could become disruptive has become particularly robust.

Some fluctuations in the Earth's temperature are inevitable regardless of human activity — because of decades-long ocean cycles, for example. But centuries of rising temperatures and seas lie ahead if the release of emissions from the burning of fossil fuels and deforestation continues unabated, according to the Intergovernmental Panel on Climate Change. The panel shared the 2007 Nobel Peace Prize with former Vice President Al Gore for alerting the world to warming's risks.

Despite the scientific consensus on these basic conclusions, enormously important details remain murky. That reality has been seized upon by some groups and scientists disputing the overall consensus and opposing changes in energy policies.

For example, estimates of the amount of warming that would result from a doubling of greenhouse gas concentrations (compared to the level just before the Industrial Revolution got under way in the early 19th century) range from 3.6 degrees to 8 degrees Fahrenheit. The intergovernmental climate panel said it could not rule out even higher temperatures. While the low end could probably be tolerated, the high end would almost certainly result in calamitous, long-lasting disruptions of ecosystems and economies, a host of studies have concluded. A wide range of economists and earth scientists say that level of risk justifies an aggressive response.

Other questions have persisted despite a century-long accumulation of studies pointing to human-driven warming. The rate and extent at which sea levels will rise in this century as ice sheets erode remains highly uncertain, even as the long-term forecast of centuries of retreating shorelines remains intact. Scientists are struggling more than ever to disentangle how the heat building in the seas and atmosphere will affect the strength and number of tropical cyclones. The latest science suggests there will be more hurricanes and typhoons that reach the most dangerous categories of intensity, but fewer storms over all.

Government figures for the global climate show that 2010 was the wettest year in the historical record, and it tied 2005 as the hottest year since record-keeping began in 1880.

Check your comprehension

~ Can you name any key points of Cancún Agreements?

~ What is palynology?

http://topics.nytimes.com/top/news/science/topics/globalwarming/index.html

Unit 12