Cosmic Imagery

18. Take It to the Limit – Koch’s Snowflake, Sierpinski’s Carpet, and Menger’s Sponge

Also by John D. Barrow

I can’t think of a single Russian novel in which one of the characters goes to a picture gallery

PREFACE

‘What is the use of a book,’ thought Alice, ‘without pictures or conversations?’

Lewis Carroll

BOOKS, ESPECIALLY BOOKS on scientific topics, generally use pictures to illustrate what they have to say. Pictures save words. They change the pace, alter the style, and make things more memorable. They are something between a thing and a thought.

This book is not intended to be like that. Its words were wrapped around the pictures and the parts they played in making a lasting and vivid contribution to our scientific understanding of the Universe. Sometimes these images recorded information in a new and impressive way; sometimes they took advantage of new ways of doing or seeing things; and at other times they simply told a story for which words alone were not enough.

Yet this is far from being a ‘picture book’. The images each carry a story that is important, unusual, or simply untold. Taken together they create a wide-ranging picture of scientific progress in which there is time for history and space for geography.

The motivation for such a book grew partly out of sociological and technical changes within science itself. In just a few years, the presentation of science at all levels, from technical seminars for fellow experts to popular expositions for the general public, has become extremely visual. The ubiquity of PowerPoint, web-streamed video, digital photography, and artificial computer simulation has meant that images dominate science in a way that would have been technically and financially impossible just 20 years ago. There is a visual culture in science and it is rapidly changing.

Visuality penetrated the practice of science just as deeply as it fashioned its presentation. Small desktop computers revolutionised research and enabled complex and chaotic behaviours to be studied visually for the first time by single individuals and small research groups armed with nothing more than an inexpensive off-the-shelf box of silicon. Small science became bigger. The results of its new forms of experimental mathematics were dramatically visual and started a trend towards the investigation of emergent complexity by means of direct simulation. ‘Publication’ no longer meant only a paper on paper.

We have witnessd a revolution in the history of science. Not the sort of revolution that philosophers of science once believed in – they don’t happen any more – but a revolution brought about by new tools, different ways of seeing, and novel ways of understanding. Nothing old needed to be overthrown to make way for the new.

The future of science will be increasingly dominated by artificial images and simulations. It will be harder for iconic images to last in the face of ever-greater technical facility. So, now is an interesting time to look backwards as well as forwards. I hope that the pictures chosen here will focus attention on the important role they played in facilitating mental pictures and guiding the way science and mathematics developed our understanding of Nature and Nature’s laws.

Unfortunately, there are some special forms of complexity where pictures actually make matters worse, and the writing of this book gradually revealed itself to be one of them. Fortunately, I was helped by many people along the way who worked tirelessly to locate pictures, ‘firsts’, high-quality images, and copyright holders. Will Sulkin, Jörg Hensgen and Drummond Moir at The Bodley Head, Random House, played the major role in sustaining the project and transforming it from black-and-white type into the volume you are now holding. Our children, although no longer children, have maintained an unexpected interest in the final product, perhaps suspecting that there will be an accompanying video game. Elizabeth has learnt that these projects do have an end, and is especially patient on hearing continually that it is nigh. Her vital support in so many ways enabled it all to get done without too many other things remaining undone.

A large number of friends and colleagues helped. For their assistance with discussions, text, pictures, and sources, I would especially like to thank Sarah Airey, Mark Bailey, June Barrow-Green, Nadine Bazar, Alan Beardon, Richard Bright, Rosa Caballero, Alan Chapman, Pamela Contractor, Jim Council, Carl Djerassi, Richard Eden, Kari Enqvist, Gary Evans, Patricia Fara, Ken Ford, Marianne Freiberger, Sandy Geis, Gary Gibbons, Owen Gingerich, Sheldon Glashow, Edward Grant, Peter Hingley, Sharon Holgate, Michael Hoskin, Martin Kemp, Rob Kennicutt, Paul Langacker, Imre Leader, Raimo Lehti, Nick Mee, Simon Conway Morris, Andrew Murray, Dimitri Nanopoulos, Chris Pritchard, Helen Quigg, Stuart Raby, Martin Rees, Simon Rhodes, Adrian Rice, Graham Ross, Martin Rudnick, Chris Stringer, Rose Taylor, Frank Tipler, John Turner, Steven Weinberg, John A. Wheeler, Denys Wilkinson, Robin Wilson, Tracey Winwood and Alison Wright. All of them answered questions, made suggestions, or provided information or images with helpful enthusiasm.

