Paradoxical effects may not make sense to those who are unfamiliar with these peculiar dose-responses. Nevertheless, these phenomena, disquieting as they may be, are irrefutable. A wide variety of paradoxical effects has been reported with fluoride5 and many other chemical substances.6 

In radiation, the paradoxical effect is known as a non-linear, quadratic and supra-linear dose-response.13,14 It is also called the Petkau effect.15 All these peculiar phenomena, associated with both chemicals and radiation, are characterized by a low concentration range within which the adverse effect increases as the dose decreases.

Gould and Goldman, in their book Deadly Deceit. Low-Level Radiation, High-Level Cover-Up,15 report the results of Charles Walden et al who observed a supra-linear effect of ionizing radiation on human chromosomes.


  "Their findings contradict the conventional scientific dogma that the dose- response is linear, and that a straight line can be used to estimate low-dose effects from studies of high doses." Gould and Goldman also discuss the "Petkau effect." In 1971, Abram Petkau, a physician and biochemist, observed an unusual and entirely unexpected effect of radiation.


He found that low levels of radiation produced more damage to fresh beef brain cellular membranes than higher doses did.

Gofman pointed out, in his book Radiation and Human Health,13 that "Enthusiasts of nuclear power and of medical irradiation are forever hoping, quite understandably, that there will be found some threshold ?a dose of radiation below which no harm would occur." But "It turns out that nuclear-power and medical-irradiation enthusiasts have all been going in exactly the wrong direction, They have consistently suggested that linearity may overestimate the true cancer risk per rad. The real problem is that linearity underestimates the true cancer risk per rad when one derives values from studies based on higher doses of radiation than the doses at which we wish to apply those values."

According to Gofman and O'Connor (in their book X-Rays: Health Effects of Common Exams), "It is natural for everyone, ourselves included, to wish that radiation would be less harmful per rad at low dose-ranges than at high dose-ranges... Those who cling to this wish, in spite of all the evidence, claim that the linear 'hypothesis' exaggerates the risk of getting cancer from irradiation at low doses. But wishful thinking is gradually yielding to evidence." 14

The books by Gofman13 and Gofman and O'Connor14 are replete with reports which prove that low doses of radiation are in many cases more harmful than higher doses. These data fit what is called a supra-linear dose response curve, which is significantly different from a linear curve. Gofman and O'Connor14 conclude that the "linear model may actually underestimate the risk of getting cancer and leukemia. There is, unfortunately, evidence which is accumulating and growing ever stronger that the cancer risk per rad of dose is worse in the low-dose range than in the high dose... Moreover, during the nearly four years of extraordinary scrutiny and widespread peer review of the book13 in professional journals, scientific symposia and in trials concerning radiation injury, no one has made a single scientifically valid refutation of any of its data, methods, or conclusions. Probably no work in this field has received more review by peers." 14