Psychometric Theory \"If it Exists,

¶ … Psychometric Theory

"If it exists, it can be measured; if it can't be measured, it doesn't exist. "

-Ludlow, 1996

That expression of professor L.H. Ludlow is actually an idea suggested much earlier by Edward Thorndike (1874-1949) and to even earlier arguments, such as those of Sir Francis Galton (1822-1911), for whom a strong case could be made that he was the first psychometrician (Ludlow, 1998). According to Ludlow (1998), Galton specifically argued that being "subjected to measurement and numbers" is a fundamental prerequisite for qualifying any branch of knowledge as a form of science. In some respects, Galton's original formulation is more accurate than subsequent versions of the same basic suggestion as expressed by Thorndike and Ludlow.

The only neat way of reconciling Thorndike and Ludlow's stronger absolute statement with Galton's suggestion is to assume that the absolute position is meant to apply only to the distinction between phenomena that are capable of accurate analysis and those that exist, but defy analysis. With that assumption, the Thorndike/Ludlow position is both consistent with that of Galton and it represents phenomenological objective reality. However, without that assumption, it would seem that the Thorndike/Ludlow formulation is inaccurate and susceptible to disproof.

The principal difference between the broader Galton concept and the much narrower Thorndike/Ludlow position is that the former does not refute the existence of that which cannot necessarily be measured. It merely suggests that until phenomena can be confirmed through objective measurement, it cannot possibly be understood and its observation cannot be regarded as a science (Ludlow, 1998).

The literal interpretation of Thorndike and Ludlow's expression is that phenomena that defy measurement cannot exist. That conclusion is rather easily refuted at the macro level of ordinary matter by the existence of vast oceans and beaches bordering such large bodies of water. At the micro level, the Thorndike/Ludlow position is definitively disproved by various elements of quantum physics (Feynman, 1995; Hawking, 2002).

Consider the prospect of measuring the exact number of all of the water molecules in the Atlantic Ocean. Even at the simplest level where, for the sake of argument, one ignores the fact that water molecules on the surface of the ocean continually evaporate into the atmosphere as water molecules fall from the sky in storms elsewhere along thousands of miles of intercontinental distances, the precise measurement of the number of water molecules in the ocean defies calculation.

Even if one could focus on a precise instant in time, computing the exact number of the water molecules in the ocean would be impossible. That is a function of the irregularity of the shape of the water container represented by the ocean floor, in addition to the physical dimensions of every single living organism and inanimate object displacing water by its physical presence in the medium. The fact that at any instant in time uncountable trillions or quadrillions of individual water molecules are either entering or leaving the ocean makes the prospect of measuring the number of water molecules in the Atlantic Ocean absolutely impossible. The same observation applies to the prospect of counting every single grain of sand along the vast Atlantic Ocean shores.

However, neither Thorndike nor Ludlow would ever have argued that the Atlantic Ocean does not exist. Therefore, even at the macro level of ordinary matter (i.e. individual water molecules and grains of sand) the only defensible interpretation of the Thorndike/Ludlow expression is that it presumes the same concept as expressed by Galton. In that regard, there is no question that an unquantifiable phenomenon may indeed exist notwithstanding its defiance of measurement. the, the meaning of the phrase "If it exists, it can be measured; if it can't be measured, it doesn't exist" would be precisely what Galton argued in 1879: that no proposed volume of the ocean at the level of individual water molecules can be considered scientific simply because there are too many variables capable of being accounted for.

In fact, the physical world around us provides equally illustrative examples that refute the absolute interpretation of the Thorndike/Ludlow expression. Every cement structure consists of a finite number of individual cement particles and of the individual molecules that each cement particle comprises; every forest contains a finite number of leaves; and every meadow a finite number of individual blades of grass and grains of pollen. None of these can be measured accurately yet they all exist.