Computer age brings sun to Italian village in shadow of the Alps

Mountainside mirror ends centuries of winter gloom
By Elisabetta Povoledo
Published: February 6, 2007

VIGANELLA, Italy: From mid-November to early February, Viganella lives in the dark shadow of a steep mountain that blocks the sun from casting direct rays on the village, a stone’s throw from the Swiss border.

For centuries, its citizens have celebrated the sun’s return Feb. 2 with a solemn religious procession and a lively auction of local delicacies.

But this year the guest of honor never really left: Since December, a 40- square-meter, or 430-square-foot, mirror placed on a mountainside above Viganella has been deflecting the sun’s rays into the town square, bringing sunlight, of a sort, in winter.

“That had never happened since the time the world began,” said Giannino Broggio, Viganella’s deputy mayor, who deemed the occasion “historic.”

There has not exactly been a run on sunglasses, and pale complexions still predominate here, but the locals seemed pleased with their artificial sun.

“It’s not like it generated much heat,” said Paola Ghensi, a housewife. “But it did make you want to stop and chat in the square for five minutes longer, instead of bolting straight home.”

Though they profess interest in the technical details of the project, what many residents really seem to marvel at has been the intensity of the media spotlight generated by the mirror.

Viganella Mirror

“We didn’t set it up because we thought it would bring people,” said Mayor Pierfranco Midali. But the mirror became an unexpected attraction, he said, adding: “More persons have passed though Viganella in the last two years than in the past two centuries.”

There is not all that much to see. The mirror — 870 meters, or 2,900 feet, above Viganella and measuring 8 meters wide by 5 meters high — is motorized and constantly tracks the sun. Computer software tilts and turns the panels throughout the daylight hours to deflect the rays downward. But from the main square, bathed in reflected sunlight, all that is visible of the false sun is a bright glare from the slope above.

“At first no one believed it could be possible, but I was certain. I have faith in physics,” said Giacomo Bonzani, an architect and sundial designer who came up with the idea of reflecting sunlight onto the square and made the necessary astronomical calculations. The project languished for a few years until funding — about €100,000, or $130,000 — came through last year from private and public sponsors.

The mirror was designed by Emilio Barlocco, an engineer whose company specializes in using reflected sunlight to light the entrances to highway tunnels. He read about Viganella’s plight in the Turin daily La Stampa and offered his expertise and services.

Solar Mirror

Solar mirror on the hill

“Whenever you do something for the first time, you’re either a pioneer or stupid,” he said. “We hope we’re the former.”

Read complete story here.

Dream Anatomy

Body Commodification

By Karen Darricades, This Magazine

Of the more than 200 human body parts roaming the globe in Dr. Gunther von Hagens’ Body Worlds and Body Worlds 2, The Anatomical Exhibition of Real Human Bodies, only six of the 25 whole body specimens are of the female sex, despite the fact that 60 percent of the body donors have been women.

The Ontario Science Centre was the first to welcome this exhibition in Canada. The space is filled with donated bodies and organs that have undergone a plastination process of von Hagens’ invention (essentially consisting of injecting plastic into donors post-mortem), bringing to mind what one might imagine Francis Bacon’s version of a wax museum would look like. This visual pairing of the bloody horrifics and clinical examination is no doubt what has prompted some to call von Hagens Dr. Frankenstein.

Anatomy Theatre

Anatomy Theatre

When questioned on the exhibition’s lack of women, von Hagens responds by saying he “did not want to appear voyeuristic by revealing too many female bodies.” In fact, five of the female figures were added to the Body Worlds 2 exhibit in response to requests from female attendees who wished to see themselves more prominently reflected in an exhibit about the science of humanity.

La Specola

Wax Anatomical Model, La Specola, Florence

According to the Body Worlds website, “He sees himself in the tradition of Renaissance anatomists, whose works traditionally included far more masculine than feminine bodies.” That begs the question: Can women’s bodies be viewed clinically or are they always sexualized by the gaze of the viewer?

Because we’ve seen Historica’s “History by the Minute” heritage series, many Canadians are aware of the ridicule Canadian suffragettes like Dr. Emily Jennings Stowe endured at medical schools in the 1870s. But, despite the current inclusion of women as students, women still continue to be excluded from many of the visual representations that serve as tools of education. The most culturally prominent of these tools are images such as Da Vinci’s Vitruvian Man and the evolutionary chart demonstrating man’s development from ape to Homo sapiens—adorning the classroom walls and home pages of every major medical and scientific institution in the western hemisphere.

Vitruvian Man

Leonardo’s Vitruvian Man

Among the iconic images that illustrate the scientific history of humankind, women are scarcely seen. And when they are, they exist in the margins as exceptions to the rule of the male norm. “Male is what it is to be human,” observes Phoebe Gloeckner, a renowned comic book artist with a master’s degree in medical illustration from the University of Texas. “[The male] doesn’t need segregation because it’s considered the base value,” Gloeckner adds. Von Hagens’ assertion that men’s and women’s anatomies are “essentially the same” is reminiscent of the lazy and confused attitudes of his second-century predecessors, who were convinced that female reproductive organs were “lesser” or smaller versions of the male’s.

