Here is what William Thompson, better known as Lord Kelvin, once said about measure:
« I often say that when you can measure what you are speaking about, and express it in numbers, you know something about it; but when you cannot measure it, when you cannot express it in numbers, your knowledge is of a meager and unsatisfactory kind; it may be the beginning of knowledge, but you have scarcely in your thoughts advanced to the state of Science, whatever the matter may be. »
William Thompson, Lecture on “Electrical Units of Measurement” (3 May 1883)
I found this quote in an early essay of the French philosopher Gaston Bachelard on what he calls “approached knowledge” (Essai sur la connaissance approchée, 1927). For him, measures cannot be considered for themselves, and he does not agree with Thompson on this point. According to him, the fact that a measure is precise enough gives us the illusion that something exists or just became real.
I quote in French, as I could find a English edition nearby, the page numbers refer to the book published by Vrin.
« Et pourtant, que ce soit dans la mesure ou dans une comparaison qualitative, il n’y a toujours qu’un jugement sur un ordre: un point vient après un autre, une couleur est plus ou moins rouge qu’une autre. Mais, la précision emporte tout, elle donne à la certitude un caractère si solide que la connaissance nous semble vraiment concrète et utile; elle nous donne l’illusion de toucher le réel. Voulez-vous croire au réel, mesurez-le. » p. 52
Bachelard criticizes what he calls “the strange equivalence that modern science has established between measurement and knowledge” («l’étrange équivalence que la science moderne a établi entre la mesure et la connaissance » p. 54). He militates in favor of an approached knowledge, i.e. a form that is simple enough to embrace a phenomenon without having to be too close to the results obtained by measures. Avoiding unnecessary variables, a formula gains in inner coherence. The difficulty is to get from the fact to the type.
He argues that knowledge often starts by an intuition (p. 149). It is better that only a normal distribution of results becomes a formula (my translations are… very approximative ! the French text is sometimes close to poetry, see here : « Tandis que la quantité fine se disperse dans une poussière de nombres qu’on ne peut plus recenser, la quantité d’ensemble prend l’aspect du continu et se géométrise. » p.154).
To put it in a nutshell, Bachelard stands for an aware and constructed exercise of science and measurement technology, and a discovery process that doesn’t search for precision itself or small details but assumes that approximation, without being too simple, is a key to knowledge acquisition.
This book may be old, but I think there is still something interesting in this approach. In my research activity, I first thought that I could lead a theoretical research and experiments on complexity that would benefit each other. But in fact, finding complexity measures has something to do with an approximation of a lot a processes that cannot be reviewed in detail. As I want to stay away from heavy parsers or neural networks in order to be able to know what is happening, what Bachelard says seems effective to me.
Last but not least, here is the Dilbert perspective on language measures!
update 2018-04-17: For a comprehensive overview of the rising trends to measure socio-economic phenomena and of the benefits and downsides of quantification, please refer to The Tyranny of Metrics, by Jerry Z. Muller, Princeton University Press, 2018.