14. Biology, ecology, molecules, and a volume of ignorance

Semantic shifts, such as when applying notions of ‘distance’ to temperature, are not the only phenomena the etymological fallacy highlights. So also are issues of the relative importance attached to different concepts, and how those affect thought. Newton’s law of inertia, for example, embodies assumptions of ‘distance’, ‘area’, and ‘space’. The three dimensions of space are axiomatic. If we are to equate the exponential law, or any other, with Newton’s law of inertia, then where are the three dimensions over which any suggested exponential law forces might act, for Newton’s laws clearly work in three? Any suggestions of equivalence must be treated with care, for Newton also has implications for the microscopic world. His concepts of space, velocity, acceleration and the like are used, with suitable quantum amendments where necessary, to explain such macroscopic phenomena as temperature and pressure. This link between the microscopic and the macroscopic is so profound that the mass of an oxygen molecule is now known to be 32.0 x 1.66 x 10-27 kilogrammes; and if the temperature is 293 kelvins, then the root-mean-square velocity of the molecules is 478 metres per second (Ohanian, 1987).

If equivalencies and correspondences between biological and physical laws are going to be suggested, then the proposed biological and ecological laws must either have been deliberately constructed with the necessary equivalences between the microscopic and the macroscopic already in situ in their accompanying deep structures; or if not so then they must be very ruthlessly examined to make sure the necessary congruencies exist. Almost invariably, they do not, for biologists and ecologists can no longer do basic science, and have lost touch with some of the most fundamental concepts in their discipline, such as volume, force, and mass … and as we shall now see.

The Avogadro constant, NA, is now accepted as a fundamental constant of nature. Modern scientists know it is essential in tracking the molecules in any system. In other words, Newton’s inertial law is both microscopic and macroscopic, and this must be explicitly recognized. Although temperature and pressure recognize this, the exponential law does not, and therefore fails this congruency test.

Thermodynamic systems have walls that—Newtonian style—their molecules can strike. Those walls are the locus for the system’s characteristic thermodynamic boundary activities—again caused by molecular mass and inertia—of work and heat. These then express themselves in forces and distances, even if heat is only being dissipated. This link between the microscopic and the macroscopic is inviolate. It must remain so under any new proposal. No law of biology can be scientific if it does not do this.

It seems trivial to state, but the three dimensions of space are the basis of this shared reality. But this complacent acceptance of three dimensions was put under trial in 1843 when James Prescott Joule conducted an important experiment to test certain of its aspects (Cardwell, 1991). What is of interest is not the experiment itself, but (a) how he described it; and (b) what chemists and physicists did as they responded to his and other similar discoveries.

Figure 14: The Joule Experiment
 The Joule Experiment

Joule’s experiment is an example of the etymological fallacy and why it is important always to properly probe and understand terms. He wanted to determine if the temperature of a sample of air would remain constant as it expanded. As in Figure 14, he took a length of piping with a stopcock in the middle; connected metal vessels to its two ends; and then submerged the whole in a water bath. He closed the stopcock; emptied one of the vessels; and filled the other with air at a pressure of 22 atmospheres. When he opened the stopcock, the air duly expanded to fill the second vessel.

But then comes the fallacy—the historical difference in terms. As was the convention of the time, Joule described the experiment by saying that the air’s “specific volume”, ν, had increased. Specific volume is the volume occupied per each unit of mass and is given by ν = volume/mass. It is the reciprocal of density. To put it in more modern style, Joule was saying not so much that the air had expanded as that it had “rarefied”. Surprisingly, he was much less concerned with its equally evident increase in volume.

There is here a clear difference in both terms and perspective. Modern scientists stand in contradistinction to Joule who was content with specific volume. They are far more concerned with volume … which has been most carefully extracted from ordinary language and is now performing the very specific function of relating the microscopic to the macroscopic:

A macroscopic observation cannot respond to those myriads of atomic coordinates which vary in time with typical atomic periods. Only those few particular combinations of atomic coordinates that are essentially time independent are macroscopically observable.

Macroscopic measurements are not only extremely slow on the atomic scale of time, but they are correspondingly coarse on the atomic scale of distance. We probe our system always with “blunt instruments.” Thus an optical observation has a resolving power defined by the wavelength of light, which is on the order of 1000 interatomic distances. The smallest resolvable volume contains approximately 109 atoms! Macroscopic observations sense only coarse spatial averages of atomic coordinates.

