Background

The single most consequential activity of any scientific work is probably that which falls under the rubric of "measurement." There is a broad awareness among educated people in the general public of the endless and unresolved debates among social scientists over what it is that they are actually counting and measuring. This awareness is stimulated by a sense that, because the phenomena they examine cannot be exactly reproduced and experiments can only examine narrowly selected pieces of the social reality of interest, the social sciences are scientific in a very different way than the engineering and "hard" sciences. This outlook conditions and frames much of the discussion of measurement issues in the social science literature up to our present day.

During the 1920s and 1930s, when the social sciences in North America were being converted into professions based on programs of post-graduate-level academic formation, many dimensions of these problems were being discussed fully and frankly in the literature. In a memorable 1931 paper, Prof. Charles A. Ellwood, who lead in professionalizing sociology, chaired the American Sociological Association in 1924, and produced (before his death in 1946) more than 150 articles and standard textbooks in the field that sold millions of copies, weighed in strongly on these matters:

A simple illustration may help to show the essence of scientific reasoning or thinking. Suppose a boy goes out to hunt rabbits on a winter morning after a fresh fall of snow. He sees rabbit tracks in the fresh snow leading toward a brush pile. He examines the snow carefully on all sides of the brush pile and finds no rabbit tracks leading away from it. Therefore he concludes that the rabbit is still in the brush pile.

Now, such a conclusion is a valid scientific conclusion if there is nothing in the boy's experience to contradict it, and it illustrates the nature of scientific reasoning. As a matter of fact, this is the way in which the great conclusions of all sciences have been reached-all the facts of experience are seen to point in one direction and to one conclusion. Thus the theory of organic evolution has been accepted by biological scientists because all the facts point in that direction-no facts are known which are clearly against this conclusion. Organic evolution is regarded as an established scientific fact, not because it has been demonstrated by observation or by methods of measurement, but rather because all known facts point to that conclusion.

This simple illustration shows that what we call scientific method is nothing but an extension and refinement of common sense, and that it always involves reasoning and the interpretation of the facts of experience. It rests upon sound logic and a common-sense attitude toward human experience. But the hyper-scientists of our day deny this and say that science rests not upon reasoning (which cannot be trusted), but upon observation, methods of measurement, and the use of instruments of precision. Before the boy concluded that there was a rabbit in the brush pile, they say, he should have gotten an x-ray machine to see if the rabbit was really there, if his conclusion is to be scientific; or at least he should have scared bunny from his hiding place and photographed him; or perhaps he should have gotten some instrument of measurement, and measured carefully the tracks in the snow and then compared the measurements with standard models of rabbit's feet and hare's feet to determine whether it was a rabbit, a hare, or some other animal hiding in the brush pile. Thus in effect does the hyper-scientist contrast the methods of science with those of common sense.

Now, it cannot be denied that methods of measurement, the use of instruments of precision, and the exact observation of results of experiment are useful in rendering our knowledge more exact. It is therefore, desirable that they be employed whenever and wherever they can be employed. But the question remains, in what fields of knowledge can these methods be successfully employed? No doubt the fields in which they are employed will be gradually extended, and all seekers after exact knowledge will welcome such an extension of methods of precision. However, our world is sadly in need of reliable knowledge in many fields, whether it is quantitatively exact or not, and it is obvious that in many fields quantitative exactness is not possible, probably never will be possible, and even if we had it, would probably not be of much more help to us than more inexact forms of knowledge.

It is worthy of note that even in many of the so-called natural sciences quantitatively exact methods play a very subordinate role. Thus in biology such methods played an insignificant part in the discovery and formation of the theory of organic evolution. (16)

A discussion of this kind is largely absent in current literature of the engineering and "hard" sciences and is symptomatic of the near-universal conditioning of how narrowly science is cognized in these fields. Many articles in this journal, for example, have repeatedly isolated the "chemicals are chemicals" fetish — the insistent denial of what is perfectly obvious to actual common sense, namely, that what happens to chemicals and their combinations in test tubes in a laboratory cannot be matched 1:1 with what happens to the same combinations and proportions of different elements in the human body or anywhere else in the natural environment.

