Imagine that one day you were greeted by your boss at work and told that you had been given a 100% pay rise because of your sterling efforts. Later that day, your bank calls to let you know that your savings and investments have doubled overnight due to an odd fluctuation in the international financial markets. But just when you thought that all your years of hard work had finally paid off,
you discover when buying your groceries that evening that the price of food and drink has also doubled – but that does not matter too much, this is just a small increase.
Are you in a better position than you were the night before? Even taking into account the rise in your cost of living, your net savings have increased, so should you be thanking your boss and your bank manager?
Whilst you may feel wealthier in this situation, this is simply an illusion. You still have to work as many hours tomorrow as you did yesterday to buy your groceries – nominal values have risen, but not real values.
Economists have long considered that financial markets limit the impact of traders trading on nominal values – irrational traders. This is because it is assumed that they are taken advantage of by smarter traders. However, new studies by Jean-Robert Tyran of the University of
Copenhagen have shown that there are situations in which money illusion can have a massive impact on the market, especially when there is a fall in nominal values.
An interesting example is the housing market. When interest rates are low, monthly nominal interest payments on mortgages are low compared to the rent on similar properties, so people start to buy. However, if inflation is decreasing, whilst current payments on the mortgage are falling, the real cost of future mortgage payments is increasing. This is because your salary is not growing and it
will take you longer to pay off your debt. These investors have fallen for the illusion. They are similar to those who pay off their credit card bill with monthly payments over 24 months, instead of over 12, as the down-payments are smaller.
Tyran’s experimental studies show that if there is a monetary contraction within the market – that is, if the nominal costs of goods and services fall – firms are reluctant to follow suit and cut their prices as this would result in lower nominal profits, even if their real profit would remain the same.
This is called nominal loss aversion and results in part from the fact that our inbuilt fear of losses tends to outweigh our desire for a gain of the same amount. It can be seen in other financial areas, such as employees accepting a nominal pay increase, even if it results in a real pay-cut if it does not match inflation. Another example is a homeowner
being more unwilling to sell a house at a real loss if it comes with a nominal loss rather than cloaked by a nominal gain.
Conversely, the experiments show that firms have no problem increasing their nominal prices should there be a rise in inflation and wages to maintain their real profit.
Laboratory work is often based on simplified economies, whilst interpretation of real data can be extremely difficult, so Tyran hopes that experimental research, combined with real observations of the market, can be used together to better understand money illusion.
If you enjoy stepping into the world of mathematics through the Plus website, now you can take maths on the move with you and enjoy Plus whereever you are! We are pleased to release our first Plus Podcast — Breaking the ice: Maths reshaping geometry and
combating climate change. In this podcast we talk to Shahn Majid about a whole new geometry of space, find out about how mathematics is combatting climate change, as well as all the latest news from the world of maths. You can subscribe to the podcasts, or just stay tuned to Plus for the next podcast due late September.
Computer scientists at the University of Alberta have solved checkers, the popular board game with a history dating back to 3,000 BC.
After 18-and-a-half years and sifting through 500 billion billion (a five followed by 20 zeroes) checkers positions, Dr. Jonathan Schaeffer and colleagues have built a checkers-playing computer program that cannot be beaten. Completed in late April this year, the program, Chinook, may be played to a draw but will never be defeated. The
results of this research were published recently in the journal Science.
"This is a tremendous achievement — a truly significant advance in artificial intelligence," said Dr. Jaap van den Herik, editor of the International Computer Games Journal. "I think we've raised the bar — and raised it quite a bit — in terms of what can be achieved in computer technology and artificial intelligence," said Schaeffer, chair of the University of Alberta Department of
Computing Science. "With Chinook, we've pushed the envelope about one million times more than anything that's been done before."
A self-described "awful" checkers player, Schaeffer created Chinook to exploit the superior processing and memory capabilities of computers and determine the best way to incorporate artificial intelligence principals in order to play checkers.
