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1 " There is indeed a fundamental beauty in mathematical abstractions. They so attracted the Greek philosopher Plato that he declared that all those things that we can see and touch are, in fact, mere shadows of the true reality and that the real things of this universe can be found only through the use of pure reason. Plato's knowledge of mathematics was relatively naive, and many of the cherished purities of Greek mathematics have been shown to be flawed. "
― , The Lady Tasting Tea: How Statistics Revolutionized Science in the Twentieth Century
2 " The early years of statistical development were dominated by men. Many women were working in the field, but they were almost all employed in doing the detailed calculations needed for statistical analysis, and were indeed called "computers". "
3 " Women tended to be more docile and patient, so went the belief, and could be depended upon more than men to check and recheck the accuracy of their calculations. A typical picture of the Galton Biometrical Laboratory under Karl Pearson would have Pearson and several men walking around, looking at output from the computers or discussing deep mathematical ideas, while all about them rows of women were computing. "
4 " Probit analysis provides a mathematical foundation for the doctrine first established by the sixteenth-century physician Paracelsus: “Only the dose makes a thing not a poison.” Under the Paracelsus doctrine, all things are potential poisons if given in a high enough dose, and all things are nonpoisonous if given in a low enough dose. To this doctrine, Bliss added the uncertainty associated with individual results. One reason why many foolish users of street drugs die or become very sick on cocaine or heroin or speed is that they see others using the drugs without being killed. They are like Bliss’s insects. They look around and see some of their fellow insects still alive. However, knowing that some individuals are still living provides no assurance that a given individual will survive. There is no way of predicting the response of a single individual. "
5 " In high school algebra, someone had already worked out the formulas. The teacher knew them or could find them in the teacher’s manual for the textbook. Imagine a word problem where nobody knows how to turn it into a formula, where some of the information is redundant and should not be used, where crucial information is often missing, and where there is no similar example worked out earlier in the textbook. This is what happens when one tries to apply statistical models to real-life problems. "
6 " In 1963, the chaos theorist Edward Lorenz presented an often-referenced lecture entitled “Does the Flap of a Butterfly’s Wings in Brazil Set Off a Tornado in Texas?” Lorenz’s main point was that chaotic mathematical functions are very sensitive to initial conditions. Slight differences in initial conditions can lead to dramatically different results after many iterations. Lorenz believed that this sensitivity to slight differences in the beginning made it impossible to determine an answer to his question. Underlying Lorenz’s lecture was the assumption of determinism, that each initial condition can theoretically be traced as a cause of a final effect. This idea, called the “Butterfly Effect,” has been taken by the popularizers of chaos theory as a deep and wise truth. However, there is no scientific proof that such a cause and effect exists. There are no well-established mathematical models of reality that suggest such an effect. It is a statement of faith. It has as much scientific validity as statements about demons or God. "
7 " What both paradoxes show is that decisions based on probabilistic arguments are not logical decisions. Logic and probabilistic arguments are incompatible... Jerry Cornfield justified the findings that smoking causes lung cancer by appealing to a piling up of evidence, where study after study shows results that are highly improbable unless you assume that smoking is the cause of the cancer. Is it illogical to believe that smoking causes cancer? "
8 " This lack of fit between logic and statistically based decision is not something that can be accounted for by finding a faulty assumption in Cohen's paradoxes. It lies at the heart of what is meant by logic. "
9 " For instance is no proof. "
10 " Gosset examined the data and determined that the counts of yeast cells could be modeled with a probability distribution known as the “Poisson distribution. "
11 " The world `out there' is an exceedingly complicated mass of sensations, events, and turmoil. With Thomas Kuhn, I do not believe that the human mind is capable of organizing a structure of ideas that can come even close to describing what is really out there. Any attempt to do so contains fundamental faults. Eventually, those faults will become so obvious that the scientific model must be continuously modified and eventually discarded in favor of a more subtle one. We can expect the statistical revolution will eventually run its course and be replaced by something else. "
12 " The proponents of chaos theory suggest that what in real life appear to be purely random measurements are, in fact, generated by some deterministic set of equations, and that these equations can be deduced from the patterns that appear in a Poincaré plot. For instance, some proponents of chaos theory have taken the times between human heartbeats and put them into Poincaré plots. They claim to see patterns in these plots, and they have found deterministic generating equations that appear to produce the same type of pattern. As of this writing, there is one major weakness to chaos theory applied in this fashion. There is no measure of how good the fit is between the plot based on data and the plot generated by a specific set of equations. The proof that the proposed generator is correct is based on asking the reader to look at two similar graphs. This eyeball test has proved to be a fallible one in statistical analysis. Those things that seem to the eye to be similar or very close to the same are often drastically different when examined carefully with statistical tools developed for this purpose. "
13 " With the coming of Nazi-inspired racial laws, many promising Jewish graduate students were also dismissed from the universities. Castelnuovo organized special courses in his home, and in the homes of other Jewish former professors, to enable the graduate students to continue their studies. In addition to writing books on the history of mathematics, Castelnuovo spent the last of his eighty-seven years examine the philosophical relationship between determinism and chance and trying to interpret the concept of cause and effect. "
14 " من الأفضل أن يكون لدينا إجابة تقريبية للسؤال الصحيح، أكثر من أن يكون لدينا إجابة دقيقة للسؤال الخطأ. "
15 " What remains of the Pearsonian revolution is the idea that the “things” of science are not the observables but the mathematical distribution functions that describe the probabilities associated with observations. "