During the 20th century and continuing today in all scientific and engineering fields pursued in universities and industry throughout North America and Europe, the dominant paradigm has been that of pragmatism — the truth is whatever works. This outlook has tended to discount, or place at a lower level, purely "scientific" work, meaning experimental or analytical-mathematical work that produces hypotheses and/or various theoretical explanations and generalizations to account for phenomena or test what the researcher thinks he or she cognizes about phenomena. The pressure has been for some time to, first, make something work and, second, to explain the science of why it works later, if ever.

This begs the question, "Is whatever has been successfully engineered actually the truth, or are we all being taken for a ride?" The first problem in deconstructing this matter is the easy assumption that technology, i.e., engineering, is simply "applied science" — a notion that defends engineering and pragmatism against any theory and any authority for scientific knowledge as more fundamental than practical.

Ronald Kline is a science historian whose works address various aspects of the relationship of formal science to technologies. In a 1995 article, he points out:

A fruitful approach, pioneered by Edwin Layton in the 1970s, has been to investigate such "engineering sciences" as hydraulics, strength of materials, thermodynamics, and aeronautics. Although these fields depended in varying degrees on prior work in physics and chemistry, Layton argued that the groups that created such knowledge established relatively autonomous engineering disciplines modeled on the practices of the scientific community. (195)

Kline does go on to note that "several historians have shown that it is often difficult to distinguish between science and technology in industrial research laboratories; others have described an influence flowing in the opposite direction - from technology to science - in such areas as instrumentation, thermodynamics, electromagnetism, and semiconductor theory." Furthermore, he points out that although a "large body of literature has discredited the simple applied-science interpretation of technology - at least among historians and sociologists of science and technology - little attention has been paid to the history of this view and why it (and similar beliefs) has [s/c] been so pervasive in American culture. Few, in other words, have [examined]... how and why historical actors described the relationship between science and technology the way they did and to consider what this may tell us about the past." It is important to note, however, that all this still leaves the question of how the relationship of engineering rules of thumb (by which the findings of science are implemented in some technological form or other) might most usefully apply to the source findings from "prior work in physics and chemistry."

One of the legacies of the pragmatic approach is that any divergence between predictions about, and the reality of, actual outcomes of a process is treated usually as evidence of some shortcoming in the practice or procedure of intervention in the process. This usually leapfrogs any consideration of the possibility that the divergence might actually be a sign of inadequacies in theoretical understanding and/or the data adduced in support of that understanding. While it may be simple in the case of an engineered process to isolate the presence of an observer and confine the process of improvement or correction to altering how an external intervention in the process is carried out, matters are somewhat different when it comes to improving a demonstrably flawed understanding of some natural process. The observer"s reference frame could be part of the problem, not to mention the presence of apparently erratic, singular, or episodic epiphenomena that are possible signs of some unknown sub-process(es). This is one of the greatest sources of confusion often seen in handling so-called data scatter, presumed data 'error/ or anomalies generated from the natural version of a phenomenon that has been studied and rendered theoretically according to outcomes observed in controlled laboratory conditions.

Professor Herbert Dingle (1950), more than half a century ago, nicely encapsulated some of what we have uncovered here:

Surprising as it may seem, physicists thoroughly conversant with the ideas of relativity, and well able to perform the necessary operations and calculations which the theory of relativity demands, no sooner begin to write of the theory of measurement than they automatically relapse into the philosophical outlook of the nineteenth century and produce a system of thought wholly at variance with their practice. (6)

He goes on to build the argument thus:

It is generally supposed that a measurement is the determination of the magnitude of some inherent property of a body. In order to discover this magnitude we first choose a sample of the property and call it a 'unit'. This choice is more or less arbitrary and is usually determined chiefly by considerations of convenience. The process of measurement then consists of finding out how many times the unit is contained in the object of measurement. I have, of course, omitted many details and provisos, for I am not criticising the thoroughness with which the matter has been treated but the fundamental ideas in terms of which the whole process is conceived and expressed. That being understood, the brief statement I have given will be accepted, I think, as a faithful account of the way in which the subject of measurement is almost invariably approached by those who seek to understand its basic principles. Now it is obvious that this is in no sense an 'operational' approach. 'Bodies' are assumed, having 'properties' which have 'magnitudes'. All that 'exists', so to speak, before we begin to measure. Our measurement in each case is simply a determination of the magnitude in terms of our unit, and there is in principle no limit to the number of different ways in which we might make the determination. Each of them-each 'method of measurement', as we call it-may be completely different from any other; as operations they may have no resemblance to one another; nevertheless they all determine the magnitude of the same property and, if correctly performed, must give the same result by necessity because they are all measurements of the same independent thing. (6-7)

Then Prof. Dingle gives some simple but arresting examples:

Suppose we make a measurement-say, that which is usually described as the measurement of the length of a rod, AB. We obtain a certain result-say, 3. This means, according to the traditional view, that the length of the rod is three times the length of the standard unit rod with which it is compared. According to the operational view, it means that the result of performing a particular operation on the rod is 3. Now suppose we repeat the measurement the next day, and obtain the result, 4. On the operational view, what we have learnt is unambiguous. The length of the rod has changed, because 'the length of the rod' is the name we give to the result of performing that particular operation, and this result has changed from 3 to 4. On the traditional view, however, we are in a dilemma, because we do not know which has changed, the rod measured or the standard unit; a change in the length of either would give the observed result. Of course, in practice there would be no dispute; the measurements of several other rods with the same standard, before and after the supposed change, would be compared, and if they all showed a proportionate change it would be decided that the standard had changed, whereas if the other rods gave the same values on both occasions, the change would be ascribed to the rod AB; if neither of these results was obtained, then both AB and the standard would be held to have changed. If an objector pointed out that this only made the adopted explanation highly probable but not certain, he would be thought a quibbler, and the practical scientist would (until recently, quite properly) take no notice of him. (8-9)

The "operational view" is the standpoint according to which the reference frame of the observer is a matter of indifference. The conventional view, by way of contrast, assumes that the observer's standard(s) of measurement corresponds to actual properties of the object of observation. However, when the physical frame of reference in which observations are made is transformed, the assumption about the reference frame of the observer that is built into the "operational view" becomes dysfunctional. Such a change also transforms the reference frame of the observer, making it impossible to dismiss or ignore:

But with the wider scope of modern science he can no longer be ignored. Suppose, instead of the length of the rod AB, we take the distance of an extra-galactic nebula, N. Then we do, in effect, find that of two successive measurements, the second is the larger. This means, on the traditional view, that the ratio of the distance of the nebula to the length of a terrestrial standard rod is increasing. But is the nebula getting farther away or is the terrestrial rod shrinking? Our earlier test now fails us. In the first place, we cannot decide which terrestrial rod we are talking about, because precise measurements show that our various standards are changing with respect to one another faster than any one of them is changing with respect to the distance of the nebula, so that the nebula may be receding with respect to one and approaching with respect to another. But ignore that: let us suppose that on some grounds or other we have made a particular choice of a terrestrial standard with respect to which the nebula is getting more distant. Then how do we know whether it is 'really' getting more distant or the standard is 'really7 shrinking? If we make the test by measuring the distances of other nebulae we must ascribe the change to the rod, whereas if we make it by measuring other 'rigid' terrestrial objects we shall get no consistent result at all. We ought, therefore, to say that the probabilities favour the shrinking of the rod. Actually we do not; we say the universe is expanding. But essentially the position is completely ambiguous.

