“I know that most men, including those at ease with problems of the greatest complexity, can seldom accept the simplest and most obvious truth if it be such as would oblige them to admit the falsity of conclusions which they have proudly taught to others, and which they have woven, thread by thread, into the fabrics of their life”. Count Leo Nicolaevitch Tolstoy 1828-1910

Compulsive in his self-examination, self-destructive in his lifestyle, gender biased with his time but brilliant in observing his contemporary foes and friends, Tolstoy’s opinion is traceable to the moral questions that were central to his work and time, questions that continue to linger and obsess our civilization where unbiased peer review remains sine que non to scientific integrity.

For example,Trofim Lysenko, the Soviet agronomist, single-handedly but with Stalin’s blessings, eliminated the science of genetics by corrupting peer review. Alfred Wegener, an astronomist and metereologist, who noticed the jigsaw fit of West Africa and South America, found fossil evidence to suggest they were once joined and proposed continental drift. Wegener was ridiculed by geologists until his hypothesis became recognized as plate tectonics long after his death in November 1930. When Sir Ronald A Fisher was knighted in 1953, each weighted average had its own variance. When geostatistics was hailed as a new science in the early 1960s, the distance-weighted average turned out to be the first and only weighted average that lost its variance during an honorific rebirth as a kriged estimate. Incredibly, the variance of the distance-weighted average was replaced with the pseudo kriging variance of a subset of some infinite set of kriged estimates. Incredible indeed!

• Central values are functionally dependent values of sets of measured values
• Each central value of a set of independently measured values has its own variance
• The arithmetic mean is the central value of a set of measured values with identical weights
• A weighted average is the central value of a set of measured values with variable weights
• The distance-weighted average is the central value of a set of measured values determined at different coordinates
• Each distance-weighted average-cum-kriged estimate has its own variance
• A set of n measured values with equal weights has df(r)=n-1 degrees of freedom
• An ordered sets of n measured values with equal weights has df(o)=2(n-1) degrees of freedom
• A set of two or more measured values determined at different coordinates gives an infinite set of kriged estimates

It is a scientific fraud to interpolate by kriging between measured values if the ordered set does not display a statistically significant degree of spatial dependence