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A mathematical explanation would involve a comparison of the density of stars throughout the universe with the inverse-square drop-off in light intensity from e

A mathematical explanation would involve a comparison of the density of stars throughout the universe with the inverse-square drop-off in light intensity from each. If you assume for the sake of argument that all stars are as bright as the sun, and that stars have a uniform density throughout the universe (either a finite-but-huge or infinite universe, it makes little difference here), then you could solve for the mean intensity of light throughout, or in our case, "how bright the sky is at night." The article makes a classic (and really hard to escape! I've seen this sort of thing called a "paradox" on many occasions.) mistake of examining two infinite quantities (infinite stars, up to an infinite distance away) and assuming that they must cancel each other out, that infinity/infinity=1. But not all infinities are the same, and infinity/infinity can work out to 0, or to 0.1, or to pi, or to infinity (as in the case of "# real numbers"/"# integers"), or to anything else; you have to look at the details -- what kind of infinity is it? -- and figure out how they compare.

jakobegger 11y ago
The article makes no mistake, it just doesn't go into enough detail. To determine the amount of energy reaching us, we need to integrate over the energy density divided by the square of the distance over the whole 3d space. As any physicist can tell you, an integral over the whole space will diverge unless the kernel falls off faster than 1/r^2. This means that one of the following must be true a) either the universe is finite, ie. the density falls off b) we don't integrate over the whole space (we can't see far enough due to age of universe) Which is exactly the argument this article is making Edit: in other words, infinite or finite-but-huge is an important difference when integrating over constant density; the former integral will diverge, the latter will not

jakobegger 11y ago

The article makes no mistake, it just doesn't go into enough detail. To determine the amount of energy reaching us, we need to integrate over the energy density divided by the square of the distance over the whole 3d space. As any physicist can tell you, an integral over the whole space will diverge unless the kernel falls off faster than 1/r^2. This means that one of the following must be true a) either the universe is finite, ie. the density falls off b) we don't integrate over the whole space (we can't see far enough due to age of universe) Which is exactly the argument this article is making Edit: in other words, infinite or finite-but-huge is an important difference when integrating over constant density; the former integral will diverge, the latter will not