For centuries the presumption was that the vagina was an inverted interior penis and testes. In fact the fallopian tubes did not get their name until Gabriele Fallopio discovered them in the late 1500s. With the 17th century came the coining of the term “ovaries.” A 17th century engraving from Casserio’s theatrum anatomicum depicts a serene woman with an open flower in the centre of her abdomen exposing a fetus. The petals are labelled A-G revealing the order of the artful cuts of Casserio’s dissection. Vesalius’ 1543 precedent-setting atlas, De Humani Corporis Fabrica (On the Fabric of the Human Body), forms the tradition of portraying primarily masculine figures. “It is like taking the skin off of Renaissance paintings where man is the hero and woman the procreator,” says Gloeckner of the Body Worlds show.

Foetus

Casserio’s theatrum anatomicum foetus

Until its arrival in North America, the Body Worlds’ 10-year stint had only used the female form as an example of reproduction—in a separate part of the exhibit equipped with warnings for those wishing to abstain from knowing this part of human anatomy. Recently, a female figure known as The Diver was added to Body Worlds 2, demonstrating that when science turns commercial—as is the case with Body Worlds—women can use their economic power to buy themselves a place in a visual history that has always been refused to them by elitist systems of education.

Medical illustrations teeter on the brink between art and science. Diagrams use symbols to convey information and create visual explanations, but those visual explanations are rendered in ways that reveal concepts of cultural norms. Frank H. Netter’s contributions to medical illustration earned him the title of “medicine’s Michelangelo” in the New York Times. His vivid illustrations brought the concept of the living patient into the textbook. But Netter’s drawings made his subjects pop off the page in a way that made the lack of diversity in his subjects, concerning gender and race, all the more glaring. His 1989 Atlas of Human Anatomy is considered the quintessential textbook for med students and medical illustrators. The fact that the organs on display in Body Worlds come primarily from the female body donors reveals von Hagens’—and von Hagens’ perception of his public’s—difficulty in accepting the female form, in its entirety, as human.

Female Anatomy

Female Reproductive Anatomy

The Body Worlds 2 exhibition finished its five-month stay at the Ontario Science Centre on February 26 to go to the Denver Museum of Nature and Science. Body Worlds and Body Worlds 2 have been seen by over 17 million people in 22 countries over the last 10 years. How many of those viewers were women?

To see my Anatomical Art page, click here.

To see my La Specola series, click here.

To see more anatomical illustrations, check out the Dream Anatomy website here.

The fallout of global warming: 1,000 years

In stark terms, scientists confirm that climate change is ‘unequivocal’

MARTIN MITTELSTAEDT

Humans have already caused so much damage to the atmosphere that the effects of global warming will last for more than 1,000 years, according to a summary of a climate-change report being prepared by the world’s leading scientists.

Katrina Aftermath

Aftermath of Hurricane Katrina

The draft, seen by The Globe and Mail yesterday, also says evidence the world is heating up is now so strong it is “unequivocal” and predicts more frequent heat waves, droughts and rain storms, as well as more violent typhoons and hurricanes. It concludes the higher temperatures observed during the past 50 years are so dramatically different from anything in the climate record that the last half-century period was likely the hottest in at least the past 1,300 years.

Moreover, 11 of the past 12 years rank among the warmest since humans began taking accurate temperature measurements in the 1850s, a record of extremes so pronounced it is unlikely to be due to chance.

Struth, An der Sweinmund

Struth, An der Swinemünder Brucke

“Warming of the climate system is unequivocal, as is now evident from increases in global average air and ocean temperatures, melting of snow and ice, and rising sea level,” says the draft, which is being reviewed in Paris before its formal release Friday by the Intergovernmental Panel on Climate Change.

The draft says concentrations of two main greenhouse gases, carbon dioxide and methane, “far exceed” anything seen over the past 650,000 years, based on data that reconstructed the atmospheric composition of earlier times using air bubbles contained in ice cores.

Ernst, Europe After the Rain II 1940

Ernst, Europe after the Rain II 1940

The changes to the atmosphere are so large the scientists estimate that warming due to human-caused increases in greenhouse gases are at least five times larger than natural changes caused by normal alterations in output of solar energy from the sun.

Although the draft doesn’t mention Canada directly, it says average Arctic temperatures have experienced a far sharper rise than elsewhere on the planet, increasing at a rate over the past 100 years that is double the global average.

Read the full article here.

Dark materials

Nuclear scientist Joseph Rotblat campaigned against the atom bomb he had helped unleash. Is it time for today’s cyber scientists to heed his legacy?