Cosmic Imagery

Key Images in the History of Science

John D. Barrow

The Globular Star Cluster NGC 6397, one of the closest to Earth, 8,500 light years away.

Leonardo da Vinci’s anatomical drawings annotated with ‘mirror’ writing, c.1510.

The number of scientists per million of population vs percentage of Gross National Product (GNP) spent on Research and Development for 2005, produced by the World Bank.

MIDNIGHT’S CHILDREN

THE CONSTELLATIONS

Lisa: Remember, Dad, the handle of the Big Dipper points to the North Star.

Homer: That’s nice, Lisa, but we’re not in astronomy class. We’re in the woods.

The Simpsons

ONCE THE NIGHT sky was dark for everyone, everywhere. There was no artificial light, and the Moon and the stars were visible to the naked eye with a clarity that is no longer possible in modern cities. The stars were also comfortingly familiar: their positions recognised and relied upon for navigation over land and sea; their patterns a portent of disasters; their regularity and predictability the seed of human faith in a Universe that was lawful and regular rather than the plaything of temperamental deities bent upon vengeance and never-ending internecine battles. The stars were important.

The most persistent and vivid picture of the star-spangled sky has remained the map of the constellations. The stars were grouped together into collections that suggested the shapes of animals or everyday objects, perhaps to enshrine some religious or mythological association between those things and their position on the sky, or simply as an aide-memoire for reading the sky. Their slow and steady progress across the darkness, night after night, as the Moon waxed and waned, and the Earth undertook its annual orbit around the Sun, allowed time to be measured in new ways, and provided mariners with a means to navigate after nightfall. If you are travelling on land and night falls, then you can stop and wait for daylight; at sea that possibility is not always open to you.

The slowly evolving map of the constellations has played a multifaceted part in human history. It has fuelled superstition, furthered scientific astronomy, aided navigation, and created a sense of oneness with the Universe. The night sky is the oldest shared human experience. Its re-creation in pictures and illuminated manuscripts has preserved and elevated that experience in many cultures and deservedly finds a place in any gallery of great scientific images.

The annual path of the Sun, viewed from our terrestrial perspective, traces out on the celestial sphere a great circle on the sky. In ancient times this was divided into twelve signs, or ‘houses’, of the zodiac by the twelve constellations through which the Sun passed in sequence on its (apparent) annual journey around the Earth.⁴ These twelve signs are still those used credulously today in the astrology columns of many magazines and newspapers around the world. Actually, the signs of the zodiac (which means literally ‘circle of animals’) differ from the constellations of the zodiac, even though they share similar names. The constellations are groups of adjacent stars that formed some discernible and suggestive pattern. The signs of the zodiac,⁵ by contrast, consist of twelve equal zones of 30 degrees in length, or one hour on a clock face, giving a total of an entire circle of 360 degrees around the sky. Conventionally, the constellations are each taken to be 18 degrees wide in extent on the sky. At first the signs and their synonymous constellations were closely related, but gradually more and more ancient constellations were named and they soon greatly outnumbered the signs. Since the signs were only used for astrological purposes they could remain twelve in number, but the constellations were crucial for navigation and so navigators in different parts of the world needed different markers and lines in the sky, hence the continual additions to the menagerie of constellations to ensure adequate sky coverage. Most people still know their star sign and astrology is still peddled in some quarters as a way of predicting human personality and behaviour by means of the character traits traditionally associated with individuals born under a particular star sign.

Another fascinating feature of the oldest constellation maps has enabled astronomers to speculate about the place and the time of their original creation. When the Earth rotates it wobbles slightly, just like a precessing top, so that its axis of rotation (currently almost, but not quite, the same as the axis through the North and South magnetic Poles) does not always point in the same direction in the sky but traces a circle that takes about 26,000 years to complete. At present, our northern rotational axis points conveniently towards a star that we have dubbed the ‘Pole Star’, or ‘Polaris’, but far in the past or the future the celestial North Pole would have pointed, or will point, in a different direction, either at another star or at no star at all. For example, in 3000 BC the Pole Star would have been Alpha Draconis, but when Shakespeare has Julius Caesar say he is ‘constant as the northern star’,⁶ this is a complete anachronism: there would have been no northern star in Caesar’s day.

