Similarity principles and intrinsic geometries: contrasting approaches to interspecies scaling.

We criticize standard allometric approaches on the grounds that they emphasize scaling to one variable at a time, whereas chemically reactive hydrodynamic systems involved in pharmacokinetic phenomena are of higher dimension. We show that attempts based on mechanical similitude to set a dosage that would be equivalent across species (for example, from mouse to humans) lead to ambiguous results. Another failing of standard allometry may be its incapability to accommodate the neoteny of Homo sapiens, even though it helped discover the phenomenon. The retarded development in our species implied by neoteny can most clearly be seen in the evidence that both our brain size and our lifespan lie well above the allometric curve for Class Mammalia for these features. In contrast to allometry, which proposes a search for scaling coefficients through invariant external measurement reference frames, we propose a search for transformations of coordinate space coefficients in an intrinsic geometry for the mammalian body plan.