“What we seek is not an ‘empirical rule’, but a law of nature that brooks no exceptions.”— Alfred Lotka (1945), “The Law of Evolution as a Maximal Principle” (pg. 167)
“An irreversible process, as the physicist uses the words, is associated with a decrease in thermodynamic potential, with capacity for yielding a balance of work, as when one gas diffuses into another gas.”— Alfred Lotka (1945), “The Law of Evolution as a Maximal Principle” (pg. 169-70)
“Short of this [Russellian] eventuality, or at any rate until it [species mass maximization] is attained, the problem [of evolution] is one of ‘distribution’. What determines the ‘distribution’ of the total matter of the system among the several species and individual organisms, and the successive changes in this distribution? Is there some significant physical quantity which these competing organisms maximize by their collective activities? Problems of distribution are not new to the physical sciences. The whole topic of ‘change of state’ deals with precisely such problems. As applied to these cases, the law of evolution is well known and clearly defined. It states, that for an isolated system, for example, the entropy of the system increases to a maximum as the system approaches equilibrium; or, more generally, that certain clearly defined functions of the parameters specifying the state of the system—its thermodynamic potentials—approach a minimum.”— Alfred Lotka (1945), “The Law of Evolution as a Maximal Principle” (pg. 174--75)
“This observation, casually introduced by Ostwald in one of his lectures in 1902, was the ‘trigger’ that set off the train of thought developed in my subsequent publications, and summarized, in part, in my Elements of Physical Biology (1925) and Analytical Theory of Biological Associations (Theorie Analytique des Associations Biologiques) (1934, 1939).”— Alfred Lotka (1945), “The Law of Evolution as a Maximal Principle” (pg. 176)
“A special example which has often been cited, because of a certain superficial analogy to the growth of a colony of bacteria in a suitable nutrient medium, is that of the crystallization from a supersaturated solution, upon the introduction of a crystal ‘germ’ of the dissolved substance. So long as the supersaturated solution is left undisturbed it may remain as such for long, perhaps indefinite periods, though seemingly spontaneous crystallization may also take place. This restricted type of stability has sometimes been spoken of as the metastable state [see: Beg-Thims interview]. Its thermodynamic potential is not at the minimum possible for the system, and hence, as soon as an available ‘path’ is presented (by the introduction of the crystal germ), the transformation to the crystal form is initiated. It continues until that particular amount of the solid has formed which is required to bring about stable equilibrium, that is, to make the thermodynamic potential a minimum.”
“If this were merely outward appearance of analogy, the oft repeated example would hardly be worth quoting again here. But it is literally true that the nutrient solution is ‘metastable’ in the absence of a germ of an organism capable of growth in it. Whether in primordial nature somewhere locally such a state presented itself, and whether the metastable state could pass over into some kind of elementary ‘living’ matter without the presence of a preexisting germ, just as crystallization of a supersaturated solution can take place even in the absence of a crystal germ, that is today still one of the unsolved problems of science. But if such was the origin of life, we know that it was followed by a long chain of evolutionary development.”Here, we see Lotka struggling with the seeming ‘origin of life’ problem, which has since been solved (see: abioism), with the patch conjecture that life originated when some type of organic-like crystal jumped from a metastable state, via thermodynamic potential decrease, into “some kind of elementary ‘living’ matter”? Lotka, however, to point out, in his “Regarding Definitions” (1925) chapter had pretty nearly arrived at a near abioism like solution. In any event, he gives the following generally correct solution to the problem of defining evolution thermodynamically:— Alfred Lotka (1945), “The Law of Evolution as a Maximal Principle” (pg. 175-76)
Correctly, while this statement is indeed prescient, the evolution function is not ‘analogous’ to thermodynamic potential, it is a thermodynamic potential function, the Gibbs function, specifically. Nevertheless, Lotka goes on to outline a general model:
“We may expect that the law of organic evolution takes the form that it is accompanied in the long run with diminution of some function, analogous to thermodynamic potential, of the parameters defining the physical state of the system as a whole.”— Alfred Lotka (1945), “The Law of Evolution as a Maximal Principle” (pg. 176)
“In organic evolution, trigger action, such as a ‘stimulus’, in the form of a very small dose of external energy, e.g. to the eye or sensor organ, which acts merely as a ‘trigger’ or ‘key’ to release energy supplied by a separate source, such as in the pulling of the trigger of a gun, plays an important role, for trigger action presupposes a fund of free energy ready to be released.”— Alfred Lotka (1945), “The Law of Evolution as a Maximal Principle” (pgs. 170+179)
“What we have before us in organic nature is a system composed of aggregates of energy transformers [e.g. bacterial, animals, humans] adapted by their composition and structure to guide available energy into such channels as lead to their maintenance and growth. A special branch of physics needs to be developed, the ‘statistical dynamics of systems of energy transformers’.”— Alfred Lotka (1945), “The Law of Evolution as a Maximal Principle” (pg. 179)
“Free energy. Associated with the transformer is a fund of free energy" ready to be released by trigger action, that is, by an expenditure of an amount of energy bearing in general no quantitative relation to the energy released, which can thus be far in excess of the energy applied at the ‘trigger’. It can be noted here, only in passing, that the possession of such a fund of free energy is what gives the opportunity for ‘purposive’ action and the exhibition of the phenomenon of ‘will’, that is, action teleologically aimed at future effects.”— Alfred Lotka (1945), “The Law of Evolution as a Maximal Principle” (pg. 181)
“The examination, and, where need be, revision of our fundamental premises is a task of a wholly different order from that of rearing upon these premises a structure of logical argumentation. It is a task that often demands the efforts of giant intellects, of men of altogether unusual independence of thought. Most of us are held back by our preconceived, intuitive judgments, which, blindly entertained, blind us also against the recognition of possible alternatives.”
“In reasoning, the selection of the premises is the all-important part of the process. The main reason for the painfully slow progress of the human race is to be found in the inability of the great mass of people to establish correctly the premises of an argument. Every school ought to give direct instruction in fact-determining and truth-seeking; and the difficulties of these processes ought to be plainly and incessantly pointed out.”
“As a matter of fact our innate perversity in this matter, our inveterate conservatism in all that concerns some of those ‘implicit and unrecognized assumptions out of which sophistry is bred’, is not due to negative influences, to sloth of mind, alone. There is a strong positive misguiding influence at work also: The wish is father to the thought.”
“There is, fortunately, a natural corrective for our inclination to allow likes and dislikes to influence our reason. This corrective is found in the instinct of curiosity, the faculty that impels men to seek the truth, even if it be unpalatable. In fact, a certain type of mind seems to take a particular satisfaction in digging up such otherwise displeasing revelations; the cynic and even the muckraker thus has his useful function. It is probably safe to say, too, that curiosity a desire to know life in all its phases, to ‘experience reality; is fundamentally the motive that impels some individuals to taste of the less savory phases of life.”
“The stabilization of our institutions rests ultimately upon our ability to know and to test assumptions, and upon a willingness to revise them without partisanship, or bitterness, or distress.”
“The life contest, then is primarily a competition for available energy, as has been pointed out by Boltzmann.  Energy in this sense and for this reason has value for the organism which is a very different thing from saying (as some have said or implied) that economic value is a form of energy. It is true that different kinds of energy are in a certain sense interconvertible into each other at fairly definite rates by exchange upon the market, in a human population. But the conversion factors here involved are of a totally different character from those that enter into the analytical expression of the law of conservation of energy.
This must be immediately apparent from the fact alone that the 'mechanical equivalents' of the several forms of energy are absolute constants, whereas the economic conversion factors are somewhat variable, though they have often a species of approximate constancy, a fact which calls for explanation.
Lotka’s 1925 model of money as a function of activation energy, from his Elements (pgs. 355-56), a form of “trigger action”, similar to a small spark triggering a dynamite explosion, which he derived from his mentor German physical chemist Wilhelm Ostwald, who was the first to realize, in the 1890s, that a catalyst acts without altering the energy relations of the reaction, i.e. the free energy changes, and that it usually speeds up a reaction by lowering the activation energy of the reaction, the logic of which Lotka compared to the input of a coin into a candy machine which sets in motion an economic mechanism yielding desired economic product.
A simple example may help to clarify the view; the case of the automatic vending machine, the penny-in-the-slot chocolate dispenser, for instance. The salient facts here are:1. A definite amount of money brings in exchange a definite amount of commodity (and of energy).
2. The physical process is a typical case of "trigger action," in which the ratio of energy set free to energy applied is subject to no restricting general law whatever (e.g., a touch of the finger upon a switch may set off tons of dynamite).
3. In contrast with the case of thermodynamic conversion factors, the proportionality factor is here determined by the particular mechanism employed.
Reflection shows that all transformation of money or of economic assets of any kind into energy by exchange upon the market is of this character. It is always a case of trigger action. Somewhere there is a store of available energy, which can be tapped with an expenditure of greater or less effort. The payment of the price sets in motion the requisite machinery for the release of that energy (or for its transfer of ownership, the release being delayed at the discretion of the buyer).”
“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.
The Lotka chocolate machine model of activation energy based social mechanism triggered by money exchanges.
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 [Die Energie (1908) (pg. 164)], for example, that the determining feature is the (physical) availability of the particular form of energy, is inadequate.”
“The inference that consciousness is absent in non-living matter reminds one somewhat of the assumption commonly made by ignorant persons that insects or similar voiceless creatures feel no pain.”— Alfred Lotka (1925), Elements of Physical Biology (pg. 390)
“Since metabolism is essentially a state of chemical flux, or chemical reaction in progress, one is led to suspect that the conscious state may be in some way correlated to that, transitional state through which matter must pass on its way from one stable molecular combination to another a state regarding which our knowledge today is extremely fragmentary. Almost the only direct evidence we have of matter actually in that state is the observation by Sir J.J. Thomson and by F.W. Aston of such molecular debris as CH3 and the like, by a method capable of detecting these fugaceous aggregations of atoms even though their life period be only a few millionths of a second.”
“This may give us at least some distant idea of the meaning of consciousness as applied to so-called non-living inorganic matter. Such consciousness as may here occur would be, it seems, of the nature of flashes of almost infinitesimally short duration.”
“The separation of "chemical" processes from other physical processes is almost certainly merely a matter of convenience. If, then we tentatively associate consciousness with certain states of chemical strain in molecules, we are forced to contemplate the possible extension of our conception to matter under physical strain generally.”
|Lotka's "strain analogy", at the end of his "consciousness" chapter, wherein he compares the surface tension bubble formation tendency of a soap bubble, to the strain an amoeba makes to engulf a food particle, to the stain of a Newton in working on a difficult problem.|
“When we say that a soap bubble, for example, tends to contract under surface tension, or perhaps when we use even less guarded language and say that it is trying to contract, our terms are commonly thought reprehensible as being more picturesque than scientific. Yet we ought to be prepared for the conception that the straining of the bubble to contract may not be so fundamentally different a thing from the straining of an amoeba to engulf a food particle, or the straining of a Newton to assimilate a new conception or to solve a problem in philosophy. The two phenomena may be far separated, indeed, upon the scale of evolution, yet they may be two rungs upon the same scale.”
“The principle of Le Chatelier is best illustrated by a simple example. Consider the simple chemical reaction:
At high temperatures this reaction is reversible; that is to say, it takes place to some extent in the direction of the upper arrow, but also to some extent in the direction of the lower arrow, and an equilibrium is finally established between these two opposing reactions. Now this is what the Le Chatelier principle tells us: If we add either H alone or alone to the system, the equilibrium is shifted in the direction of the upper arrow, that is to say, in such direction as to absorb some of the added constituent. Similarly, if we heat the system, the equilibrium is shifted in the direction of the lower arrow, that is to say, in the direction of the reaction which absorbs heat. The principle, as enunciated by Le Chatelier himself, is: ‘Every system in chemical equilibrium, under the influence of a change of any single one of the factors of equilibrium, 3 undergoes a transformation in such direction that, if this transformation took place alone, it would produce a change in the opposite direction of the factor in question. The factors of equilibrium are temperature, pressure, and electromotive force, corresponding to three forms of energy heat, electricity and mechanical energy.’
The second paragraph of the principle as quoted above, requires special emphasis. It is often omitted, even by authors of the highest repute with the result that a vagueness is introduced for which Le Chatelier himself cannot justly be made responsible. This vagueness is then often rendered still worse by departures from, the original wording, aimed at an extension of the scope of the law to all conceivable systems and "factors," an extension which is gained with a total sacrifice of all validity of the principle.”
“As has been shown by Ehrenfest (1911) the error arises through failure to discriminate, in the application of the principle, between the intensity factor (e.g., pressure) and the capacity factor (e.g. volume) of an energy. Ehrenfest points out that the explanation lies in the very vagueness of the principles, which permits it to be construed in each case to suit circumstances. The principle is commonly applied fix post facto, and its competence to predict thus escapes any serious test.”
“The broadest definition of the principle of Le Chatelier is that a system tends to change so as to minimize an external disturbance.”— Wilder Bancroft (1911), 
“Every external action produces in, a body or system changes in such direction, that in consequence of this change the resistance of the body or system against the external action is increased. If we regard the faculty of adaptation of animals and plants from the point of view that the organisms undergo, under the influence of external actions, changes which render them more resistant to those actions, then the property of non-living matter which is expressed by the principle of Le Chatelier-Braun may be regarded as a sort of adaptation of such non-living matter.”— Orest Khovolson (1909), Trait de Physique 
“If the equilibrium of a natural complex (system of masses, organism, system of ideas) is disturbed, it adapts itself to the stimulus (Reiz) which causes the disturbance, in such manner that the said stimulus continually diminishes until finally the original or a new equilibrium is again established.”— J. Lowy (1911), Cosmos 
|A rent ($/mo) vs area (ft²) diagram (Ѻ) of New York City, the general model of which Lotka attempts (pg. 288) to map into a conjugate variables formulation of energy model, similar to the PV diagram calculation of work.|
“The second direction in which the analysis, on general grounds, of the principle, enlarges its field of warrant, is in the matter of the kinds of "factors" to which it is properly applicable. It has already been pointed out that, in its physico-chemical application, it must be used with proper discrimination as to the distinction between the capacity and the intensity factor of an energy, as, for example, volume and pressure. It is found, upon analysis, that the applicability of the principle to the effect of a change in pressure, for example rests upon the following fundamental property of the pressure and volume of a system in stable equilibrium.
1. For every value of v, the volume of the system, there is a definite value of pi the pressure which it exerts, the internal pressure, as we may term it.
2. The volume v increases or decreases according as the internal pressure pi is greater or less than the external pressure p upon the enclosure, that is to say:
3. It can be shown that, given (1) and (2), stability demands that the curves representing the relative between p (ordinates) and v (abscissae) must slope from left to right downwards. For if such a curve slopes in the opposite direction, then the slightest displacement from equilibrium will immediately cause the system to travel with cumulative effect, avalanche-like, along the pv curve further and further away from the starting point.
Now these fundamental properties (1), (2) and (3), of a capacity and an intensity factor of an energy are shared by certain parameters that have no direct or simple relation to energy whatsoever [Lotka footnotes the following]:Owing to the custom of counting heat absorbed by a system as positive, but work done upon it as negative, the relation analogous to that of (2) takes the form, in the case of heat energy:
where Q is the quantity of heat absorbed by the system at a temperature from a source at the temperature T. Here the QT curves slope upward from left to right. [Cf. A. J. Lotka, loc. cit., p. 36].
and since the applicability of the principle depends upon these properties, it will extend to such other parameters possessing them. As an example may be mentioned the relation between area a occupied by a population, and the rent per unit area Ri that an (average) individual is willing to pay. If Ri is greater than Re, the rent at market rate, the individual will move into a more spacious apartment, and a will increase, and vice versa; so that:
On the other hand the curves representing, in rectangular coordinates, the relation between rent and area available per head, necessarily slope from left to right downward. If it were true, as sometimes stated, that the more a man has, the more he wants, economic equilibrium would be an unstable condition.”
“In physico-chemical systems the topographic parameter v (volume) is the capacity factor of an energy, as had already been noted; and associated with v is what may be termed a conjugate parameter Pi (pressure), which is the intensity factor of the energy in question, i.e., that factor which determines the direction of any change in
the capacity factor v, according to the scheme:
where pe is the external pressure. This relation is essentially the Helm-Ostwald Intensity Law. Although this law is not as universal as its sponsors would make it appear, yet it has a certain field of utility. For a critique of this law see Max Planck, Eight Lectures on Theoretical Physics, Columbia University Press, 1915, p. 11. The
form of this relation may be taken as the definition of a pair of conjugate parameters.”
“We may speak of the rent per unit area that the representative individual is willing to pay as a measure or at least an index of the ‘population pressure’.”
|Lotka's mechanical walking sensor-induced table edge turning beetle (pg. 341), which he cites in the latter sections of this book in discussions of models of human and animal movement and reactions, along with issues such as the falsities of teleology models.|
See also: Cartesian automaton; Neumann automatonLotka, in his section on “correlating apparatus” (pgs. 340-41), i.e. inputs and outputs of animal reactions, modeled as: receptors, adjustors, and effectors, employs mechanical walking beetle as an example model; about which he says the following:
“Some time ago there appeared on the market an ingenious toy, primarily designed, no doubt, merely to amuse; but, in point of fact, highly instructive. Its general appearance and simple mechanism are illustrated in figure 69. The beetle "walks" on two toothed wheels, of which one is an idler, while the other is rotated by a spring whose gradual release is ensured by a simple escapement device. At its forward end reckoning in the direction of motion (at the "head") the toy is provided with a pair of antennae, of which one is a dummy, and rises clear of the table upon which the beetle is placed to exhibit its talents. The other antenna is operative and is so bent downward as to glide along the table top, in contact with it.Lotka, later, in his 27§§: “Mechanistic and Teleological Interpretation of Adjustors” (pgs. 281-85), elaborates on the nature of the adjustor or sensor input as follows:
A little in advance of the propelling wheel is another smaller toothed wheel, running idle, and disposed transversely to the direction of the driving wheel. This transverse wheel clears the table without contact in the normal working position of the beetle. The animal, if placed somewhere near the center of the table, makes a straight track, apparently intent [purpose] upon reaching the edge and seeking destruction in a species of mechanical suicide. But the moment the operative antenna clears the edge of the table, the body of the toy, till then held up by the contact of the antenna with the table surface, sinks down a fraction of an inch, and the transverse wheel now contacts with the table. In consequence the toy rotates until the running wheel is parallel with the table edge, and the insect continues its peregrinations with the operative antenna hugging the side of the table top.
Clearly here the antenna is a receptor, which "apprises" the insect of certain features in its environment, which depicts, in a crude but sufficient manner the environment in the toy. The law of depiction is here extremely simple; a depression in the external world (table top) is translated into a downward tilt in the angle of repose of the toy.
The adjuster, in this case, is the transverse wheel, about as simple an example of an adjuster as can well be imagined. It "construes" the information furnished by the receptor antenna, and modifies in accordance with this information the law of motion of the toy, in such manner as to preserve the beetle from a fall which might destroy that stability of form on which the continued operation, according to schedule, of the mechanism depends.”
Lotka's mechanical model of a scaled measurement (pg. 382) of sensory induced mechanical "teleology", so to say, which for the mechanical beetle (above) is exact and for humans involves a lag or delay, or something along these lines.
“We have seen, from the example of a simple toy, that typical and fully competent adjusters can very well be provided in and by purely mechanical structures. In the toy beetle anticipatory correlation between the reaction of the beetle and untoward variations of the environment is established as follows: The beetle is progressing along the straight line AB (see fig. 72) . Its law of motion is that of uniform progression along this straight line. Suppose a scale of centimeters is laid along AB. Successively higher scale divisions along AB are reached at successively later intervals. In fact, this scale, with the beetle moving along it (at constant velocity, we may suppose, to simplify the argument) constitutes a clock. If at the time t the driving wheel of the beetle is at the zero mark, scale divisions to the left correspond to and represent past instants, and those to the right represent future instants. Suppose the antenna is 5 divisions long, and that the table edge is at division mark 15. If for any reason the adjuster apparatus failed to function, at time t = 15 the driving wheel of the beetle would pass the table edge and fall over. When the adjuster apparatus is functioning, five time units in anticipation of the threatened catastrophe the antenna "senses" the danger, and the creature turns aside into the path of safety.
Note that this anticipatory reaction depends upon the correspondence between points forward upon the line of advance, and future instants of time. A supposititious future, & future that may be, is depicted, instant by instant, by successive points in the line of advance of the beetle on the supposition that its law of motion continues unchanged. The behavior of the beetle is determined in terms of this depiction of a supposititious future.”
“The depiction in this case is plainly mechanical or geometric. We, as living, conscious organisms, in certain circumstances exhibit a precisely analogous behavior; our action is determined by a picture (psychic in this case) of the future that we seek to avoid or to attain. We are directly conscious of our own volition (whatever its precise physical significance may be.) We hesitate not at all in describing our action as purposive, as directed to and determined by an end, by a final cause. As to the tin beetle, we have dissected him and fully understand his mechanism. We would think it foolish, with our peep behind the scenes, to impute to him volition or purpose; we describe his action as mechanical, as fully determined by an efficient cause.”
|Lotka’s mechanical beetle vs human vs amoeba example brings to mind Alfred Roger’s 2014 human vs geyser vs paramecium example, in respect to classifying one as “alive” and the others as “non-life”, about which, in respect to whether he believes the hydrogen atom is alive, he comments: “There is no essential difference between ‘life’ and ‘non-life.’ The perceived difference is complexity. Old Faithful (Ѻ) has ‘life-like’ movement but is easier to understand than a paramecium (Ѻ). The hydrogen atom is NOT alive.” |
“But what shall we do when confronted with a case that falls into neither of these categories? An amoeba, for example? We cannot enter the amoeba in spirit and become parties to its conscious experience; we do not even know whether it has any such experience. On the other hand its mechanism is not completely known to us. To class it among purposive, teleological beings so long as we are ignorant of its working, and to be prepared to reclassify it among ‘purely mechanical’ structures us soon as we come to understand its physical operation, seen is hardly a very commendable way to marshal our mental stock-in-trade.”
“The mystery may be in part of our own making. The difficulty in answering a question sometimes arises from the fact that the question has been badly put. Certainly no harm can come from an effort to make a survey of some of the relevant facts and their relations. To such a survey we shall proceed forthwith. Here it may be well to summarize briefly three cardinal points in our observations so far:1. Mechanisms teleological in their operation can be constructed, which we would not in any ordinary sense of the word describe as conscious.
2. The active types of teleological mechanisms in nature (animals) impress us as being in some sense conscious, though in the case of the lower rungs on the scale we feel very doubtful as to just what meaning to assign to this statement.
3. In our own selves we feel that consciousness (volition) plays a dominant role in the teleological operation of our bodies, and, in particular, in the operation of the adjusters.
In all that has been said so far the individualistic character of tastes has been emphasized. A man's likes and dislikes are essentially his own personal affair. This does not mean, as might perhaps at first sight appear, that tastes of different individuals are wholly random collections of likes and dislikes, dealt out purely haphazard, like the cards from a well shuffled pack. However erratic human desires may appear in detail, in the gross they display a species of uniformity, of law, of constancy.”
|Left: Lotka says that the tropisms of the moth to light work or operate with the same mechanical inevitableness of the mechanical beetle towards the table edge. Right: an toy Tamiya Mechanical Beetle (Ѻ), that one can by, and study, similar to Lotka's mechanical beetle.|
“The tropisms of a moth apparently draw it toward a light with the same mechanical inevitableness as the gears of the toy beetle constrain it to follow the table edge.”— Alfred Lotka (1925), Elements of Physical Biology (pg. 395)
“Just as a man has learned, in the progress of ages, to think logically, to think in accord with reality, so he must yet learn to will rightly, that is, in harmony with Nature's scheme. We have here a thought that seems fundamental for a natural system of ethics.”— Alfred Lotka (1925), Elements of Physical Biology (pgs. 386-87)
“The choice may not be made simply in response to instinctive impulse. It may be more or less consciously guided by "principles," such as may be given either empirically, on the word of an accepted authority, the Church for example; or as worked out systematically by the agent himself (philosophy of conduct, ethics). These two types of choice may be respectively termed instinctive and reflective, or, in analogy with the terms employed with regard to thought, the instinctive may also be classed as autistic, the reflective as realistic, since the former seeks no basis outside the individual himself, the latter tends to seek an objective basis.”— Alfred Lotka (1925), Elements of Physical Biology (pg. 412)
|Lotka's version of the photon mill model of life.|
“The circulation of substance in the organic world and its inorganic background, which was considered in an earlier chapter in its purely material relations, now acquires a new significance. We recognize in it now a typical characteristic of the great world engine which, for continued operation, must of necessity work thus in cycles. The picture presented to our minds is that of a gigantic overshot mill wheel, receiving from above the stream of sunlight with its two hundred twenty-seven million gross horsepower though much of this is split without effect and discharging below its dissipated energy in the form of heat at the general temperature level. The main outstanding features of the wheel are represented diagrammatically in figure 68. But in detail the engine is infinitely complex, and the main cycle contains within itself a maze of subsidiary cycles. And, since the parts of the engine are all interrelated, it may happen that the output of the great wheel is limited, or at least hampered, by the performance of one or more of the wheels within the wheel. For it must be remembered that the output of each transformer is determined both by its mass and by its rate of revolution. Hence if the working substance, or any ingredient of the working substance of any of the subsidiary transformers, reaches its limits, a limit may at the same time be set for the performance of the great transformer as a whole”
|A rendition of Lotka's conception of an energy flux driven evolution mill wheel, i.e. what has come to be called the "photon mill" model in recent years.|
“The law of evolution adumbrated as a law of maximum energy flux 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.”
“The general effect will be to increase the rate 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’.”
“I wanted to remind the biologists that in the early stages of life what they are accustomed to speak of as natural selection passes over into what might be described as a mere physical selection of stabler compounds.”— Karl Pearson (c.1900), cited by Lotka in Elements of Physical Biology (pg. 152)
“In the population of molecules here under consideration the relation between birth rate and death rate is of the simplest possible form. Each molecule of S1 that ‘dies’ becomes a molecule of S2, and vice versa.”Here we see Lotka mentally vacillating on and or water-testing the view that anthropisms such as ‘born’ and ‘die’ are funny (non-cogent) terms when scaled down into the conceptual physicochemical reaction range of evolution.— Alfred Lotka (1925), Elements of Physical Biology (pg. 153)
“In equilibrium, the molecules are present in amounts proportional to their respective mean lengths of life, although, they are ‘born’ in equal numbers, since k2n2 = k1n1.”— Alfred Lotka (1925), Elements of Physical Biology (pg. 153)
“Thus, in the struggle for existence the stabler (fitter) molecules of S1 have the advantage, being, on an average, longer-lived. There is thus an obvious analogy between the course of events in such a population of different species of molecules, on the one hand, and a mixed population of different species of organism on the other, an analogy which extends into details for the exposition of which space is lacking here.”— Alfred Lotka (1925), Elements of Physical Biology (pg. 153)
“Every complete reaction consists of three separate stages, with each of which is associated its characteristic energy change. In general, molecules in the free state exist in a phase which is non-reactive, and in order to carry out any reaction it is first of all necessary to bring them into a reactive phase. This, which is the first stage of the reaction, requires that a definite amount of energy should be supplied to each molecule, the amount necessary being the difference in energy contents of the initial phase and the particular phase necessary for the reaction in question.
The second stage of the reaction is the atomic rearrangement whereby new molecules are produced, and it is this stage, and this stage alone, which is represented by the equation of the reaction.
The third and final stage is the change in phase of the newly synthesized molecules, whereby they pass into their normal and non-reactive phases. These last two stages are both accompanied by an escape of energy. If the sum of the amounts of energy evolved in the second and third stages is greater than that absorbed in the first stage, the reaction is exothermic; whilst an endothermic reaction is one in which the energy necessary for the first stage is greater than the total amount evolved in the second and third stages.”
“It should be remarked that the second stage is, apparently, passed through in an exceedingly brief space of time, so that at any instant only an imperceptibly small amount of substance exists in the transitional state. We are, in fact, almost wholly devoid of any information regarding matter in this state, and the words of Schonbein hold true in almost their full force today: "Presumably, between the state in which two portions of matter exist after completion of chemical combination, and the state in which they previously existed separately, there is a series of transition states of which the chemistry of today knows nothing."
Probably the only positive and direct experimental evidence we have of matter in this intermediate state between two compounds is furnished by the superlatively refined methods of Sir J. J. Thomson and Dr. F. W. Aston, which not only reveal but actually weigh such decapitated molecules as CH3, whose length of life is measured in ten-millionths of a second.
As to the agencies, the "fluctuations" that provide, every now and again, the requisite energy to carry a transforming molecule "over the crest of the hill," there is first the thermal agitation of the molecules, second the influence of incident light in photochemical reactions, and third the influence of catalysts, whose action probably depends on a flattening of the path over the hill crest, the point of departure and the final state remaining unchanged. For discussions of these technical details the reader must be referred to the literature, a few of the more recent publications being noted in a footnote below.
While the details of the manner of the "birth" and "death" of the molecules in chemical transformation are, as yet beyond the range of the observation of the physicist, the fundamental laws of energetics, which hold true generally, and independently of particular features of mechanism, are competent to give substantial information as to the end product, at any rate, of the evolution of such a system as considered in the simple example above. The final equilibrium must accord, as regards its dependence on temperature, pressure and other factors, with the second law of thermodynamics, which may thus be said to function as a law of evolution for a system of this kind.
This is a point worth dwelling on a little at length, inasmuch as our knowledge of the form and character of the law of evolution for this special type of system may be expected to serve as a guide in the search for the laws of evolution in the more complicated systems, belonging to an essentially different type, which confront us in the study of organic evolution. The second law of thermodynamics can be expressed in various ways, but the form in which it serves our present purpose best is that which states that the system evolves toward a state in which certain functions (thermodynamic potentials) of the variables defining its condition are at a minimum, somewhat as a ball placed in a hemispherical bowl ultimately comes to rest in the position in which its (gravitational) potential is a minimum, namely, at the lowest point of the bowl.
Mary laws of nature are conveniently expressed in this form, as minimum (or maximum) laws, and it is to be expected that the law of evolution in life-bearing systems also, (where, as we shall see later, mechanism cannot be lightly waved aside into the convenient catch-all of the laws of thermodynamics), will be found to receive its most convenient expression in this form. In another respect the case of chemical evolution may confidently be expected to be found a good model in the treatment of the broader problem of evolution. It is to be noted that the law of chemical evolution is expressed in terms of the system as a whole. It is the thermodynamic potential of the entire system that approaches a minimum. Biologists have rather been in the habit of reflecting upon the evolution of individual species. This point of view does not bear the promise of success, if our aim is to find expression for the fundamental law of evolution.”
“Generally it can be said that in equilibrium the thermodynamic potential is a minimum, but the expression for this potential will vary according as pressure and temperature, or volume and temperature, for example, are held constant. Only this shall be noted in passing: Whereas, in the thermodynamical treatment of physico-chemical phenomena a function Φ is given (essentially as the expression of the laws of thermodynamics), and whereas certain consequences are derived from this known function, the type of problems with which we are here concerned is of inverse nature. We are given certain data regarding the behavior of these systems, for example, the fact that their evolution follows more or less closely a system of equations of the type of the general equations (1) (Chapter VI) of the Kinetics of Material Transformation; and the problem may be raised, as to whether there exist functions Φ analogous to the functions known as thermodynamic potentials, in terms of which the behavior of the system can be concisely epitomized, after the manner of thermodynamics. If such a plan could be successfully carried out, the result would be a species of quasi-dynamics of evolving systems, in which certain parameters P played a role analogous to forces, without being in any sense identical with forces (or even with generalized forces); certain other conjugate parameters p would play a role analogous to displacements, and certain functions Φ would resemble in their relations to certain events in the system, the energy functions Φ (free energy, thermodynamic potentials) of thermodynamics.”— Alfred Lotka (1925), Elements of Physical Biology (pgs. 319-21)
“Truth comes out of error more readily than out of confusion.”— Francis Bacon (1620), New Instrument of Science (§2:Aphorism 20) (Ѻ); cited by Lotka in Elements of Physical Biology (§1:Regarding Definitions, pg. 3)
|In 1901, Lotka, aged 21, as a student in the physical chemistry lectures of Wilhelm Ostwald, listened to a lecture of the growth of bacteria (Ѻ) as compared to crystal (Ѻ) growth, both described by one and the same physicochemical principles, which, as he later (1945) recalled, acted as the “trigger” for the train of thought that led to his Elements of Physical Biology (1925).|
“In any case, the similarity between physical-chemical and biological systems had first struck Lotka much earlier, while he was attending Friedrich Wilhelm Ostwald's lectures in Leipzig in 1901. In one of these lectures, Ostwald compared the growth of a bacterial colony to the formation of crystals in a supersaturated liquid. Such a liquid existed in what he called a "meta-stable" state, that is, it was in equilibrium until disturbed by the addition of a crystal which would act as a "seed" for the formation of more crystals until a second equilibrium of concentration was attained. The whole process was accompanied by energy changes within the system. In a similar manner, the bacterium "seed" in a nutrient broth grew by extracting solid matter from the surrounding liquid, a process accompanied by energy changes in the living colony. Ostwald's analogy introduced in passing at the end of a lecture was only a heuristic device used to illustrate how biological processes might be understood by reference to inorganic processes. As Lotka later recalled, it was this comparison which had acted as the "trigger" for the train of thought that led eventually to the Elements. The important difference was that Lotka's argument rested not on superficial resemblance, but on the demonstration of a true identity between physical-chemical and biological systems. This demonstration required an elaboration of Ostwald's sketch.”
“The time is ripe. I see many signs of the fact. Have you seen a recently published book by Burns and Paton, An Introduction to Biophysics? It also dug a spur into my side—not that there is anything to get excited over, the book would hardly be described as either inspired or inspiring. But it shows the undercurrent, which one of the days must break through to the surface.”
|Lotka's table 17 (pg. 197) showing a 13 elemental composition of a human (see: periodic table; human molecular formula; hmolscience periodic table).|
|Lotka's table of 17 elements comprising organisms (plants and animals), via citation to Henry Osborn (1917).|
“On the whole it may be said the living organisms are composed of comparatively rare elements. We are, indeed, earth-born, but yet not altogether common clay. Indeed, taken literally the expression "common clay," as applied to man, is an extreme case of poetic license; for aluminum and silicon the chief constituents of clay, and taking second and third place in rank of abundance among the components of the earth's crust, are both present only in traces in the human body.”
“Physical biology, as here conceived and discussed, is essentially a branch of the greater discipline of the ‘general mechanics of evolution, the mechanics of systems undergoing irreversible changes in the distribution of matter among the several components of such system. In introducing the term ‘physical biology’ the writer would suggest that the term ‘biophysics’ be employed (as hitherto) to denote that branch of science which treats of the physics of individual life processes, as exhibited IN THE INDIVIDUAL organism (e.g., conduction of an impulse along nerve or muscle); and that the term ‘physical biology’ be reserved to denote the broader field of the application of physical principles in the study of life-bearing systems AS A WHOLE. Physical biology would, in this terminology, include biophysics as a subordinate province.”
See also: Darwin on higher and lowerIn 1942, Joseph Needham published a critique of Lotka’s mention that:
“The passage 'from lower to higher forms', which are often used to describe the direction of evolution, are vague, and undoubtedly contain an anthropomorphic element [and his suggestion that] these be replaced by proceeds 'from simpler to more complex forms'.”
|Lotka's diagram of his program of physical biology (pg. 53), a subset of which he defines as "biophysics", aka physiology.|
“In the era BC (before cybernetics) it [Elements of Physical Biology] was an important source of education and encouragement for few souls who had gleam in their eyes about the prospective mathematization of the social sciences. It had a substantial influence on Henry Schultz and Paul Samuelson, and, I am sure, many others besides myself. As a matter of fact, most of the ideas of Wiener emphasizes—for example, the relation of entropy to organizational behavior—can be found in Lotka, and I have felt some annoyance at the lack of recognition of the latter’s contributions.”— Herbert Simon (c.1990) (Ѻ)
|Lotka's periodic table (pg. 207), at a point in time when "90 elements" were known, with elements highlighted being the elements of a human, according to his table 17 (pg. 197), thus defining a person, in modern parlance, as a "CHNOPS+7 phase", according to Lotka's cited measurements.|
“When the elements have been ‘mingled’ in the fashion of a man, and come to the light of day, or in the fashion of the race of wild beasts or plants or birds, then men say that these ‘come into being’, and when they are ‘separated’, they call that in common parlance, death .... let not the error prevail over the mind that there is any other source of all the perishable creatures that appear in countless numbers.”— Empedocles (c.450BC), cited by Alfred Lotka (1925) in Elements of Physical Biology (pg.185)“There is no coming into being of aught that perishes, nor any end for it, but only mingling, and separation of what has been mingled.”— Empedocles (c.450BC), cited by Alfred Lotka (1925) in Elements of Physical Biology (pg. 246)
“It is to be hoped that these men, finding that they cannot longer write impertinently and absurdly will be reduced either to write nothing, or books that may teach us something; and so, ceasing to trouble the world with riddles or impertinencies, we shall either by their books receive an advantage, or by their silence escape an inconvenience.”— Robert Boyle (1661), The Skeptical; cited by Lotka (pg. x)
“In all such cases there is one common circumstance, the system has a quantity of potential energy, which is being transformed into motion, but which cannot begin to be so transformed until the system has reached a certain configuration, to attain which requires an expenditure of work which in certain cases may be infinitesimally small, and in general bears no definite proportion to the energy developed in consequence thereof. Every existence above a certain rank has its singular points, the higher the rank, the more of them. At these points influences too small to be taken into account by a finite being may produce results of the greatest importance. All great results produced by human endeavor depend on taking advantage of these singular states when they occur. In the course of this our mortal life we more or less frequently find ourselves on a physical or moral watershed, where an imperceptible deviation is sufficient to determine into which of two valleys we shall descend.”— James Maxwell (c.1870), “Article”, in: Life of Clerk Maxwell (editors: Lewis Campbell and William Garnett (1882) (pgs. 441-43); cited by Lotka in Elements of Physical Biology (pg. 408)
“An abandonment of willfulness without extinction of will, but rather by means of a great development of will, whereby, instead of being consciously free and really in subjection to unknown laws, it becomes consciously acting by law, and really free from the interference of unknown laws— James Maxwell (c.1870), Ethics; cited by Lotka in Elements of Physical Biology (pg. 414)
“Not only do the body fluids of the lower forms of marine life correspond with sea water in their composition, but there are at least strong indications that the fluids of the highest animals are really descended from sea water.”— Lawrence Henderson ( 1913), The Fitness of the Environment (pg. 187); cited by Lotka in Elements of Physical Biology (pg. 203)
“Mind is merely the ‘integration’ of the organism’s motor responses to stimuli.”— A.G. Tansley (1916), summary of the views of Edwin Holt in The Freudian Wish (pg.76-94); cited by Lotka in: Elements of Physical Biology (pg. 405)
“The preface is that part of a book which is written last, placed first, and read least.”— Alfred Lotka (1925), Elements of Physical Biology (pg. vii)
“In the struggle for existence, the advantage must go to those organisms whose energy-capturing devices are most efficient in directing available energies into channels favorable to the preservation of the species.”— Alfred Lotka (1922) (Ѻ)
“Evolution is the history of a system undergoing irreversible changes.”— Alfred Lotka (1925), Elements of Physical Biology (pg. 24)
“Problems of evolution are in large measure problems of probabilities, statistical problems. Incidentally, this reflection disposes of the rather foolish objection sometimes raised against the theory of evolution, that it ascribes the course of events in an evolving system to chance. When we describe a phenomenon as being governed by chance, we do not, of course, mean that there are no definite causes (determining factors) at work; we merely state in these terms that the causes are complex and not known to us in detail.”— Alfred Lotka (1925), Elements of Physical Biology (pg. 25)
“The law of evolution is the law of irreversible transformations; that the direction of evolution (which, we saw, had baffled description or definition in ordinary biological terms), is the direction of irreversible transformations. And this direction the physicist can define or describe in exact terms. For an isolated system, it is the direction of increasing entropy. More generally, it is the direction of decreasing thermodynamic potential, this potential being variously defined, according to the conditions of transformation. The law of evolution is, in this sense, the second law of thermodynamics.”— Alfred Lotka (1925), Elements of Physical Biology (pg. 26)
“What is needed is an altogether new instrument—a microscope for elephants; one that shall envisage the units of a biological population as the established statistical mechanics envisage molecules, atoms and electrons; that shall deal with such average effects as population density, population pressure, and the like, after the manner in which thermodynamics deal with the average effects of gas concentration, gas pressures, etc.; that shall accept its problems in terms of common biological data, as thermodynamics accepts problems stated in terms of physical data; and that shall give the answer to the problem in the terms in which it was presented.”— Alfred Lotka (1925), Elements of Physical Biology (pgs. 39-40); cited by Roderick Seidenberg (1950) in Post-Historic Man (pgs. 153-54)
“Physical chemistry views the progressive changes in a system comprising several chemical species, that is to say elements, compounds, phases, etc. It describes the system by enumerating these components, by stating their character and extent (mass); and by further indicating the values of certain quantities or parameters, such as volume or pressure, temperature, etc., which, together with the masses of the components, are found experimentally to be both necessary and sufficient, for the purposes in view, to define the state of the system. With the instantaneous state of the system thus defined, physical chemistry investigates by observation and by deductive reasoning (theory) the history, the evolution of the system, and gives analytical expression to that history, by establishing relations, or equations, between the variables defining these states (after the manner set forth above), and the time.”— Alfred Lotka (1925), Elements of Physical Biology (pg. 41)
