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Philosophy, sociology and religion

Philosophy, sociology and religion

Love on the edge of the universe

03 Jul 2002

How the Universe Got Its Spots: Diary of a Finite Time in a Finite Space
Janna Levin
2002 Weidenfeld and Nicholson 218pp £16.99/$22.95hb

Different style

In October 1998 Janna Levin arrived to start a postdoc at Sussex University’s Astronomy Centre. She had just said good-bye to her beloved California, swapping the sun of Berkeley for the grey skies of Brighton. However, when she first arrived in the UK the customs and excise officers were surprised to find a stack of identical CDs in her luggage. Their suspicions aroused, they placed most of her possessions in a warehouse and decided to interview her.

The CDs were, in fact, personal copies made by her partner Warren, a blues musician. Also locked up in the warehouse were her transparencies, which she needed for a conference in Rome that we both were about to speak at. To cap it all, the computer with her presentations on it blew up when Warren plugged it into a socket: they had forgotten that UK mains voltage is twice that in the US.

A few days later, Levin arrived in Rome and gave her presentation, grabbing the audience’s attention with the story of her customs nightmare. She then proceeded to draw by hand a number of the topological spaces that she was guiding us through. One of just two people at the 100-strong conference trying to determine the topology of the universe, Levin stole the show with her natural talent for presentation and the quality of her material.

While at Sussex, Levin was offered two lectureships, both of which she subsequently turned down. These were brave decisions. Postdocs usually live a precarious life, taking short-term contracts and travelling around the world from one position to the next. The goal is a hallowed faculty position, where roots can, at last, be laid down and the administration can begin. Levin’s choices reflect her independent streak. Despite the pressure to accept, the posts simply did not feel right.

I am not surprised that Levin has been bold enough to write this book. Through a series of letters to her “mom”, she chronicles the development of her research over a two-year period, while also providing an intimate insight into various aspects of her personal life, many of which return time after time to torment her. The decision to share her innermost thoughts could have failed miserably. The fact that the concept does not fail – but instead develops into a fascinating story – is testament to Levin’s skills and courage.

She gives clear explanations of difficult mathematical concepts, often patiently repeating herself to give us a second chance. Many have done that, but Levin goes further – simultaneously confiding in us her innermost thoughts about her turbulent relationship with Warren, the role that physics plays in her life, and the importance of art in determining how she appreciates her work.

There is something gripping about Levin’s diary style. She acknowledges that the dates of events are not always accurate – in one entry describing a traumatic week at a meeting in a Moscow sanatorium, for example, she suddenly realizes that she was actually there four months earlier. But what binds the book together is the way her thoughts and ideas developed.

There are two main threads to the book: Levin’s desire to understand the shape of our universe and the development of her relationship with Warren. It is a relationship that eventually breaks down, primarily because of Levin’s need to follow the first thread. It is a sad, moving story, yet full of humour, unfolding as the physics that she has to share gets more and more exciting.

Levin believes that the universe is finite, that it does not extend forever. General relativity, for all its success, can only tell us about the local geometry of the universe. It has no feel for the topological nature or shape of the universe. In particular, it cannot say whether the universe has any holes in it, or if a light ray sent from a point could travel all the way round the universe to return to where it was emitted.

Before we can fully follow the more detailed tests that she proposes for a finite universe, Levin has to teach us some basic topology. To my surprise, she succeeds. The topological circle is introduced through her frustration with the London underground’s circle line, something that will be familiar to anyone having to travel on it. The two-dimensional world of the flat-landers lets her introduce the effect of probing from higher dimensions. For example, five fingers intersecting a flat-lander’s world would appear as five disconnected blobs to them.

Levin tantalizes the reader with the prospect that we live in a projection of a higher-dimensional space, or “hyperspace”. Using ideas from topology, she explains how we might test for such an idea. It is all linked to the question of whether the universe is finite or infinite. From where you sit reading this review, the Earth looks flat – as if it could go on forever. But as the beautiful NASA pictures remind us, when we look back at the Earth from space, we see our planet as a two-dimensional sphere – finite, compact and connected.

What about the universe as a whole? Is it infinite or finite, with holes or without? Answering these questions is at the heart of Levin’s work. The party line adopted by most cosmologists is that the universe is spatially flat and infinite in extent. The data, mainly from the distortions seen in the cosmic-microwave-background radiation, appear to favour this outcome, although we cannot be sure. Levin, however, appears confident that the universe cannot be infinite, arguing forcefully that infinities simply do not occur in nature, even if they appear in mathematics.

It is a moot question whether π which is clearly made up of an infinite sequence of numbers, actually appears in nature. Testing the shape of the universe is made all the more difficult by the fact that we cannot step outside of it, by moving up a dimension and peering down on the universe to look for evidence of finiteness. Our task is analogous to the flat-landers trying to understand the origin of the five blobs, which would indicate to them the presence of a third dimension.

Levin sets about the task, patiently introducing us to the powers of topology. Like all good teachers, she tries lots of examples and analogies, hoping that we will cotton on to the basic ideas. It works, and before long we are working with equivalence classes, understanding how coffee cups have the same topology as doughnuts and seeing how light in a compact space will always come back on itself. This last point is crucial. By coupling it with the tiling of geometries, which allows us to view multiple images of the same geometry, Levin is able to propose a scheme to determine the shape of the universe.

By looking at the distribution of the hot and cold spots in the cosmic-microwave-background radiation, it is possible to look for patterns of repeating spots or some other periodic behaviour that would indicate that the universe has a non-trivial topology associated with it. Unfortunately, the task Levin sets herself is ambitious and will probably not work because the universe is so large that – even if it were compact – light would not have had time to traverse it by today. Nevertheless, her explanation of the physics behind the idea is so compelling that I, for one, have been convinced that it is worth trying harder to find evidence for non-trivial topology in the universe.

This is a special book, written by someone who has a gift for science together with the skill and bravery to place that science in the context of her personal life. She describes the struggles facing many postdocs establishing a career in academia as they move constantly between temporary positions while at the same time trying to continue with a life outside of academia. Although she and Warren pay a heavy price as their relationship ends, at the end of the book Levin tantalizingly hints that they may get back together after meeting on a sidewalk in her beloved California, where the book began. In doing so, she even keeps open the possibility of a Hollywood film.

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How the Universe Got Its Spots: Diary of a Finite Time in a Finite Space: Amazon UK/Amazon US

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