Elements of Physical Biology

In view of the entire absence of any general law regulating the ratio of energy released to energy applied in such cases of trigger action, we may ask the question, how does it come about that economic conversion factors, economic ratios-in-exchange of different forms of energy, display any regularity whatever? The answer is not far to seek. The approximate constancy of the economic conversion factors is traceable to the approximate constancy in type of the mechanism involved, namely the human organism and its social aggregations. Just as one particular slot machine will always deliver a certain package of chocolate, so a certain social organization under similar conditions will render (approximately) the same amount of selected form of energy in return for a stated sum of money. As to the circumstances that quantitatively determine these economic conversion factors, for a discussion of these the reader must be referred to the literature;!® only this may be remarked here, that the conception advanced by Ostwald,!* for example, that the determining feature is the (physical) avazlability of the particular form of energy, is inadequate.

Collective Effect of Individual Struggle for Energy Capture. Our reflections so far have been directed to the selfish efforts of each organism and species to divert to itself as much as possible of the stream of available energy. But if we recall once more the admonition of Bunge—Nature must be considered as a whole if she is to be understood in detail—we shall be led to enquire: What must be the effect, upon the world-as-a-whole, of the general scrimmage for available energy?

It has already been pointed out that the operation of the correlating apparatus is of the nature of a cycle beginning and terminating in the external world; that the grazing cow is able to subsist because the grass is “hungry for oxygen,” that animals are essentially catalysers, oiling the machinery, as it were and assisting energy in its downhill path to levels of lower availability (higher entropy). If we had only the animal kingdom to consider we should in the first instance be disposed to conclude that the cosmic effect of the scrimmage for available energy would be to increase the total energy flux, the rate of degradation of the energy received from the sun. But plants work in the opposite direction. And even among animals, greater efficiency in utilizing energy, a better husbanding of resources, and hence a less rapid drain upon them, must work to the advantage of a species talented in that direction.2? There are thus two opposing tendencies in operation, and it is difficult to see how any general principle can be applied to determine just where the balance will be struck.

The Law of Evolution Adumbrated as a Law of Maximum Energy Flux. This at least seems probable, that so long as there is an abundant surplus of available energy running “to waste” over the sides of the mill wheel, so to speak, so long will a marked advantage be gained by any species that may develop talents to utilize this ‘lost portion of the stream.” Such a species will therefore, other things equal, tend to grow in extent (numbers) and this growth will further increase the flux of energy through the system. It is to be observed that in this argument the principle of the survival of the fittest yields us information beyond that attainable by the reasoning of thermodynamics.?!

As to the other aspect of the matter, the problem of economy in husbanding resources will not rise to its full importance until the available resources are more completely tapped than they are today. Every indication is that man will learn to utilize some of the sunlight that now goes to waste. The general effect will be to increase the rate 20 Compare J. Johnstone, The Mechanism of Life, 1921, p. 220. 21 This fact has been recognized independently by the writer and also by H. Guilleminot. For details see A. J. Lotka, Proc. Natl. Acad. Sci., 1922, p.

of energy flux through the system of organic nature, with a parallel increase in the total mass of the great world transformer, of its rate of circulation, or both.” One is tempted to see in this one of those maximum laws which are so commonly found to be apt expressions of the course of nature. But historical recollections here bid us to exercise caution; a prematurely enunciated maximum principle is liable to share the fate of Thomsen and Berthelot’s chemical ‘‘principle of maximum work.”

Let us call to mind once more the picture of the life conflict viewed as the interplay of organisms moving over a topographic chart and suffering a succession of collisions with each other and with features of their environment. We might seek to develop, for such a system, a discipline of statistical mechanics similar to that which the physicist has developed to deal with the kinetic theory of gases and allied problems. No attempt will be made here to carry out this project in any degree of completeness, or to carry it to such ultimate conclusions as it may be competent to furnish. But it may not be out of place to indicate at least a few points, in addition to the pertinent matter contained in the preceding paragraph, that can be offered as first steps toward the development of such a discipline.