With the help of some top-level checkers players, Schaeffer programmed heuristics — rules of thumb — into a computer software program that captured knowledge of successful and unsuccessful checkers moves. Then he and his team let the program run, while they painstakingly monitored, fixed, tweaked, and updated it as it went.
An average of 50 computers, with more than 200 running at peak times, were used everyday to compute the knowledge necessary to complete Chinook. Now that it is complete, the program no longer needs heuristics — it has become a database of information that knows the best move to play in every situation of a game. If Chinook's opponent also plays perfectly the game would end in a
"We've taken the knowledge used in artificial intelligence applications to the extreme by replacing human-understandable heuristics with perfect knowledge," Schaffer said. "It's an exciting demonstration of the possibilities that software and hardware are now capable of achieving."
Schaeffer started the Chinook project in 1989, with the initial goal of winning the human world checkers championship. In 1990 it earned the right to play for the championship. The program went on to lose in the championship match in 1992, but won it in 1994, becoming the first computer program to win a human world championship in any game — a feat recognized by the Guinness Book of
Chinook remained undefeated until the program was retired in 1997. With his sights set on developing Chinook into the perfect checkers program, Schaeffer restarted the project in 2001. "I'm thrilled with this achievement," he said. "Solving checkers has been something of an obsession of mine for nearly two decades, and it's really satisfying to see it through to its
"I'm also really proud of the artificial intelligence program that we've built at the University of Alberta," he added. "We've built up the premier games group in the world, definitely second-to-none. And we've built up a strong, international, truly world-class reputation, and I'm very proud of that."
Understanding embryo development moves forward thanks to biology and maths
Research aimed at understanding the mechanisms underlying embryo development has taken a step forward thanks to collaborative work between biology and mathematics. A study of wing formation in the fruit fly (Drosophila melanogaster), led by the researchers Marco Milán and Javier Buceta, both in Barcelona, has led to the discovery of a new genetic function involved in this process, and furthers
our understanding of the internal laws which regulate it.
The development of a living being is based on general laws written into the genetic code of each cell and which enable the cell to develop a specialist function, modifying the way they divide, their form and their behaviour. These changes are coordinated through a series of instructions that must be correctly interpreted within the cell, and this means that the information must pass along a
pathway of signalling molecules. These pathways have been conserved across evolution, and therefore studies using models such as the fruit fly provide information about these same processes in humans and other animals.
The Developmental Biology of Drosophila Group from the IRB Barcelona, led by Marco Milán, studies the signals that guide wing development in Drosophila. The wings are generated from a set of cells grouped into different segments or compartments that never mix with one another, and which enable the symmetrical construction of the dorsal and
ventral parts starting from a given limit or border. This process of subdivision into compartments also takes place during the formation of the vertebrate central nervous system, and the genes and signalling pathways involved are conserved in both Drosophila and vertebrate species.
Although biologists already had an intuitive idea of how the limit or border between these compartments was generated, there had been no systematic study taking into account all the relevant elements. Therefore, and with the backing of a group led by Javier Buceta, they decided to use mathematical modelling to better understand the internal mechanisms which regulated this process. In this way
they identified certain interactions in the signalling pathways that brought to light a number of contradictions and showed that a key step was missing in their model. As Milán explains: “Thanks to this computer simulation we have found a new genetic function that ensures the stability of the system and has enabled us to test its robustness. This study shows that modelling is a highly useful tool
for describing in silico new properties of a biological system and being able to corroborate them subsequently in vivo”.
In this regard, Buceta, who leads the SiMBioSys group, dedicated to modelling biological processes, explains that “the advantage of these modelling techniques is that they can simulate genetic and cell interactions as a set of mathematical equations and, therefore, to determine the feasibility of a biological mechanism”. In order to study the
stability of the system they conducted around 45,000 different in silico experiments, introducing variations in twenty parameters. The results have enabled them to identify the most important system parameters and showed that the biological mechanism maintained its functionality in 91% of the cases analyzed. According to Milán and Buceta “this study confirms the hypothesis that if this gene
network has been maintained across evolution in both vertebrates and insects, it is precisely because it is highly stable and robust”.
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.