Measurement is the identification of a relationship—a quantitative relationship established by means of a standard that serves as a unit. Entities (and their actions) are measured by their attributes (length, weight, velocity, etc.) and the standard of measurement is a concretely specified unit representing the appropriate attribute. Thus, one measures length in inches, feet and miles—weight in pounds—velocity by means of a given distance traversed in a given time, etc.
It is important to note that while the choice of a given standard is optional, the mathematical rules of using it are not. It makes no difference whether one measures length in terms of feet or meters; the standard provides only the form of notation, not the substance nor the result of the process of measuring. The facts established by measurement will be the same, regardless of the particular standard used; the standard can neither alter nor affect them. The requirements of a standard of measurement are: that it represent the appropriate attribute, that it be easily perceivable by man and that, once chosen, it remain immutable and absolute whenever used. (Please remember this; we will have reason to recall it.)
Now what is the purpose of measurement? Observe that measurement consists of relating an easily perceivable unit to larger or smaller quantities, then to infinitely larger or infinitely smaller quantities, which are not directly perceivable to man. (The word “infinitely” is used here as a mathematical, not a metaphysical, term.) The purpose of measurement is to expand the range of man’s consciousness, of his knowledge, beyond the perceptual level: beyond the direct power of his senses and the immediate concretes of any given moment. Man can perceive the length of one foot directly; he cannot perceive ten miles. By establishing the relationship of feet to miles, he can grasp and know any distance on earth; by establishing the relationship of miles to light-years, he can know the distances of galaxies.
The process of measurement is a process of integrating an unlimited scale of knowledge to man’s limited perceptual experience—a process of making the universe knowable by bringing it within the range of man’s consciousness, by establishing its relationship to man. It is not an accident that man’s earliest attempts at measurement (the evidence of which survives to this day) consisted of relating things to himself—as, for instance, taking the length of his foot as a standard of length, or adopting the decimal system, which is supposed to have its origin in man’s ten fingers as units of counting.
It is here that Protagoras’ old dictum may be given a new meaning, the opposite of the one he intended: “Man is the measure of all things.” Man is the measure, epistemologically—not metaphysically. In regard to human knowledge, man has to be the measure, since he has to bring all things into the realm of the humanly knowable. But, far from leading to subjectivism, the methods which he has to employ require the most rigorous mathematical precision, the most rigorous compliance with objective rules and facts—if the end product is to be knowledge.
Observe the multiple role of measurements in the process of concept-formation, in both of its two essential parts: differentiation and integration. Concepts cannot be formed at random. All concepts are formed by first differentiating two or more existents from other existents. All conceptual differentiations are made in terms of commensurable characteristics (i.e., characteristics possessing a common unit of measurement). No concept could be formed, for instance, by attempting to distinguish long objects from green objects. Incommensurable characteristics cannot be integrated into one unit.
Tables, for instance, are first differentiated from chairs, beds and other objects by means of the characteristic of shape, which is an attribute possessed by all the objects involved. Then, their particular kind of shape is set as the distinguishing characteristic of tables—i.e., a certain category of geometrical measurements of shape is specified. Then, within that category, the particular measurements of individual table-shapes are omitted.
Please note the fact that a given shape represents a certain category or set of geometrical measurements. Shape is an attribute; differences of shape—whether cubes, spheres, cones or any complex combinations—are a matter of differing measurements; any shape can be reduced to or expressed by a set of figures in terms of linear measurement. When, in the process of concept-formation, man observes that shape is a commensurable characteristic of certain objects, he does not have to measure all the shapes involved nor even to know how to measure them; he merely has to observe the element of similarity.
Similarity is grasped perceptually; in observing it, man is not and does not have to be aware of the fact that it involves a matter of measurement. It is the task of philosophy and of science to identify that fact.
As to the actual process of measuring shapes, a vast part of higher mathematics, from geometry on up, is devoted to the task of discovering methods by which various shapes can be measured—complex methods which consist of reducing the problem to the terms of a simple, primitive method, the only one available to man in this field: linear measurement. (Integral calculus, used to measure the area of circles, is just one example.)
There is no exact method of measuring the intensity of all psychological processes, but—as in the case of forming concepts of colors—conceptualization does not require the knowledge of exact measurements. Degrees of intensity can be and are measured approximately, on a comparative scale. For instance, the intensity of the emotion of joy in response to certain facts varies according to the importance of these facts in one’s hierarchy of values; it varies in such cases as buying a new suit, or getting a raise in pay, or marrying the person one loves. The intensity of a process of thought and of the intellectual effort required varies according to the scope of its content; it varies when one grasps the concept “table” or the concept “justice,” when one grasps that 2 + 2 = 4 or that e = mc2.
Observe that the attacks on the conceptual level of man’s consciousness, i.e., on reason, come from the same ideological quarters as the attacks on measurement. When discussing man’s consciousness, particularly his emotions, some persons use the word “measurement” as a pejorative term—as if an attempt to apply it to the phenomena of consciousness were a gross, insulting, “materialistic” impropriety. The question “Can you measure love?” is an example and a symptom of that attitude.
As in many other issues, the two allegedly opposite camps are merely two variants growing out of the same basic premises. The old-fashioned mystics proclaim that you cannot measure love in pounds, inches or dollars. They are aided and abetted by the neo-mystics who—punchdrunk with undigested concepts of measurement, proclaiming measurement to be the sole tool of science—proceed to measure knee-jerks, statistical questionnaires, and the learning time of rats, as indices to the human psyche.
Both camps fail to observe that measurement requires an appropriate standard, and that in the physical sciences—which one camp passionately hates, and the other passionately envies—one does not measure length in pounds, or weight in inches.
Measurement is the identification of a relationship in numerical terms—and the complexity of the science of measurement indicates the complexity of the relationships which exist in the universe and which man has barely begun to investigate. They exist, even if the appropriate standards and methods of measurement are not always as easily apparent nor the degree of achievable precision as great as in the case of measuring the basic, perceptually given attributes of matter. If anything were actually “immeasurable,” it would bear no relationship of any kind to the rest of the universe, it would not affect nor be affected by anything else in any manner whatever, it would enact no causes and bear no consequences—in short, it would not exist.
The motive of the anti-measurement attitude is obvious: it is the desire to preserve a sanctuary of the indeterminate for the benefit of the irrational—the desire, epistemologically, to escape from the responsibility of cognitive precision and wide-scale integration; and, metaphysically, the desire to escape from the absolutism of existence, of facts, of reality and, above all, of identity.