Category Archives: Mathematics

Revisiting the scientific past for new breakthroughs

A March 2, 2017 article on features a thought-provoking (and, for some of us, confirming) take on scientific progress  (Note: Links have been removed),

The idea that science isn’t a process of constant progress might make some modern scientists feel a bit twitchy. Surely we know more now than we did 100 years ago? We’ve sequenced the genome, explored space and considerably lengthened the average human lifespan. We’ve invented aircraft, computers and nuclear energy. We’ve developed theories of relativity and quantum mechanics to explain how the universe works.

However, treating the history of science as a linear story of progression doesn’t reflect wholly how ideas emerge and are adapted, forgotten, rediscovered or ignored. While we are happy with the notion that the arts can return to old ideas, for example in neoclassicism, this idea is not commonly recognised in science. Is this constraint really present in principle? Or is it more a comment on received practice or, worse, on the general ignorance of the scientific community of its own intellectual history?

For one thing, not all lines of scientific enquiry are pursued to conclusion. For example, a few years ago, historian of science Hasok Chang undertook a careful examination of notebooks from scientists working in the 19th century. He unearthed notes from experiments in electrochemistry whose results received no explanation at the time. After repeating the experiments himself, Chang showed the results still don’t have a full explanation today. These research programmes had not been completed, simply put to one side and forgotten.

A March 1, 2017 essay by Giles Gasper (Durham University), Hannah Smithson (University of Oxford) and Tom Mcleish (Durham University) for The Conversation, which originated the article, expands on the theme (Note: Links have been removed),

… looping back into forgotten scientific history might also provide an alternative, regenerative way of thinking that doesn’t rely on what has come immediately before it.

Collaborating with an international team of colleagues, we have taken this hypothesis further by bringing scientists into close contact with scientific treatises from the early 13th century. The treatises were composed by the English polymath Robert Grosseteste – who later became Bishop of Lincoln – between 1195 and 1230. They cover a wide range of topics we would recognise as key to modern physics, including sound, light, colour, comets, the planets, the origin of the cosmos and more.

We have worked with paleographers (handwriting experts) and Latinists to decipher Grosseteste’s manuscripts, and with philosophers, theologians, historians and scientists to provide intellectual interpretation and context to his work. As a result, we’ve discovered that scientific and mathematical minds today still resonate with Grosseteste’s deeply physical and structured thinking.

Our first intuition and hope was that the scientists might bring a new analytic perspective to these very technical texts. And so it proved: the deep mathematical structure of a small treatise on colour, the De colore, was shown to describe what we would now call a three-dimensional abstract co-ordinate space for colour.

But more was true. During the examination of each treatise, at some point one of the group would say: “Did anyone ever try doing …?” or “What would happen if we followed through with this calculation, supposing he meant …”. Responding to this thinker from eight centuries ago has, to our delight and surprise, inspired new scientific work of a rather fresh cut. It isn’t connected in a linear way to current research programmes, but sheds light on them from new directions.

I encourage you to read the essay in its entirety.

The mathematics of Disney’s ‘Moana’

The hit Disney movie “Moana” features stunning visual effects, including the animation of water to such a degree that it becomes a distinct character in the film. Courtesy of Walt Disney Animation Studios

Few people think to marvel over the mathematics when watching an animated feature but without mathematicians, the artists would not be able to achieve their artistic goals as a Jan. 4, 2017 news item on makes clear (Note: A link has been removed),

UCLA [University of California at Los Angeles] mathematics professor Joseph Teran, a Walt Disney consultant on animated movies since 2007, is under no illusion that artists want lengthy mathematics lessons, but many of them realize that the success of animated movies often depends on advanced mathematics.

“In general, the animators and artists at the studios want as little to do with mathematics and physics as possible, but the demands for realism in animated movies are so high,” Teran said. “Things are going to look fake if you don’t at least start with the correct physics and mathematics for many materials, such as water and snow. If the physics and mathematics are not simulated accurately, it will be very glaring that something is wrong with the animation of the material.”

Teran and his research team have helped infuse realism into several Disney movies, including “Frozen,” where they used science to animate snow scenes. Most recently, they applied their knowledge of math, physics and computer science to enliven the new 3-D computer-animated hit, “Moana,” a tale about an adventurous teenage girl who is drawn to the ocean and is inspired to leave the safety of her island on a daring journey to save her people.

A Jan. 3, 2017 UCLA news release, which originated the news item, explains in further nontechnical detail,

Alexey Stomakhin, a former UCLA doctoral student of Teran’s and Andrea Bertozzi’s, played an important role in the making of “Moana.” After earning his Ph.D. in applied mathematics in 2013, he became a senior software engineer at Walt Disney Animation Studios. Working with Disney’s effects artists, technical directors and software developers, Stomakhin led the development of the code that was used to simulate the movement of water in “Moana,” enabling it to play a role as one of the characters in the film.