Mean Free Path. In the elementary kinetic theory of gases it is shown that the mean free path / of a molecule ina gas is given by?4 *4 See, for example, Winkelmann, Handbuch der Physik, 1906, vol. 3, p. 696. This elementary result is based on the simplifying assumption that the velocity of all the moving molecules is the same. Taking into account the velocities ranging according to the Maxwellian law, it is found that | = me But for our purposes it is quite sufficient to accept the simple elementary method and its result,

where N is the number of moleeule, per unit volume, and s their diameter. This, of course, relates to motion in three dimensions. We may apply similar methods to the case of two species, NV, individuals of S; and Ny» individuals of Sz, operating on a square mile, say, of ground. If the field of influence of S; is a circular field of diameter s it is easily shown that (according to the elementary theory) the mean free path for the individuals of S, is, expressed in miles, nr (26) Frequency of Collisions and of Capture. If v is the average velocity of the individuals of S;, the frequency collision will be, approximately at any rate,

In general not all collisions, but only a certain fraction c, will result in capture. The total captures per unit of time, per square mile, will then be It may be noted in passing that the expression thus found represents, in certain cases at any rate, the term kN, N:2 which appears in equation (38) of Chapter VIII, where it was introduced without analyzing its precise physical significance. Influence of Size of Organism. It is interesting to observe the influence of size of the predatory organism on the frequency of capture. Suppose, leaving all other factors the same, we halve the size of the predatory organisms, so that the new value of Ni, which we may designate by a prime, is given by

If the velocity of the smaller organisms is unchanged, we shall have for the new frequency of capture More appropriate, perhaps, is the supposition that the new velocity v’ is related to the old v in the proportion of the linear dimensions, There is then, other things equal, an advantage for predatory species in small size. In nature, presumably, there is a tendency to strike a compromise between the advantage thus gained, and certain disadvantages, such as relative defencelessness, incurred by decreased stature.

Curves of Pursuit. The coefficient c which occurs in (28) is open to further discussion and analysis. A collision is characterized by the fact that through its duration the law of motion differs essentially and discontinuously from the law of motion between collisions. The coefficient c evidently depends on the law of motion during collision. During collision the two individuals follow a course of the type known as a curve of pursuit. For a discussion of these curves so far as they have been studied, the reader must be referred to the pertinent literature. The mathematical theory of problems in pursuit and conflict generally has hitherto been developed principally, if not exclusively, in connection with warfare. In any effort to deal with the more ‘general theory of conflict between biological species it may be well to have an eye open to the methods followed in the treatment of problems of military and naval tactics. Here, however, this mere hint must suffice.

Random Motion under a Bias. Various problems relating to the motion of a point following in part a random course, but at the same time controlled by some kind of directing influence, have been dealt with by L. Bachelier in his Calcul des Probabilités, 1912, to which the reader may be referred. Chapter XX, on Probabilités Cinématiques, may be found suggestive in connection with the type of motion presented by living organisms, a motion that can be regarded as containing both a systematically directed and also a random element.

Use of Models. Another point shall be passed over here with a mere suggestion. The mathematical treatment of the statistical mechanics of the kind of systems here taken in view may appear to threaten formidable difficulties. It is to be hoped that this will not *° See, for example, Boole, Differential Equations. fourth edition, p. 251. altogether prevent its attack, even if at first sweeping simplifications must be made in the fundamental assumptions. But the writer wishes to draw particular attention to one method that in the past has not been used to any considerable extent, and which may be found serviceable where ordinary analytical methods become forbidding. The method to which I refer is a special form of the graphic method, namely the method of working models. It is well worth considering whether interesting light may not be thrown on various problems of biological conflict, by the use of models designed to imitate the biological warfare somewhat after the manner in which the war game imitates the armed conflict of nations.

Let us now consider the character of the material Nature whose necessary results have been made available . . . . for a final cause.—Aristotle. In preceding pages we have dealt with the correlating apparatus, and its functions, in the gross, without paying more than passing attention to the details of its constitution and operation. It is desirable now to fill in some of these omitted details; we shall consider in turn the depictors, elaborators, effectors and adjustors, with especial attention to the case of the human species. For it goes without saying that a particular interest attaches to the study of the correlating apparatus in man, if only because in no other creature has it developed such singular excrescences as that which prompts, for example, the writing of this book and furnishes the means for the accomplishment of the task. Man thus stands out, if not as a superior being, at any rate as a highly peculiar creature. One might perhaps dispute the propriety of the study so unhesitatingly advocated by Pope; but one cannot truthfully deny the fundamental fact of man’s inordinate interest in himself. Moreover, there are certain very important phenomena that play a prominent réle in the operation of the correlating apparatus, phenomena for the study of which our chief source, indeed our only altogether indisputable source of data, lies in our own self: that group of phenomena briefly summarized under the term consciousness. In- evitably therefore, a study of the correlating apparatus, if carried out in any detail, will center largely about the manifestation of this apparatus in the human species.

In dealing with the several elements of the correlating apparatus it will be convenient to depart somewhat from what might appear the most natural order. Receptors and effectors, though functionally separated at the two extreme ends of the operative cycle, are in certain respects rather closely related in practice. Similarly there is in certain respects an approach between the elaborators and the adjustors. We shall, accordingly, consider the several elements in the order Receptors, Effectors, Klaborators, Adjustors.

