杏吧原创

THE Universe is big. The Earth is a tiny cosmic backwater. So a question as simple as 鈥淲hat shape is the Universe?鈥� is distinctly tricky when all you鈥檝e got to go on is what you can see from here. Bob Osserman is a distinguished research mathematician, and Poetry of the Universe is his vision of humanity鈥檚 changing views about the geometry of the space in which it lives. Or the space-time in which it lives, which is one of those changes.

There鈥檚 an awful lot of mathematics between the ancient notion of a flat Earth and the big bang, and Poetry makes a fair stab at explaining all of it. The prototype question for 鈥淲hat shape is the Universe?鈥� is 鈥淲hat shape is the Earth?鈥�. We can learn a lot about how to answer the first by seeing what happened to the second.

Osserman tells of the voyages of discovery that mapped the surface of the Earth as his intention is to explore the relation between the map and the territory. Depicting a curved sphere on a flat plane, maps represent reality without reproducing it. Similarly, mathematics provides conceptual maps of the Universe.

Karl Friedrich Gauss pioneered the view of curvature as an intrinsic feature of a space, rather than as a property of how it is situated within some larger space. The idea of representing curved surfaces by maps led to the realisation that there is not a single unique geometry but an infinite variety. From there to Einstein is a convoluted historical tale, but a relatively, as it were, simple conceptual one. The key new ingredient is the idea that time can be considered as an additional dimension. This led Einstein to replace dynamic entities in a changing space by static entities in a frozen space-time. This mathematical trick converts dynamics into geometry, but it also expands the meaning of the word 鈥渦niverse鈥�.

So, what shape is the Universe? I don鈥檛 want to give away Osserman鈥檚 punch line 鈥� or even to give away whether there is a punch line 鈥� but one plausible answer is 鈥渁 hypersphere鈥�, a four-dimensional analogue of the ordinary sphere. Among the many other possibilities are fractals, which bring us to the irregular distribution of matter in the Universe and the 鈥渞ipples at the edge of time鈥� detected by the COBE satellite.

Poetry is a gentle, measured, elegant read that takes us effortlessly from Egyptian surveying to galactic superclusters. Most books on cosmology emphasise the physics; it makes a welcome change to find one that tells the mathematical side of the story. And it also makes a welcome change to find a popular science book that 鈥� unless I am mistaken 鈥� waxes enthusiastic about the Universe without once invoking the word 鈥淕od鈥�.