Month: August 2005

The ouzo phase diagram. The full figure legend can be found in the corresponding journal paper.

Mathematicians at Loughborough University have turned their attention to a fascinating observation that has intrigued scientists and cocktail enthusiasts alike: the mysterious way ouzo, a popular anise-flavored liquor, turns cloudy when water is added.

The researchers’ exploration of this seemingly simple phenomenon, known as the “Ouzo Effect,” has resulted in a new mathematical model that offers insights into the spontaneous formation of microscopic droplets and how they can remain suspended in a liquid for a long time.

Revealing the math taking place in the glass could have far-reaching implications beyond the world of beverages, such as the creation of new materials.

“Ouzo is essentially three things: alcohol, anise oil, and water,” explains Dr. David Sibley, an expert in mathematical modeling.

“When water is added, microscopic droplets form that are made mostly of oil, and these are a result of the anise oil separating from the alcohol-water mixture. This causes the drink to turn cloudy as the droplets scatter light.”

He continued, “This emulsification—the suspension of well-mixed oil droplets in the liquid—is something that requires a lot of energy in other systems and foods. For example, food emulsions such as mayonnaise and salad dressings require vigorous whisking to achieve a smooth and stable mixture. For ouzo, however, the emulsification happens spontaneously.

“What’s also surprising is how long these droplets, and the resulting cloudiness, remain stable in the mixture without separating, especially when compared to other food emulsions. If you’ve ever made an olive oil and balsamic vinegar dressing, you’ll notice that the two liquids start to separate after a short time, requiring more whisking to bring them back together. The ouzo-water emulsion remains stable for a much longer period.

“Understanding how and why this happens in ouzo could lead to the development of new materials, especially in fields such as in pharmaceuticals, cosmetics, and food products, where the stability and distribution of microscopic particles are critical.”

The Loughborough researchers, in collaboration with experts from the University of Edinburgh and Nottingham Trent University, have uncovered the mathematical principles that explain how the droplets and surrounding liquid—two distinct ‘phases’ within the mixture—form and can remain stable together for long periods.

By mixing alcohol, oil, and water in varying proportions, they were able to observe phase separation and measure key properties like surface tension.

They used this data and a statistical mechanical modeling method known as ‘classical density functional theory’ to develop their mathematical model.

This model has been used to calculate a phase diagram that details the stable combinations of the ouzo ingredients.

The research has been published in the journal Soft Matter and is featured on the front cover of the latest issue. The paper is titled “Experimental and theoretical bulk phase diagram and interfacial tension of ouzo.”

“You could say, what looks cloudy is now clearer,” said Professor Andrew Archer, the first author of the journal paper.

“What is also fun is that simple models like this can predict a lot—similar to recent, parallel research we did that reveals how long droplets we sneeze into the air can persist.

“As is often the case, ‘blue skies’ fundamental research can say something profound about an experience that occurs in regular life—like serving and drinking ouzo.”

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Credit of the article to be given  Meg Cox, Loughborough University

The notebooks of Sir Isaac Newton, who was famously reported to have suffered a (scientifically) earth-shaking blow to the head from an apple, are being scanned and published online by the University of Cambridge.

Newton, a Biblical numerologist when he wasn’t developing calculus or building the first reflecting telescope, founded classical mechanics with Philosophiæ Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy), which was first published in 1687. In the book that made his name, Newton set out his three laws of motion, and his theory of universal gravitation (prompted by pondering what force plummeted the fruit straight down onto his head, or so goes the apocryphal tale).

Newton studied and later held the Lucasian Chair of Mathematics at Cambridge, which was given numerous manuscripts of his in 1872 and has since bought more. The online publication has started with Newton’s mathematical works of the 1660s and more papers will become available over coming months.

A philosopher of science at Flinders University, George Couvalis, said that Newton’s gravitational experiments – which largely corrected ancient observations of gravity – were sparked by his interest in magic and magnetism. “The idea that things might naturally attract one another is an idea that he got from magical ideas. He adapted it across to mathematical theory because it was a mystical theory,” Dr Couvalis said

It was important to remember that scientists of Newton’s era did not have what we would consider a modern sceptical outlook and – with the exception of the “exceptional” Galileo Galilei – instead held a fusion of views that we would consider deeply irrational, Dr Couvalis said.

“It was certainly far more common in the 17th and 18th centuries for scientists to be interested in magical beliefs and alchemical beliefs and religious beliefs. Johannes Kepler, for example, had all kinds of strange views about the music of the spheres, Copernicus had strange views about the sacredness of the sun, and Newton famously had views about the mysterious numerical meanings of Biblical passages and about alchemical material,” Dr Couvalis said.

