TOWARD CULTURAL ONCOLOGY: THE EVOLUTIONARY INFORMATION DYNAMICS OF CANCER

B1 ≡ bk+1, ..., bm.

Thus we permit a graded response, supposing that if

h(x) ∈ B0

the pattern is not recognized, and if

h(x) ∈ B₁

the pattern is recognized and some action bj , k + 1 ≤ j ≤ m takes place.

We are interested in paths x which trigger pattern recognition-and-response
exactly once. That is, given a fixed initial state a0 , such that h(a0) ∈ B0 ,
we examine all possible subsequent paths x beginning with a0 and leading
exactly once to the event h(x) ∈ B₁. Thus h(a₀, ..., aj) ∈ B₀ for all j < m,
but h(a₀, ..., a_m) ∈ B₁.

For each positive integer n let N (n) be the number of paths of length
n which begin with some particular a0 having h(a0) ∈ B0 and lead to the
condition h(x) ∈ B1. We shall call such paths ‘meaningful’ and assume N(n)
to be considerably less than the number of all possible paths of length n -
pattern recognition-and-response is comparatively rare. We further assume
that the finite limit

H ≡ lim ^log[N(ⁿ)∣
n→∞   n

both exists and is independent of the path x. We will - not surprisingly
- call such a pattern recognition-and-response cognitive process ergodic.

We may thus define an ergodic information source X associated with
stochastic variates Xj having joint and conditional probabilities P (a0, ..., an)
and P (an|a0, ..., an-1) such that appropriate joint and conditional Shannon
uncertainties may be defined which satisfy the relations

H[χ] = lim ^log∣N(n)∣ =
n→∞   n

lim H(Xn|X0,...,Xn-1)=
n→∞

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