Essay by Martin Rees
Saturday June 10, 2006
The Guardian

Joseph (Jo) Rotblat was a nuclear scientist. He helped to make the first atomic bomb. But for decades he campaigned against what he had helped unleash. Until he died last year, aged 96, he pursued this aim with the dynamism of a man half his age, inspiring others to join the cause. He was born in Poland in 1908. His family suffered great hardship in the first world war but he was exceptionally intelligent and determined, and managed to become a nuclear physicist. After the invasion of Poland, he came as as a refugee to England to work with James Chadwick at Liverpool University. He then went to Los Alamos, New Mexico, as part of the British contingent involved in the Manhattan Project to make the first atom bomb.

In his mind there was only one justification for the bomb project: to ensure that Hitler did not get one first. As soon as this ceased to be a credible risk, Jo left Los Alamos – the only scientist then to do so. He returned to England and became a professor of medical physics, an expert on the effects of radiation on human health, and a compelling and outspoken campaigner.

In 1955, he met Bertrand Russell and encouraged him to prepare a manifesto stressing the extreme gravity of the nuclear peril. He secured Einstein’s signature too; this “Russell-Einstein manifesto” was then signed by 10 other eminent scientists.

Atom Bomb

The authors claimed to be “speaking on this occasion not as members of this or that nation, continent or creed, but as human beings, members of the species Man, whose continued existence is in doubt”. This manifesto led to the initiation of thePugwash Conferences – so called after the village in Nova Scotia where the inaugural conference was held. There have been 300 meetings since then. Jo attended almost all of them.

When the achievements of these conferences were recognised by the 1995 Nobel peace prize, half the award went to the Pugwash organisation, and half to Jo Rotblat personally, as their “prime mover” and untiring inspiration. Particularly during the 1960s, the Pugwash Conferences offered crucial “back-door” contact between scientists from the US and the Soviet Union when there were few formal channels. These contacts eased the path for the partial test ban treaty of 1963, and the later anti-ballistic missile treaty.

But this catastrophic threat could be merely in abeyance. In the next 100 years, geopolitical realignments could lead to a nuclear standoff between new superpowers, which might be handled less well than the Cuba crisis was. Moreover, we are confronted by a proliferation of nuclear weapons (in North Korea and Iran for instance). There is now a growing risk of nuclear weapons going off in a localised conflict, and the Bulletin’s clock stands at seven minutes to midnight. The nuclear threat will always be with us.

But what are the promises and threats from 21st-century science? Science offers immense hope, and exciting prospects. There are genuine grounds for being a techno-optimist.

The technologies that fuel economic growth today – IT, miniaturisation and biotech – are environmentally and socially benign. They are sparing of energy and raw materials. They boost quality of life in the developing and the developed world, and have much further to go. That is surely good news. But opinion polls reveal public concern that science may be advancing too fast to be properly controlled. It is not only advancing faster than ever, it is opening up the prospects of new kinds of change.

Whatever else may have changed over preceding centuries, humans have not for thousands of years. But in this century, targeted drugs to enhance memory or change mood, genetic modification, and perhaps silicon implants into the brain, may alter human beings themselves. That is something qualitatively new in our history.

Our species could be transformed within a few centuries. And there are other disquieting prospects. Collective human actions are transforming, even ravaging, the biosphere – perhaps irreversibly – through global warming and loss of biodiversity. We have entered a new geological era, the anthropocene. We do not fully understand the consequences of rising populations and increasing energy consumption on the interwoven fabric of atmosphere, water, land and life.

We are collectively endangering our planet, but there is a potential threat from individuals too. “Bio” and “cyber” expertise will be accessible to millions. It does not require large, special-purpose facilities as do nuclear weapons. Even a single person will have the capability to cause widespread disruption through error or terror. There will always be disaffected loners, and the “leverage” each can exert is ever-growing. It would be hard to eliminate such risks, even with very intrusive surveillance.The global village will have its global village idiots.

Kruger, Your Manias Become Science 1980s

Kruger, Your Manias 1984

Some commentators on biotech, robotics and nanotech worry that when the genie is out of the bottle, the outcome may be impossible to control. They urge caution in “pushing the envelope”. But we cannot reap the benefits of science without accepting some risks. The best we can do is minimise them. The typical scientific discovery has many applications, some benign, others less so. Even nuclear physics has its upside: its medical uses have saved more people than nuclear weapons actually killed.

The uses of academic research generally cannot be foreseen. Ernest Rutherford, the leading nuclear physicist of his time, famously said in the mid-1930s that nuclear energy was “moonshine”; the inventors of lasers did not foresee that an early application of their work would be to eye surgery; and the discoverer of x-rays was not searching for ways to see through flesh.

