of causes as compared to effects have been identified through the Second Law of Thermodynamics, confirming the ancient, medieval and Cartesian view that "the cause is greater than the effect" for the particular case of thermodynamic free energy. That in turn is challenged by popular interpretations of the concepts of nonlinear systems and the butterfly effect in which small events cause large effects because of, respectively, unpredictability and an unlikely triggering of large amounts of potential energy. Causality construed from counterfactual states Intuitively, causation seems to require not just a correlation, but a counterfactual dependence. Suppose that a student performed poorly on a test and guesses that the cause was his not studying. To prove this, one thinks of the counterfactual – the same student writing the same test under the same circumstances but having studied the night before. If one could rewind history, and change only one small thing (making the student study for the exam), then causation could be observed (by comparing version 1 to version 2). Because one cannot rewind history and replay events after making small controlled changes, causation can only be inferred, never exactly known. That is referred to as the Fundamental Problem of Causal Inference – it is impossible to directly observe causal effects. A major goal of scientific experiments and statistical methods is to approximate as best possible the counterfactual state of the world. For example, one could run an experiment on identical twins who were known to consistently get the same grades on their tests. One twin is sent to study for six hours while the other is sent to the amusement park. If their test scores suddenly diverged by a large degree, that would be strong evidence that studying (or going to the amusement park) had a causal effect on test scores. In that case, correlation between studying and test scores would almost certainly imply causation. Well-designed experimental studies replace equality of individuals as in the previous example by equality of groups. The objective is to construct two groups that are similar except for the treatment that the groups receive. That is achieved by selecting subjects from a single population and randomly assigning them to two or more groups. The likelihood of the groups behaving similarly to one another (on average) rises with the number of subjects in each group. If the groups are essentially equivalent except for the treatment they