TOWARD CULTURAL ONCOLOGY: THE EVOLUTIONARY INFORMATION DYNAMICS OF CANCER

F(K1,...Km)= lim

V→∞

log[Z (K1,..,Km )]
V

(1)

where the Kj are parameters, V is the system volume and Z is the ‘par-
tition function’ defined from the energy function, the Hamiltonian, of the
system.

For an adiabatically piecewise memoryless ergodic information source
[57], the equivalent relation associates source uncertainty with the number
of ‘meaningful’ sequences N (n) of length n, in the limit

H[X] = lim ^log[N^(n)].
n→∞   n

‘Meaningful’ sequences are those with a high degree of internal serial
correlation, having grammar, syntax, and higher order structures, in the limit
of ‘infinite’ length. H [X] then represents the ‘splitting criterion’ between
small high and much larger low probability sets of sequences, which we call
‘paths’ (e.g. [17]).

Note that this approach, since it is asymptotic, precludes ‘semantic’ or
‘semiotic’ analysis of short symbol sequences.

We appropriately parametize the information source to obtain the crucial
expression on which our version of information dynamics will be constructed,
writing

.о              log[N (Kι,....Km)]

H [Ki. ∙∙∙, Km. χ] = lim -------------------

n→∞       n

(2)

The Kj represent the parameters.

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