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A mirror that's in shape

03/09/2008

Words can sometimes say a lot and mean very little. Whereas a picture, like the recent one of the GTC's completed primary mirror, can mean a great deal. At last the Universe has a mirror big enough to look at itself in; but it's the shape, not the size that we're going to think about today. Building a mirror over ten metres in diameter meant dividing it up into 36 hexagonal segments. Does that make you think of something else?

In nature, some shapes occur more frequently than others. Spheres, for example, are the commonest basic shape. Bubbles, planets and stars are all spheres that protect, rotate and confine. The sphere is the most symmetrical and stable of shapes, and it will surround any amount of matter with the smallest surface area possible. Objects are as complex as the environment around them: shapes are normally born in response to a need. If an object cannot deal with the demands of its immediate reality it will go the same way as a bicycle that doesn't move: the scrap heap. This means that the more often we see a shape, the surer we can be that it works!

Spheres are most likely to appear in conditions where there are few restraints, where space is homogeneous and where nothing is pushing in a particular direction. In very uniform environments, like a near-empty Universe or a water-covered planet, the sphere will logically be the shape we see most. However, shapes change as conditions become more complex. If we were to put several circles or spheres into a restricted area, they would start competing with one another for the available space. A circle can happily exist with six equal circles surrounding it and in contact with it but, if the pressure continues to grow, the space between the points of contact disappears and the circles become a group of hexagons. You can try this yourself by applying pressure to a handful of drinking straws; it doesn't take long before they change from cylinders into hexagonal prisms.

In other words, when a large number of circles compete for space they form hexagons. This shape is so successful that it is found in many places: beehives, tortoise shells, insects' eyes; and, as we have discovered, in the GTC's primary mirror. This is no coincidence. Engineering often, sometimes unconsciously, looks to nature for simple solutions to apparently impossible problems.

Focusing on the differences between natural and man-made objects is a useful academic exercise; but focusing on the similarities makes them easier to understand. Like the compound eyes of insects, which are made up of thousands of hexagonal lenses, the GTC's primary mirror is divided into 36 hexagonal segments. In both cases the individual lenses work like pixels, creating an image from a single patch of light. This technique, of concentrating light rays with lenses, means that arthropods and telescope mirrors have excellent vision. For an insect, the better it can see its environment the more chance it has of finding food and escaping attack; for a telescope, better vision means seeing faint, distant objects in the Universe that can help us understand more about the moving parts of the cosmos.

The hexagon is also an ideal space-saving shape as it eliminates the empty spaces left by circles. Space is at a premium in a beehive and at the GTC, although at the telescope it is needed for storing light rather than honey. In nature, the hexagon is particularly good at 'paving' space, especially on spherical surfaces like a tortoise shell or the bark of a pine tree. The use of hexagons means that the GTC's primary mirror is a perfect hyperbolic concave surface. It collects and concentrates the light that reaches it like an open container, relaying it on to the secondary and tertiary mirrors from where it is forwarded to the foci for examination.

It is no coincidence that Jorge Luis Borges endowed his Library of Babel, where all knowledge was stored, with an infinite number of hexagonal galleries duplicated in the reflection of a mirror in the hallway. Like pieces of a jigsaw puzzle, hexagons and mirrors were always destined to come together. In the end, hexagons offered not only the best alternative to building, handling and moving an enormous monolithic mirror whilst saving space; it turns out that, combined with the huge size of the GTC, they also offer the best geometry for reflecting the Universe.

Iván Jiménez Montalvo

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