By Alfred J. Lotka
In the 50 years that experience handed due to the fact Alfred Latka's loss of life in 1949 his place because the father of mathematical demography has been safe. together with his first demographic papers in 1907 and 1911 (the latter co authored with F. R. Sharpe) he laid the rules for good inhabitants conception, and over the subsequent many years either mostly accomplished it and located handy mathematical approximations that gave it functional applica tions. on account that his time, the sphere has moved in numerous instructions he didn't foresee, yet basically it really is nonetheless his. regardless of Latka's stature, although, the reader nonetheless must hunt throughout the outdated journals to find his significant works. As but no exten sive collections of his papers are in print, and for his half he by no means as sembled his contributions right into a unmarried quantity in English. He did so in French, within the half Theorie Analytique des institutions Biologiques (1934, 1939). Drawing on his parts of actual Biology (1925) and so much of his mathematical papers, Latka provided French readers insights into his organic proposal and a concise and mathematically available precis of what he referred to as fresh contributions in demographic analy sis. we might be exact in additionally calling it Latka's contributions in demographic analysis.
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It is in this direction that the mathematical analysis of the problem ought to be developed. It is likely that this analysis will profit from an artifice that might seem bizarre. It is CHAPTER3 23 not necessary that the transformers on which our discussion is based be biological organisms that actually exist. It is only necessary that they have the characteristic properties that a biological organism can possess. To reduce the problem to its fundamental elements it will probably be advantageous to concern ourselves with idealized transformers much simpler than those we encounter in nature.
But this observation belongs to psychology and not to physics. It is nonetheless very important, for it definitively coordinates with certain subjective data, that is, our impressions of the length of a lapse of time, objective data, that is, the lengths corresponding to the displacements of a certain mass. , objective data, that is, certain wavelengths of light. But when we seek an objective base for the direction from the past to the future, classical mechanics fails us. And, without entering into details, we note briefly that relativistic mechanics also does not give us satisfactory indications on this subject.
Is the impression we have of a specific direction to the passage of time a purely subjective illusion? If it were, what sense could it give to the idea of a progressive evolution? The answer to this question escapes us today. It is without doubt intimately tied to the classical problem of causality. CHAPTER 3 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.
Analytical Theory of Biological Populations by Alfred J. Lotka