The receptors, as has already been noted, are one of the two classes of organs or faculties concerned with the depiction of the environment in the organism (the other class being the elaborators). A typical receptor is the eye, which, in the most literal sense, depicts the external world upon the retina. The law of depiction, in this case, is given by the principles of geometrical optics, and is most easily expressed in terms of two systems or reference frames of codrdinates, the one fixed with regard to suitably chosen features in the external world, the other fixed with regard to the eye that forms the image. So, for example, the impression my eye received at noon today was determined by the fact that it was located at the N.W. corner of Monument Square and was pointed upward at an angle of about 45 degrees, and turned in the E. §.E. direction. The tip of the Washington Monument, whose coérdinates in the “external world” system are 2, y Zz, say, was thus depicted upon my retina! by a point with the codrdinates x’, y’, 2’. This appearance in the analytical, expression of the depicting process, of two codrdinate reference frames, or at least something equivalent, is very characteristic and should be particularly noted. We shall have occasion to refer to this matter again.

But the picture formed by the eye, typical as it is of the process of depiction, is nevertheless essentially incomplete. We know our own world picture as something much more expansive, much more intimate and profuse in detail. When I view a landscape I have not merely in my eye a dead photograph of the rolling hills and placid valleys, in their garb of green, and stirring with life. These things I see; but at the same time I hear the bells of the grazing herd, and all those familiar noises that belong to the tout ensemble of the rustic scene; while the fragrance of the sun-scorched woods, or perhaps the perfume of flowers, enters to fill out another aspect of the picture. So all our receptors or sense organs are, in a larger sense, depicting organs, each supplying its special share toward that composite world picture into which their several contributions are united and further

1 Strictly speaking this is an inverted statement of the facts. We are directly cognizant of sense impressions x’ y’z’, as our prime data, and we infer, or hypothecate, as secondary data, corresponding codrdinates x, y, 2, of an external world. See Chapter XXXIV, footnote 2. But for our present purpose the more usual (naive) viewpoint will serve. developed by certain special faculties, the Elaborators, notably the Memory and Imagination. Artificial Receptors. A detailed discussion of the natural receptors with which our body is supplied by the physiological processes of embryological development and growth is unnecessary here, since these things are fully discussed in special works devoted to these subjects, such as for example, Ladd and Woodworth’s Elements of Physiological Psychology (Scribner’s, 1915). But a special development of the receptors in man, which has had, and is destined still to have, an altogether superlative importance in the evolution of the world is passed over in total silence in most works of the character cited, and calls for discussion here in some proportion to the importance of this phase of the subject: the artificial aids and adjuncts to our senses which the ingenuity of man has pressed into his service. With prophetic eye Robert Hooke in 1665 foresaw—no doubt very imperfectly—what these aids were destined to accomplish for the human race.

The next care to be taken, in respect to the senses, is asupplying of their infirmities with instruments, and, as it were, the adding of artificial organs to the natural; this . . . . hasbeen of late years accomplished with prodigious benefit to all sorts of useful knowledge. . . . . It seems not improbable, but that by these helps the subtility of the composition of bodies, the structure of their parts, the various texture of their matter, the instruments and manner of their inward motions, and all the other possible appearances of things, may come to be more fully discovered.

That the artificial adjuncts to our correlation apparatus are subject to a process of evolution by selection, by trial and error, was clearly recognized by David Hume,’ who in this, as in other important points, anticipated the conceptions of Darwin and Spencer. The last mentioned was the first to realize fully and to point out clearly the rdle of man-made contrivances, as artificial sense organs on the one hand, and as artificial members (effectors) on the other? As we

* Dialogues concerning Natural Religion, 1757, Edition of 1907, pp. 189-190. Hume’s reflections relate particularly to the artificial effectors (as represented by a ship, for example), but the underlying principle is, of course, the same. * Compare Herbert Spencer, Principle of Psychology, Chapter VII, Section 164; Emerson, The Conduct of Life, Everyman’s Library Edition, pp. 159-190 (original edition, 1860); Wiener, Die Erweiterung unserer Sinne, Leipzig 1900; Lehmann, Die Kinematographie, Leipzig, 19M py 1