This precession of the celestial North Pole means that the sky looks different in significant ways to observers located at different latitudes on the Earth and at different times in history. Most interesting of all, an ancient astronomer observing from a latitude of, say, L degrees north would have been unable to see a disc of the sky centred on the south celestial pole and spanning an angle of 2L degrees on the sky. By looking at maps of the ancient constellations, several nineteenth-and twentieth-century astronomers have claimed to locate the latitude of the earliest known constellation mappers close to 35 degrees north from the angular extent of the empty zone in their maps of the southern sky.

This 35-degree line of latitude runs through the Mediterranean Sea, intersecting the Minoans, the Phoenicians (modern-day Lebanon) and the Babylonians (modern-day Iraq). Then by locating the centre of that empty zone it is possible to extrapolate the history of the precession backwards to find out when the South Pole was at the centre of the empty zone. This gives an interval of time between about 1800 and 2500 BC for when the ancient constellations were laid down.⁷

The reasons for their suggestive shapes and names are lost. But if we assume that the inventors were Mediterranean navigators then many of the animal shapes make good sense, tracing the rising of stars on the sky and permitting the setting of a sailing course at night. They also took on a wider significance. Maps symbolise a human desire to understand and be in control of our surroundings. To map a territory was tantamount to possessing it. Maps of the heavens offered an ultimate reassurance that all was well in the Universe, that we were at a focal controlling point within it, and had a special part to play in its unfolding story.

Each religious tradition embraced the zodiac and the constellations in its own way. Julius Schiller produced a Christianised picture of the constellations in which the strange pagan symbols were replaced by names from the Old and New Testaments. But the greatest draughtsman and artist of all those who strove to represent the constellations was the Dutch-German mathematician and cosmologist Andreas Cellarius. His Celestial Atlas of Universal Harmony, the Atlas Coelestis seu Harmonica Macrocosmica of 1660, is one of the most beautiful books ever created. The hand-coloured engravings are the Sistine Ceiling of the map-maker’s art, combining vivid colours and exuberant figures within the geometrical constraints of a sky map of the constellations.⁸

The oldest image of the ancient constellations available to us today is one that is enshrined in stone rather than on paper and associated with a very different type of ‘atlas’. In the National Archaeological Museum of Naples, famed for its ancient Egyptian remains, is the Farnese Atlas, a second-century AD Roman statue of the bearded figure of Atlas bearing a white marble globe of the constellations on its shoulders. The statue, standing more than two metres tall, is bending on one knee and is partly covered by a cloak. The celestial globe it bears is 65 cm in diameter and is damaged only by a hole through the top that cuts through the constellations of Ursa Major and Minor. In all, forty-one constellations are shown drawn in positive relief; no single stars are shown. The equator, the two tropics, the colures,⁹ and the polar circles are shown as coordinate lines in relief around the sky on the surface. The globe is laid out with remarkable precision and the positions of defining points on the sky are accurate to about 1.5 degrees. In 2005, Bradley Schaefer¹⁰ of the University of Louisiana re-analysed the layout of the constellations shown on the Farnese globe and showed that with high probability they are an image of the long-sought lost star catalogue of Hipparchus of Rhodes, the greatest astronomer of the ancient world. One of Hipparchus’ many accomplishments, made possible by the extraordinary precision of his observations, was the discovery of the 26,000-year precession of the Earth’s rotation axis that we discussed above. By studying the locations of the constellations and the blind spots in the sky coverage alone, Schaefer dated the constellation map shown on the Farnese globe to 125 BC with an uncertainty of only about fifty-five years either way. Hipparchus created his star catalogue in 129 BC but it vanished in antiquity and has remained unknown until now except for references to it by others.¹¹ Ironically, Hipparchus’ own discovery of the precession was the key tool in dating the globe that bears an image of his map.

