Reply to Nespolo's paper entitled "New invariants and dimensionless numbers: futile renaissance of old allacies?".

included an article by R. F. Nespolo with a very unusual title: " New invariants and dimensionless numbers: futile renaissance of old fallacies? " This paper contains a rather ranting criticism of our paper " Homeostasis and heterostasis: from invariant to dimensionless numbers " (Biol. Res. 36: 211-221, 2003), and therefore we are obliged to respond to Nespolo's comments in detail. A) GENERAL OBJECTIONS Our disagreements with Nespolo's commentary begin with the title. What are the so-called " old fallacies " that he refers to? He fails to clearly identify them. Furthermore, we believe that the concept of " new invariant numbers " does not infer a " renaissance of old fallacies, " but rather the addition of new aspects of current research. It is commonly known that dimensionless and invariant numbers can be obtained by that finally yield " pure " numbers. Moreover, an invariant number simply means devoid of physical dimensions (M 0 L 0 T 0), while dimensionless numbers can maintain a significant dependence on body mass, a fact that can be exemplified by " residual mass exponents. " From this perspective, an invariant number should be a constant, although in Charnov's words, " how constant is constant enough to be considered invariant is worthy of much thought " (1993, p: 5). As is well known, some " invariant " numbers can be obtained by combining universal constants, although the numerical values of these universal constants are experimentally determined and subject to statistical variations. The different values obtained for these universal constants can lead to significant contributions in cosmology, such as the prediction of the existence of innumerable parallel universes (Barrow and Webb, 2005). From this perspective, the matter of dimensionless or invariant numbers is not a " fallacy, " and therefore " not futile. " The subject of dimensionless and invariant numbers is currently an active field of investigation, and certainly not restricted to physics. For example, the " Handbook of Physics and Chemistry, " features several hundred dimensionless groups with applications in modern engineering (Weast, 1983). The biological sciences also include many contributions in When Buckhingham's theorem is used to calculate dimensionless numbers from a set of dimensional variables, dimensionless parameters that are independent of body mass are obtained first and their ratio is not only dimensionless, but also independent of body mass. In this sense, they are considered invariant numbers as well as dimensionless …