Читать книгу Planning and Executing Credible Experiments - Robert J. Moffat - Страница 29

Only the simplest attributes of systems can be directly measured – the rest are inferred.

For example, tensors, complex numbers,² and vectors cannot be ordered and, therefore, cannot be “measured.” These can be described by ordered sets of scalars (dyads, triads, and two or three‐dimensional arrays of scalars), but those are simply the components of the entity, not the entity itself.

Many times people seem to recognize this problem but don't know how to describe their malaise. They want information but find themselves talking about measurements. For example, a former governor of Mississippi has been quoted as saying (and I paraphrase), “When putting money in education, everyone wants to see some measurable return for the money. Yet it is the one area that has the greatest degree of intangibles.” There is no measurable attribute of education except a purely artificial one: “test scores.” Teachers know that test scores don’t measure educational achievement. But when people insist on measurements, they will get measurements.

A great deal of the information we use in daily decision‐making is nonscalar and, therefore, intrinsically not measurable. For example, we cannot measure the appearance of a face, the sound of a voice, or the taste of tomato soup, and yet with no difficulty at all, we greet our friends, recognize their voices, and enjoy our dinners. The information transfer by sight, hearing, and through taste represents very complex information handling using arrays of scalars and correlations between pairs of scalars (temporal and spatial). No instrumentation system can do as sophisticated a job of pattern recognition as the human eye/mind combination, or of frequency analysis/correlation as the ear/mind combination, or of chemical analysis as the taste‐bud/mind combination. We are not denying the improving capabilities of neural networks, wavelet transformations, or AI deep learning – we are just marveling.