In the early eighteenth century it was discovered that in many situations the amount of information in a set of data was only proportional to the square root of the number n of observations, not the number n itself.

it being taken for granted that at least one other hypothesis (Divine Providence or Newtonian dynamics) would yield a much higher probability for the observed data than the probability found under a hypothesis of “chance.”

with exactness, and subducted, the residual facts are constantly appearing in the form of phenomena altogether new, and leading to the most important conclusions.

Granted that more evidence is better than less, but how much better? For a very long time, there was no clear answer.

He computed exactly what the inclination of the chutes must be (he called it a coefficient of reversion) in order for intergenerational balance to be preserved,

The second pillar, Information Measurement, is logically related to the first: If we gain information by combining observations, how is the gain related to the number of observations?

In even approximate equilibrium, the variability Darwin both required and demonstrated existed was in conflict with the observed short-term stability in populations.

Clearly the calculation of a single probability is not the answer to all questions. A probability itself is a measure and needs a basis for comparison. And clearly some restriction on allowable hypotheses is needed, or else a self-fulfilling hypothesis such as “the data are preordained” would give probability one to any data set.

statistical comparisons do not need to be made with respect to an exterior standard but can often be made in terms interior to the data themselves.