Rather than describe the atomic state of the system by specifying the position of each atom, it is more convenient (and mathematically equivalent) to specify the instantaneous amplitude of each normal mode. These amplitudes are called normal coordinates, and the number of normal coordinates is exactly equal to the number of atomic coordinates.

… For the purpose of illustration … we think of a macroscopic observation as a kind of “blurred” observation with low resolving power; the spatial coarseness of macroscopic measurements is qualitatively analogous to visual observation of the system through spectacles that are somewhat out of focus. … The amplitude of this mode describes the length (or volume, in three dimensions) of the system. The length (or volume) remains as a thermodynamic variable, undestroyed by the spatial averaging, because of its spatially homogeneous (long wavelength) structure.

… if we were to consider systems with very large numbers of atoms, the frequency of the longest wavelength mode would approach zero …. Thus all the short wavelength modes are lost in the time averaging, but the long wavelength mode corresponding to the “volume” is so slow that it survives the time averaging as well as the spatial averaging.

This simple example illustrates a very general result. Of the enormous number of atomic coordinates, a very few, with unique symmetry properties, survive the statistical averaging associated with a transition to a macroscopic description. Certain of these surviving coordinates are mechanical in nature—they are volume, parameters descriptive of the shape (components of elastic strain), and the like. … The study of mechanics (including elasticity) is the study of one set of surviving coordinates.

Thermodynamics, in contrast, is concerned with the macroscopic consequences of the myriads of atomic coordinates that, by virtue of the coarseness of macroscopic observations, do not appear explicitly in a macroscopic description of a system.

Among the many consequences of the “hidden” atomic modes of motion, the most evident is the ability of these modes to act as a repository for energy. Energy transferred via a “mechanical mode” (i.e., one associated with a mechanical macroscopic coordinate) is called mechanical work. Energy transferred via an “electrical mode” is called electrical work. Mechanical work is typified by the term -P dV (P is pressure, V is volume), and electrical work is typified by the term -E dB (E, is electric field, B is electric dipole moment). … But it is equally possible to transfer energy via the hidden atomic modes of motion as well as via those that happen to be macroscopically observable. An energy transfer via the hidden atomic modes is called heat. [Italics in original]. (Callen, 1985, pp. 6–8)

Volume, in modern scientific eyes, establishes the distances over which molecules can interact and exchange their energies both with each other and with the environment. Again in modern eyes, to state a system’s volume is to give an implicit count, and a description, of molecules and their energy density across its extent. The triplet of concepts ‘volume, number-of-molecules and mass-of-molecules’ should be as indissolubly yoked together in every biologist’s and ecologist’s mind as are ‘hypotenuse, right-angle, opposite side’. If not so, then no amount of reasoning in these disciplines is going to be scientific.

Volume when interpreted in this more modern way, and used as such in science, has proved to be an eminently more useful concept than the specific volume Joule had to work with. Unlike volume, V, which is an extensive property, specific volume, ν, is an intensive property—i.e. one whose properties do not vary with the size of the system. The temperature Joule sought to measure is also intensive meaning that if a first system held at 50 °C is added to a second at that same temperature, the temperature is preserved.

If scientists of Joule’s era did not use volume to establish the sizes of their systems, then what did they use? Just as important, what was the deep structure of that alternative, for it might prove useful to biology? It might also account for the numerous wrong turns biology and ecology have taken.

Most thermodynamic systems are described with two intensive and two extensive properties. The ratio between any two extensive properties is an intensive one. Density, for example, is intensive, and is mass divided by volume … both of which are extensive. It is also the inverse of Joule’s specific volume. Although intensive properties tend to remain conserved as smaller and smaller samples are taken, this does not hold indefinitely. Sample sizes will eventually become so small that atomic and microscopic forces and issues become relevant, and new forces independent of the original size must be taken into account.

Specific volume, with its concept of “rarefying” and “condensing”, did not allow scientists of the early molecular era to properly account for molecular numbers, configurations and behaviours in the systems they chose to study, and so was gradually abandoned. And in choosing to abandon specific volume and turn instead to volume, scientists also chose to make pressure—an intensive variable—more important.

A prison officer, for example, is generally confident that the pressure exerted upon the cell walls by any single prisoner is of no concern. No one prisoner can independently exert enough force to stage a breakout. But should 900 prisoners suddenly congregate at, and push upon, the same wall, then the officer’s attitude is likely to be very different … and even though the pressure exerted by any one has not changed. In this case, the system’s size is better reckoned by counting the prisoners. That determines the total potential force.

