  The unknown amplitude law q(x) defining an observed effect may be found using
the principle of Extreme Physical Information. EPI is derived as follows. The
observations follow an information flow J --> I, with J the information
intrinsic to the source and I the Fisher information level in its data, obeying
(i) I=4 Integral dx q' -squared. Here q'= dq/dx and p(x) = q(x)-squared is the
probability. It was previously shown, using L. Hardy's 5 axioms defining
physics, that I = max. Therefore, its variation (ii) delta I = 0. Note that I
is generic, obeying (i) for all source effects, whereas J is specific to the
particular effect. Hence, rather than having form (i), J obeys (iii) J =
Integral dx j[q(x),s(x)] with j some function of its arguments and s(x) a known
source, such as of mass, biological fitness, etc. Information I decreases under
any irreversible operation such as measurement, so that I l.e. J or,
equivalently, I = kJ where 0 l.e. k l.e. 1. Then the variation delta I = k
delta J so that property (ii) gives (iv) delta J = 0 as well. Then combining
(ii) and (iv), delta(I - J) = 0. Or, I - J = L = extremum. What kind of
extremum? Eqs. (i) and (iii) give (v) L=4q'^2 - j[q(x),s(x)]. Differentiating
(v), (d^2 L )/(dq'^2) = +8. Then by the Legendre condition the extremum is a
minimum. The unknown source effect obeys (vi) I - J= minimum, EPI.
