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Alessandro Baricco paints a lively portrait of the modern-age barbarian in his 2014 book, The Barbarians. He initially frames the issue as a simple struggle between the shallow and the profound: Mickey Mouse versus Flaubert, Big Mac against the bouillabaisse. The barbarian is superficial, abhors depth, and spreads knowledge as thinly as possible across the globe. The favorite means of transport is the Internet, which connects everything and everyone at the speed of light.

But in his last chapter, Baricco visits the ultimate barrier built against the advancing hordes: the Great Wall of China. When he stands on the meandering wall and looks over the empty steppes, he is suddenly in doubt. On which side are the Barbarian hordes?

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This existential question is especially appropriate for modern science, whose border with society is longer, more winding, and more porous than it has ever been. It’s rather like a coastline seen on a map, seemingly easy to draw and measure. If you were to view it from an airplane window and zoom in, though, an incredibly rich set of twists and turns would become discernible. Magnifying the perspective further would reveal even more complexity: This pattern repeats itself at smaller and smaller scales, persisting down to the levels of individual pebbles and grains of sand. As you descend further still, to the scale of molecules and atoms, the whole concept of a border becomes fuzzy and ambiguous. Where does the land end and the sea begin? On which side are the scientific experts, and on which side the barbarian hordes?

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The gap between research and everyday life is not growing, but instead rapidly decreasing. More and more, we are touched by science in all aspects of our lives.

The mathematician Benoit Mandelbrot famously introduced the idea of a fractal with exactly this example, in a 1967 paper titled “How Long Is the Coast of Britain?” The answer is that, taken to its logical extreme, the natural border of the coast of Britain is so deceptively twisted, with self-similar complexity at all levels of magnification, that it becomes infinitely long—the very definition of a fractal in mathematics. When looking at this form, the sense of scale becomes tricky: Is a particular image an island or a grain of sand?

I propose that the natural border between science and society should also be considered fractal-like and will become ever more so. In what I like to call the “knowledge paradox,” the remarkable growth of science—both in complexity and in the presence in our everyday lives—means that the frontier of knowledge simultaneously moves away from us and toward us.

On the one hand, research, by its very definition, moves further away from our everyday experiences as it digs deeper into unexplored layers of knowledge. As this happens, the path from cutting-edge science to the public domain becomes longer with more winding, inscrutable hairpin bends. Science becomes less visible to the general public—metaphorically, but also literally, since much present-day research is done behind the closed doors of laboratories and universities and published in specialist journals behind paywalls.

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On the other hand—and here resides the paradoxical element—science becomes more useful and relevant as its fractal border lengthens, often because of its growing complexity, which allows for much more targeted and precise applications. The latest scientific research can literally be found in our bloodstream and in our pockets, in the form of the latest drug or smartphone. If 50 years ago the genetic information stored in our DNA was mainly a grand concept guiding basic biological research, nowadays it is used every day in diagnoses and treatments. Similarly, in the pioneering days of computing, some thought that a few of these massive machines would be enough for the world’s demands. Now, almost every appliance has some computing and communication power.

As science moves to matters of greater complexity and relevance, moral values also become more integral to research practices.

The same applies to the infiltration of science into the veins of society. There is hardly a policy issue that does not crucially depend on basic research, from climate change to financial regulation, from water shortages to the spread of the Zika virus. So, viewed from this perspective, the gap between research and everyday life is not growing, but instead rapidly decreasing. More and more, we are touched by science in all aspects of our lives.

Both sides of this paradox—the simultaneously increased and shortened distance between science and society—stem from the complexity of science itself. As is often said, knowledge is the only natural resource that grows when used. We see the increased complexity also reflected in the infrastructure of science itself: the growing number of institutions, researchers, and publications; larger and more interdisciplinary collaborations; and a language that in many areas has become impenetrable for the layperson.

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It is estimated that a century ago there were only 1,000 professional physicists in the world. By comparison, the construction and operation of the Large Hadron Collider in CERN, Geneva, requires more than 10,000 scientists and engineers. The complexity of societal problems—the Earth’s climate and biodiversity, the worldwide energy supply, the spread of infectious diseases, the global economy—is also increasing. All of these issues involve the combination of a large number of disciplines, huge databases, sometimes erroneous or incomplete measurement data, and governments and citizens who impatiently seek solutions.

And so science and society are entangled in an ongoing feedback loop. Just like the coastline of Britain, when viewed in all its detail, the border between science and society grows ever more complex and diffuse, changing from a simple straight line into an endlessly branching fractal. Scientific knowledge becomes, like the title of the 1993 Wim Wenders film Faraway, So Close!, infinitely distant and near at the same time.

What does the evolving frontier of knowledge mean for society’s relationship with science? Long borders are difficult to patrol. Professional gatekeepers of scientific knowledge can no longer control the flow of information as they used to. In an age of the “University of Google,” people no longer rely on established, peer-reviewed literature but rather seek out manifold sources on the Internet. Fragments of scientific knowledge get absorbed into society this way, as do some scientific values and thinking—which by itself is good. But many of these fragmented bits of knowledge are also invalidated, politicized, and of dubious quality.

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This self-driven accumulation of “knowledge” has created a healthy dose of skepticism among the public toward facts and arguments, as well as a more intense public engagement. Some speak of the modern citizen as a “proto-scientist,” emulating, no doubt incompletely, some of the well-established practices of academia. It is no longer enough for experts to argue by means of what mathematicians fondly call “proof by intimidation.” The authority of science has been eroded by these public debates, a subject that deserves a separate discussion. One of the immediate consequences is that the scientific community will have to spend much more time engaging with policy makers and the public, not only communicating the products of research, but also the scientific method itself.

A coastline is shaped by two forces that work against each other: The sea erodes the land and sediments fill in the water, twisting the boundary. In the same way science affects society as much as society affects science. As science moves to matters of greater complexity and relevance, moral values such as care for our fellow human beings and our planet, and our sense of justice and equity, also become more integral to research practices. Science increasingly becomes a public good. History shows that its products cannot be captured by a few, and will, in the end, benefit all. A dynamic interface between science and society, where science and scientists are enriched by the public spirit, is a good thing.

At the end of The Barbarians, Baricco wonders whether the image of advancing barbarians is just a projection. Aren’t we all barbarians in some sense? Or, more precisely, don’t we all have barbaric tendencies—so that we are, in effect, on both sides of the fractal border? Like that border’s self-similar patterns, every generation is given the opportunity to explore a world of intriguingly complex behaviors, experiences, and meanings. The distance and depths to which science can go depends crucially on the fears and imagination of not just scientists, but also the public.

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Don’t miss Robbert Dijkgraaf’s video interview in this issue, “Ingenious: Robbert Dijkgraaf.”

Robbert Dijkgraaf is the director and Leon Levy Professor at the Institute for Advanced Study in Princeton, NJ.

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