Yet, the constellations have created one strange mystery of history. The trick of using the Earth’s precession history in conjunction with empty regions of ancient sky maps to date and locate the creators of the knowledge those maps contain was first exploited by a little-known Swedish amateur astronomer, Carl Swartz, who in 1807 published a book¹² on the subject in Swedish and French, with a second edition in 1809. From the maps available to him, he deduced that the original constellation map-makers probably lived around 1400 BC near a latitude of 40 degrees north and he suggested the city of Baku, on the coast of Armenia, as their likely home. Subsequently, other astronomers, such as the Astronomer Royal, Edward Maunder,¹³ in 1909, and Michael Ovenden¹⁴ in 1965 (neither of whom seemed to know of Swartz’s book), narrowed the map-makers’ latitude down to around 36 degrees north and their epoch to the range 2500–1800 BC. Ovenden believed (unjustifiably in the minds of many historians)¹⁵ that the Minoans were the prime candidates because they were seafarers with an advanced culture at the target latitude who suddenly disappeared owing to a natural disaster in about 1450 BC. But he noticed a strange historical conundrum. One of the most useful records of ancient astronomical knowledge is contained in a long and detailed prose poem by Aratus of Soli,¹⁶ which is entitled the Phaenomena (The Appearances) and was published in about 270 BC. He listed forty-eight constellations and their relative positions on the sky in his poetic tribute to the great Greek astronomer and mathematician Eudoxus of Cnidus,¹⁷ who lived between 409 and 356 BC. Ancient literature talks of ‘the sphere of Eudoxus’ and it is generally believed that he possessed a celestial globe, but nothing more is known about it or about his astronomical writings and maps. Fortunately, Aratus used Eudoxus’ now-lost writings to create his poetic description of the sky and so he gives us a constellation-by-constellation guide to Eudoxus’ sky. But when Hipparchus studied the poem 150 years later he was puzzled. The sky according to Aratus and Eudoxus was not one they could ever have seen. Taking precession into account, they included constellations that were not visible to them when and where they lived, and they omitted some of the constellations that were visible. Ovenden’s analysis of the poem indicates that it describes a sky that would have been visible at latitudes between 34.5 and 37.5 degrees north at a time between about 3400 and 1800 BC – very similar to the time and place we have deduced from the ancient constellation maps as well.¹⁸

Back view, showing the equator, the ecliptic, the equinoctial colure and the two tropics. The rim of the horn of Aries lies right on the colure.

One possible conclusion to draw is that Eudoxus inherited ancient knowledge from another civilisation in another location that he didn’t know how to update – probably he didn’t realise it needed updating – because he didn’t know about precession. If he was in possession of a very ancient celestial globe, he might have reported the sky that was inscribed upon the globe rather than the sky that he saw. Was there a mysterious ancient globe from Egypt or some other Mediterranean civilisation, such as that in Babylonia?

This is a strange story but alas, in this case at least, fact does not seem to be as strange as fiction. A careful scrutiny of the evidence for a void in the southern sky of the size and location claimed by Ovenden and others before him reveals a number of serious errors¹⁹ in their analysis and large uncertainties concerning the practical visibility of stars. In an attempt to distil out the fact from the fiction, Bradley Schaefer has subjected the problem to a modern astronomical analysis,²⁰ checking all the historical information available, reviewing past analyses, and introducing a new and more reliable technique to isolate when the constellation makers might have worked. He tracks the visibility of stars in six key southern constellations Altar (Ara), Southern Crown (Corona Australis), Southern Fish (Pisces Australis), Water (Aquarius), Centaur (Centaurus), and Argo from 3000 BC onwards, and computes the most northerly latitude²¹ at which the creators of each of these constellations could have lived, at any given epoch. The results are interesting because the maximum latitude of visibility has a rather different variation with the passage of time for each of these constellations.²² Two constellations (Water and Southern Fish) become visible increasingly further north as time passes, while all the others become visible only at less and less northerly latitudes. As a result, the curves of latitude of visibility versus time of the first two have to intersect the four others. Intriguingly, we see that all the curves roughly intersect in a fairly narrow range of latitudes and epochs. If all these constellations were created by a single civilisation (rather than being invented separately over a significant period of time) then this crossover indicates when and where it would have to have been done.

The latitude limit coincidence has a spread of only about 6 degrees around 500 BC and only about 2.5 degrees around 300 BC. Schaefer concludes that his realistic treatment of the uncertainties leads to a range from 900 BC to 330 BC for the date of these six constellation makers with 30 to 34 degrees north as their likely latitude.²³ This is very different to the older estimates and is historically much easier to understand. It rules out the Minoans and the ancient Greeks, but it is a perfect fit for the Babylonians at 32.5 degrees north. This is an appealing conclusion because we already know that the Babylonians contributed about 16 constellations to the celestial picture in about 500 BC, and one of those was the Fish, which was in Schaefer’s sample of six.

Realistic latitude limits and epochs, for the makers of six distinctive constellations.

It is remarkable that the ancient picture of the constellations remains something that we not only admire for its beauty and drama but can use to discover vital facts about those who first framed the story that it tells.

EMPIRE OF THE SUN

THE COPERNICAN WORLD PICTURE

Heliocentric model, published by Nicolaus Copernicus (1473–1543) in 1543 in his book De revolutionibus orbium coelestium (On the Revolutions of the Heavenly Spheres). This Sun-centred model revolutionised astronomy, replacing the previous Earth-centred (geocentric) model. The diagram, labelled in Latin, shows concentric spheres around the Sun (centre). The outer, fixed sphere (I, the stars) surrounds rotating spheres (II–VII) for Saturn, Jupiter, Mars, Earth (and the Moon), Venus, and Mercury.

