It is possible to view an inconsistent change in body weight in causal terms by reference to a nonlinear model, just as it is possible to view a consistent change in body weight in causal terms by reference to a linear model. How? Let Wi be the weight of the ith animal, and assume that it is absolutely determined by the instantaneous value of the variables xj, j=1, 2, J. Some xj are exogenous, such as temperature, and some are endogenous, such as the level of enzyme X; the xj depend on time and on each other. The ith and kth animals are selected because they are identical with respect to all internal and external factors that affect body weight; the kth animal is exposed to an EMF for time T while the ith animal is maintained in a field-free but otherwise identical region. If EMF exposure caused an increase in enzyme X which, in turn, caused an increase in body weight, we could validly identify the EMF as the cause of the increase in body weight. But the ultimate effect on body weight due to the change in enzyme X induced by the EMF will also depend on the particular combination of values of the j-1 variables other than enzyme X. An identical effect on enzyme X might occur in each of a group of reasonably homogeneous animals exposed to the EMF, but an identical effect on body weight will not necessarily occur because, in general, the animals will differ from one another with regard to the instantaneous value of each non-X variable. Thus, the EMF may increase or decrease body weight, or cause no change at all; such changes may sum to zero in a particular group of animals, but each change biases toward an effect on sample variance. In this manner, by allowing that an animal response is determined by both its outer environment (which can be controlled by the investigator), and its internal environment (which is not well controlled), EMF causality can be reconciled with apparent inconsistency.


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