6. The importance of defining terms

Before we proceed, it is important to clarify how important rigour in its terms is to science, and why it is important to apply those terms consistently. More specifically, we must be completely clear what ‘mass’ and ‘joules’ are before we provide any figures. They may seem straight forwards, but a subtle and important point is at stake. For example, in his paper Does Population Ecology Have General Laws Peter Turchin says “The similarity between the exponential law and the law of inertia is striking” (Turchin, 2001). But unfortunately, the proposed similarity does not exist: or at least, not in the specific way he proposes.

There is a particular fallacy in debating called ‘the etymological fallacy’. Since we do not wish to be accused of it, it is important to be clear what it is. The linguistic phenomenon ‘pejoration’ is an example of this fallacy. Pejoration is the process of semantic change by which a word that used to mean one thing gradually depreciates in its meaning (McArthur, 1992, p. 758). It can sometimes even come to mean the opposite.

It is perhaps best to first consider a word that has not undergone pejoration such as the mathematically precise ‘hypotenuse’. Since it has never entered popular currency, it has remained associated with geometry, and its meaning has never changed. According to Steven Schwartzman’s The Words of Mathematics, An Etymological Dictionary of Mathematical Terms used in English, it derives from the Greek hypo- or “under” and teinein or “to stretch” (Schwartzman, 1994). When a right angle is inscribed in a circle, the circle’s diameter “subtends” that right angle … which is the Latin for sub- “under” and -tendere “to stretch”. Even when a right triangle is not inscribed in a circle, its hypotenuse is still the side that “stretches” from one of its legs to the other, and so “under” its right angle. It could not possibly be anything else, and the understanding it evokes has a stark and simple clarity.

Hypotenuse stands in complete contrast to the English word ‘silly’, a classic example of pejoration. Up until the fifteenth century it was associated with the Old German selig or ‘blessed’. Previously spelt ‘sely’, it meant “holy, innocent, helpless, deserving of sympathy”. Country people, who were certainly worthy of receiving sacredness and blessings, were also deserving of sympathy because they lacked their own priests to do this. They were therefore ‘silly’—i.e. worthy to be blessed—because they received ministrations from the Church in the shape of regular visitations from priests in the nearest town. But then gradually, ‘silly’ attached itself to the traits associated with country people: including being ‘simple’ and ‘weak in the head’. It therefore gradually came to have today’s meaning of “showing lack of good sense, frivolous”. The etymological fallacy is the attempt to insist, in a debate, that a word clearly intended in its current meaning should instead be understood with reference to some prior historical meaning.

Most words—including those characteristically used in science, in biology, and in ecology—live in an uneasy terrain somewhere between ‘hypotenuse’ and ‘silly’ and exhibit slow, and often inadvertent, semantic shifts. Such semantic shifts sometimes occur because people deliberately choose to use a word differently. But sometimes they occur because they don’t quite properly understand it in the first place, or else have forgotten something very important about it. Whichever the cause, the inaccuracies and differences in denotation can be significant. So for example, the words ‘mass’ and ‘inertia’ should be as inextricably conjoined in mathematics and science as are hypotenuse and right-angle. As soon as ‘hypotenuse’ is used, we know exactly where to look for the appropriate right-triangle. The same should hold for mass and inertia. We should therefore exercise the greatest of care that mass and inertia do not get divorced.

The question is, of course, whether or not biology and ecology are conducive to the kinds of regularities—often called “laws”—found with such ease in other so-called ‘harder’ sciences. Physics is the most oft-cited reference. In Laws in biology Rejane Bernier decides that the best policy is to excuse biologists and ecologists from compliance by saying:

Biological investigation is related more to inductive inference than to deductive inference. One cannot deny that general laws do exist in biology, but, at the same time, one must admit that they are quite rare, and that biologists have very seldom had recourse to deduction. (Bernier, 1983, p. 270).

It is hard to know how to interpret this. Does it mean that biologists and ecologists should be excused for misunderstanding a basic scientific word like ‘mass’? But since Galileo and Newton’s clarification of mass is where the modern adventure with science begins, it is hard to see how biologists can truly regard themselves as scientific if they do not thoroughly respect its usage and, indeed, refuse to engage in its abusage.