Science in the 21st century will present new threats more diverse and more intractible than nuclear weapons did. It will pose ethical dilemmas. But a blanket prohibition on all risky experiments and innovations would paralyse science and deny us all its benefits.
Scientists sometimes abide by self-imposed moratoria on specific lines of research. A precedent for this was the so-called “Asilomar declaration” in 1975 whereby prominent molecular biologists refrained from some experiments involving the then new technique of gene-splicing. Just last month, experts in the more advanced techniques of “synthetic biology” proposed a similar ban.

Holzer, Protect Me 1980s

Jenny Holzer, Protect Me 1984

But a voluntary moratorium will be harder to achieve today: the academic community is larger, and competition (enhanced by commercial pressures) is more intense. To be effective, the consensus must be worldwide. If one country alone imposed regulations, the most dynamic researchers and companies would migrate to another that was more sympathetic or permissive. This is happening already in stem cell research.

How can we prioritise and regulate, to maximise the chance that applications are benign, and restrain their “dark side”? How can the best science be fed in to the political process?

There is an ever-widening gap between what science allows, and what we should actually do. There are many doors science can open that should be kept closed, on prudential or ethical grounds. Choices on how science is applied should not be made just by scientists. That is why everyone needs a “feel” for science and a realistic attitude to risk – otherwise public debate won’t get beyond sloganising. Jo Rotblat favoured a “Hippocratic oath” whereby scientists would pledge themselves to use their talents to human benefit.

Holzer, Abuse

Holzer, Abuse of Power 1980s

Scientists surely have a special responsibility. It is their ideas that form the basis of new technology. They should not be indifferent to the fruits of their ideas. They should forgo experiments that are risky or unethical. More than that, they should foster benign spin-offs, but resist dangerous or threatening applications. They should raise public consciousness of hazards to environment or health.

At the moment, scientific effort is deployed sub-optimally. This seems so whether we judge in purely intellectual terms, or take account of likely benefit to human welfare. Some subjects have had the inside track. Others, such as environmental research, renewable energy, biodiversity studies and so forth, deserve more effort. Within medical research the focus is disproportionately on ailments that loom largest in prosperous countries, rather than on the infections endemic in the tropics. The challenge of global warming should stimulate a whole raft of manifestly benign innovations – for conserving energy, and generating it by “clean” means (biofuels, innovative renewables, carbon sequestration, and nuclear fusion).

These scientific challenges deserve a priority and commitment from governments, akin to that accorded to the Manhattan Project or the Apollo moon landing. They should appeal to the idealistic young. But to safeguard our future and channel our efforts optimally and ethically we shall need effective campaigners, not just physicists, but biologists, computer experts, and environmentalists as well; latter-day counterparts of Jo Rotblat, inspired by his vision and building on his legacy.

· Martin Rees is president of the Royal Society. This essay is based on a talk he gave at the Guardian Hay literary festival

Source: Guardian Online

For more information on Martin Rees, click here.

Earthly Paradise

In the later 18th century in the west, with the new philosophical emphasis on the sublime and the Romantic championing of nature and the natural, landscape painting began to be an important art form. Romantics saw the landscape in a new light, as able to express lofty ideals on its own without illustrating stories from history or classical myth. For some Romantics, art was a product of divine religious inspiration and the mystic experience of the dynamic forces of the universe was to be found in nature. The idea that landscape could convey an image of divine power was a new and radical one in the nineteenth century.

;Church, Heart of the Andes

Church, The Heart of the Andes

In the early to mid nineteenth century American religious art took the form of landscapes that were “Edenic, majestic, gorgeous and bombastic, rather than historical scenes of biblical enactment” (Arthur Danto) in the works of the so-called Hudson River School of which these paintings by Church are two.

Church, Cotopaxi

Church, Cotopaxi

In the later nineteenth and early twentieth centuries the ability of technology to master and control the environment, the conversion of nature into culture and the expansion of industrial capitalism all affected the way people felt about their place in the world. The world was becoming increasingly unfamiliar and alien: a gigantic impersonal maze of bewildering urban spaces, new experiences of space and time caused by new modes of travel, dislocation, flux, change.

Burtynsky, Wan Zhou

Burtynsky, Wan Zhou

Is it the case that the great 19th century revolutionary political and social projects which had promised personal and societal liberation have created instead a world in which the individual’s fate seemed to be more than ever dominated by vast impersonal and unknowable bureaucratic political and economic structures? The empowerment offered by industrial technology is increasingly offset by the terrible price paid for technological advances: pollution, devastation of resources, human bondage and large scale war.

Burtynski, Oil Fields 13

Burtynsky, Oil Fields 13

Burtynsky, Nickel Tailings 34

Burtynsky, Nickel Tailings 43

Polidori, Cafeteria Chernobyl

Polidori, Cafeteria Pripyet Chernobyl

To see more works by Edward Burtynsky, click here.

Apocalypse Then and Now II: Whither Winter?

