Untitled [On Energetics and Uncertainty]

  • Alfred J. Lotka
Part of the The Springer Series on Demographic Methods and Population Analysis book series (PSDE)


The model with which we are occupied is capable of illustrating still other principles which are important for our study. In a certain sense the operation of random drawings is irreversible. It would be vain to continue to make drafts in the fashion indicated, in hopes of one day seeing all of the black balls again reassemble in urn A, where they were found after the hundredth draft. Not that this event is impossible, but it is of such a high improbability that it would be senseless to expect to see it realized in a practicable length of time. We know well that if we are permitted to look into the urns and select the balls we withdraw with the aid of sight, we can very easily reassemble all the black balls in urn A. The operation of “drawing” is thus irreversible or reversible according to the means we are permitted to employ in choosing the balls that we extract from the urns. It is because we lack the means to operate on individual molecules that the process of molecular diffusion is irreversible in thermodynamics. But in their operations on masses of macroscopic size, biological organisms also frequently find themselves facing a type of irreversibility practically as insurmountable as that of thermodynamics. If a substance of great economic value, such as gold, for example, is found in some location in a state of extreme dispersion, mixed with valueless materials, its dispersion is for us practically an irreversible process, in the sense that it cannot be reversed (so as to concentrate the ore) without employing means excluded for reasons of economy. Now the inorganic forces of nature are in large part forces tending toward dispersion. Biological organisms, by contrast, depend for their existence on sources of matter and energy in a somewhat concentrated state. For this reason they possess more or less perfected organs and faculties, by which they effectuate the concentration of the materials they need. This concentration often takes the form of a “sorting” of valued materials which are found dispersed among other materials or objects without value for the organism. Whether this dispersion is irreversible or reversible for a given species will thus depend on the degree of perfection of its organs and its faculties of sorting. In addition, we see that in this case it no longer suffices to distinguish in an absolute manner between reversibility and irreversibility; it is necessary to envisage different degrees of irreversibility, corresponding to different degrees of perfection of the organs and faculties of sorting among different biological species. A dispersion that is irreversible for an organism of low intelligence, which depends almost entirely on chance encounters with the materials it wants, can be reversible (that is, quite capable of reconcentration) for an organism, such as man, which clearly recognizes the situation and possesses more or less refined means to take advantage of it.


Uncertainty Principle Biological Species Biological Organism Random Drawing Vital Force 
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© Springer Science+Business Media New York 1998

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  • Alfred J. Lotka

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