An example of a teaching analogy used to explain an abstract idea in a popular science book,
"the galaxies are rushing away from each other at enormous speeds…
the analogy of a balloon with a large number of dots marked on its surface. If the balloon is blown up the distances between the dots increase in the same way as the distances between the galaxies. Here I should give a warning that this analogy is must not be taken too strictly. There are several respects in which it is definitely misleading. For example, the dots on the surface of a balloon would themselves increase in size as the balloon was being blown up. This is not the case for the galaxies, for their internal gravitational fields are sufficiently strong to prevent any such expansion. A further weakness of our analogy is that the surface of an ordinary balloon is two-dimensional – that is to say, the points on its surface can be described by two coordinates; for example, by latitude and longitude. In the case of the Universe we must think of the surface as possessing a third direction.. …
But then what does the radius of the balloon represent, and what does it mean to say the balloon is being blown up? The answer to this is, that the radius of the balloon is a measure of time, and the passage of time has the effect of blowing up the balloon.…The balloon analogy brings out a very important point. It shows we must not imagine that we are situated at the centre of the universe, just because we see all the galaxies to be moving away from us. For, whichever dot you care to choose on the surface of the balloon, you will find that the other dots all move away from it. In other words, whichever galaxy you happen to be in, the other galaxies will appear to be receding from you."
Fred Hoyle (1960) The Nature of the Universe (Revised ed.)
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