Into the white

Bruegel, Hunters

Peter Bruegel, Hunters in the Snow 1565

In the Renaissance, falling temperatures cast a blanket of snow over Europe. It was the Little Ice Age – and people were terrified the Earth would freeze over. Jonathan Jones looks at how artists reacted to a crisis we’re still grappling with today

Monday December 18, 2006
The Guardian

The mountains are the clue to the hidden meaning of Pieter Bruegel the Elder’s masterpiece Hunters in the Snow. Flinty precipices rise up beyond the frosted valley, with its church and houses muffled in white, and children wrapped up like little balls, skating on frozen ponds. Mountains like this are not that common in the Low Countries. Why did the Flemish master make them such a prominent part of the greatest Christmas card scene ever painted?

Snow scenes are one of the delights of European painting, and at Christmas they’re everywhere. Yet these homely pictures have a troubling pertinence: their true subject is climate change. Bruegel invented the snow scene, a unique achievement. All the other genres of painting – still life, portraiture, battles and histories, landscape – originate in antiquity. Depictions of snow originate with one man, and one terrible winter.

The year 1565 saw the coldest winter anyone could remember. The world turned white, birds froze, fruit trees died, the old and young faded away. It was a shock – and a foreboding. This seemed to be more than just a cold winter. The climate was perceptibly changing, and that is what Bruegel’s snow scenes eerily record. All of them – from Hunters in the Snow painted in 1565, to Census in Bethlehem in 1566, to The Adoration of the Magi in 1567 – were made in response to that year and what it presaged. The key to their prophetic quality is right there in the mountains in Hunters in the Snow.

Those mountains are Alps. In 1552, Bruegel crossed the Alps on an artistic pilgrimage from his native Netherlands to Italy. His experience of western Europe’s highest and coldest mountain range, which he recorded at the time in drawings that survive, stayed with him all his life, sharpening his mind’s landscape, yet never as tellingly as in Hunters in the Snow. Here he seems to say that all the world is turning Alpine – in a new Ice Age.

Bruegel, The Numbering at Bethlehem

Bruegel, Census in Bethlehem 1565

He’s right. Once, when the first painters made their marks on cave walls, all Europe was crushed and churned by glaciers that only survive now in the high Alps. In the 1500s and 1600s, these European glaciers were on the move, swallowing up pastures and devastating communities. The villagers of Chamonix, as the historian Emmanuel Le Roy Ladurie discovered, petitioned their lords to do something about climate change: “We are terrified of the glaciers … which are moving forward all the time and have just buried two of our villages and destroyed a third.”

In Hunters in the Snow, the glaciers have reached the villages around Antwerp. Bruegel’s prophecy is accurate. The climate was changing dramatically and dangerously, although in the opposite direction from today’s impending crisis. The world was getting colder. Temperatures dropped globally in the Renaissance, so severely that climatologists call the era from 1400 to 1850 the Little Ice Age. The winter of 1565 was one of the first when everyone could see something had changed. But what was to be done?

This was a pre-industrial society that had only the most limited control over its environment. The Little Ice Age was a naturally caused phenomenon, and humanity – puny then in the face of nature – could only try to adapt. Bruegel’s paintings are not just prophecies. They are recipes of adaptation, illustrating new ways to live with the cold: how to inhabit it, even enjoy it. Ice and snow turn the world upside-down. In Bruegel’s paintings, the very chill that threatens life provokes vitality. People don’t just shiver in the snow. In his Census at Bethlehem, while adults huddle miserably, children skate and sledge on the ice, as they do in Hunters.

Dutch artists took up Bruegel’s new snow scene genre as winters deepened and hardened and the frosts that seemed novel in 1565 became routine (though still magical). In making everything look new and alien – stopping school and work, severing the chains of rural habit – snow created a wonderland that is celebrated, for example, in the paintings of Hendrick Avercamp, where entire Dutch towns are shown out on the ice while old people sit watching, wrapped up warm.

Bruegel, The Slaughter of the Innocents

Bruegel, Slaughter of the Innocents 1565

In Britain, the 17th-century English diarist John Evelyn recorded that when the Thames froze over, from December 1683 to February 1684, people treated it as a “carnival of winter”. A carnival was a mad collective escape from drudgery, and in Abraham Hondius’s painting, A Frost on the Thames, you can see what Evelyn means. Long-haired dandies glide across the solid river, visiting booths and tents, while cannons fire to salute a royal visit and children play ball games.

Yet, Evelyn points out, this midwinter celebration skated over the chilling facts: the poor were perishing from cold and hunger, the next year’s harvest was dead in the ground, and trees were dying. It was a catastrophe. Somehow, the Thames “frost fairs” turned it all into a joyous Bruegelian celebration of life.

