This week, researchers from the University of Cambridge will be arriving at the Summer Science Exhibition of the Royal Society armed not with the latest in cutting-edge lab technology, but an assortment of simple toys.
But while many of these playthings may look like Christmas stocking-fillers purchased from the gift shop at a museum, their behaviour is helping scholars to understand the evolution of weather patterns and the magnetohydrodynamics of spinning stars and planets. They include spinning eggs that rise against gravity, objects that spontaneously reverse their sense of spin and discs that roll at an
accelerating rate before coming to a standstill. In each case, their behaviour has been baffling some of the sharpest scientific minds for years.
"Understanding the behaviour of spinning toys can teach us a lot about some of the fundamental principles of dynamics," Dr Tadashi Tokieda, College lecturer at Trinity Hall, Cambridge, explained. "The toys themselves are very simple, but the way in which they behave is so strange that they have intrigued anyone who has studied mechanics at graduate level. One of the things we hope to point out
is that some of the most important experiments can take place not in the lab, but in daily life. Good scientists take toys seriously."
One example of a toy that seems to defy the laws of physics is the "rattleback" - a small, symmetrical canoe-shaped object that spins smoothly in one direction, but when spun the other way rattles and reverses its motion. Its mysterious behaviour was this year explained in a paper by Professor Keith Moffatt FRS, also at Cambridge University, and Dr
Tokieda, as being a subtle effect of what is known as chirality – the result of the object's skewed mass distribution.
The behaviour of this toy could offer insight into a bigger problem. Every million years or so, the Earth's magnetic field reverses, causing the planet's magnetic north and magnetic south to interchange. Scientists are still at a loss as to what causes this, but the rattleback toy mimics certain fluid dynamical processes in the Earth's liquid core that are responsible for the excitation of its
"In the case of each toy that will be on display, mathematics, coupled with computation and high-speed photography, and above all simple, imaginative experiments that everyone can do, is helping us to explain their surprising and behaviour," Dr Tokieda added.
The Royal Society's Summer Science Exhibition is held annually at the Royal Society, the UK's national academy of science. The event is free and open to the public. This year, 23 interactive exhibits will be on show presenting the best in UK science, engineering and technology. During the four days, more than 4,000 people are expected to explore the exhibition. The event will run from Monday 2
to Thursday 5 July. Other maths on display at the exhibition include sound waves, extreme pressure and optical illusions.
The geometry that gives rise to rainbows may help scientists to find out whether other planets contain water, which is necessary to sustain life. Rainbows are formed because light rays are bent, or refracted, and scattered as they enter droplets of liquid that hang in the atmosphere. The refraction occurs because light waves are slowed as they enter the droplet — think of a shopping trolley
slowing down as you push it onto a lawn at an angle, and changing its direction as a result. The amount by which the light rays are slowed, and hence bent, depends on the liquid's consistency and is measured by its refractive index. Thus, different liquids give rise to rainbows at different angles, a fact that enabled researchers to determine that the clouds of Venus are droplets of
concentrated sulfuric acid. Researchers now suggest that the same approach could be used to detect clouds made of liquid water in a planet's atmosphere.
Plasma astrophysicists at the University of Warwick have found that key information about the Sun's "storm season" is being broadcast across the solar system in a fractal snapshot imprinted in the solar wind. This research opens up new ways of looking at both space weather and the unstable behaviour that affects the operation of fusion powered power plants.
Solar wind consists of a stream of plasma, mainly protons and electrons, that are ejected by the Sun's corona. On its way out the wind interacts with the Sun's magnetic field, broadcasting it across the universe. The researchers, led by Sandra Chapman, measured the strength of the magnetic field in the solar wind. They found that when the Sun is at the peak of its 11-year cycle, the graph they
were plotting turned into a fractal. At this point the solar corona was at its most active, stormy and complex, due to sunspot activity, solar flares, etc. When the corona was quieter no fractal patterns were found in the solar wind.
This new information will help astrophysicists understand how the solar corona heats the solar wind and the nature of the turbulence of the solar wind with its implications for cosmic ray flux and space weather.
The techniques used to find and understand the fractal patterns in the solar wind are also being used to assist the quest for fusion power. Researchers in the University of Warwick's Centre for Fusion, Space and Astrophysics (CFSA) are collaborating with scientists from the EURATOM/UKAEA fusion research programme to measure and understand fluctuations in the world leading fusion experiment
MAST (the Mega Amp Spherical Tokamak) at Culham. Controlling plasma fluctuations in tokamaks is important for getting the best performance out of future fusion power plants.
