Spencer Heath Archive

Item 1273

Carbon of a letter to William Marias Malisoff, 51 West 86th Street, New York City

August 26, 1939

Dear Doctor Malisoff:

    I am impelled to acknowledge my double gratitude to you, first, for publishing your own article, “What Is an Atom?” in the July number of Philosophy of Science, and then for that other excellent article, “Science: Natural and Social,” by Mr. T. I. Cook, in the same number.

   

    It seems to me these two articles are singularly complementary one to another. Just as structure and function must be taken together as a totality in any adequate appre­hension of reality, so does the development of any science require two basic essentials before it can proceed. There must be some specific apprehension of reality and there must be a specific process or mode of procedure, with respect to the reality apprehended, to constitute the development of the particular science. Since science depends on measurement it is quantitative; there must be, therefore, units of quantity, and since the units must be manipulated in a meaningful way, there must be a method of procedure, a scientific process.   

    The first article sets out with fine distinctness that the unit need not be atomic but only “atomistic,” that it need not be impossible of analysis or further division, so only that it be treated without analysis or division in the process to which it is being subjected. This is what makes it possible to discover simple scientific relationships among similar units at different levels of unit complexity. Given the units, or, as he calls them, facts, Mr. Cook makes it clear that the relationships which exist among assembled or associated units — among a “homogeneous body” of facts, (for facts when classified become units “in terms of continuing uni­formities”) — are not usually discovered, even if dis­coverable, by any uniform, or prescribed rule for scien­tific procedure but from the “genius that perceives relation­ships not generally visible to others.” But this is with the important proviso that a relationship, when discovered, must be susceptible of integration with all the relation­ships previously discovered in the relevant field and, thereby, capable of independent verification.

    It seems probable that scientific discovery is made rather by synthesis than by analysis and that the synthesis takes the form of analogy. There are observed among the classified facts or homogeneous units in the field of undiscovered relationships certain partial but not complete correspondences with relations previously verified in other fields. This gives a measure wherewith to mark off and separate that which in the new field duplicates the old from that which transcends the old. Synthesis of these two parts discloses the new relationship. This relation­ship is analogous instead of identical only by the fact of the correspondence breaking down at the point at which the new relationship extends beyond and transcends the old. A nexus is thus established for integration of the new relationship with those previously verified, and in this the process of verification consists.

    Prior to all method, however, is the determination of the field of homogeneous units or classified facts among which new relationships will be sought. This is induction. It begins with observation and terminates with classification of homogeneous units, of facts “in terms of continuing uniformities.” These units of facts merit consideration as to their characteristics.

    A unit conceived as having less than four dimensions can have no objective counterpart. There are no static structures. All are subject to and in process of change. Energy is constantly taken on and as constantly modified or transformed and given off. The structure also changes; it is, in itself, but a manifestation of energy in only relatively stabilized forms. And since structure is as inseparable from change as from its other dimensional at­tributes, all structures are manifestations of facts, and, conversely, all facts are manifestations of structures; and the facts manifested in specific structures are termed the functions of those structures. Facts, indeed, may be regarded as the energy or change aspects, the functional manifestations of structures.

    Specific structures are such only because, under inductive classification, they are found to be units or members of a specific (definable) class or species. “Their systematic arrangement in terms of continuing uniformities that allow the formulation of laws which help to interpret the universe, or some section of it,” is this inductive classification.