Scientists of the period saw their work touching on many illogical and occult fields of interest, including Robert Boyle, a founder of modern chemistry, who had “an interest in doing experimental research on magical mirrors, which to us would sound bizarre but at the time it was thought to be a possibility,” said Dr Couvalis, who added that Boyle pulled back from some experiments for religious reasons. “He thought it might get him in touch with demons.”

Demonology may have fallen out of favour amongst scientists, but “the view that we’re getting everything right would be a serious mistake,” Dr Couvalis said. “To some degree science is always in the sway of the time it’s in; this is now the standard view of philosophers and historians.”

“Newton’s mechanics is in certain respects pretty much right, but in other respects it was shown by Einstein and others to be wildly wrong. By about 1900 we had people saying to their graduate students ‘You should give up physics because it’s all been done,’ but Einstein managed to show that it was wildly wrong in certain respects,” Dr Couvalis said.

The ideal of the scientific method is never met, and our beliefs and discoveries will likely on day be seen as flawed but perhaps useful stepping stones in the continuum of science, Dr Couvalis said. “People make mistakes, people have a lot of trouble leaving assumptions behind, and our tests are never rigorous enough to be absolutely certain that we’re getting things right. Future experimental studies and the sheer empirical facts will show us to be wrong in many ways that we can’t anticipate.”

“We work with what we have because we just don’t know anything better at the moment. It might turn out that Einstein’s special and general theories of relativity are wrong in some deep-seated way. It might turn out that some of our theories of the universe are wrong. It’s starting to look in biology as if neo-Darwinism isn’t completely right, so where will that go – I don’t know. Research will determine the direction. That doesn’t mean that we’re going to go back to being creationists – that view has been thoroughly debunked. Imre Lakatos wrote in the 1970s there are no good scientific theories, there’s only the best rotten theory we have.”

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Credit of the article given to Matthew Thompson, The Conversation

Children do better at math when music is a key part of their lessons, an analysis of almost 50 years of research on the topic has revealed.

It is thought that music can make math more enjoyable, keep students engaged and help many ease fear or anxiety they have about math. Motivation may be increased and pupils may appreciate math more, the peer-reviewed article in Educational Studies details.

Techniques for integrating music into math lessons range from clapping to pieces with different rhythms when learning numbers and fractions, to using math to design musical instruments.

Previous research has shown that children who are better at music also do better at math. But whether teaching music to youngsters actually improves their math has been less clear.

To find out more, Turkish researcher Dr. Ayça Akın, from the Department of Software Engineering, Antalya Belek University, searched academic databases for research on the topic published between 1975 and 2022.

She then combined the results of 55 studies from around the world, involving almost 78,000 young people from kindergarten pupils to university students, to come up with an answer.

Three types of musical intervention were included the meta-analysis: standardized music interventions (typical music lessons, in which children sing and listen to, and compose, music), instrumental musical interventions (lessons in which children learn how to play instruments, either individually or as part of a band) and music-math integrated interventions, in which music is integrated into math lessons.

Students took math tests before and after taking part in the intervention and the change in their scores was compared with that of youngsters who didn’t take part in an intervention.

The use of music, whether in separate lessons or as part of math classes, was associated with greater improvement in math over time.

The integrated lessons had the biggest effect, with around 73% of students who had integrated lessons doing significantly better than youngsters who didn’t have any type of musical intervention.

Some 69% of students who learned how to play instruments and 58% of students who had normal music lessons improved more than pupils with no musical intervention.

The results also indicate that music helps more with learning arithmetic than other types of math and has a bigger impact on younger pupils and those learning more basic mathematical concepts.

Dr. Akin, who carried out the research while at Turkey’s National Ministry of Education and Antalya Belek University, points out that math and music have much in common, such as the use of symbols symmetry. Both subjects also require abstract thought and quantitative reasoning.

Arithmetic may lend itself particularly well to being taught through music because core concepts, such as fractions and ratios, are also fundamental to music. For example, musical notes of different lengths can be represented as fractions and added together to create several bars of music.

Integrated lessons may be especially effective because they allow pupils to build connections between math and music and provide extra opportunities to explore, interpret and understand math.

Plus, if they are more enjoyable than traditional math lessons, any anxiety students feel about math may be eased.

Limitations of the analysis include the relatively small number of studies available for inclusion. This meant it wasn’t possible to look at the effect of factors such as gender, socio-economic status and length of musical instruction on the results.

Dr. Akin, who is now based at Antalya Belek University, concludes that while musical instruction overall has a small to moderate effect on achievement in math, integrated lessons have a large impact.

She adds, “Encouraging mathematics and music teachers to plan lessons together could help ease students’ anxiety about mathematics, while also boosting achievement.”

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Credit of the article given to Taylor & Francis