Born: 11th of November 1904 in Madras, India
Died: 8th of May 1960 in Princeton, New Jersey, USA
"He would have been more successful in mathematics if he had been less so at cricket," is what Whitehead's maths teacher wrote about him on his graduation from Eton. Once at Oxford, to which he'd nevertheless gained entry, Whitehead's distraction diversified to include squash, tennis, boxing and poker, at which he reportedly staked large sums of money. Worse, Whitehead did not even seem to
want to become a mathematician at first, instead he joined a stockbrokers firm in London on completion of his degree.
But luckily, all turned out well for maths in the end. Working in the City wasn't to Whitehead's taste, and after a detour to Oxford he enrolled for a PhD at Princeton in the US. Here he began to work on two areas which benefitted greatly from his contributions: topology and differential geometry. Both differential geometry and topology deal with surfaces like the sphere or the torus, or their
higher dimensional analogues. While differential geometry looks at rigid properties that depend on a metric, for example the curvature of a surface, in topology metric properties are irrelevant. Topologists regard two objects as being the same if you can deform one into the other without tearing. The famous example is that a coffee cup and a doughnut are topologically the same.
Whitehead contributed two major works to differential geometry, now considered classics. In topology he is best remembered for his work on "homotopy equivalence", a central notion when it comes to pinning down whether two objects are topologically equivalent. Notably, Whitehead spent quite some time working on the now famous Poincare conjecture and even thought that he had found a proof.
However, an inconspicuous pair of interlinked circles, now known as the "Whitehead link", gave rise to a structure that Whitehead had assumed not to exist. This toppled his proof and the Poincare conjecture was to remain open for another 70 years.
Whitehead also contributed to maths in another, less theoretical way. The percecution of Jews in Nazi Germany troubled him greatly, and he helped a number of eminent mathematicians to escape, including Erwin Schroedinger, one of the founders of quantum mechanics.
Had Whitehead not died suddenly of a heart attack at only 56, he certainly would have gone on to contribute even more.
Scientists are currently building the largest machine in the world in order to understand the smallest fragments of our universe. Their insights will throw light on some of the biggest questions there are - how did the universe start, what is it made of, and how will it end? The machine is the Large Hadron Collider (LHC) and it is buried up to 175m below ground in a huge circular tunnel close
to Geneva. To prepare for its inauguration at the end of this year, the Science Museum has put on a special exhibition entitled "Big Bang". The accompanying website tells you all you need to know about the collider and the science behind it. It's accessible for everyone from school age onwards, no previous knowledge required.
Live maths - tangled DNA, the Big Bang and musical superstrings
Twisting, Coiling, Knotting: Maths and DNA Replication
The proportions of a DNA molecule in a human cell are equivalent to a 2000-mile-long rope packed inside the Millennium Dome. When DNA replicates, it spins at an astonishing 10 turns per second. Therefore, it is hardly surprising that DNA can become highly twisted, super-coiled and even knotted! To understand this phenomenon, the molecular biologist must grapple with the mathematical concepts
of twisting, writhing and knotting. In this highly-illustrated talk Professor Michael Thompson FRS will experiment with strings and rubber bands (bring your own!) to explore the geometrical rules which underlie the transmission our genetic code.
In honour of the Large Hadron Collider, the Dana Centre is holding an evening dinner and discussion attended by the expert James Gillies from CERN. There'll be slide shows and photographs and a two-course meal inspired by particle physics.
When: 15th of May 2007, 6.30pm - 8.30pm
Where: Dana Centre, 165 Queen's Gate, London SW7 5HE
Tickets: £15 per person, including a two-course meal and a drink. Tickets have to be booked by calling 0207942 4040 or e-mailing firstname.lastname@example.org.
Age range: this event is open only to those over 18 years of age.
More information: Visit the Dana Centre site.
Also the Science Museum in London has put on an exhibition in honour of the Large Hadron Collider. The exhibition is free and will run until the 7th of October 2007.
Superstrings - a Musical Journey through Time and Space
You probably knew that Einstein was a great scientist, but did you also know that he played the violin? In this unique double act a virtuoso violinist and the head of the department of particle physics at Oxford University combine the electricity of a live musical performance with an insight into the deepest corners of the Universe. The lecture explores Einstein's life, both in science and in
music, from his theories that shaped space and time, to modern ideas in particle physics.
When: 18th of May 2007 5pm-7pm
Where: Science Oxford, 1-5 London Place, Oxford, OX4 1BD
Tickets: £6.50, £4.50 concession, available from The Oxford Playhouse on 01865 305305.
More information: The Oxford Trust