The last frost fair on the Thames was in 1814, when Regency fops were just as keen to get on the ice to flirt, as a cartoon by Thomas Rowlandson, of skaters on the Serpentine, shows. But in the 19th century, the communal hilarity Bruegel bequeathed gives way to a terrible solitude. Snow is no longer made homely by winter sports and braziers. It becomes the white shroud of death. Caspar David Friedrich’s painting The Watzmann imagines a snowbound Alp, seen across green foothills, as a smooth, inhuman spectre remote from the fleshy concerns of the everyday. It is extreme, it is desired, and it will kill you. The Alps in Friedrich’s day were still a menace to the economic and political life of Europe. The Little Ice Age still had the continent in its grip – crossing from France to Italy was terrifying. JMW Turner made the trip several times and glaciers and blizzards swirl in his paintings, most fantastically in his traumatic vortex of a painting, Snow Storm: Hannibal and His Army Crossing the Alps.

By the middle of the 19th century, it was over. London would not see another frost fair. Today, to see people larking about on a frozen river in the heart of a great city, you have to go to St Petersburg. What changed? The industrial revolution had an impact on the climate as long ago as the 1850s, together with massive forest clearances in the US. A tendency for the world to become colder, which had been noticeable since the middle ages, was reversed by the stirrings of modernity.

Friedrich, The Watzmann

Friedrich, The Watzmann 1824

Ice started to roll back from the world – but not from art. It is arguable that abstract art begins with all those snow scenes of the Old Masters, from Bruegel to Turner. When you look at fallen snow, the erasure of detail, the disappearance of perspective is what makes it so magical. Bruegel captures this: in his Adoration of the Magi, the action is partly obscured by falling snowflakes. He recognises the disengaging visual quality of snow, an insight that has surprising consequences. It would be fascinating to hang Hunters in the Snow next to a painting by the 20th-century Dutch visionary Piet Mondrian. The white emptiness of Mondrian’s space, the pulses and chunks of colour animating it, uncannily (and not, I think, accidentally) resemble the patterns of white nothingness and human warmth in Bruegel’s art.

The ghosts of the Hunters and the skating butterball children can be glimpsed in some of modern art’s most haunting encounters with whiteness – in Jasper Johns’ White Flag, in Robert Ryman’s white monochromes, right through to the feathery snow in Peter Doig’s paintings of winter sports.

Ice and snow are on the retreat now. This year is Britain’s warmest on record. You’ve seen the news. Christmas card scenes suddenly look different when the north pole is vanishing. Can art respond to this, can it help resist climate change? The best work I’ve seen about global warming is Rachel Whiteread’s installation of crumbling white plastic mountains in the Tate Modern Turbine Hall, created after she visited the Arctic. This homage to icebergs – at once colossal and disintegrating, its very material speaking of human destructiveness – conveyed the incomprehensible scale and dismal entropy of meltdown.

Whiteread, Embankment

Whiteread, Embankment

In modern cities, icy conditions are easily recreated by technology. Synthesised ice rinks have spread from Manhattan’s Rockefeller Centre to parks and museum terraces everywhere. Maybe this is what winter will become: a refrigerated carnival, an attempt to recreate artificially the cherished memories and folk tales of winters lost for ever. In Tarkovsky’s film Solaris, a space station orbiting a distant planet has a print of Bruegel’s Hunters in the Snow in its lounge. It is the astronauts’ memento of Earth. It’s a chilling thought that, for future generations on a radically altered Earth, Hunters in the Snow may fulfil just this purpose: preserving the idea, at least, of what a snowbound planet looked like, how human it was, how paradoxically warm and fun.

St Mary's Lake, Montana

St Mary’s Lake, Glacier National Park, Montana

Bruegel captured humanity’s double relationship with winter: we fear it and we love it. Surviving winter is part of what makes us human. For Whiteread as for Bruegel, whiteness is wondrous, frightening – and the world would be a poorer place without it.

Apocalypse Then and Now …

When it comes to climate change, I’ll take a small bet that Pascal was right

By Gerard Baker, Times on Line September 2006

Unless the sceptics are really, really certain that we’re all going to be OK, we must act now.

Moonscape

Painting by Basil Wolverton from the Apocalypse series, 1950s

IF I WERE inclined to be agnostic I’ve always thought I’d be tempted to take a punt on Pascal’s Wager. Blaise Pascal, as you know, was a theologian-mathematician back in the days when it was still respectable for Frenchmen to be clever and religious. His combined musings on probability theory and the human condition led him to a formulation that belief in a God and the afterlife was the only prudent intellectual course of action.

The calculation is simple. If you believe in God and live a God-fearing life, and it turns out there is a God, then, when the time comes, you’ll be rewarded with a place in paradise for ever. If there isn’t one, and you’ve lived the religious life, then you will end up, infinitely speaking, the same as everyone else, and no worse off than the atheist who spent his life deriding religious belief as superstitious nonsense.

