Olbers’ Paradox: Why Is the Sky Dark at Night? (2000)
Subsequent edit: Assuming the universe is infinite, is where the problem begins. There is no reason to assume that.<p>Original comment:
Is this really not obvious to people?  It's about subtended angles - simple geometry.  As the Earth's distance from a star increases, it subtends a decreasing angle in that star's "sky."  Assuming radiation does indeed proceed radially and in straight lines, at increasing distance the Earth is capable of catching a decreasing portion of that star's radiation.  As the distance approaches infinity, the subtended angle approaches zero and the amount of light reaching us approaches zero.  The star is just as bright, but most of its radiation goes somewhere else besides Earth.<p>Imagine building a giant spherical shell around a star.  Its radius equals the distance between earth and the star.  It catches 100% of that star's radiated energy.  Now paint the Earth on the inside of the shell, actual size.  It looks, to someone standing on the surface of that star, like the real earth, i.e. a tiny dot.  Now divide the surface area of the dot, by the surface area of the sphere (4)(pi)(r^2).  That's how much of that star's energy our planet catches.  Assuming zero degradation across space.<p>So imagine you're in a forest of trees the closest of which are 800 miles away from you.  You'd see the goddamned sky just fine.