How many students does it take to change a light bulb on the campus of a Scottish university? At Edinburgh, just one – he holds the bulb and the world revolves around him.

Anonymous Scottish academic²⁴

NICOLAUS COPERNICUS IS generally regarded as a revolutionary – the scientist who dethroned humanity from a central position in the Universe. But, if he was a revolutionary at all, he was certainly a reluctant one and the reality has turned out to be more complicated and far less dramatic.²⁵ Copernicus’ great book, De revolutionibus orbium coelestium (On the Revolutions of the Celestial Spheres), was delivered to the printers in 1543, shortly before his death, and its impact was muted. Not many copies were printed and few of those ever read. Yet, in time, Copernicus’ work became the rallying point for the transformation of our view of the Universe. It began a slow war of attrition that would eventually overthrow the ancient Ptolemaic picture of a Universe with the Earth at its centre in favour of a heliocentric model that is firmly established today.²⁶ Yet, its impact on our worldview was arguably greater than that on our world model.

The advances in printing during the early sixteenth century meant that Copernicus’ illustrated book could be accurately printed with diagrams embedded in the text at the points where they are discussed. The most famous of his diagrams at the beginning of his discussion shows a simple model of the solar system with the Sun located at its centre. The outermost circle marks the boundary of the ‘immobile sphere of the fixed stars’ beyond our solar system. The other six outer circles are the spheres for the orbits of the six then-known planets. Going from the outside inwards, they denote Saturn, Jupiter, Mars, Earth (with its adjacent crescent Moon), Venus and Mercury, respectively. All follow circular tracks around the central Sun (Sol). The Moon was believed to move in a circle around the Earth.

The systems of Copernicus and Ptolemy were not the only pictures of the Universe that were on offer by the sixteenth and seventeenth centuries. The accompanying picture from Giovanni Riccioli’s Almagestum Novum (The New Almagest)²⁷ of 1651 nicely summarised the world pictures on offer to astronomers in the post-Copernican era. It shows six different models of the solar system (labelled I–VI). Model I is the Ptolemaic system with the Earth located at the centre and the Sun’s orbit around it lies outside the orbits of Mercury and Venus; Model VI is the Copernican system we have just seen illustrated by Copernicus himself. Model II is the Platonic system, where the Earth is central. The Sun and all the planets are in orbit around it but the Sun lies inside the orbits of Mercury and Venus. Model III is the so-called Egyptian system, in which Mercury and Venus revolve around the Sun, which, along with the outer planets, revolves around the Earth. Model IV is the Tychonic system (of Tycho Brahe, 1546–1601) in which the Earth is fixed at the centre and the Moon and the Sun revolve around the Earth, but all the other planets revolve around the Sun. The orbits of Mercury and Venus are therefore partly between the Earth and the Sun, while the orbits of Mars, Jupiter, and Saturn encircle both the Earth and the Sun. Model V, called the semi-Tychonic system, was invented by Giovanni Riccioli, the author of Almagestum Novum and the creator of this picture. In his model the planets Mars, Venus, and Mercury orbit the Sun which, together with Jupiter and Saturn, orbits the Earth. Riccioli wanted to distinguish Jupiter and Saturn from Mercury, Venus, and Mars because they were known to have moons like the Earth (the two moons of Mars had not yet been discovered) and so their orbits must be centred on the Earth rather than on the Sun.

Copernicus has given his name to an entire philosophy of the world. An ‘anti-Copernican’ view of anything in science is a pejorative description of a view looked upon as blinkered or biased towards a human perspective or position in some unjustified way. In cosmology the ‘Copernican principle’ is often used to add prestige to the idea that we should always assume our position in the Universe is not special – that we have a typical view of the Universe and should build our theories accordingly. Sometimes it is used as a philosophical underpinning for the assumption of a universe model that is on the average the same everywhere throughout space. While this cosmic egalitarianism is an important general lesson for scientists, we have come to appreciate that it contains pitfalls of its own. For while we have no reason to expect that our position in the Universe is special in every way, we would be equally misled were we to assume that it could not be special in any way. We now understand that life can only exist in regions of the Universe that have certain features – we could not exist at the centre of a star or in a region of the Universe where the density of matter is too low for stars to form – and at special times – we could not exist when the Universe was too young to have produced elements like carbon in the stars.²⁸

Giovanni Riccioli’s summary in 1651 of the six world pictures of the post-Copernican era, from his Almagestum Novum.

If ‘typical’ places in the Universe do not allow life to develop there then we cannot be in a typical position. This moderation of the Copernican perspective plays a crucial role in the testing of predictions in modern cosmology²⁹ and draws us back into the issue of what the Universe is like in an unexpected and un-Copernican way. By way of compensation, the development of our scientific descriptions of the Universe have become Copernican in a far deeper way. Newton’s famous laws of motion unfortunately only hold for a very special type of observer – one who does not rotate or accelerate relative to the most distant stars. If you rotate, then, contrary to Newton’s first law of motion for unaccelerated observers, you will see stars accelerating past your window even though they are acted upon by no forces. Einstein recognised and cured this problem in the way our laws of Nature were formulated. It was scandalous that we could have a description of natural laws that picked on some special collection of observers for whom, by virtue of their motion, the world looks simpler. It is okay that they should find Nature to be simpler in some respects but unacceptable that they should find Nature simpler in all respects. Einstein’s great achievement was to find a system of laws of Nature which will be seen to be the same by all observers no matter how they are moving. The true Copernican perspective lives in the realm of the unseen laws of Nature rather than in the complicated world of their outcomes where we find planets, stars, and galaxies. Copernicus’ picture did more than picture the solar system correctly: it painted a new world picture.

STARRY, STARRY NIGHT

THE WHIRLPOOL GALAXY

The Earl of Rosse’s original 1845 drawing of M51, with its counterpart, a modern NASA image, below.

Starry, starry night, paint your palette blue and grey

Don McLean

ON 13 OCTOBER 1773, Charles Messier was busy observing a comet that had appeared in the night sky that year. He was rewarded with the discovery of something much more spectacular – a pair of galaxies³⁰ with brilliant centres. This doublet became the fifty-first entry in Messier’s great catalogue of astronomical objects and is known to astronomers today by Messier’s catalogue number, M51, or by the more evocative name of the ‘Whirlpool Galaxy’.

In the spring of 1845, William Parsons, the third Earl of Rosse, began observing with his great six-foot reflecting telescope – the ‘Leviathan of Parsonstown’ at Birr Castle, in Ireland’s County Offaly. After he had put up with bad weather for a few weeks, conditions became cold and dry and he turned the world’s largest telescope towards M51. The Earl was excited by what he was the first human to see: spiral patterns of stars, seemingly swirling in great ‘spiral convolutions’ about the centre of the galaxy. This was before the availability of photographic plates and so the Earl did what all astronomers then did: he made careful drawings of his observations. These meticulous drawings, first made in April 1845, began to circulate in the scientific world and generated considerable interest when they were first shown at the meeting of the British Association for the Advancement of Science, in Cambridge, that June. And so began the study of the spiral structure of galaxies. These swirling patterns of stars are so familiar to us now, because we have seen countless pictures of beautiful spiral galaxies in magazines, that we have to make some effort to take ourselves back to the nineteenth century and appreciate the impact of these striking pictures, which resolved stars in other galaxies for the first time.³¹

Soon afterwards, at the Paris Observatory, the French astronomer Camille Flammarion (1842–1925), who had also been among the first to have observed the Whirlpool, published an extremely successful and influential book entitled L’Astronomie populaire in 1879, of which over 100,000 copies were sold. It was translated into English as Popular Astronomy in 1894 by John Ellard Gore. It was the continental Brief History of Time of its day and was widely read by educated people of all interests and persuasions. Flammarion included Rosse’s striking drawing of the double galaxy and it was thereby exposed to the whole of the French-reading world and eventually to English readers as well.

I believe that one of the readers of that book must have been the great Post-Impressionist painter Vincent Van Gogh. If you look at his most famous work, The Starry Night, with the eyes of an astronomer, there is something familiar about the sky in this small painting that now hangs in the Metropolitan Museum of Art in New York. Despite its title, the dominant impression is one of great spiral swirls of light joining two centres. No one could ever have seen the spiral pattern of stars in a galaxy unless they had looked through Rosse’s telescope or seen his drawings. The similarity with the Earl of Rosse’s drawings is remarkable and I believe that Van Gogh would have seen those drawings in the press following the publicity attracted by them, or in Flammarion’s book during the 1880s when it was big news all over France, and gained his astronomical inspiration from them.³²

We know that Van Gogh was very interested in the sky – his painting Moonrise has been precisely dated by reference to the appearance of the sky, while others, like Starry Night over the Rhone and Café Terrace, have overtly astronomical content. Some astronomers have even argued about whether the background stars at the top of The Starry Night follow closely the pattern of stars in the constellation of Aries, which was Van Gogh’s own sign of the zodiac (he was born on 30 March 1853). ‘For my part,’ Van Gogh once remarked, ‘I know nothing with any certainty but the sight of the stars makes me dream.’³³ The Starry Night was completed in Saint-Rémy, Provence, in June 1889. Just thirteen months later, driven to despair, Van Gogh shot himself.