But if you don’t believe in God and live a generally irreligious life, you’re taking one hell of a gamble. If it turns out you were right all along, and there’s no God and no afterlife, so what? You won’t even have the pleasure of a nanosecond of gloating at the ineffable stupidity of your God-bothering fellow ex-human beings. The very moment of your intellectual triumph and existential vindication is also the precise moment at which its significance collapses to literal nothingness. That will be it. Lights out. For ever.

Bruegel Triumph of Death

Bruegel, The Triumph of Death 1563

But if it turns out there is a God, and you’ve spent your earthly span denying his existence and generally poking fun at believers you’re going to feel a bit sick when St Peter shows up on the other side, ledger in one hand and one-way ticket to the Underworld in the other.

Therefore, Pascal said, the sensible thing to do is to resist the atheist temptation. The best on offer is a lifelong sense of smug superiority in this world. The worst is eternal damnation. The costs of being wrong are so high that they would require a level of confidence in your unbelief that is humanly impossible. Why chance it? Pascal’s Wager, it seems to me, is a good starting point for consideration of climate change. Belief in global warming and its human provenance seems to have replaced traditional religion as the faith of the secular.

Memling, Last Judgment

Memling, Last Judgment c 1470

Politicians and the media accept the wisdom of climate-change belief with the same unquestioning devotion that medieval peasants and monarchs used to bring to the Church. Scientists predict earthly conflagration with all the confidence with which 17th-century divines used to caution about eternal hellfire.

For myself, I prefer the old religion, and count myself still a bit of an agnostic on climate change. Certainly, the evidence is clear that the earth has been getting warmer, and certainly the preponderance of scientific opinion is that our emissions of greenhouse gases have played at least a highly significant role in that.

But there remains enough doubt in there to merit a cautious agnosticism. Unquestioning faith in current scientific hypothesis opinion is not always rewarded with consistent conclusions (ask Pluto).

Wolverton Giant Tsunami

Wolverton, Giant Tsunami

On this as on any other subject we agnostics don’t have the luxury of being hermits, whose philosophy is summed up in the injunction: don’t just do something, stand there! What are we actually supposed to do in a world of high uncertainty?

This is where our friend Pascal comes in. If we believe in global warming and do something about it and it turns out we’re right, then we’re, climatologically speaking, redeemed — if not for ever, at least until some other threat to our existence comes along.

Manifest Destiny

Manifest Destiny by Alexis Rockman

If we’re wrong about it, what is the ultimate cost? A world with improved energy efficiency and quite a lot of ugly windmills.

If we don’t believe in global warming and do nothing about it, and we’re right, so what? Our distant posterity will be able to cite us approvingly in future opinion columns. But if our unbelief turns out to be unsupported by the outcome and we’ve done nothing about global warming in the meantime, then we’re in a position analogous to the atheist at the gates of heaven. We will spend not eternity, but perhaps the rest of the earth’s existence, ruing our folly.

Now there is one significant risk that makes this equation slightly different from Pascal’s. There could be high costs of believing in the human role in global warming and being wrong about it. We may have to trade off a lot of economic activity in the next 50 years to lower our carbon emissions.

It is certainly a risk. And yet these costs might actually be lower than is sometimes feared. Like virtue, improving energy efficiency is its own reward. Individual companies such as Wal-Mart are already discovering that the costs of reducing their carbon footprint are offset heavily by efficiency gains.

For whole economies the equation is not necessarily as attractive but there’s still reason to believe that efficiencies can reduce the long-term net costs of investment in alternative energy sources. There are, besides, other incalculable benefits of shifting our energy-use patterns — reducing our economic and strategic dependence on Middle Eastern oil, for one.

In modern game theory Pascal’s Wager is called the maximin criterion. When confronted with a choice of actions in conditions of uncertainty, the correct choice is the course whose worst outcome is least harmful. That puts the burden of proof on to the global-warming sceptics. Unless you’re really, really certain that we’re all going to be fine, then the only prudent course is to act now to reduce emissions. The costs of understating the threat are much higher than the costs of overstating it.

Post Apocalypse

After the Apocalypse

The wise thing to do, then, is to invest in alternative energy and change public policy so as to raise fuel emission standards and penalise overconsumption. Kyoto, of course, is a dead letter, but renewed efforts at international co-operation are also essential. If I were a betting man, I’d wager that old Pascal is, even now, smiling in agreement.

Wasteland

Wolverton, Apocalypse

For more on Pascal’s wager, click here.

For other illustrations/graphs on the issue of global warming, click here.

For more on Alexis Rockman, click here.

For a review of Rockman’s work, click here.

From the Golden Ratio to Polytopes

Golden Ratio and Fibonacci numbers:

Consider the line ABC in the following diagram:

Golden rectangle

Point B divides the line in such a way that the ratio between the longer segment (AB) and the shorter segment (BC) is the same as that between the whole line (AC) and the longer segment (AB).

