You can often save money by doing your research on a model of the real problem, though this is not necessarily as simple as it sounds. In making a scaled-up or a scaled-down model you cannot always assume that every dimension can be blindly modified in the same fixed ratio.

Suppose you are still watching your television football match and are shown a distant view to enable you to see the whole field and the progress of the play. The players look like dwarfs. But how can you be certain that they aren't dwarfs? Perhaps the manager of the match has decided to save capital outlay by reducing the size of the pitch and has trained a number of dwarfs to play the game; as they might drink less he wouldn't have to pay them so much. How do you know, merely from watching your television screen, that you are not seeing a consistently scaled-down version of the match? You will probably be able to guess by looking at how the players behave. Soon after the beginning of the match they may well become more interested in kicking each other than in kicking the ball. Why doesn't the referee blow his whistle and send someone off? But the wretched little man is blowing into his whistle with all his might, to no effect. A scaled-down whistle will either produce an unrecognizable squeak or else a sound above the human range of detectable frequencies.