“The increased demand for realism and complexity in animated movies makes it preferable to get assistance from computers; this means we have to simulate the movement of the ocean surface and how the water splashes, for example, to make it look believable,” Stomakhin explained. “There is a lot of mathematics, physics and computer science under the hood. That’s what we do.”

“Moana” has been praised for its stunning visual effects in words the mathematicians love hearing. “Everything in the movie looks almost real, so the movement of the water has to look real too, and it does,” Teran said. “’Moana’ has the best water effects I’ve ever seen, by far.”

Stomakhin said his job is fun and “super-interesting, especially when we cheat physics and step beyond physics. It’s almost like building your own universe with your own laws of physics and trying to simulate that universe.

“Disney movies are about magic, so magical things happen which do not exist in the real world,” said the software engineer. “It’s our job to add some extra forces and other tricks to help create those effects. If you have an understanding of how the real physical laws work, you can push parameters beyond physical limits and change equations slightly; we can predict the consequences of that.”

To make animated movies these days, movie studios need to solve, or nearly solve, partial differential equations. Stomakhin, Teran and their colleagues build the code that solves the partial differential equations. More accurately, they write algorithms that closely approximate the partial differential equations because they cannot be solved perfectly. “We try to come up with new algorithms that have the highest-quality metrics in all possible categories, including preserving angular momentum perfectly and preserving energy perfectly. Many algorithms don’t have these properties,” Teran said.

Stomakhin was also involved in creating the ocean’s crashing waves that have to break at a certain place and time. That task required him to get creative with physics and use other tricks. “You don’t allow physics to completely guide it,” he said.  “You allow the wave to break only when it needs to break.”

Depicting boats on waves posed additional challenges for the scientists.

“It’s easy to simulate a boat traveling through a static lake, but a boat on waves is much more challenging to simulate,” Stomakhin said. “We simulated the fluid around the boat; the challenge was to blend that fluid with the rest of the ocean. It can’t look like the boat is splashing in a little swimming pool — the blend needs to be seamless.”

Stomakhin spent more than a year developing the code and understanding the physics that allowed him to achieve this effect.

“It’s nice to see the great visual effect, something you couldn’t have achieved if you hadn’t designed the algorithm to solve physics accurately,” said Teran, who has taught an undergraduate course on scientific computing for the visual-effects industry.

While Teran loves spectacular visual effects, he said the research has many other scientific applications as well. It could be used to simulate plasmas, simulate 3-D printing or for surgical simulation, for example. Teran is using a related algorithm to build virtual livers to substitute for the animal livers that surgeons train on. He is also using the algorithm to study traumatic leg injuries.

Teran describes the work with Disney as “bread-and-butter, high-performance computing for simulating materials, as mechanical engineers and physicists at national laboratories would. Simulating water for a movie is not so different, but there are, of course, small tweaks to make the water visually compelling. We don’t have a separate branch of research for computer graphics. We create new algorithms that work for simulating wide ranges of materials.”

Teran, Stomakhin and three other applied mathematicians — Chenfanfu Jiang, Craig Schroeder and Andrew Selle — also developed a state-of-the-art simulation method for fluids in graphics, called APIC, based on months of calculations. It allows for better realism and stunning visual results. Jiang is a UCLA postdoctoral scholar in Teran’s laboratory, who won a 2015 UCLA best dissertation prize.  Schroeder is a former UCLA postdoctoral scholar who worked with Teran and is now at UC Riverside. Selle, who worked at Walt Disney Animation Studios, is now at Google.

Their newest version of APIC has been accepted for publication by the peer-reviewed Journal of Computational Physics.

“Alexey is using ideas from high-performance computing to make movies,” Teran said, “and we are contributing to the scientific community by improving the algorithm.”

Unfortunately, the paper does not seem to have been published early online so I cannot offer a link.

Final comment, it would have been interesting to have had a comment from one of the film’s artists or animators included in the article but it may not have been possible due to time or space constraints.

Maths gallery at the UK’s Science Museum takes flight

Mathematics: The Winton Gallery at the Science Museum, Zaha Hadid Architects’ only permanent public museum exhibition design. London. Photograph: Nicholas Guttridge/NIck Guttridge

This exhibition looks great in the picture, I wonder what the experience is like. Alex Bellos is certainly enthusiastic in his Dec. 7, 2016 posting on the Guardian’s website,

Mathematics underlies all science, so for a science museum to be worthy of the name, maths needs to included somewhere. Yet maths, which deals mainly in abstract objects, is [a] challenge for museums, which necessarily contain physical ones. The Science Museum’s approach in its new gallery is to tell historical stories about the influence of mathematics in the real world, rather than actually focussing directly on the mathematical ideas involved. The result is a stunning gallery, with fascinating objects beautifully laid out, yet which eschews explaining any maths. (If you want to learn simple mathematical ideas, you can always head to the museum’s new interactive gallery, Wonderlab).

