Julia Dream

by Nicholas Mee on July 20, 2019

Many naturally occurring objects have a complicated appearance, and when we look closer the complexity only increases. As we zoom in we see what appear to be miniature replicas of the original object. For instance, a branch of a fir tree might resemble a scaled down version of an entire fir tree, and a broccoli floret might look like a miniature broccoli.

This is true of many organic structures including some within our own bodies, such as the arteries, veins and capillaries of the circulatory system, and the branching components of the respiratory system from our trachea to our lungs. Self-similar objects such as these are known as fractals.

Gaston Julia

It is rather surprising that the idea of fractals can be traced back to the musings of a seriously injured soldier amidst the horrors of the First World War.

That soldier was Gaston Julia who was born in French Algeria in 1893. In his teens he won a scholarship to study in Paris, but within months of completing his maths degree war broke out and he was conscripted into the French army the following day.

Early in 1915 Julia suffered a terrible wound during a German attack. According to the military report, on

January 251915, he showed complete contempt for danger. Under an extremely violent bombardment, he succeeded despite his youth in giving a real example to his men. Struck by a bullet in the middle of his face causing a terrible injury, he could no longer speak but wrote on a ticket that he would not be evacuated. He only went to the ambulance when the attack had been driven back. It was the first time this officer had come under fire.

No Man’s Land by Gregory Manchess

After a series of unsuccessful operations Julia’s injury resulted in the loss of his nose. He was left like a twentieth century counterpart to the sixteenth century Danish astronomer Tycho Brahe who lost his nose to a duelling sword. Whilst Tycho wore a brass prosthesis to hide his loss (with a gold one for special occasions), Julia wore a leather strap to conceal his disfigurement.

Gustav Herglotz and Gaston Julia

During convalescence Julia occupied himself with mathematics. Whereas Tycho investigated outer space, tracking the positions of stars and planets with greater precision than ever before, Julia investigated inner space, plotting the intricate mathematical properties of points in the plane. This involved long sequences of simple calculations, ideally suited to the number-crunching capabilities of a modern computer. But Julia’s work was published long before computers were available.

Gaston Julia with his wife and six children.

In 1917 Julia submitted his doctoral dissertation, much of which had been completed in hospital. It was published as a ground-breaking 200-page paper the following year. That year Julia married Marianne Chausson, daughter of the composer Ernest Chausson, one of the nurses who looked after him while in hospital.

Julia’s work was celebrated when published, but almost forgotten in later years as further investigation was extremely difficult without a computer.

Luckily, Julia lived long enough to see a revival of interest in his research. By the 1970s computers were producing crude low resolution images based on his work. Julia died in 1978 at the age of 85.

Google commemorated the 111th anniversary of Julia’s birth on 3 February 2004.

The illustration below was generated on my PC. It is a colour-coded representations of Julia’s ideas known as a Julia set. Julia sets have a fractal structure and are like relief maps. The colours are arbitrary, but they are determined by a mathematical property of each region of the map as deduced by the computer following Julia’s algorithm and regions sharing the same property are given the same colour.

An Example of a Julia Set.

Computer generated imagery has really taken off in recent decades. It now has many applications, especially in video games and special effects in the film industry. These effects employ sophisticated mathematical algorithms and many involve fractals.

Part of the Mandelbrot set, a close relative of the Julia sets.

Further Information

I have long been interested in the interplay of maths and the arts and the often surprising influences that pass between one and the other. Next year Oxford University Press is publishing a book I have written on the subject called: Celestial Tapestry: The Warp and Weft of Art and Mathematics.

This is a short video in which I discuss Gaston Julia’s work.

There are many more videos on The Cosmic Mystery Tour YouTube Channel. Please don’t forget to subscribe.


Sex and the Cosmos

by Nicholas Mee on June 2, 2019

Looking up at a clear night sky can be quite overwhelming. It puts the world into perspective and invites some deep reflection. Two big questions have puzzled humanity through the ages. What are the stars made of? And just how vast is the universe?

The Milky Way, with the Large and Small Magellanic Clouds to the left of the picture. Credit: ESO/Y. Beletsky.

The philosophers of classical Greece 2400 years ago offered some speculative answers. Aristotle believed the Earth was made of four elements: Earth, Air, Fire and Water, whereas the heavens, stars and planets were composed of a fifth element known as Aether or quintessence, which just means fifth element. According to Aristotle the stars were attached to the outermost sphere of the cosmos and this was just beyond the sphere of the outer planet Saturn. So the heavens were big, but not really that big.

These ideas held sway for two thousand years. The process of replacing Aristotle with something better started just over four hundred years ago, with our modern understanding of the cosmos beginning to take shape less than one hundred years ago in the 1920s. Two female astrophysicists (quite separately) played pivotal roles in finding the answers to the age old questions: What are the stars made of? And just how big is the universe? Unfortunately, you may not have heard of either of them.

Before saying a bit about their work I will say a few words about a recent controversy which might help explain why their work has been overshadowed. Towards the end of last year at a conference on gender issues in physics at CERN, the European particle physics lab, it was reported that an Italian physics professor Alessandro Strumia suggested that physics was invented by men and that women don’t have an automatic right to participate just because they want to be involved. This caused outrage and Prof. Strumia has since been dismissed. 