Pressure is generally of very little in a single prisoner situation, although it remains of value when pondering whether or not it is a good idea to keep prisoners in tents. We do not do so because it is immediately apparent that the force per unit area is too great. Total force is not required to make a decision in this latter system, but it certainly is in a mass prison breakout one.

Force and pressure are distinct, but both always exist. Indeed, force is to pressure as volume is to specific volume. Force has a specific line or boundary upon or around which it works. It thus compares to volume which establishes a boundary within which, and/or upon which, molecular forces can operate. In contrast to that, pressure does not indicate a specific line of macroscopic force. Nor does specific volume establish a suitable scope or locale for macroscopic operations. But when taken together, pressure and volume achieve what is required. The one provides the boundary that the other lacks. Science requires that intensive and extensive work together in this way or there is no hope of reckoning the fundamental constituents of all known matter … including the biological and ecological.

In most thermodynamic systems—such as with a box sitting upon a table—the sum of all the molecular forces upon the walls balance each other out, and there is no net or spontaneous motion by the box across the table. Therefore, the total force exerted upon the box’s entire surface area is of little interest. Force per unit area can still vary, however, as the system changes in state. The link between pressure and volume is then extremely revealing about the system’s net energy behaviour. So although we do not reckon the total simultaneous macroscopic force on all those external walls, we still reckon the force and mass of its individual components.

The volume V does remain as a relevant mechanical parameter. Furthermore, a simple system has a definite chemical composition which must be described by an appropriate set of parameters. One reasonable set of composition parameters is the numbers of molecules in each of the chemically pure components of which the system is a mixture. Alternatively, to obtain numbers of more convenient size, we adopt the mole numbers, defined as the actual number of each type of molecule divided by Avogadro’s number (NA = 6.02217 X 1023).

This definition of the mole number refers explicitly to the “number of molecules,” and it therefore lies outside the boundary of purely macroscopic physics. An equivalent definition which avoids the reference to molecules simply designates 12 grams as the molar mass of the isotope 12C. …

The macroscopic parameters V, N1, N2, … Nr, have a common property that will prove to be quite significant. Suppose that we are given two identical systems and that we now regard these two systems taken together as a single system. The value of the volume for the composite system is then just twice the value of the volume for a single subsystem. Similarly, each of the mole numbers of the composite system is twice that for a single subsystem. Parameters that have values in a composite system equal to the sum of the values in each of the subsystems are called extensive parameters. Extensive parameters play a key role throughout thermodynamic theory. (Callen, 1985, pp. 9, 10).

If we return to meteorology, then no matter what may be its inaccuracies in prediction, and no matter how great may be the derision at those failures, the subject has been explicitly constructed to take molecular behaviour into account, and it recognizes—through that—the fundamental structure of its objects of study. Many of meteorology’s difficulties exist because the size of an air mass is almost by definition fluid and so does not in that sense have a measurable volume. The boundary on which the forces act is extremely difficult to determine … which is certainly not a flaw in the underlying theory. When atmospheric temperatures and pressures are being measured, meteorologists are immediately taking molecular behaviour into account, and as science requires.

Meteorologists—and again virtually by definition—study what thermodynamicists also study: boundary activities. In the former case it is air masses and ocean currents. Their boundary activities remain work and heat. The sizes of air masses and of ocean currents are left unfixed because climate, the intended object of study, is their interaction—their net external and combined forces—across their unspecifiable boundaries as they do work and exchange heat. The size of the terrain over which a climatological event is manifest might well be of concern to the ultimate consumers of meteorological information, but the fluid nature of these objects makes those areas and volumes extremely difficult to determine. It is, however, the force between those air masses and ocean currents and upon their boundaries that is of primary interest to meteorologists. The individual sizes and extents of air masses and ocean currents are less important, less relevant, and less determinable as variables, although of course critical to determining the likely areas impaced. Weather is always the interaction between such air masses.

Just because we can generally ignore a given system’s externally directed forces over all its walls does not mean that we can or should similarly ignore it for all systems. Sometimes force and specific volume are more important, sometimes pressure and volume. Both are capable of giving correct measures for thermodynamic events, entirely according to circumstance. We now have both a planimeter and Green’s theorem ready for situations when we must reckon the total force circulating all about pertinent areas.