The four laws of biology

LAW 1: The law of existence

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

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

[(dm̅/dt ≤ 0) ∧ ( > 0)] ⇒ [(dn/dt ≥ 0) ∧ (dA/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; M > 0
Biology is “the study of those systems that can replace their internal energy” (See explanation of terms and variables).

pdt + mdt = dh + du = δq; m > 0
Ecology is “the study of the processes systems use to replace their internal energy” (See explanation of terms and variables).

The Gibbs-Duhem equation governs all biological energy:
m̅μ = dS = dU + dH - Σi μi(dvi - dmi)
The Euler equation governs all biological activity:
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.

All biological populations are subject to the three constraints of:

(a) constant propagation,
0 =  T0dP < P’ = N’p̅’
;
(b) constant size,
0 =  T0dM < M’ = N’m̅’ ( = R’)
;
(c) constant equivalence,
0 =  T0dS < S’ = N’s̅’
.

The four maxims of ecology

brassica rapa experiment

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

MAXIM 2: The maxim of number
∇ • H = H/n =

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

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