TOWARD CULTURAL ONCOLOGY: THE EVOLUTIONARY INFORMATION DYNAMICS OF CANCER

the Rate Distortion or Joint Asymptotic Equipartition Theorems. K is an
inverse coupling parameter between system and environment [56, 57]. Ac-
cording to our development, at punctuation - near some critical point KC -
the systems begin to interact very strongly indeed, and we may write, near
KC , taking as the starting point the simple physical model of equation (4),

I[K] ≈ Io[KC-K]^α

KC

For a physical system α is fixed, determined by the underlying ‘univer-
sality class’. Here we will allow α to vary, and, in the section below, to itself
respond explicitly to selection pressure.

Normalizing KC and Io to 1, we obtain,

I[K] ≈ (1 -K)^α.

(6)

The horizontal line I [K] = 1 corresponds to α = 0, while α = 1 gives
a declining straight line with unit slope which passes through 0 at K = 1.
Consideration shows there are progressively sharper transitions between the
necessary zero value at K = 1 and the values defined by this relation for
0 < K, α < 1. The rapidly rising slope of transition with declining α is, we
assert, of considerable significance.

The instability associated with the splitting criterion I[K] is defined by

Q[K] ≡ -KdI[K]/dK = αK(1 -K)^α-1,

(7)

and is singular at K = KC = 1 for 0 < α < 1. Following [51, 52, 56,
59], we interpret this to mean that values of 0 < α ≪ 1 are highly unlikely

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