Good Notation Is Valuable
Good Notation Is ValuableDespite common sneering (SyntacticSugar, SyntacticSalt etc), GoodNotationIsValuable.
The most famous example is the replacement in Western Civilization of roman numerals by Indo-Arabic numerals, with positional notation and an explicit zero.
"One of the effects of the introduction of the positional notation was to popularise mathematics: to take what was previously the concern only of specialists and make it available to the general public...[also to make arithmetic operations] almost completely mechanical, thus allowing mathematical minds to start thinking about something else instead. It is by no longer having to think about things that civilisation progresses. (For a more extended discussion of this, see Whitehead[68], particuarly Chapter V on 'The Symbolism of Mathematics.'"
"In fact a good notation is more than mere 'convenience', for it also allows us to structure our ideas hierarchically: we can focus our attention at the appropriate level. For example, when we actually need to consider the structure of a numeral (to find out what number it represents), the details of the positional notation are important. At higher levels of abstraction, however, the notation is so concise and compact that it is easy to regard the numeral as a single object (a molecule, perhaps). A good notation thus conceals much of the inner workings behind suitable abbreviations, while allowing us to consider it in more detail if we require: matrix and tensor notations provide further good examples of this. It may be summed up in the saying: 'A notation is important for what it leaves out.'"
And then there's exceptions which prove the rule. For example, Hubble's constant is given in terms of kilometers per second per megaparsecs, which is immediately useful in astronomy, instead of just doublings per second, which is not.
Contrast with the discredited SapirWhorfHypothesis, LinguisticDeterminism
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