Wednesday, November 6, 2013

As well as we like: accurate(ly) versus efficient(ly)

Doing something well can mean to do it accurately or efficiently, or both. Julian Havil is asking the question how well an irrational number can be approximated by a rational number; and—within this context—he discusses the distinction between the adjectives accurate and efficient or, to be more accurate, the adverbs accurately and efficiently:

If by well we mean accurately, then the answer is as well as we like. It is intuitively clear that the accuracy of rational approximation can, in theory, be chosen to be what we will: there are plenty of rationals and as many as we could desire as close as we desire to our chosen number; consider the decimal expansion of the irrational number, truncated as we please. Yet, there is a hidden cost, as we shall see. Alternatively, if by well we mean efficiently the story is more complex since some numbers are more amenable to rational approximation than others - and from this relative compliance we can draw important distinctions [...]
Julian Havil, 2012.

Well done! 

Keywords: semantics, adjectives, adverbs, word disambiguation, approximation.

Julian Havil: The Irrationals. Princeton University Press, Princeton and Oxford, California, 2012; page154.

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