Much of the attention on Mathematics: The Winton Gallery – the main funders are David Harding, founder and CEO of investment firm Winton, and his wife Claudia – has been on Zaha Hadid’s design. The gallery is the first UK project by Zaha Hadid Architects to open since her unexpected death in March [2016], and the only permanent public museum exhibition she designed. Her first degree was in maths, before she turned to architecture.

Hanging from the ceiling is an aeroplane – the Handley Page ‘Gugnunc’, built in 1929 for a competition to build safe aircraft – and surrounding it is a swirly ceiling sculpture that represents the mathematical equations that describe airflow. In fact, the entire gallery follows the contours of the flow, providing the positions of the cabinets below.

The Science Museum’s previous maths gallery, which had not been updated in decades, contained about 600 objects, including cabinets crammed with geometrical objects and many examples of the same thing, such as medieval slide rules or Victorian curve-drawing machines. The new gallery has less than a quarter of that number of objects in the same space.

Every object now is in its own cabinet, and the extra space means you can walk around them from all angles, as well as making the gallery feel more manageable. Rather than being bombarded with stuff, you are given a single object to contemplate that tells part of a wider story.

In a section on “form and beauty”, there is a modern replica of a 1920s chair based on French architect’s Le Corbusier’s Modulor system of proportions, and two J W Turner sketches from his Royal Academy lectures on perspective.

The section “trade and travel” has a 3-metre long replica of the 1973 Globtik Tokyo oil tanker, then the largest ship in the world. In its massive cabinet it looks as terrifying as a Damien Hirst shark. The maths link? Because British mathematician William Froode a century before had worked out that bulbous bows were better than sharp bows at the fronts of boats and ships.

The new maths gallery is a wonderfully attractive space, full of interesting and thought-provoking objects, and a very welcome addition [geddit?] to London’s museums. Go!

A Dec. 8 (?), 2016 [London, UK] Science Museum press release is the first example I’ve seen of the funders being highlighted quite so prominently, i.e., before the press release proper,

Mathematics: The Winton Gallery designed by Zaha Hadid Architects opens at the Science Museum

  • A stunning new permanent gallery that reveals the importance of mathematics in all our lives through remarkable historical artefacts, stories and design
  • Free to visit and open daily from 8 December 2016
  • The only permanent public museum exhibition designed by Zaha Hadid anywhere in the world

Principal Funder: David and Claudia Harding
Principal Sponsor: Samsung
Major Sponsor: MathWorks

On 8 December 2016 the Science Museum will open an inspirational new mathematics gallery, designed by Zaha Hadid Architects.

Mathematics: The Winton Gallery brings together remarkable stories, historical artefacts and design to highlight the central role of mathematical practice in all our lives, and explores how mathematicians, their tools and ideas have helped build the modern world over the past four centuries.

More than 100 treasures from the Science Museum’s world-class science, technology, engineering and mathematics collections have been selected to tell powerful stories about how mathematics has shaped, and been shaped by, some of our most fundamental human concerns – from trade and travel to war, peace, life, death, form and beauty.

Curator Dr David Rooney said, ‘At its heart this gallery reveals a rich cultural story of human endeavour that has helped transform the world over the last four hundred years. Mathematical practice underpins so many aspects of our lives and work, and we hope that bringing together these remarkable stories, people and exhibits will inspire visitors to think about the role of mathematics in a new light.’

Positioned at the centre of the gallery is the Handley Page ‘Gugnunc’ aeroplane, built in 1929 for a competition to construct safe aircraft. Ground-breaking aerodynamic research influenced the wing design of this experimental aeroplane, helping to shift public opinion about the safety of flying and to secure the future of the aviation industry. This aeroplane encapsulates the gallery’s overarching theme, illustrating how mathematical practice has helped solve real-world problems and in this instance paved the way for the safe passenger flights that we rely on today.

Mathematics also defines Zaha Hadid Architects’ enlightening design for the gallery. Inspired by the Handley Page aircraft, the design is driven by equations of airflow used in the aviation industry. The layout and lines of the gallery represent the air that would have flowed around this historic aircraft in flight, from the positioning of the showcases and benches to the three-dimensional curved surfaces of the central pod structure.

Mathematics: The Winton Gallery is the first permanent public museum exhibition designed by Zaha Hadid Architects anywhere in the world. The gallery is also the first of Zaha Hadid Architects’ projects to open in the UK since Dame Zaha Hadid’s sudden death in March 2016. The late Dame Zaha first became interested in geometry while studying mathematics at university. Mathematics and geometry have a strong connection with architecture and she continued to examine these relationships throughout each of her projects; with mathematics always central to her work. As Dame Zaha said, ‘When I was growing up in Iraq, math was an everyday part of life. We would play with math problems just as we would play with pens and paper to draw – math was like sketching.’