CERN’s Large Hadron Collider during maintenance. Credit: CERN Geneva.

In response to remarks such as those of Prof. Strumia, I would offer two points.

Firstly, women have made important contributions to physics, especially astrophysics, as I will describe, but often their contributions have not been appreciated until much later.

Secondly, comments such as Prof. Strumia’s assume there has always been a level playing field in science and the wider world. They are equivalent to an assertion such as: ‘All nineteenth century British prime ministers were men, so why do women think they should participate in politics’, which is readily countered by pointing out that women weren’t even allowed to be MPs in the nineteenth century so it was impossible for a woman to become prime minister in the nineteenth century.

Clearly, we should look at Prof Strumia’s remarks in a sociological and historical context. Women have made their contributions to physics and the other sciences, but this has been despite the obstacles that have been placed in their way, as we can see through the careers of two of the twentieth century’s most important astrophysicists. 

How Vast is the Universe?

The devices we know today as computers are named after a now obsolete occupation. Computers were people, mainly women, who were employed to perform mundane repetitive calculations. In the late nineteenth and early twentieth centuries Edward Charles Pickering recruited over 80 women to work as computers for astronomy projects at the Harvard College Observatory. 

The Harvard College Observatory computers.

Henrietta Swan Leavitt completed the Harvard degree course in June 1892 and was presented with a certificate to say that, had she been a man, she would have qualified for a B.A. degree. Leavitt was almost deaf following a childhood illness, but she was financially secure so she offered to work for free and Pickering was delighted to take her on, so she became one of his computers. She was later paid 30 cents an hour or $10 a week.

Today this all sounds rather exploitative and demeaning, but Pickering was actually quite progressive in encouraging women to be involved in such work. The project that Pickering gave to Henrietta Swan Leavitt was to analyse stars in the Magellanic Clouds as recorded on a series of photographic plates taken at the Boyden Observatory in Peru. The Large and Small Magellanic Clouds are dwarf galaxies that orbit our own Milky Way galaxy. They are visible from the southern hemisphere and were unknown to Europeans before Magellan’s circumnavigation of the globe in the sixteenth century. (They can be seen to the left of the image at the top of this post.)

Henrietta Swan Leavitt

Leavitt’s task was to study variable stars. Many stars vary in brightness over time, sometimes in a regular way and sometimes quite unpredictably. There are many reasons why this might happen. There are eclipsing variables, for instance. These are binary stars, which appear to be a single star, but are in fact two stars that orbit each other, and when one star blocks the light of the other as viewed from Earth there is a dip in brightness. Because the orbits of the stars are very regular these variations in brightness are also very regular and predictable. (There is more about eclipsing binaries here: The Gorgon’s Head.) Other types of star change in brightness quite unpredictably for a number of reasons.

Leavitt discovered a very important relationship for a type of variable star known as Cepheid variables. These are very bright stars whose luminosity varies regularly over a period of several days. You may have seen the closest Cepheid variable. It is known as Polaris – the Pole Star or North Star. It is about 430 light years away and it varies in brightness over a period of around four days. 

The Pole Star can be found by using two stars of the Plough or Big Dipper as pointers.

Cepheid variables get their name from another northern star Delta Cephei, which is about 880 light years away and varies in brightness over a period of around five days and nine hours.

When comparing stars, we cannot easily tell whether a star is very bright, but at an immense distance, or not so bright and relatively nearby. For instance, Sirius is the brightest star in the night sky, much brighter than the Pole Star, but we know today that Sirius is one of our closest stellar neighbours, just over eight and a half light years distant, whereas Polaris is fifty times further away. If these two stars were equally distant then Polaris would easily be the brighter of the two.

When Henrietta Swan Leavitt was working, over a century ago, the distance to the Small Magellanic Cloud was unknown. But she assumed that, as it consists of a dense cluster of stars, these stars must all lie at essentially the same distance from us, so any differences in their apparent brightness must reflect true differences in their luminosity. This enabled her to make an important breakthrough. She realised that the brighter a Cepheid variable the longer the period of its variation. Leavitt’s initial results were published by Pickering in 1908 in a Harvard College Observatory circular and this was followed up with a second paper in 1912.

Big deal, you might say, Henrietta Swan Leavitt found a pattern in the brightness of a fairly obscure type of star. But, as she pointed out, this might prove to be a very important pattern indeed by offering a measuring rod to the heavens. Cepheid variables are particularly bright stars, so with powerful telescopes they can be observed at great distances, and it is easy to monitor the brightness of a Cepheid variable to determine its period of variation. Once this period is known the period-luminosity relationship can be used to deduce the intrinsic brightness of the star. Then by comparing this to how bright the star appears in the sky we can determine its distance. 

So, as Leavitt suggested, the period-luminosity relationship could be used to determine a relative distance scale for the Cepheids. She referred to them as standard candles, a term that is still used today.