“We envisage the life-bearing system, in the progress of evolution, as an assembly of a number of components: Biological species; collections or aggregations of certain inorganic materials such as water, oxygen, carbon dioxide, nitrogen, free and in various combinations, phosphorus, sulfur, etc. rate of growth dX/dt of any one of these components will depend upon, will be a function of, the abundance in which it and each of the others is presented; this rate of growth will also be a function of the topography, climate, etc. Terrestrial species have an essentially two-dimensional distribution, so that area functions here in a manner somewhat analogous to that in which volume enters into physicochemical relations. Aquatic life, with its three-dimensional sphere of activity, is enacted in systems whose extension is described in terms of volume. More detailed topographic parameters may be required to define in sufficient completeness the configuration, the structure of these systems.”— Alfred Lotka (1925), Elements of Physical Biology (pg. 43)
|A physicochemical sociology depiction of micro-mechanics (individualism and interaction view) and macro-mechanics (system-view), as Lotka refers to them, generally, for chnopsological systems.|
“It so happens that many of the components that play an important role In nature, both organic and inorganic, are built large numbers of individuals, themselves very small as compared with the with the aggregations which they form. Accordingly the study of systems of this this kind can be taken up in two separate aspects, namely, first with the attention centered upon the phenomena displaced by the component aggregates in bulk; we may speak of this as the ‘bulk mechanics’ or ‘macro-mechanics’ of the evolving system. And, secondly, the study of such systems may be conducted with the attention centered primarily upon the phenomena displayed by individuals of which the aggregates are composed. This branch of the subject may suitably be termed the ‘micro-mechanics’ of the evolving system. It is evident that between these two branches or aspects of the general discipline there is an inherent relation arising from the fact that the bulk effects observed are of the nature of a statistical manifestation or resultant of the detail working of the micro-individuals.”— Alfred Lotka (1925), Elements of Physical Biology (pgs. 50)
“If the population of the United States continues to follow this [Pearl-Reed equation] growth curve in future years, it will reach a maximum of some 197 million souls, about double its present population, by the year 2060 or so. Such a forecast as this, based on a rather heroic extrapolation, and made in ignorance of the physical factors that impose the limit, must, of course, be accepted with reserve.”— Alfred Lotka (1925), Elements of Physical Biology (pg. 67)
“The evidence points clearly that the elements, such as we know them, are the product of ‘the general brewing of material which occurs under the intense heat in the interior of the stars.’ Out of such foundry came our own abode, if we accept the well-considered views of Eddington (1923): ‘I do not say that the earth was a gaseous body when it first became recognizable as an independent planet, but I am convinced that its material was at one time merged in a completely gaseous sun.’ And since we are of earth, ours also is the same origin. The hand that writes these words and the eye that reads them alike are composed of the selfsame atoms that came into being, ages and ages ago, in the young sun. Far, far more wonderful than any dream of old mythology is the story of our creation.”— Alfred Lotka (1925), Elements of Physical Biology (pgs. 272-273); an early "star stuff" type quote
“The last things to receive critical scrutiny are always the fundamental premises of our arguments.”— Alfred Lotka (1925), a general statement made in context of misuse of Le Chatelier’s principle; in: Elements of Physical Biology (pg. 282)
“Facts are stubborn things; it seems a pity to demolish the idol of a pretty generalization, but in such things we cannot permit the wish to be father to the thought.”— Alfred Lotka (1925), Elements of Physical Biology (pg. 289)
“As Pareto remarks, if a man dislikes spinach, it is useless trying to prove to him, as one would demonstrate a proposition in geometry, that spinach tastes good.”— Alfred Lotka (1925), Elements of Physical Biology (pg. 385) 
“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.”— Alfred Lotka (1925), Elements of Physical Biology (pg. 358)
“Gilbert and Pogue in their memoir on Power 9 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.”— Alfred Lotka (1925), Elements of Physical Biology (pg. 366); an early energy slave type of statement
“In a most real way, the artificial extension of our natural body, e.g. artificial ears (telephones, artificial eyes (microscope), etc., have bound men together into one body: so very real and material is the bond that modern society might aptly be described as one huge multiple Siamese twin. That a species of ‘slavery’, that is to say of ownership of one person's body [artificial or not] by another or by others, should prevail, is in the last analysis an absolutely unavoidable situation, once we recognize that no sharp lines are drawn to separate the individual from his fellow; willy-nilly we must accept the fact..”— Alfred Lotka (1925), Elements of Physical Biology (pgs. 369-70)
“It is a singular fact possessing a certain psychological interest, that as soon as we understand the modus operandi of a teleological mechanism we are disposed to reject its interpretation in terms of ‘final causes’.”— Alfred Lotka (1925), Elements of Physical Biology (pg. 384)
“To say that a necessary condition for the wilting of these words is the willing of the author to write them, and to say that a necessary condition for the writing of them is a certain state and configuration of the material of his brain, these two statements are probably merely two ways of saying the same thing.”— Alfred Lotka (1925), Elements of Physical Biology (pg. 403)
“Aimed collisions imply a correlation between a present state or event and a future occurrence or eventuality (a future that will be or a future that may be). Psychologically this correlation is apprehended as purposive forethought. Physically it implies the disposal of a fund of free energy], since the energy for bringing about (or for avoiding) a future encounter cannot itself be derived from that encounter. There is thus of necessity a fundamental connection between purposive action and the disposal of a fund of free energy.”— Alfred Lotka (1925), Elements of Physical Biology (pg. 409)
“An agent is not always conscious of the relation of his actions to the beneficiary. Thus, for example, the scientific investigator, working under the stress of the instincts of curiosity, workmanship, and self-expression, may have little or no thought of conferring a benefit on society. Such benefit nevertheless follows. The choice may not be made simply in response to instinctive impulse. It may be more or less consciously guided by ‘principles’, such as may be given either empirically, on the word of an accepted authority, the Church for example; or as worked out systematically by the agent himself (philosophy of conduct, ethics).”— Alfred Lotka (1925), Elements of Physical Biology (pg. 412)
“The role of the hands in the evolution of man's intelligence seems to have been clearly recognized by the Greek philosopher Anaxagoras (500-428 BC). He explained, as cited by Will Durant, that ‘man's intelligence by the power of manipulation that came when the forelimbs were freed from the tasks of locomotion’.”— Alfred Lotka (1925), Elements of Physical Chemistry (pg. 440)“To say with the great stoic ‘0 universe, whatsoever is in harmony with thee, is in harmony with me.’ The being whose will is so adjusted is fortune's favorite; all things must bend to his will as they bend to nature's law. For his will is nature's law.”— Alfred Lotka (1925), Elements of Physical Biology (pg. 434); concluding sentence of book; possibly his philosophical creed or belief statement motto