False rigor

There is a way in which this happens, I think. It occurs through a phenomenon that one might call false rigor, in which a model masquerades as a more respectable theory than it really is. This is caused not by duplicity on the part of the model s proponents, but most frequently by the fuzzy thinking of those of us who use it. A somewhat related idea has been presented by Bhushan and Rosenfeld (1995). I will cite here an example that will be developed in more detail in the next section. 

To see where false rigor can get us in trouble, let s first examine another use of symmetry. Near the end of the book The Conservation of Orbital Symmetry, in which Woodward and Hoffmann described their rules for understanding pericyclic reactions, the authors included a section entitled "Violations" (Woodward Hoffman, 1970). The first, single-sentence paragraph proclaims "There are none "... 

Solution A rigorous treatment of a reversible reaction with variable physical properties is fairly complicated. The present example involves just two ODEs one for composition and one for enthalpy. Pressure is a dependent variable. If the rate constants are accurate, the solution will give the actual reaction trajectory (temperature, pressure, and composition as a function of time). If ko and Tact are wrong, the long-time solution will still approach equilibrium. The solution is then an application of the method of false transients. 

Eight combinations are possible with the true/false answers to the following three questions (1) is 5res, i = ires,2 , (2) is b = bjl, (3) is ymean.I = ymean.z A rigorous treatment is given in Ref. 34. First, question 1 must be answered if Hq is retained, question 2 must be answered. Only if this also leads to a positive result can question 3 be posed. 

Finally we hope to see that more validation studies are conducted to compare any new search method with the reference exhaustive search (of course on a smaller validation virtual space of 104-106). Only through this type of rigorous validation studies, one can truly probe the rates of false positives and false negatives as well as the fold increase in search speed. This in turn allows end users to make informed decisions on which search method will be a best match for their specific tasks. 

Although junk science has no rigorous definition, it is characterized by one or both of two properties (1) data that do not meet the normal criteria for being unbiased and objective, and (2) inappropriate or incomplete representations of tests of the predictive accuracy of of models that create a false impression of reliability. 

The hypothetical experiment discussed in the previous section, though now rigorous in design in that it cannot lead to false conclusions, is in some cases capable of further refinement... 

Valid conclusions cannot be based on controls which have been carried out on non-representative samples sampling is thus an essential link in the chain of assessment of the quality of raw materials as well as that of semi-finished of finished product. Consequently, it is an important operation in which a small fraction of a batch, sometimes an infinitesimally small one, is taken to represent the whole of it. Different controls are carried out on this fraction, leading to acceptance or rejection of the batch. If suitable means for the rigorous and rational organization of sampling are not provided, controls are likely to give a false sense of security. Since controls cannot be carried out on the entire batch, steps must be taken to ensure that the samples withdrawn are as representative as possible. 

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