Bertram Murray raises similar issues in his paper Are ecological and evolutionary theories scientific?:

… my colleagues and I approach the study of biology in fundamentally different ways, reflecting different philosophies of science, and these may be worth examining.

My biological colleagues seem to be verificationists. They usually propose ad hoc hypotheses, which are tested directly by observation or experiment. Sometimes they propose inductive general hypotheses, which more often than not have numerous exceptions. By contrast, with regard to theory structure and evaluation, I am a Popperian in search of universal laws and initial or background conditions from which I can predict or deduce biological facts. … (p. 257)

Only one textbook mentions deduction (Solomon et al., 1993). … These authors do not discuss the deductive methods of Popper, much less that of Newton, Einstein, Bohr, Feynman, and many other physicists, whose general laws, when applied under a variety of initial conditions, produce a deductive theory with an enormous information content.

Inasmuch as biologists are not introduced to the scientific method of Newton, Einstein, Bohr, Feynman and Popper, it is no wonder that they follow the inductive method of Bacon, taught in virtually every textbook and practised by virtually every biologist. The evidence indicates that biological explanation relies on ad hoc hypotheses and induction. (p. 259). (Murray, 2001).

Figure 2: Inertia and Force: A Marble in Motion
 Inertia and Force: A Marble in Motion

Scientific-mathematical terms such as ‘mass’, ‘inertia’, and ‘hypotenuse’ are introduced to promote clarity of thought and language, and to avoid semantic shifts and pejoration in the efforts to understand the surrounding environment. It is not, therefore, to invoke the etymological fallacy to probe the original and historic meanings of such terms, and as their usage is intended in the classic scientific figure we are initially introduced to in Figure 2.

We are all introduced to the problems this figure raises because it is how we should all learn to think. It allows us to see the consequences of the differences in attitude Murray refers to, howsoever they may be caused. It is a prime example of the clarity in thought and linguistic terminology we are all asked to emulate.

We rapidly remember—we are, after all, still working scientists!—that the forces acting on this marble are gravity, friction, air resistance, and the reaction force normal to both the hypotenuse, which is the inclined plane, and to the horizontal plane after it, and on which the marble will roll until it runs off the ledge—from which it then falls. There is a dependency here, for the behaviour of mass and inertia are somehow linked to right-triangles and hypotenuses.

It will not take much jogging of our memory to recollect that we can solve all relevant problems by equating the marble’s potential energy to its rotational and kinetic energies through mgh = ½mv2 + ½Ir2ω2 where m is the marble’s mass, g is gravitational attraction, h is its initial height on the inclined plane, v is its velocity, I is its moment of inertia with respect to its axis of rotation (i.e. its diameter), r is its radius, and ω is its angular velocity. But we don’t do this kind of thing every day any more, so when our son or daughter asks for our help, because his or her physics teacher wants him or her to figure out the effects of air resistance once that marble rolls off the ledge, then determining the correct answer is suddenly not so easy! We know there is a ‘catch’ here somewhere because we vaguely remember Galileo’s important demonstration that the vertical and the horizontal components of velocity are independent … but we have forgotten so much we have become somewhat hazy on how to apply such basic terms and concepts to this relatively simple situation.

This kind of dim haziness regarding ‘mass’, ‘inertia’, ‘forces’ and the like is now—unfortunately—how most of us as working biologists and ecologists live. Even if they don’t remember it, most physicists can work out the correct formula for air displacement and the drag force, = ½dAv2, from first principles. Unlike many biologists and ecologists, they are still in touch with those principles. They will also be immediately clear that the retarding drag force will at some point equal the weight presented, by the marble’s mass, to gravity; and they will soon tell their son or daughter what additional information might be required—if any?!—to solve this problem.

This is no time for an excursion into linguistic philosophy, but hypotenuse never induces a myopic fog of this kind. The larger point is that it is not possible to develop coherent biological or ecological theories with such haziness on such fundamental scientific concepts as mass, inertia, work, and joule, nor concerning which term is measuring what with respect to what. It all also means that we are unlikely to recognize them for what they are, when they show themselves in a different context—such as in these biological and ecological contexts. We are also likely to think we have correctly identified them when we have not, which is all too often the case in contemporary biology and ecology.