Ian Blatchford, Director of the Science Museum Group, said, ‘We were hugely impressed by the ideas and vision of the late Dame Zaha Hadid and Patrik Schumacher when they first presented their design for the new mathematics gallery over two years ago. It was a terrible shock for us all when Dame Zaha died suddenly in March this year, but I am sure that this gallery will be a lasting tribute to this world-changing architect and provide inspiration for our millions of visitors for many years to come.’

From a beautiful 17th century Islamic astrolabe that uses ancient mathematical techniques to map the night sky, to an early example of the famous Enigma machine, designed to resist even the most advanced mathematical techniques for code breaking during the Second World War, each historic object within the gallery has an important story to tell. Archive photography and film helps to capture these stories, and introduces the wide range of people who made, used or were impacted by each mathematical device or idea.

Some instruments and objects within the gallery clearly reference their mathematical origin. Others may surprise visitors and appear rooted in other disciplines, from classical architecture to furniture design. Visitors will see a box of glass eyes used by Francis Galton in his 1884 Anthropometric Laboratory to help measure the physical characteristics of the British public and develop statistics to support a wider social and political movement he termed ‘eugenics’. On the other side of the gallery is the pioneering Wisard pattern-recognition machine built in 1981 to attempt to re-create the ‘neural networks’ of the brain. This early Artificial Intelligence machine worked, until 1995, on a variety of projects, from banknote recognition to voice analysis, and from foetal growth monitoring in hospitals to covert surveillance for the Home Office.

A richly illustrated book has been published by Scala to accompany the new gallery. Mathematics: How it Shaped Our World, written by David Rooney, expands on the themes and stories that are celebrated in the gallery itself and includes a series of newly commissioned essays written by world-leading experts in the history and modern practice of mathematics.

David Harding, Principal Funder of the gallery and Founder and CEO of Winton said, ‘Mathematics, whilst difficult for many, is incredibly useful. To those with an aptitude for it, it is also beautiful. I’m delighted that this gallery will be both useful and beautiful.’

Mathematics: The Winton Gallery is free to visit and open daily from 8 December 2016. The gallery has been made possible through an unprecedented donation from long-standing supporters of science, David and Claudia Harding. It has also received generous support from Samsung as Principal Sponsor, MathWorks as Major Sponsor, with additional support from Adrian and Jacqui Beecroft, Iain and Jane Bratchie, the Keniston-Cooper Charitable Trust, Dr Martin Schoernig, Steve Mobbs and Pauline Thomas.

After the press release, there is the most extensive list of ‘Abouts’ I’ve seen yet (Note: This includes links to the Science Museum and other agencies),

About the Science Museum
The Science Museum’s world-class collection forms an enduring record of scientific, technological and medical achievements from across the globe. Welcoming over 3 million visitors a year, the Museum aims to make sense of the science that shapes our lives, inspiring visitors with iconic objects, award-winning exhibitions and incredible stories of scientific achievement. More information can be found at

About Curator David Rooney
Mathematics: The Winton Gallery has been curated by Dr David Rooney, who was responsible for the award-winning 2012 Science Museum exhibition Codebreaker: Alan Turing’s Life and Legacy as well as developing galleries on time and navigation at the National Maritime Museum, Greenwich. David writes and speaks widely on the history of technology and engineering. His critically acclaimed first book, Ruth Belville: The Greenwich Time Lady, was described by Jonathan Meades as ‘an engrossing and eccentric slice of London history’, and by the Daily Telegraph as ‘a gem of a book’. He has recently authored Mathematics: How It Shaped Our World, to accompany the new mathematics gallery, and is currently writing a political history of traffic.

About David and Claudia Harding
David and Claudia Harding are associated with Winton, one of the world’s leading quantitative investment management firms which David founded in 1997. Winton uses mathematical and scientific methods to devise, evaluate and execute investment ideas on behalf of clients all over the world. A British-based company, Winton and David and Claudia Harding have donated to numerous scientific and mathematical causes in the UK and internationally, including Cambridge University, the Crick Institute, the Max Planck Institute, and the Science Museum. The main themes of their philanthropy have been supporting basic scientific research and the communication of scientific ideas. David and Claudia reside in London.

About Samsung’s Citizenship Programmes
Samsung is committed to help close the digital divide and skills gap in the UK. Samsung Digital Classrooms in schools, charities/non-profit organisations and cultural partners provide access to the latest technology. Samsung is also providing the training and maintenance support necessary to help make the transition and integration of the new technology as smooth as possible. Samsung also offers qualifications and training in technology for young people and teachers through its Digital Academies. These initiatives will inspire young people, staff and teachers to learn and teach in new exciting ways and to help encourage young people into careers using technology. Find out more

