what is the function and origin of ramental scale?
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The main point is that size functionsare invariant for every transformation preserving the measuring function. Hence, they can be adapted to many different applications, by simply changing the measuring function in order to get the wanted invariance.
The scales (specifically, a two-pan, beam balance) are one of the traditional symbols of justice, as wielded by statues of Lady Justice. This corresponds to the use in metaphor of matters being "held in the balance". It has its origins in ancient Egypt. Scales are also the symbol for the astrological sign Libra.
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