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This web site uses the four fundamental theorems of the vector calculus,
in conjunction with an experiment conducted with Brassica rapa,
to prove the following five propositions:
- PROPOSITION I
That biology is “the study of those thermodynamic systems that can replace their internal energy”; that it is described by the general equation dU = Mdt = δQ - dH; and that it is governed by the four laws of biology summarized upon the left.
- PROPOSITION II
That ecology is “the study of the exact processes by which a thermodynamic system replaces its internal energy”; that it is described by the equation pdt + mdt = dh + du; and that it is governed by the four maxims of ecology summarized upon the right.
- PROPOSITION III
That all biological populations are subject to three constraints …:- the constraint of constant propagation, P > 0 = ∫0T dP;
- the constraint of constant size, R > 0 = ∫0T dR;
- the constraint of constant equivalence, W > 0 = ∫0T dW.
- PROPOSITION IV
That every species can be uniquely characterized by stating:- its generation length, T;
- its average individual mass, m̅; and
- its average individual energy, p̅,
- with T being a boundary condition set by the Liouville theorem; and with m̅ and p̅ being the decompositions of the Helmholtz theorem and so the scalar and vector potentials.
- PROPOSITION V
(A) That the Gibbs-Duhem equation
m̅μ = m̅dS = dU + dH - Σi μi(dvi - dmi)
governs all biological energy;
(B) That the Euler equation
μ = dS = (∂S/∂U)V,Ni dU + (∂S/∂V)U,Ni dV + Σi (∂S/∂ui)U,V,{Nj≠i} dui + Σi (∂S/∂vi)U,V,{Nj≠i} dvi
governs all biological activity;
(C) That it is impossible for the summation terms in the above Gibbs-Duhem and Euler equations ever to be zero; and therefore that a population free from Darwinian competition and evolution is impossible.