About MathWorks
MathWorks is the leading developer of mathematical computing software. MATLAB, the language of technical computing, is a programming environment for algorithm development, data analysis, visualisation, and numeric computation. Simulink is a graphical environment for simulation and Model-Based Design for multidomain dynamic and embedded systems. Engineers and scientists worldwide rely on these product families to accelerate the pace of discovery, innovation, and development in automotive, aerospace, electronics, financial services, biotech-pharmaceutical, and other industries. MATLAB and Simulink are also fundamental teaching and research tools in the world’s universities and learning institutions. Founded in 1984, MathWorks employs more than 3000 people in 15 countries, with headquarters in Natick, Massachusetts, USA. For additional information, visit

About Zaha Hadid Architects
Zaha Hadid founded Zaha Hadid Architects (ZHA) in 1979. Each of ZHA’s projects builds on over thirty years of exploration and research in the interrelated fields of urbanism, architecture and design. Hadid’s pioneering vision redefined architecture for the 21st century and captured imaginations across the globe. Her legacy is embedded within the DNA of the design studio she created as ZHA’s projects combine the unwavering belief in the power of invention with concepts of connectivity and fluidity.

ZHA is currently working on a diversity of projects worldwide including the new Beijing Airport Terminal Building in Daxing, China, the Sleuk Rith Institute in Phnom Penh, Cambodia and 520 West 28th Street in New York City, USA. The practice’s portfolio includes cultural, academic, sporting, residential, and transportation projects across six continents.

About Discover South Kensington
Discover South Kensington brings together the Science Museum and other leading cultural and educational organisations to promote innovation and learning. South Kensington is the home of science, arts and inspiration. Discovery is at the core of what happens here and there is so much to explore every day.

About Zaha Hadid: Early Paintings and Drawings at the Serpentine Sackler Gallery
This week an exhibition of paintings and drawings by Zaha Hadid will open at the Serpentine Galleries that will reveal her as an artist with drawing at the very heart of her work. It will include calligraphic drawings and rarely seen private notebooks, showing her complex thoughts about architecture’s forms and relationship to the world we live in. Zaha Hadid: Early Paintings and Drawings at the Serpentine Sackler Gallery is free to visit and runs from 8th December 2016 – 12th February 2017.

I found the mentions of Zaha Hadid fascinating and so I looked her up on Wikipedia, where I found this (Note: Links have been removed),

Dame Zaha Mohammad Hadid, DBE (Arabic: زها حديد‎‎ Zahā Ḥadīd; 31 October 1950 – 31 March 2016) was an Iraqi-born British architect. She was the first woman to receive the Pritzker Architecture Prize, in 2004.[1] She received the UK’s most prestigious architectural award, the Stirling Prize, in 2010 and 2011. In 2012, she was made a Dame by Elizabeth II for services to architecture, and in 2015 she became the first woman to be awarded the Royal Gold Medal from the Royal Institute of British Architects.[2]

She was dubbed by The Guardian as the ‘Queen of the curve’.[3] She liberated architectural geometry[4] with the creation of highly expressive, sweeping fluid forms of multiple perspective points and fragmented geometry that evoke the chaos and flux of modern life.[5] A pioneer of parametricism, and an icon of neo-futurism, with a formidable personality, her acclaimed work and ground-breaking forms include the aquatic centre for the London 2012 Olympics, the Broad Art Museum in the US, and the Guangzhou Opera House in China.[6] At the time of her death in 2016, Zaha Hadid Architects in London was the fastest growing British architectural firm.[7] Many of her designs are to be released posthumously, ranging in variation from the 2017 Brit Awards statuette to a 2022 FIFA World Cup stadium.[8][9]

Dubbed ‘Queen of the curve’, Hadid has a reputation as the world’s top female architect,[3][62][63][64][65] although her reputation is not without criticism. She is considered an architect of unconventional thinking, whose buildings are organic, dynamic and sculptural.[66][67] Stanton and others also compliment her on her unique organic designs: “One of the main characteristics of her work is that however clearly recognizable, it can never be pigeonholed into a stylistic signature. Digital knowledge, technology-driven mutations, shapes inspired by the organic and biological world, as well as geometrical interpretation of the landscape are constant elements of her practice. Yet, the multiplicity and variety of the combination among these facets prevent the risk of self-referential solutions and repetitions.”[68] Allison Lee Palmer considers Hadid a leader of Deconstructivism in architecture, writing that, “Almost all of Hadid’s buildings appear to melt, bend, and curve into a new architectural language that defies description. Her completed buildings span the globe and include the Jockey Club Innovation Tower on the north side of the Hong Kong Polytechnic University in Hong Kong, completed in 2013, that provides Hong Kong an entry into the world stage of cutting-edge architecture by revealing a design that dissolved traditional architecture, the so called modernist “glass box,” into a shattering of windows and melting of walls to form organic structures with halls and stairways that flow through the building, pooling open into rooms and foyers.”[69]

Hadid’s architectural language has been described by some as “famously extravagant” with many of her projects sponsored by “dictator states”. [emphasis mine] [70] Rowan Moore described Hadid’s Heydar Aliyev Center as “not so different from the colossal cultural palaces long beloved of Soviet and similar regimes”. Architect Sean Griffiths characterised Hadid’s work as “an empty vessel that sucks in whatever ideology might be in proximity to it”.[71] Art historian Maike Aden criticises in particular the foreclosure of Zaha Hadid’s architecture of the MAXXI in Rome towards the public and the urban life that undermines even the most impressive program to open the museum.[72]

If you think about it, most of the world’s great monuments were built by dictators or omnipotent rulers of one country or another. Getting the money and commitment can present an ethical/moral issue for any artist or architect who has a ‘grand design’.

