The four laws of biology

LAW 1: The law of existence

n >= 1; δW = (δQ - dU) > 0; m → ∞; m̅ > 0

There is an entity such that it must always lift a weight; and such that it must, and by this means, at some time increase in its mass.

Explanation

LAW 2: The law of equivalence

(δW1 = δW2) ∧ (δW2 = δW3) ⇒ (δW1 = δW3)

If a first entity can follow a path such that Law 1 is satisfied; and if a second entity can follow the same path to the same effect; then the first and second entities are equivalent.

Explanation

LAW 3: The law of diversity

A ⇒ 0; F ⇒ M

The sum of all the paths that satisfy Law 2 constitutes the allowed set for the entity and its equivalents; while that which permits them to satisfy Law 1 constitutes the required set.

Explanation

LAW 4: The law of reproduction

dA/dt > 0; dm̅/dt < 0; m̅ > 0; dn/dt >= 0

In the allowed set is at least one path such that mass is surrendered, and such that a further entity possessing the required set, and satisfying these four laws results.

Explanation

 

G  O    T  O    M  A  X  I  M  S

dU = Mdt = δQ - dH
Biology is “the study of those thermodynamic systems that can replace their internal energy”.

pdt + mdt = dh + du
Ecology is “the study of the exact processes by which a thermodynamic system replaces its internal energy”.

The Gibbs-Duhem equation:
m̅μ = m̅dS = dU + dH - Σi μi(dvi - dmi)
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.

The three constraints: constant propagation, P > 0 = ∫0T dP; constant size, R > 0 = ∫0T dR; constant equivalence, W > 0 = ∫0T dW.

The four maxims of ecology

brassica rapa experiment

MAXIM 1: The maxim of dissipation
[Darwin's theory of competition]
∫dm < 0; ∇• M → 0; M = nm̅

MAXIM 2: The maxim of number
∇• H = δW = Pdt = nh̅

MAXIM 3: The maxim of succession
[Darwin's theory of evolution]
∇ x M = ∂m̅/∂t - ∂n/∂t

MAXIM 4: The maxim of apportionment
∇ x H = ∂m̅/∂t - ∂n/∂t - ∂V/∂t