Leavitt’s work did indeed lead to a revolution in our understanding of the distance scales of the universe. But tragically she died of stomach cancer in 1921 at the age of 53 just too soon to see the revolution come about. In 1924 Edwin Hubble used her relationship to show that our Milky Way galaxy is just one among many galaxies. He found Cepheid variables in the Andromeda nebula and his estimates of their distance demonstrated that this nebula is in fact a separate galaxy, much more distant than any stars in our own galaxy. By the end of the decade Hubble had used Leavitt’s standard candles to show the universe contains vast numbers of galaxies and that the universe itself is expanding.

The universe contains vast numbers of galaxies. Credit: NASA/HST.

Henrietta Swan Leavitt’s discovery led to a total re-evaluation of the scale of the universe. Her discovery still forms a very important rung in the cosmic distance ladder, which is the basis for measuring the size of the cosmos. We now know it is 25,000 light years to the centre of the Milky Way galaxy. But it is 2.3 million light years to the Andromeda galaxy, which is about the same size as our own galaxy. And the Andromeda galaxy is a near neighbour. We can see galaxies that are billions of light years distant.

Henrietta Swan Leavitt never obtained a doctorate or an academic position. If she had lived a few more years, however, she probably would have been nominated for a Nobel Prize.

What are the Stars made of?

Henrietta Swan Leavitt was not alone in making important contributions to astrophysics. There are stories about a number of female astrophysicists in my new book The Cosmic Mystery Tour and the career of one of them Cecilia Payne illustrates the difficulties faced by female scientists of the following generation.

Report on Eddington’s eclipse expedition of 1919 from the London Illustrated News.

Cecilia Payne went to Cambridge University in 1919 to study botany, chemistry and physics. Soon after arriving she was transfixed by a talk given by the leading astrophysicist Arthur Eddington who had just returned from an eclipse expedition to West Africa where he tested Einstein’s brand new theory of general relativity. 

Einstein and Eddington

Cecilia Payne was so amazed by the talk that she was in a daze afterwards. A few days later she plucked up the courage to go and see Eddington and tell him she was thinking of studying astronomy. He was very supportive and encouraging, so Cecilia Payne continued her studies for the next few years, completed her course and did her exams. But she realised she could not pursue an academic career in Britain because even though women could attend lectures and do the exams at Cambridge University, which was Britain’s leading academic establishment for science and mathematics, the university did not confer degrees on women. So she couldn’t graduate with a degree. She would have to go to America to further her studies. Fortunately, she obtained a scholarship to Harvard University where she did her PhD, and this was later described as the most brilliant PhD ever in astronomy. What Cecilia Payne did in her PhD was to show that the Sun and stars are essentially huge balls of hydrogen and helium with just traces of all the other elements.

The Sun is a huge ball of hydrogen and helium. Credit: NASA.

Prior to this time astronomers assumed the Sun had a similar composition to the Earth, which implied it was composed of carbon, oxygen, calcium, aluminium, iron, all the elements that are common on Earth. And they assumed that if a ball of Earth-like material were heated to the temperature of the Sun, it would look pretty much the same as the Sun. Cecilia Payne showed that this is actually incorrect. This was a very significant breakthrough because, unless you know what stars like the Sun are made of, it isn’t possible to work out how they generate their energy. During the following decade, physicists worked out how stars generate energy by converting hydrogen into helium and this was the key to understanding why stars exist.

Cecilia Payne made important contributions to astrophysics throughout her career, but it wasn’t until 1956 that she obtained a full professorship at Harvard, so even in America she wasn’t really acknowledged until towards the end of her career.

Cecilia Payne

It is worth noting that although Cambridge University has conferred degrees on women since 1948 this hasn’t automatically made it a level playing field. All the colleges were single sex and just two out of about thirty colleges were women’s colleges and the men’s colleges were all the old historical colleges, the ones with long academic traditions. It was only in the 1980s that most colleges became mixed. And it takes a long time to change a culture, so it’s only in very recent times that we are even approaching a level playing field for women in science in the UK.

Trinity College, Cambridge, founded by Henry VIII in 1546. Women were first admitted in 1978. Credit: Wikimedia – Cmglee.

So why should we care about the lack of recognition of these two female astrophysicists when it all happened around a century ago?

It is easy to argue that everything is different now. But Prof Strumia’s remarks show that there is, perhaps, still some way to go. Science is a collaborative endeavour, but it is also very competitive. There are only so many university places and there is only so much research funding. It is easy for a male scientist to intimidate a more able female scientist by pointing to the male dominance of the physical sciences. So the work of important female scientists of the past should be highlighted in order to burst this bubble. And just to be clear, the discoveries of Henrietta Swan Leavitt and Cecilia Payne were not lucky chance discoveries they were the outcome of sophisticated and very technical research – physics at its best. Their contributions have been slow to receive their deserved recognition simply because they were restricted to subordinate positions in a male-dominated academic hierarchy.

Further Information

There is much more about the deep questions of the cosmos and the research of astrophysicists such as Henrietta Swan Leavitt and Cecilia Payne in my new book: The Cosmic Mystery Tour.

This is a short video in which I discuss Cecilia Payne’s work and some of the issues raised in this article.

There are many more videos on The Cosmic Mystery Tour YouTube Channel. Please don’t forget to subscribe.


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