As long as the transformation of the frame of reference of the phenomenon is taken properly into account, the operational view will overcome ambiguity. However, the comparison of what was altered by means of the preceding transformation serves to establish that there is no such thing as an absolute measure of anything in physical reality:

Let us look at another aspect of the matter. On the earth we use various methods of finding the distance from a point C to a point D: consider, for simplicity, only two of them-the so-called 'direct' method of laying measuring rods end to end to cover the distance, and the indirect method of 'triangulation' by which we measure only a conveniently short distance directly and find the larger one by then measuring angles and making calculations. On the earth these two methods give identical results, after unavoidable 'experimental errors' have been allowed for, and of course we explain this, as I have said, by regarding these two processes as alternative methods of measuring the same thing. On the operational view there are two different operations yielding distinct quantities, the 'distance' and the 'remoteness', let us say, of D from C, and our result tells us that, to a high degree of approximation, the distance is equal to the remoteness. Now let us extend this to the distant parts of the universe. Then we find in effect that the 'direct' method and the triangulation method no longer give equal results. (Of course they cannot be applied in their simple forms, but processes which, according to the traditional view, are equivalent to them, show that this is what we must suppose.) On the view, then, that there is an actual distance which our operations are meant to discover-which, if either, gives the 'right' distance, direct measurement or triangulation? There is no possible way of knowing. Those who hold to the direct method must say that triangulation goes wrong because it employs Euclidean geometry whereas space must be non-Euclidean; the correct geometry would bring the triangulation method into line with the other, and the geometry which is correct is then deduced so as to achieve just this result. Those who hold to triangulation, on the other hand, must say that space is pervaded by a field of force which distorts the measuring rods, and again the strength of this field of force is deduced so as to bring the two measurements into agreement. But both these statements are arbitrary. There is no independent test of the character of space, so that if there is a true distance of the nebula we cannot know what it is. On the operational view there is no ambiguity at all; we have simply discovered that distance and remoteness are not exactly equal, but only approximately so, and then we proceed to express the relation between them.

The nature-science approach takes what Prof. Dingle has outlined to the final stage of considering nature four-dimensional. If time is taken as a characteristic measure of any natural phenomenon and not just of the vastnesses of distance in cosmic space, then the observer's frame of reference can be ignored if and only if it is identical to that of the phenomenon of interest. Otherwise, and most if the time, it must be taken into account.

That means, however, that the assumption that time varies independently of the phenomena unfolding within it may have to be relaxed. Instead, any and all possible (as well as actual) non-linear dependencies need to be identified and taken explicitly into account. At the time Prof. Dingle's paper appeared in 1950, such a conclusion was neither appealing nor practicable. The capabilities of modern computing methods since then, however, have reduced previously insuperable computational tasks to almost routine procedures.

In mentioning the "operational view," Prof. Dingle has produced a hint of something entirely unexpected regarding the problemspace and solution-space of reality according to Einstein's relativ-istic principles. Those who have been comfortably inhabiting a three-dimensional sense of reality have nothing to worry about. For them, time is just an independent variable. In four-dimensional reality, however, it is entirely possible that the formulation of a problem may never completely circumscribe how we could proceed to operational-ize its solution. In other words, we have to anticipate multiple possible, valid solutions to one and the same problem formulation. It is not a 1:1 relationship, so linear methods that generate a unique solution will be inappropriate. The other possibilities are one problem formulation with multiple solutions (l:many) or multiple formulations of the problem having one or more solutions in common (many:l, or many:many). In modelers' language, we will very likely need to solve non-linear equation descriptions of the relevant phenomena by non-linear methods, and we may still never know if or when we have all possible solutions. (This matter of solving non-linear equations with non-linear methods is developed further at §§4-5 supra.) At this moment, it is important to establish what operational-izing the solution of a problem — especially multiple solutions — could mean or look like. Then, contrast this to how the scenario of one problem with multiple solutions is atomized and converted into a multiplicity of problems based on different sub-portions of data and data-slices from which any overall coherence has become lost.

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