Epic Scottish poetry and social network science

It’s been a while since I’ve run a social network story here and this research into a 250-year controversy piqued my interest anew. From an Oct. 20, 2016 Coventry University (UK) press release (also on EurekAlert) Note: A link has been removed,

The social networks behind one of the most famous literary controversies of all time have been uncovered using modern networks science.

Since James Macpherson published what he claimed were translations of ancient Scottish Gaelic poetry by a third-century bard named Ossian, scholars have questioned the authenticity of the works and whether they were misappropriated from Irish mythology or, as heralded at the time, authored by a Scottish equivalent to Homer.

Now, in a joint study by Coventry University, the National University of Ireland, Galway and the University of Oxford, published today in the journal Advances in Complex Systems, researchers have revealed the structures of the social networks underlying the Ossian’s works and their similarities to Irish mythology.

The researchers mapped the characters at the heart of the works and the relationships between them to compare the social networks found in the Scottish epics with classical Greek literature and Irish mythology.

The study revealed that the networks in the Scottish poems bore no resemblance to epics by Homer, but strongly resembled those in mythological stories from Ireland.

The Ossianic poems are considered to be some of the most important literary works ever to have emerged from Britain or Ireland, given their influence over the Romantic period in literature and the arts. Figures from Brahms to Wordsworth reacted enthusiastically; Napoleon took a copy on his military campaigns and US President Thomas Jefferson believed that Ossian was the greatest poet to have ever existed.

The poems launched the romantic portrayal of the Scottish Highlands which persists, in many forms, to the present day and inspired Romantic nationalism all across Europe.

Professor Ralph Kenna, a statistical physicist based at Coventry University, said:

By working together, it shows how science can open up new avenues of research in the humanities. The opposite also applies, as social structures discovered in Ossian inspire new questions in mathematics.”

Dr Justin Tonra, a digital humanities expert from the National University of Ireland, Galway said:

From a humanities point of view, while it cannot fully resolve the debate about Ossian, this scientific analysis does reveal an insightful statistical picture: close similarity to the Irish texts which Macpherson explicitly rejected, and distance from the Greek sources which he sought to emulate.”

A statistical physicist, eh? I find that specialty quite an unexpected addition to the team stretching my ideas about social networks in new directions.

Getting back to the research, the scientists have supplied this image to illustrate their work,

Caption: In the social network underlying the Ossianic epic, the 325 nodes represent characters appearing in the narratives and the 748 links represent interactions between them. Credit: Coventry University

Caption: In the social network underlying the Ossianic epic, the 325 nodes represent characters appearing in the narratives and the 748 links represent interactions between them. Credit: Coventry University

Here’s a link to and a citation for the paper,

A networks-science investigation into the epic poems of Ossian by Joseph Yose, Ralph Kenna, Pádraig MacCarron, Thierry Platini, Justin Tonra.  Complex Syst. DOI: Published: 21 October 2016

This paper is behind a paywall.

Complex networks to provide ‘grand unified theory’

Trying to mesh classical physics and quantum physics together in one theory which accounts for behaviour on the macro and quantum scales has occupied scientists for decades and it seems that mathematicians have discovered a clue so solving the mystery. A Sept. 13, 2015 news item on Nanotechnology Now describes the findings,

Mathematicians investigating one of science’s great questions — how to unite the physics of the very big with that of the very small — have discovered that when the understanding of complex networks such as the brain or the Internet is applied to geometry the results match up with quantum behavior.

A Sept. 9, 2015 Queen Mary University of London press release, which originated the news item, describes the collaboration between Queen Mary and Karlsruhe Institute of Technology mathematicians,

The findings, published today (Thursday) in Scientific Reports, by researchers from Queen Mary University of London and Karlsruhe Institute of Technology, could explain one of the great problems in modern physics.

Currently ideas of gravity, developed by Einstein and Newton, explain how physics operates on a very large scale, but do not work at the sub-atomic level. Conversely, quantum mechanics works on the very small scale but does not explain the interactions of larger objects like stars. Scientists are looking for a so called ‘grand unified theory’ that joins the two, known as quantum gravity.

Several models have been proposed for how different quantum spaces are linked but most assume that the links between quantum spaces are fairly uniform, with little deviation from the average number of links between each space. The new model, which applies ideas from the theory of complex networks, has found that some quantum spaces might actually include hubs, i.e. nodes with significantly more links than others, like a particularly popular Facebook user.

