Alfred LotkaThis is a featured page

Alfred Lotka nsIn evolution thermodynamics, Alfred Lotka (1880-1949) was an Austrian-born American physical chemist and mathematician noted for his 1922 articles “Contribution to the Energetics of Evolution”, “Natural Selection as a Physical Principle”, which introduced the term trigger action, and his 1925 book Elements of Physical Biology, in which he used thermodynamics and energetics to explain evolution. Lotka was one of the first to explain collision theory in biology. [2] Lotka coined the term "biophysical economics" in his Elements. Lotka is the eponym of the of the Darwin-Lotka energy law.

Chemical evolution | Natural selection
Lotka, in his ripe §12: “Chemical Equilibrium as an Example of Evolution Under a Known Law”, opens to the following chapter quote:

“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)

On this platform, Lotka equates stability to fitness, and ventures the assertion that evolution operates according to thermodynamic potential minimum transformational states; the main quotes of which are as follows:

“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.”
— 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)

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.

“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)

On this “space lacking” point, Lotka cited his 1907 article “Studies on the Growth of Material Aggregates.” [9] Lotka then cites the following quote by Edward Baly to explain the three phases of transition states: [10]

“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.”

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Thermodynamic potentials
Lotka, following the above, then goes into (pgs. 156-58) the following very-good discussion of evolution described via thermodynamic potential minimas:

“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.”

On maxima and minima, Lotka cites: J. Petzold (1891), Pierre Duhem (1911), and F. Michaud (1921).

Life | Definitions
Lotka, in his opening chapter, "Regarding Definitions", opens to the following quote:

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)

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Physical vs Biological (Crystal vs Bacteria growth)
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).

Ostwald | Bacterial growth | Crystal growth
In 1901, Lotka attended the physical chemistry lectures of Wilhelm Ostwald, wherein he gleaned the connection between biological phenomena (e.g. bacterial growth) and physical phenomena (crystal growth) both informally described physico-chemical methods; which Sharon Kingsland (1995) describes as follows: [8]

“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.”

In 1902, Lotka, during his student days at Leipzig, began to outline the "first plan" for his theory of the physics of biology. In 1907, he began to publish some of his ideas, the first appearing in American Journal of Science. The result was 1925 Elements of Physical Biology; noted sections of which are as follows:

Human elemental composition (Lotka, 1925)
Lotka's table 17 (pg. 197) showing a 13 elemental composition of a human (see: periodic table; human molecular formula; hmolscience periodic table).
Elements | Organisms / Humans
Lotka, in his §15: “The Stages of the Life Drama”, lists 13 elements that comprise the human. He also gives the following diagram:
Lotka figure 42
Elements in Organisms A
Elements in Organisms B
Elements in Organisms C
Lotka's table of 17 elements comprising organisms (plants and animals), via citation to Henry Osborn (1917).

Lotka, of note, in commentary on these two elemental listings (in humans), seems to be the first to address the so-called “aluminum disproof”, of the various disproofs of the existence of god, i.e. in indirect reference to the clay creation myth of humans, he states:

“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.”

This, in short, is indirect implicit Bible debunking, wherein he relegates the creation of humans according to Genesis (or Heliopolis creation myth) as being but a form of poetry.

Lotka, also lists, in life drama chapter, citing Henry Osborn’s “the Origin and Evolution of Life” (1917), a table of 17 element composition of living organisms (plants and animals), shown adjacent.

Lotka seems to have been one of the first to take note of the relatively unknown 1919 work of American economist Julius Davidson, one of the first to attempt to explain facets of economics in terms of Gibbsian thermodynamics and equilibrium chemical reactions models. [7]

Free energy | Available energy
Lotka seems to use both the terms "free energy" and "available energy", though possibly not in the absolute correct sense, e.g. speaking about the conservation of free energy (below). This is evidenced by the fact that in his section on the "world engine" he seems to equates the boiler to the working substance. Working outside of academic mainstream, Lotka began his studies of the energetics of evolution in the early 1900s; in this isolation he soon came to the view that there was no distinction between biology and physical systems, but that life existed in terms of the exchange of energy. [4] Lotka proposed that natural selection was, at its root, a struggle among organisms for "available energy"; organisms that survive and prosper are those that capture and use energy at a rate and efficiency more effective than that of its competitors. Lotka extended his energetic framework to human society. In particular, he suggested that the shift in reliance from solar energy to nonrenewable energy would pose unique and fundamental challenges to society. [5] In commentary on James Johnstone’s 1921 entropy retardation logic, in particular that “in living processes, the increase in entropy is retarded,” Lotka tells us, in his 1922 "Contributions to the Energetics of Evolution" article, “he points out that this is true, primarily, of plants; but that among animals also natural selection must work toward the weeding out of unnecessary and wasteful activities, and thus toward the conservation of free energy, or, what amounts to the same thing, toward retarding energy dissipation.” [4]

Physical biology | Biophysics
Lotka, in his “Preface” (pg. viii), defined the term “physical biology” to mean physical principles applied to systems of biological entities, and “biophysics” as the study of certain physical aspects of the life process of the individual; according to which the latter is a subset of the former. Lotka, citing Alexander Forbes (1920) and Walter Porstmann (1925), in his §5:Program of Physical Biology”, gave the following bold type definition:

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.”