look back today upon the progress in recent centuries, it is plain beyond all possible misunderstanding that the ushering in of the era of the man-made adjuncts to his natural body has given not only a new direction to the process of evolution, but has speeded up its progress to an extent without the remotest parallel in the history of our globe. How long it may have taken man to develop his organ of sight by the slow processes of physiological evolution we are quite unable to say, but this is certain, that the time is reckoned in many millions of years. Contrast with this the following brief historical record: The use of spectacles was introduced about 1350.4 The invention of the microscope is credited to the Dutch optician Janssen, 1590. A modern microscope is capable of a magnification of several thousand diameters. (This, however, does not indicate its “separating”’ power, which in point of fact, is only about 200 times greater than that of the naked eye.) Particles too small to be formed into a distinct image by the microscope can still be detected by the ultra microscope, invented by Zsigmondy in 1903. By the method of X-ray photography developed chiefly by Laue 1912 and Bragg 1915, direct optical evidence of the arrangements of atoms in a crystal is obtained, and the distance between the layers, of the order of so0.0bv.000 Of an inch, is measured. This represents, in effect, a million-fold improvement on the separating power of the eye. The method of C. T. R. Wilson® 1912 renders visible to the eye the track of an electron, whose diameter is of the order of one ten-millionmillionth of aninch. The power of the natural vision is, in such case as this, virtually multiplied by two hundred billion.

The step from the use of a crude pair of spectacles in 1300 to this was taken in the space of about six centuries—and much of the progress is condensed within a space of less than three decades. The evolution of man’s artifical sense organs has proceeded at a pace so utterly out of scale with that of his natural equipment that the aid of diagrammatic representation quite forsakes us here. Any attempt to plot such progress as this on a single scale in rectangular codrdinates could

4 Darmstaedter in his Handbuch der Gechichte der Naturwissenschaftem states that the Emperor Nero in A.D. 63 employed a cut emerald to view the gladiator contests. Roger Bacon in A.D. 1250 recommended the use of lenses for persons of weak sight. The chronicle of St. Catherine’s Convent at Pisa mentions Alessandro de Soina as maker of spectacles. merely result in two limbs of a curve, the first essentially coinciding with the time axis, the second rising abruptly, at an angle indistinguishable from a right angle.®

The historical sketch thus drawn represents but a diminutive fragment of the total development of man’s artificial correlating apparatus. It is out of the question to cover here in any exhaustive manner even the aids to vision alone. We must pass by with a mere mention the astronomical telescope, which opens the pupils of our eyes one hundred inches wide;’ or that fantastic application of the stereoscope to astronomical objects, which enables us to see the universe as it would appear to a gigantic being with his eyes many millions of miles apart. As for a general survey of the entire field of our artificial sense organs, to give this would amount to nothing less than the writing of a work, in several volumes, on general observational methodology. For our purpose here these hints must suffice.

The natural effectors, like the natural receptors, have received their full share of attention, and it is not proposed to add here to the existing literature’ on this special phase of the subject. As to the artificial aids to the effectors, these are plainly evident on every hand, and do indeed give a stamp altogether its own to this unprecedented industrial era in which we live. Gilbert and Pogue in their memoir on Power? estimate that the use of power derived from coal and other extraneous sources (i.e., not from the human body) gives to each man, woman and child the service equivalent of 30 servants. But in point of fact this figure, based merely on the total horsepower developed, gives an altogether inadequate picture of the real facts. Machinery has not only increased our energy output, it has immensely multiplied the speed of production. One extreme

® Compare also H. Heath Bawden, T i i epee , The Evolution of Behavior, Psychol. 7 Or more than double this, with the aid of Michelson’s interference device ® The following may here be mentioned: J. Amar, Le Moteur Humain 1914: A. Keith, Engines of the Human Body, 1920; O. Fisher (Teubner), 1906 Grundlagen fiir eine Mechanik der lebenden Kérper; C. Bell, Animal Meotane ics, 1838 (Library of Useful Knowledge); W. M. Feldmann, Bicmathenmntiad Lippincott 1923; L. L. Burlingame, General Biology, (Jonathan Cape) 1923. ® Smithsonian Institution Bulletin, 102, Part 5. ;

example of this is seen in the printing plant. A modern newspaper press, with a crew of 6 to 10 men, can turn out 80,000 complete 16-page papers per hour, all folded, counted and delivered ready for the carrier boys. It may be left to the reader to make some kind of estimate of the time that would be required to write the same matter out in longhand, to say nothing of the folding and counting. 200 miles. Fria. 70. Toe Evo.iutrion or Man’s Mpans or TRANSPORTATION

Distance travelled in one hour by different means of conveyance Artificial Effectors; Industrial Evolution. In the development of our artificial effectors, as with the receptors, the progress of evolution has been a rocket-like ascent. To take a simple and very moderate example, the evolution of means of personal transportation is exhibited diagrammatically in figure 70, which, is in essence a target of zones of operation of the kind referred to in Chapter XXV. The figures on which the diagram are based, some of which may very well have been superseded, are the following: