Stranger Than We Can Imagine (30 page)

Thanks to the butterfly effect, climate modelling has proved to be exponentially more difficult than von Neumann expected. But the need for weather forecasting and longer-range predictions has not gone away, so climate modellers have worked hard. In the
half-century since Lorenz first coded a virtual atmosphere, climate models have become massively more detailed and computationally intensive. They have to be run many times in order to obtain the statistical likelihood of their results. As the models improved, they became far less likely to flip into ‘snowball earth’ or other unlikely states. And in doing so they confirmed a finding that had shocked the pioneers of chaos mathematics. Whenever they studied complexity and looked deeply at the frothing, unpredictable turbulence, they found the strangest thing. They found the emergence of order.

The fact that our ecosystem was so complicated was what was keeping it so stable.

Benoît Mandelbrot was a magpie-minded Polish mathematician with a round, kindly face and the type of personality that found everything intensely interesting. He was a Warsaw-born Jew who fled the approaching Nazis as a child, first to France and then to America. In 1958 he joined the IBM Thomas J. Watson Research Center in New York to undertake pure research. This allowed him to follow his curiosity wherever it might take him.

In 1979 he began feeding a short equation into a computer. Like Lorenz’s waterwheel model, Mandelbrot’s equation was incredibly simple. It was little more than a multiplication and an addition, the sort of mathematics that could have been attempted at any point in history. The reason why it hadn’t was because the equation was iterative, and needed to be calculated millions of times. The answer that came out at the end was fed back into the start, at which point the equation was performed again, and again, and again. This was why Mandelbrot needed a computer. Even the shabbiest early computer was happy to run a simple bit of maths as many times as you liked.

Mandelbrot wanted to create a visual representation of his equation, so he performed the same iterative mathematics for every pixel on his computer display. The outcome would be one of two things. Either the number would become increasingly small, and ultimately head towards zero, at which point Mandelbrot would mark that pixel on the screen black. Or the number would become
massive and race off towards infinity, in which case that pixel would be coloured. The choice of colour varied with the speed at which that number increased. The set of numbers that created this image became known as the
Mandelbrot Set
.

The result, after the equation had been applied to the whole screen, was an appealing black splodge in the centre of the screen with coloured, crinkly edges. It wasn’t a circle, exactly, but it was satisfyingly plump. The shape resembled a cross between a ladybird and a peach, or a snowman on its side. It wasn’t a shape that anyone had ever seen before, yet it felt strangely familiar.

It was when he looked closely at the edges of the Mandelbrot Set that things got interesting.

The edges of the shape weren’t smooth. They were wrinkled and unpredictable, and sometimes bulged out to form another near-circle. Zooming in to them should have clarified their shape, but it only revealed more and more detail. The closer you looked, the more you found. There were swirls that looked like elephant trunks, and branching shapes that looked like ferns or leaves. It didn’t matter how closely you dived in, the patterns kept coming. There were even miniature versions of the initial shape hidden deep within itself. But at no point did the patterns repeat themselves exactly. They were always entirely new.

Mandelbrot had discovered infinite complexity hidden in one short equation.

It might have been expected that such complexity should have been entirely random and discordant, but that was not the case. It was aesthetically appealing. Mathematicians are notoriously quick to describe whatever they are working on as ‘beautiful’, but for once they had a point. There was something very natural and harmonious about the imagery. They were nothing like the sort of images then associated with computer graphics. Instead, they resembled the natural world of leaves, rivers or snowflakes.

Mandelbrot coined the word
fractal
to describe what he had discovered. A fractal, he said, was a shape that revealed details at all scales. An example of this would be the coastline of an island. This
will always remain crinkly, regardless of whether you are looking at headlands, or rocks, or individual pebbles on the shore. The smaller the scale, the more detail that emerges.

For this reason, measuring the length of a coastline is an arbitrary exercise entirely dependent on the amount of detail factored into the measurements. The length of the British coastline is 17,820 kilometres, according to the Ordnance Survey, yet the
CIA Fact-book
reckons that it is 12,429 kilometres, or nearly a third shorter. Those measurements are entirely dependent on the scale from which they were taken. The figure is essentially meaningless without that context. The observed can, once again, only be understood if we include its relation to the observer.

Having found fractals on his computer, Mandelbrot looked again at the real world and realised they were everywhere. He saw them in the shapes of clouds, and in the whirls of rising cigarette smoke. They were in the branching of trees and the shape of leaves. They were in snowflakes, and ice crystals, and the shape of the human lungs. They described the distribution of blood vessels, and the path of a flowing river. At one point Mandelbrot was invited to give a talk at the Littauer Center at Harvard University, and was surprised to turn up and find what looked like one of his diagrams already on the blackboard. The diagram Mandelbrot intended to talk about depicted income variation, which was data in which he discerned fractal patterns. The Harvard diagram already on the board had nothing to do with income variation. It represented eight years of cotton prices. Yet that data had also produced remarkably similar fractal patterns.

Every time Mandelbrot stepped outside his front door and into the fractal landscape of nature, he was confronted by a world that now appeared entirely different to the one imagined by the mathematics of Euclid and Newton. A mountain may roughly be the shape of a pyramid, but only roughly. The classic Euclidian geometric shapes of spheres, cubes, cones and cylinders didn’t actually exist in the natural world. There was no such thing as a straight line
until mathematicians invented one. Reality was far messier than it had been given credit for. Like it or not, reality was fractal and chaotic.

Through the insights of people like Lorenz and Mandelbrot, and the arrival of brute computational power, a major shift occurred in our understanding of both mathematics and nature. As the research accumulated, two surprising facts became apparent. When you looked closely at what appeared to be order, you would find outbreaks of chaos around the edges, threatening to break free. And yet when you looked deeply into chaos, you would find the rhythms and patterns of order.

The discovery of order in chaos was of intense interest to biologists. The existence of complex life never really appeared to be in the spirit of the second law of thermodynamics, which stated that, in an isolated system, entropy would increase. Ordered things must fall apart, in other words, so it was odd that evolution kept generating increasingly intricate order. With the arrival of chaos mathematics, biologists now had a key that helped them study the way order spontaneously arose in nature. It helped them understand the natural rhythms of life, both in the internal biology of individual animals and in the larger ecosystems around them.

It was not long before someone applied this insight to the largest ecosystem we have: planet Earth itself, and all the life that exists on it.

In the 1960s the English polymath James Lovelock was working at NASA when they were preparing to launch unmanned probes to Mars. Lovelock’s work was focused on studying the Martian atmosphere. It led to him inventing chlorofluorocarbon (CFC) detectors, which later proved invaluable when CFCs were discovered to be the cause of the growing hole in the ozone layer.

The atmosphere of a dead planet should be very different to that of a living planet like Earth, and so analysing the Martian atmosphere would prove to be a useful clue in determining whether or not there was life on Mars. As it turned out, the atmosphere of Mars was very close to a natural chemical equilibrium, being predominantly
carbon dioxide with very little of the more interesting gases such as oxygen or methane, and this strongly suggested that Mars was a dead planet.

As Lovelock pondered the atmospheric differences between a living planet and a dead one, he became increasingly intrigued by the processes in which living organisms altered their atmosphere. This could occur in many different ways. For example, an increase in temperature would stimulate the growth of phytoplankton, which are tiny plants that live on the surface of the ocean and which excrete a compound called dimethyl sulphide. Those extra plants produced extra dimethyl sulphide, which entered the atmosphere and made it easier for clouds to form. Those extra clouds then reflected more of the sun’s energy back into space, which had a cooling effect on the climate and helped reduce the amount of phytoplankton back towards their initial quantity. The whole system was a feedback loop, which constantly acted upon itself.

Wherever Lovelock looked, at all manner of chemical, biological, mineral and human processes, he found countless similar examples of feedback loops. Order was spontaneously being generated by chaos. The ecosystems of earth were unwittingly stabilising the very conditions they needed to survive.

The work of Lovelock and his colleague, the microbiologist Dr Lynn Margulis, led to Gaia Theory. They argued that our planet could be considered to be a self-regulating organism that altered its physical state in order to maintain the necessary conditions for life. Life on earth was generating the conditions needed for the existence of life on earth, in other words, and the magnitude of its complexity had created an extraordinary amount of stability. The planet was behaving like a living thing. If you damaged it, it would heal itself – assuming, of course, that the wound was not too severe. This was still a chaotic system, after all, and there was no reason why it could not be pushed out of its stable equilibrium into the chaotic states studied by Lorenz. This is the fear that keeps climate scientists awake at night: not gradual climate change, but runaway climate change, where the natural rhythms of the planet tip into
unpredictable chaos and the goal of growing sufficient food to feed 7 billion people becomes impossible.

Gaia Theory was naturally controversial, especially among those unfamiliar with non-linear mathematics. Scientists of the calibre of the evolutionary biologist Richard Dawkins and the biochemist Ford Doolittle criticised it on the grounds that they could see no mechanism whereby individual natural selection could allow for environmental-level concerns. But stability seemed to be an emergent property of nature. It was just something that happened, in a similar way to how life was something that just happened to matter, or consciousness was something that just happened to life. This idea made many scientists deeply uneasy. They understood that Lovelock was employing a metaphor, and that he was saying that the planet was acting
like
it was a living thing. But few wanted to be drawn into the problem of defining the difference between a system that was acting like a living thing, and one that actually was one.

Lovelock’s ideas gradually became accepted, but only after some very specific definitions were put in place. They are now studied under the name Earth Systems Science, which differentiates itself from Gaia Theory by being extremely clear that it in no way suggests that the planet is regulating itself
consciously
.

The name ‘Gaia’ had been suggested to Lovelock by the English novelist Sir William Golding, the author of
Lord of the Flies
, and it proved to be something of a double-edged sword. It helped popularise the idea among the general public, but it also scared away many members of the scientific community. ‘Gaia’ was the ancient Greek goddess of the earth, and scientists were cautious about anything that might encourage the idea that the earth was some form of conscious deity. This was a sensitive area because, as the twentieth century progressed, a lot of people were indeed coming to view the earth as some form of conscious deity.

One of the more surprising aspects of twentieth-century Western spirituality was the growth of a wide variety of broadly sympathetic practices that are most simply generalised as pagan or neopagan. Paganism is focused on respect for the natural world, which it
views as both living and divine. A prominent example would be the Wiccan faith founded by the Crowley-inspired English witch Gerald Gardner, which has grown to the point that it is now recognised by organisations ranging from the US Armed Forces to the UK’s Pagan Police Association. Gardner’s faith is largely unique in British history, for while Britain has a long history of giving the rest of the world stories, inventions, sport and music, it had never before given it a religion.

For those familiar with the power and influence of organised religion, it was easy to be unimpressed by paganism and its grass-roots, distributed nature. In the eyes of religions which claim authority from a central divine text, the sheer unstructured and contradictory variety inherent in paganism, and its focus on personal experience, rob it of any credibility. It was obviously all just made up. In the eyes of the pagans, however, it was the ‘People of the Book’ who lacked credibility. The notion that a single text could function as an ultimate authority in a post-omphalos individualist society appeared naive in the extreme. Individual personal experience, to a pagan, was the only authority they needed. This was the clash between the hierarchical imperial mind, in which a person is defined by their service to a higher Lord who takes responsibility for their protection and threatens them with punishment, and the individualism of the world after Einstein and the First World War.