    The most abstract science, mathematics, is founded inductively upon the classification of structures, facts or events with respect to their wholeness or unity. This constitutes the homogeneous species or series of units /words missing? check original/ quantitative relationships among which this science reveals. Unity is the “terminus” of mathematical as of “Atomistic” analysis and synthesis because it is the only point at which relationships have any beginning or any end. And it matters not whether the series or species be arithmetical or geo­metrical, each of its members or terms is either a given unity or some composite of them. In arithmetical relationships the unit or “atom” is the integer, one. In the higher quantitative relationships called “geometrical” the unit is composite, as a + b, and is always treated as unity whether the process be evolution or the reverse, and there can be no point of beginning or end in either series except at the point of unity. It is not that the “atom” or unit be actually structureless, only that it be so treated. But if the process be contra-evolutionary or disintegrative, then the unit is taken as being indefinitely composite. In physical nature, however, there is much evidence of there being definite limits to analysis or the disintegrative processes without evidence of there being any limits whatever to the synthetic or evolutionary process. And while this may suggest, it still does not necessitate the assumption of an infinite universe, for there are said to be infinite non-repeating relationships among finite numbers and even within the finiteness of some of the planetary satellites. But the indefinite extension of synthesis and its therefore necessary preponderance does establish the evolutionary principle as an indefinitely abiding characteristic of energy in the totality of its manifestation, as the basic reality in or of even a finite universe. This suggests the indefinitely synthetic or evolutionary character of energy as a fifth manifestation or dimension of reality in addi­tion to change, which is identifiable with time, as the fourth — a fifth dimension not lacking in qualitative connotation.

    Because mathematics, besides being abstract, is definitely verifiable and quantitative and not subject to feeling or opinion, it is the pattern and discipline and the instrument for the development of the concrete and particular sciences.

    Physical nature is objective upon the basis of its fundamental units which manifest themselves indifferently either as particular and discrete particles or as energy waves of basic and indivisible magnitude. Here there can be no disintegration without previous integration, no destruction without previous creation, no analysis but upon prior synthesis. Mathematics is formal, without objective reality, and subjective upon the basis of any units that may be assumed and no unit is assumed as fundamental in the sense of ultimate or indivisible. This is why mathe­matical analysis can be applied only to that which is composite and not to the fundamental units of nature as objectified in physical science. Mathematics, being ab­stract, does not bear the limitations of concrete physical nature. Hence at the fundamentals, and therefore, pre­eminently, it can correspond with objective nature only in the direction of synthesis and evolutionary process.

    But science doubtless owes its quantitative character, and with this its practical capacity of anticipating physic­ally conditioned events, to the fact that there are ultimate units in nature capable of definite synthesis into mul­tiples as the commensurable units with which science mathematically deals. This is what gives science its positive character and creative possibilities. These scientific units are of length, (spatial), mass (energy stabilized in space) and time (energy in process or change). Each of these units is itself a synthesis capable of only a definite and limited amount of analysis or disintegration into lesser units but, by the warrant of all objective experience, capable of indefinite and unlimited extension and interrelation by synthetic processes.

    It is, in fact, by the mathematical interrelation of these units that all exact science proceeds. In solar astronomy it is the diameter of the earth or of its orbit, the mass of the earth and the period of its revolution or rotation to which all other relevant data are referred. Geology borrows the same units. In terrestrial physics and chemical science fractional divisions of the astronomical units are employed. The degree of development of any science may be said to be measured by the extent to which its units have been mathematically related to the changes observed to occur in its phenomenal field. And the pseudo-sciences or quasi-sciences remain such because of the absence or the insufficiency with which mathematical relationships among the objects, facts and events that constitute their phenomena have been described. Beyond all doubt this is due to the lack of units or standards derived or definitely derivable from those employed in the authentic sciences. When it is reflected that no science has any inception objectively as a science until its facts have been not merely observed but also classified in terms of their uniformities, under adequate standards or units, it can be no mystery that a science of society takes so long to be born and that only the blindest empiricism prevails in all political and public affairs.

    In the societal field adequate physical units must be sought — units that constitute a homogeneous body and ex­hibit continuing uniformities as to function and behavior. But it is not required that the units exhibit uniformity in all respects but only in those respects which are the basis of their classification and thus initially relevant.