This proportion is known by various names: the golden section, the golden mean, the golden ratio, the extreme and mean ratio, the divine proportion, or phi (φ). If the distance AB equals 1 unit, then BC = 0.6180339887… and AC = 1.6180339887… . The second of these two numbers is the golden section, or phi (sometimes this name is also given to the first number). Many designs in nature are related to the golden section, and it has been widely used in sacred architecture and artwork throughout the ages.

The golden section is part of an endless series of numbers in which any number multiplied by 1.618 gives the next higher number, and any number multiplied by 0.618 gives the next lower number.

The large rectangle below is a golden rectangle, meaning that its sides are in the proportion 1.000:1.618. If a square is removed from this rectangle, the remaining rectangle is also a golden rectangle. Continuing this process produces a series of nested golden rectangles. Connecting the successive points where the ‘whirling squares’ divide the sides of the rectangles in golden ratios produces a logarithmic spiral, which is found in many natural forms (see next section). A similar spiral can be generated from a golden triangle (an isosceles triangle whose sides are in the golden ratio), by repeatedly bisecting one of the angles to generate a smaller golden triangle.

Spiral

Spiral 2

A number series closely related to the golden section is the Fibonacci sequence: it begins with 0 and 1, and each subsequent number is generated by adding the two preceding numbers:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987 …

If we take these numbers two at a time, and divide the larger one by the smaller one, the value will oscillate alternately above and below the golden section, while gradually converging on it.

Many of nature’s patterns are related to the golden section and the Fibonacci numbers. For instance, the golden spiral is a logarithmic or equiangular spiral – a type of spiral found in unicellular foraminifera, sunflowers, seashells, animal horns and tusks, beaks and claws, whirlpools, hurricanes, and spiral galaxies. An equiangular spiral does not alter its shape as its size increases. Because of this remarkable property (known as self-similarity), it was known in earlier times as the ‘miraculous spiral’.

Spiral galaxy

Whirlpool Galaxy

Nautilus

Nautilus shell

Geometrical forms: polygons and polyhedra

While pentagonal patterns abound in living forms, the mineral world favours twofold, threefold, fourfold, and sixfold symmetry. The hexagon is a ‘close-packing’ shape that allows for maximum structural efficiency. It is very common in the realm of molecules and crystals, in which pentagonal forms are almost never found. Steroids, cholesterol, benzene, TNT, vitamins C and D, aspirin, sugar, graphite – all show sixfold symmetry. The most famous hexagonal architecture is built by bees, wasps, and hornets.

Honeycomb

Honeycomb

Fly eye

Fly’s eye

Snow

Six water molecules form the core of each snow crystal.

Snow

The great majority of viruses are icosahedral, including the polio virus and the 200 kinds of viruses responsible for the common cold. Icosahedral symmetry is believed to allow for the lowest-energy configuration of particles interacting on the surface of a sphere. The five platonic solids are also found in radiolarian skeletons.

Platonic solids in sea

The platonic solids have been found living in the sea. The tetrahedron, somewhat rounded as if from internal pressure, is embodied in a protozoan called Callimitra agnesae, the cube is Lithocubus geometricus, the octahedron Circoporus octahedrus, the dodecahedron Circorrhegma dodecahedrus, and the icosahedron Circognia icosahedrus.

From: http://ourworld.compuserve.com/homepages/dp5/pattern1.htm

Polyhedra in four dimensions

From: http://math.ucr.edu/home/baez/platonic.html

While there are 5 Platonic Solids in 3 dimensional space, in 4 dimensions, there are exactly six regular polytopes.

How can we visualize these? Well, a Platonic solid looks a lot like a sphere in ordinary 3-dimensional space, with its surface chopped up into polygons. So, a 4d regular polytope looks a lot like a sphere in 4-dimensional space with its surface chopped up into polyhedra! A sphere in 4-dimensional space is called a ‘3-sphere’, since people living on its surface would experience it as a 3-dimensional universe with the curious feature that if you hop aboard a rocket and shoot off straight in any direction, you eventually wind up back where you started. (This is just like what happens when you start walking in a straight line in any direction on an ordinary sphere.)

So, we can visualize the regular polytopes in 4 dimensions by taking a 3-sphere and drawing it chopped up into polyhedra. A 3-sphere is hard to draw until you realize it looks just like ordinary 3d space except that it ‘wraps around’… very far away from here. But if we ignore that, and just draw a nearby portion of the 3-sphere chopped up into polyhedra, with everything outside this portion being one big polyhedron, we’ll do okay. And this is what we get:

5 cell

Hypertetrahedron 5 tetrahedral faces

8 cell

Hypercube (tesseract) 8 cubical faces

16 cell

Hyperoctahedron: 16 tetrahedral faces

120 cell

Hyperdodecahedron: 120 dodecahedral faces

600 cell

Hypericosahedron: 600 tetrahedral faces

24 cell

24 cell: 24 octahedral faces