Calculations run with this model show that these spaces are described by well-known quantum Fermi-Dirac, and Bose-Einstein statistics, used in quantum mechanics, indicating that they could be useful to physicists working on quantum gravity.

Dr Ginestra Bianconi, from Queen Mary University of London, and lead author of the paper, said:

“We hope that by applying our understanding of complex networks to one of the fundamental questions in physics we might be able to help explain how discrete quantum spaces emerge.

“What we can see is that space-time at the quantum-scale might be networked in a very similar way to things we are starting to understand very well like biological networks in cells, our brains and online social networks.”

Here’s a link to and a citation for the paper,

Complex Quantum Network Manifolds in Dimension d > 2 are Scale-Free by Ginestra Bianconi & Christoph Rahmede. Scientific Reports 5, Article number: 13979 (2015) doi:10.1038/srep13979 Published online: 10 September 2015

This is an open access paper.

Michelangelo, clinical anatomy, mathematics, the Golden Ratio, and a myth

I would have thought an article about Michelangelo, mathematics, and the Golden Ratio would be in a journal dedicated to the arts or mathematics or possibly both. Not even my tenth guess would  have been Clinical Anatomy. As for the myth, not everyone subscribes to the Golden Ratio theory of beauty.

A July 20, 2015 Wiley Periodicals press release (also on EurekAlert) announces the publication of the research,

New research provides mathematical evidence that Michelangelo used the Golden Ratio of 1.6 when painting The Creation of Adam on the ceiling of the Sistine Chapel. The Golden Ratio is found when you divide a line into two parts so that the longer part divided by the smaller part is equal to the whole length divided by the longer part.

The Golden Ratio has been linked with greater structural efficiency and has puzzled scientists for centuries due to its frequent occurrence in nature–for example in snail shells and flower petals. The Golden Ratio can also be found in a variety of works by architects and designers, in famous musical compositions, and in the creations of many artists.

The findings suggest that the beauty and harmony found in the works of Michelangelo may not be based solely on his anatomical knowledge. He likely knew that anatomical structures incorporating the Golden Ratio offer greater structural efficiency and, therefore, he used it to enhance the aesthetic quality of his works.

“We believe that this discovery will bring a new dimension to the great work of Michelangelo,” said Dr. Deivis de Campos, author of the Clinical Anatomy study.

Here’s a link to and a citation for the paper,

More than a neuroanatomical representation in The Creation of Adam by Michelangelo Buonarroti, a representation of the Golden Ratio by Deivis De Campos, Tais Malysz,  João Antonio Bonatto-Costa, Geraldo Pereira Jotz, Lino Pinto De Oliveira Junior, and Andrea Oxley da Rocha. Clinical Anatomy DOI: 10.1002/ca.22580 Article first published online: 17 JUL 2015

© 2015 Wiley Periodicals, Inc.

This paper is open access.

Golden Ratio myth

One final comment, it seems not everyone is convinced that the Golden Ratio plays an important role in design, art, and architecture according to an April 13, 2015 article by John Brownlee for Fast Company titled: The Golden Ratio: Design’s Biggest Myth,

In the world of art, architecture, and design, the golden ratio has earned a tremendous reputation. Greats like Le Corbusier and Salvador Dalí have used the number in their work. The Parthenon, the Pyramids at Giza, the paintings of Michelangelo, the Mona Lisa, even the Apple logo are all said to incorporate it.

It’s bullshit. The golden ratio’s aesthetic bona fides are an urban legend, a myth, a design unicorn. Many designers don’t use it, and if they do, they vastly discount its importance. There’s also no science to really back it up. Those who believe the golden ratio is the hidden math behind beauty are falling for a 150-year-old scam.

Fascinating, non?

April 2015 (US) National Math festival; inside story on math tournaments; US tv programme: The Great Math Mystery; and the SET Award (tech women in the movies and on tv)

I have three math items for this posting and one women in technology item, here they are in an almost date order.


A British movie titled X+Y provides a fictionalized view of a team member on the British squad competing in an International Mathematics Olympiad.The Guardian’s science blog network hosted a March 11, 2015 review by Adam P. Goucher who also provides an insider’s view (Note: Links have been removed),

As a competition it is brutal and intense.

I speak from experience; I was in the UK team in 2011.

So it was with great expectation that I went to see X+Y, a star-studded British film about the travails of a British IMO hopeful who is struggling against the challenges of romance, Asperger’s and really tough maths.

Obviously, there were a few oversimplifications and departures from reality necessary for a coherent storyline. There were other problems too, but we’ll get to them later.

In order to get chosen for the UK IMO team, you must sit the first round test of the British Mathematical Olympiad (BMO1). About 1200 candidates take this test around the country.