    The physical foundation of society is population. Its units or “atoms” while possessing a high degree of homogeneity in structure and uniformity of functioning within themselves as individuals are in these respects the proper subjects of observation and generalization in the individual sciences such as anatomy, physiology and psy­chology, they not in these respects the homogeneous units that constitute them into a society. /Sentence? check original/ Here it is only the continuing uniformities in their relationship toward each other and among themselves that constitute the units of a population into a functioning society. Not any analy­sis of the societal atoms themselves, nor any qualities peculiar to the individual units, but the continuing uni­formities that can be observed in their functioning and behavior towards each other are the facts relevant to a science of society. It is in these facts and relations alone that the individual plays “the role of an indivisible (relative to that analysis).”

    But the capacity of the individuals composing a population to form, maintain and develop societal relations, and hence a society, is highly relevant to the possibili­ties of its maintenance and growth. For this examination, since individual differences are wholly or at least chiefly differences of degree, there must be an average individual capacity which, pending the perfection of methods and instruments for measuring it in absolute terms, may very properly be taken as unity or one hundred. If we multiply this by the number of individuals composing the population we have an expression for the energy rate but not of the total energy manifested in the lives of that population. To obtain this total energy, the energy rate of the popu­lation already obtained must be multiplied by its duration, which is the average duration of its individual lives. In this then, we have the total energy expression as an actual four-dimensional unit made up of the number of three-dimensional individuals times the total amount of energy flowing and functioning through them, and this latter is made up, as we have seen, by the average energy rate per individual taken as unity (or 100) times the average dur­ation of individual life. Thus the average unit or “atom” of the population is not merely the individual in three dimensions, but the individual times the average energy rate times the average duration of life, or, more shortly, the individual as average structure times its average total energy potential or endowment. This may also be expressed briefly, keeping the average energy rate as unity, by say­ing that the unit of life in a population is not the in­dividual but the individual life-year and the whole life of the population is the total number of life-years embraced within its average life span. Thus, in a population averag­ing a million lives with an average span of twenty-five years, the average individual would exhibit twenty-five life-years, and the population as a whole would exhibit the total energy of twenty-five million life years every twenty-five years.

    Though the above-suggested scientific units or standards for a population may seem strange and, perhaps, impractical of application, it will be found upon examination that they are in all respects analogous to the standards for energy measurements employed in the authentic sciences. The energy rate of a stream at any point is measured by the number of physical structures or units passing at one time multiplied by the average velocity of their flow (their average mass being taken as unity), and the total energy for a given duration is this rate into the duration period. The rate of an electric flow is the number of electrons passing times the speed with which they move, and the total flow is this rate into their duration of flow. From these analogies it is apparent that the energy manifested in a population is susceptible of the same mathematical treat­ment as any other energy flow and should be as accurate in its results as any other statistical or average calculation. The energy content of different populations or of the same population at different times can be cal­culated upon the simple data of average numbers and average duration and, thus, they can be usefully compared. This mode of procedure not only shows quantitative differences in population energy but it discloses, also by mathematical expression, qualitative differences as well, and it does this independently of quantitative difference and the more strikingly where there is none.

    The method here suggested, based on average capacity, number, and duration of lives, has been outlined under the heading, “The Energy Concept of Population,” copy of which I enclose, in case it should interest you to follow and examine it. It has been passed upon favorably by a number of well qualified persons almost invariably with the suggestion that it should be printed in one of the quarterly journals for readier access.

    If you consider it a promising foundation on which to base analyses of particular social institutions, I hope for permission to submit for your comment and suggestion a functional analysis of the institution of private property in land in which the Energy Concept is implicit throughout and in which some interesting possibilities of rational and automatic social advance seem to appear.

    Although the Energy Concept outline is strictly and very fundamentally sociological and would, therefore, be appropriate for a strictly sociological publication, never­theless, I feel that it is more likely to be useful and desired for a journal less circumscribed in its general outlook. I will be glad to have you consider whether it is appropriate for publication in Philosophy of Science. Although but a recent subscriber, I have found this pub­lication of the greatest interest and, I believe, of greater effectiveness than any I see for the extension of sound science into the field too long preempted by empiric ineptitude.

    You are absolved from any obligation to make extensive reply to this very long communication.

Sincerely yours,

 

 Spencer Heath

 

Enc. “The Energy Concept of Population”