Today we can experience the magnificence of the Whirlpool anew thanks to the resolving power of modern telescopes. Although M51 is 37 million light years away, the Spitzer Space Telescope images on the following page show the details of the spiral arms and the companion galaxy in vivid contrast. They also show one of the most important developments in twentieth-century astronomy – multi-wavelength observations. Modern telescopes on mountain tops and in space are able to observe the radiation coming from celestial objects across a wide range of wavelengths. This capability has revealed that stars and galaxies look very different in different wavebands. There is no longer a unique image of a galaxy such as M51 and its companion. Here we see, side by side, an image in optical light, quite close to the sensitivity range of the human eye,³⁴ alongside one taken in the infra-red, which preferentially ‘sees’ the clouds of gas and lanes of dust from which the stars are formed. Images taken in the radio, x-ray, ultra-violet or gamma ray wavebands would give us further pictures of the galaxy that are sensitive to other aspects of its make-up and energetics. Just as an x-ray picture of a person will look very different to an optical image taken with the digital camera on your mobile phone, so all cosmic objects have a complicated spectrum of light emission that spans a range of wavelengths.

M51 in two wavebands taken by the Spitzer Space Telescope, showing the stars (visible) and the dust (infrared) as two separate components.

Astronomers believe that the gravitational influence of the smaller companion played a vital role in creating the spectacular spiral pattern that its larger neighbour displays. The spiral arms are not solid or fixed features. They are places where the gravitational forces are largest and material gets squeezed the most. This facilitates the formation of the bright young stars that illuminate the spiral pattern. As the galaxy rotates, different material passes through these regions and illuminates the spiral pattern. It is like a traffic jam of stars. Look from the air and you will see that cars are more densely packed in a slow-moving traffic jam if a lane has been closed on a section of the motorway, but the jam is always composed of different cars. It is a density wave of cars and the cars flow through it at a different speed to the speed of the wave as a whole. The same is true in the spiral galaxy. The spiral pattern rotates at a speed that differs from that of the stars themselves as they rotate about the centre of the galaxy. In some places the speeds are the same and there is a longer and stronger gravitational encounter between different stars. This is where stars preferentially form and where there is more starlight. These are the places we notice most.

Van Gogh’s famous picture is not a scientific image; it plays no part in the study of galaxies; but over the past century it has served as the impressionistic signature of the stars, impressing itself upon the minds of scientists and art lovers as a point of contact between art and the Universe. Its author combined original astronomical observations with his innovative vision of light and reality in an enduring way that looks as fresh and exciting now as the day he finished it. And today, by virtue of the growth in telescopic and photographic techniques, the stars and galaxies he could only imagine in simple form have indeed assumed the larger significance for our place in the Universe that his painting suggests. Their part in our mental sky is as prominent as the one they played in Van Gogh’s starry night.

SO, YOU WANNA BE A STAR

THE HERTZSPRUNG–RUSSELL DIAGRAM

Modern Hertzsprung – Russell diagram showing populations of stars according to their luminosities and temperatures (in degrees Kelvin).

Man hath weaved out a net, and this net throwne upon the Heavens, and now they are his own.

John Donne

THE MOST FAMOUS diagram in astronomy was devised by the independent efforts of a Danish astronomer, Ejnar Hertzsprung (1873–1967), and an American, Henry Norris Russell (1877–1957). It was first drawn by Hertzsprung in 1911 and then by Russell later that year, using more data, and became known thereafter to astronomers as the ‘Hertzsprung–Russell diagram’, or ‘HR diagram’. Put simply, it tells the life story of stars.