I sat BMO1 on a cold December day at my sixth form, Netherthorpe School in Chesterfield. Apart from the invigilator and me, the room was completely empty, although the surroundings became irrelevant as soon as I was captivated by the problems. The test comprises six questions over the course of three and a half hours. As is the case with all Olympiad problems, there are often many distinct ways to solve them, and correct complete solutions are maximally rewarded irrespective of the elegance or complexity of the proof.

The highest twenty scorers are invited to another training camp at Trinity College, Cambridge, and the top six are selected to represent the UK at an annual competition in Romania.

In Romania, there was much maths, but we also enjoyed a snowball fight against the Italian delegation and sampled the delights of Romanian rum-endowed chocolate. Since I was teetotal at this point in time, the rum content was sufficient to alter my perception in such a way that I decided to attack a problem using Cartesian coordinates (considered by many to be barbaric and masochistic). Luckily my recklessness paid off, enabling me to scrape a much-coveted gold medal by the narrowest of margins.

The connection between the UK and Eastern Europe is rather complicated to explain, being intimately entangled with the history of the IMO. The inaugural Olympiad was held in Romania in 1959, with the competition being only open to countries under the Soviet bloc. A Hungarian mathematician, Béla Bollobás, competed in the first three Olympiads, seizing a perfect score on the third. After his PhD, Bollobás moved to Trinity College, Cambridge, to continue his research, where he fertilised Cambridge with his contributions in probabilistic and extremal combinatorics (becoming a Fellow of the Royal Society in the process). Consequently, there is a close relationship between Hungarian and Cantabrigian mathematics.

Rafe Spall’s character was very convincing, and his eccentricities injected some much-needed humour into the film. Similarly, Asa Butterfield’s portrayal of a “typical mathmo” was realistic. On the other hand, certain characters such as Richard (the team leader) were unnatural and exaggerated. In particular, I was disappointed that all of the competitors were portrayed as being borderline-autistic, when in reality there is a much more diverse mixture of individuals.

X+Y is also a love story, and one based on a true story covered in Morgan Matthews’ earlier work, the documentary Beautiful Young Minds. This followed the 2006 IMO, in China, where one of the members of the UK team fell in love and married the receptionist of the hotel the team were staying at. They have since separated, although his enamourment with China persisted – he switched from studying Mathematics to Chinese Studies.

It is common for relationships to develop during maths Olympiads. Indeed after a member of our team enjoyed a ménage-a-trois at an IMO in the 1980s, the committee increased the security and prohibited boys and girls from entering each others’ rooms.

The film was given a general release March 13, 2015 in the UK and is on the festival circuit elsewhere. Whether or not you can get to see the film, I recommend Goucher’s engaging review/memoir.

The Great Math Mystery and the SET award for the Portrayal of a Female in Technology

David Bruggeman in a March 13, 2015 post on his Pasco Phronesis blog describes the upcoming première of a maths installment in the NOVA series presented on the US PBS (Public Broadcasting Service), Note: Links have been removed,

… PBS has announced a new math special.  Mario Livio will host a NOVA special called The Great Math Mystery, premiering April 15.  Livio is an astrophysicist, science and math writer, and fan of science/culture mashups.  The mystery of the title is whether math(s) is invented or was discovered.

You can find out more about The Great Math Mystery here.

David also mentions this,

The Entertainment Industries Council is seeking votes for its first SET Award for Portrayal of a Female in Technology. … Voting on the award is via a Google form, so you will need a Google account to participate.  The nominees appear to be most of the women playing characters with technical jobs in television programs or recent films.  They are:

  • Annedroids on Amazon
  • Arrow: “Felicity Smoak” played by Emily Bett Rickards
  • Bones: “Angela Montenegro” played by Michaela Conlin

Here’s a video describing the competition and the competitors,

More details about the competition are available in David’s March 13, 2015 post or here or here. The deadline for voting is April 6, 2015. Here’s one more link, this one’s to the SET Awards website.

(US) National Math Festival

H/t to David Bruggeman again. This time it’s a Feb. 6, 2015 post on his Pasco Phronesis blog which announces (Note: Links have been removed),

On April 18 [2015], the Smithsonian Institution will host the first National Math Festival in Washington, D.C.  It will be the culmination of a weekend of events in the city to recognize outstanding math research, educators and books.

On April 16 there will be a morning breakfast briefing on Capitol Hill to discuss mathematics education.  It will be followed by a policy seminar in the Library of Congress and an evening gala to support basic research in mathematics and science.

You can find out more about the 2015 National Math Festival here (from the homepage),

On Saturday, April 18th, experience mathematics like never before, when the first-of-its-kind National Math Festival comes to Washington, D.C. As the country’s first national festival dedicated to discovering the delight and power of mathematics, this free and public celebration will feature dozens of activities for every age—from hands-on magic and Houdini-like getaways to lectures with some of the most influential mathematicians of our time.

The National Math Festival is organized by the Mathematical Sciences Research Institute (MSRI) and the Institute for Advanced Study (IAS) in cooperation with the Smithsonian Institution.

There you have it.