This definition, of significant note, was preceded by his ripe §1:Regarding Definitions, wherein he goes into persuasive argument about how there are issues with the attempts to define “life”, i.e. the “bio-”, according to physicochemical principles, but that he does not know presently how to resolve the issue, and thereby retains the term “life”, and related, for practical purposes.

Influential to Lotka was the 1921 work of English oceanographer James Johnstone. [3] Lotka's work later came to be influential to those as American mathematician Norbert Wiener, Russian-born American mathematical biologist Nicolas Rashevsky, founder of mathematical biophysics, American biophysicist Jeffrey Wicken, and possibly to Belgian thermodynamicist Ilya Prigogine in his dissipative structures theory in relation to equilibriums in biology.

Physical Biology (Lotka, 1925)
Lotka's diagram of his program of physical biology (pg. 53), a subset of which he defines as "biophysics", aka physiology.
Lotka began his study at Birmingham University, England in 1898 and earned his BS degree in 1901. He then spent a year studying chemistry at Leipzig University from 1901 to 1902. During this period, he developed his interest in the mathematical theory of evolution, which would be the foundation for his life's work. [6] Lotka came to the United States in 1902, where he worked as an assistant chemist at the General Chemical Company in New York until 1908. While there, he published his first papers on the mathematical theory of evolution and on population analysis. He entered Cornell University as a graduate student and assistant in physics in 1908 and received his MA degree in 1909. Following his education at Cornell University, Lotka worked as an examiner at the United States Patent Office (1909), assistant physicist at the United States Bureau of Standards (1909-1911), and as an editor of the Scientific American Supplement (1911-1914). He received his Doctor of Science degree from Birmingham University in 1912. Lotka then returned to General Chemical Company, where he worked as a chemist from 1914 to 1919. While he held these various positions, Lotka continued his investigations into the mathematical theory of evolution. From 1922 to 1924, he accepted a temporary research appointment in Raymond Pearl's Human Biology group at Johns Hopkins University to focus on his studies. The result of his work was the publication Elements of Physical Biology (1924). [6]

Quotes | On
The following are noted tributes:

“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 periodic table (1925)
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.

Quotes | Employed
The following is the title page quote:

“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)

“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)

“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)

The following are notable quotes:

“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)

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)
Physicochemical Sociology
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)

(add discussion)

1. (a) Lotka, Alfred J. (1922a). “Contribution to the energetics of evolution” (pdf). Proceedings of the National Academy of Sciences, 8:147–51.
(b) Lotka, Alfred J. (1922b). “Natural selection as a physical principle” (pdf). Proceedings of the National Academy of Sciences, 8:151–54.
2. Thims, Libb. (2007). Human Chemistry (Volume One) (pg. 98-103). Morrisville, NC: LuLu.
3. Johnstone, James. (1921). The Mechanism of Life in Relation to Modern Physical Theory, (pgs. 192-203). New York: Longmans, Green & Co.
4. Whitfield, John. (2006). In the Beat of a Heart: Life, Energy, and Unity of Nature, (pg. 97-98). The National Academies.
5. Alfred Lotka – Encyclopedia of Earth.
6. Alfred J. Lotka Papers (1881-1966) – Princeton University Library.
7. Lotka, Alfred J. (1925). Elements of Physical Biology (republished (Ѻ) as: Elements of Mathematical Biology, which includes: corrections from Lotka’s notes and a completed list of his publications) (pdf) (Ѻ) (txt) (thermodynamics, 21+ pgs; evolution equilibrium quote, pg. 23; Julius Davidson, pgs. 304, 356). Dover, 1956.
8. (a) Ostwald, Wilhelm. (1901). Vorlesungen uber Naturphilosophie (342-44). Leipzig, 1902.
(b) Lotka, Alfred. (1945). “The Law of Evolution as a Maximal Principle”, Human Biology, 17, 176n.
(c) Kingsland, Sharon E. (1995). Modelling Nature: Episodes in the History of Population Ecology (Ostwald, pg. 35). University of Chicago Press.
9. Lotka, Alfred. (1907). “Studies on the Growth of Material Aggregates”, American Journal of Science, 24:199,375.
10. (a) Baly, Edward C. (1922). “Photosynthesis”, Nature (pg. 344).
(b) Lotka, Alfred J. (1925). Elements of Physical Biology (republished (Ѻ) as: Elements of Mathematical Biology, which includes: corrections from Lotka’s notes and a completed list of his publications) (pdf) (Ѻ) (txt) (pgs. 155-56). Dover, 1956.

Further reading
● Lotka, Alfred. (1921). “Note on Moving Equilibria” (pdf), communicated by R. Pearl, Proceedings of the National Academy of Sciences, 7(6):168-72, Mar 12.
● Lotka, Alfred. (1921). “Note on the Economic Conversion Factors of Energy” (Ѻ), Proceedings of the National Academy of Sciences, 7:192-97.
● Lotka, Alfred. (1924). “Biased Evolution”, Harpers Magazine, May.
● Lotka, Alfred. (1924). “The Intervention of Consciousness in Mechanics”, Science Progress, Jan.

External links
Alfred Lotka – Wikipedia.

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