Hertzsprung came from a very wealthy family. His father had wanted to be an astronomer but could not find a job after his studies finished, so he moved into the commercial world and ended up as the director of a successful insurance company. The younger Hertzsprung graduated in chemistry but, perhaps influenced by his father’s unfulfilled ambitions and his own strong interest in photography, gradually developed a strong amateur interest in astronomy. He was lucky. His family’s wealth enabled him to set up as a private scientist, needing neither salary nor position.³⁵ It was a good investment on their part. Ejnar became one of the most important astronomers of the twentieth century, producing a prodigious amount of research, even when in his nineties. He soon got a position as well. In 1908 he was made an ‘extraordinary’ professor at the Potsdam Observatory; in 1919 he became the assistant director of the Leiden Observatory, then in 1935 director, in which post he remained until his retirement ten years later.

Russell was equally successful and became the foremost American astronomer of his day.³⁶ He was the son of a church minister and graduated from Princeton before working at the Cambridge University Observatory, returning to Princeton as an instructor; he then became professor in 1911, and finally director of the Observatory in 1912. For forty-three years, beginning in 1900, he contributed an astronomical column to Scientific American. In many ways Hertzsprung and Russell had careers that appear indistinguishable to the layperson. It is rather fitting that their names are forever linked by the stars they devoted their lives to studying.

Up until the mid-nineteenth century very little was known about stars save for their positions and apparent brightnesses on the sky; only a few nearby stars had their distances from the Earth known with reasonable accuracy. Gradually, though, the application of the new technique of spectral analysis allowed astronomers to determine information about the different colours contributing to the spectrum of starlight and, by using the Doppler effect, to use any systematic shift in their wavelengths³⁷ to determine how rapidly they were moving, and in which direction, along our line of sight towards them. By the end of the century, stars had been divided into four principal groupings according to their colours – white, yellow (like the Sun), orange, and red – and it was suspected that this colour sequence might be a reflection of temperature variations. Large catalogues of data started to be accumulated, notably by Henry Draper, an accomplished New York medical professor who as a sideline became one of the most brilliant pioneers of astrophotography, and stellar astronomers found themselves in possession of a huge population of objects to make sense of by using statistical methods.

Hertzsprung and Russell both sought correlations between different properties of stars – looking for correlations is what astronomers do because they cannot carry out experiments on the Universe in the way that experimental physicists can. If you think stars get hotter the bigger they are, you search out all the stars that you can and see if there is a correlation between their temperatures and their sizes.

In 1905, Hertzsprung published a paper³⁸ in a slightly obscure journal of scientific photography where he pointed out that bright red stars must be very large, and the scarcity of large red stars must mean that they evolve very quickly through that phase of their lives, so there must be a connection between the brightness and the colour of a star. He first met Russell, his scientific twin, in 1910 while on a visit to the USA and was able to share his findings with him. In 1911, Hertzsprung finally discovered that if he plotted a graph of the apparent brightnesses of stars in the Pleiades and Hyades star clusters against their colours, then a definite correlation emerged, showing the stars getting redder in colour as they got fainter in brightness. Russell presented a similar graph (rotated by 90 degrees) for all known stars in a talk to the Royal Astronomical Society at their monthly meeting in London in 1913.³⁹

They both found that about 90 per cent of all stars lay along a narrow diagonal band in an HR diagram that is now called the ‘main sequence’. Until then, astronomers had thought that it was just as likely for a star to be hot but dim, or hot and bright, as it was to be cool and bright. Suddenly it was clear that this was not the case. There were rules of physics to be discovered that governed how stars could be. Their properties were not haphazard.

Hertzsprung’s 1905 diagram showing the relationship between stars’ luminosities and spectral types. Absolute magnitudes are plotted vertically and spectral types (revealing temperatures) are plotted horizontally.

If we look at the HR diagram it is clear that it is neither uniformly nor randomly populated with stars. Conventionally, the bottom axis runs from high temperatures on the left to low temperatures on the right, as the colours change from blue (O) to red (M). The vast majority of stars fall along the diagonal, or main-sequence band. Our Sun sits there, with a surface temperature of about 6000 degrees Kelvin, and reveals itself to be a typical hydrogen-burning star: a so-called ‘main-sequence star’. Most stars are found on the main-sequence diagonal because this is where they spend most of their lifetimes as they evolve and change, consuming their fuel by nuclear burning of hydrogen into helium in a nice steady way.

About 10 per cent of stars are giants and supergiants and do not lie on the main sequence of the HR diagram. They must have very large diameters and surface areas from which to radiate their energy in order to explain how they can be very bright even though they are comparatively cool. Down in the other corner of the diagram is a small population of ‘dwarf’ stars which must have very small sizes – many similar to the size of the Earth, yet a million times heavier –