Download The Biology of Numbers: The Correspondence of Vito Volterra by Giorgio Israel, Ana M. Gasca PDF

By Giorgio Israel, Ana M. Gasca

Foreword the trendy advancements in mathematical biology came about approximately among 1920 and 1940, a interval now often called the "Golden Age of Theoretical Biology". The eminent Italian mathematician Vito Volterra performed a decisive and extensively said function in those advancements. Volterra's curiosity within the program of arithmetic to the non actual sciences, and to biology and economics specifically, dates again to the flip of the century and was once expressed in his inaugural handle on the college of Rome for the tutorial 12 months 1900/01 (VOLTERRA 1901). however, it used to be purely within the mid-twenties that Volterra entered the sector in individual, on the instigation of his son in legislations, Umberto D'Ancona, who had faced him with the matter of festival between animal species, asking him even if a mathematical remedy used to be attainable. From that point on, till his loss of life in 1940, Volterra produced a tremendous output of courses at the topic. Volterra's particular venture was once to move the version and the thoughts of classical mechanics to biology, developing a kind of "rational mechanics" and an "analytic mechanics" of organic institutions. the hot topic used to be hence to be outfitted with an outstanding experimental or a minimum of empirical foundation, additionally to that end following the attempted and validated instance of mathematical physics. even if only a few particular good points of this reductionist programme have truly survived, Volterra's contribution used to be decisive, as is now universally stated, in en­ couraging clean experiences within the box of mathematical biology.

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The majority of us can make use of mathematics by simply applying ready-made formulae as is done, if I am not mistaken, also in statistics. Therefore, in order to encourage the dissemination of the paper among naturalists, it would be advisable in this case to pinpoint some equations to be applied to individual cases and to give examples of such applications. It might be a good idea to do this later. For example, apply your calculations to Chapman's numerical data and see whether the theoretical results can be made to fit the empirical data of population increase.

What emerges from all our work is only partial confirmation. D'Ancona had evolved towards a more modem "modellistic" point of view, resembling Brelot's, in which mathematical theory was considered an independent development to be subjected only to a rather soft likelihood control. The utility of mathematics was not questioned, and neither subordinate to a direct empirical verification. Gause's research program seemed meaningless or useless from this point of view. After some weeks, D'Ancona wrote on Chapman's research a more favourable opinion (Cat.

In the following pages we shall see to what extent the laws formulated in this 38 1 Mathematical Theories versus Biological Facts way agree with the experimental data available to us. They could be considered as a good start on experimental demonstration. This is why the solution to the problems of the coexistence between different species, although necessarily having to be inferred mainly from observation and experience, can find firm support in mathematical calculation and prediction, thanks to which the experimental research can be directed and the results of experiment and observation can be more clearly interpreted.

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