Friday, March 22, 2013

A Cosmic Egg?

News came yesterday of the completion of another survey of cosmic radiation, this one begun in 2009 by the European Space Agency (ESA) using the Planck satellite. The image shown in the papers is the by now familiar cosmic egg we’ve become accustomed to since images were stitched together from the NASA/WMAP (Wilson Microwave Anisotropy Probe) launched in 2001. The latest is best, of course. It has a higher resolution. The age of the cosmos has been tweaked a little: older by 80 million years.

It may have been the illustrations—invariably showing an egg in a surrounding black field. I got to wondering. Is the cosmos really an egg? The answer to that last. First, what are we looking at?

The best way to picture this survey is to imagine that we had a camera able to look through rock. Let’s put it at the center of the earth. It will be able to take photographs of the earth’s surface, its lenses so adjusted that it would see the surface but nothing beyond it. Well, the Planck satellite does just that. It is up in space with its camera able to swivel and move in all directions so that it can take slice-after slice of the night sky. Its lenses are adjusted to pick up only microwave radiation.

To map the results from either of these projects onto a two-dimensional surface requires projection. Let’s recall briefly the Mercator projection. The globe is placed in a tube sized so that it will touch the equators. The image of the earth’s surface is projected onto the tube. The tube is then cut and flattened. The Mercator, and all similar projections, stretch the map in the southerly and northerly directions, therefore deforming distances, shapes, and measurable areas. Alas, no matter what we do in mapping three-dimensional objects in Flat Land, distortion is a given.

World maps and cosmic maps make use of another, the Aitoff projection. That’s what we see when contemplating the cosmic egg. It is named after David A. Aitoff (1854-1933), a Russian geographer. His aim was to produce good global maps, his object being to preserve what he could of shapes and areas while minimizing the space the global image would take up. He began with what is called an equidistant azimuth scale. Such a scale preserves true distances, so that distance on the map is proportional to distance on the ground. But Azimuthal projection significantly distorts continental shape at the borders of the map. Aitoff’s solution, which is, note well, applicable only to spheres, has distortions in all of the measurements, but all of these are minimized. Hence his scale is called a good compromise. He makes his projection by re-scaling the map so that his central meridian is only half as long as his equator. The whole shape of the globe is thus distorted; we get an egg for a sphere; but the contents are reasonably true to reality. Here is the earth mapped using the Aitoff scale:

Let me next deal to the black stuff that surrounds the usual depictions of our cosmic egg. Needless to say, no camera ever took a picture of Nothing. The Planck satellite no more saw the end of the cosmos than our imaginary earth-centered camera could ever see the sky; it only sees hard matter. Therefore we don’t really know what lies beyond the visible. We assume there is nothing there because we believe in Hubble and the Big Bang.

So is the universe an egg? Well, I had a chuckle this morning. In the process of trying to hatch this egg, I came upon two stories (link, link). They suggests that, no matter what the Planck saw or didn’t see, NASA thinks that the cosmos is, even if only ever so slightly, ellipsoid. Well, maybe Ahura Mazda had it right after all….
My images come from ESA and Wikipedia (link).

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