ellauri066.html on line 360: Is Pynchon’s equation of motion a standard differential equation used by specialists to calculate the path of a rocket’s flight or to control its yaw? No: Pynchon’s equation does not resemble anything one might reasonably expect. […] Not only are most of the symbols in Pynchon’s equation obscure, but the general structure of the terms in the equation also makes it impossible to identify with one or other of the equations describing the position and orientation of a rocket in flight. This equation, then, is not a genuine mathematical expression in this context. It may appear authoritative to the layperson, but it is unlikely to fool a rocket scientist. (Schachterle/Aravind, 2001: 162)...
ellauri066.html on line 368: Moore’s intuition that Pynchon’s Second Equation is real proved to be correct, and he and his colleague correctly assign the angle ϕ to the orientational range of the rocket. But since they did not know that this formula is only one in a set of equations that describe the flight path, the orientation, and the steering of the V-2, the research team was misled in their interpretation of the other parameters and terms. With Müller’s paper, we can finally determine the meaning of each term and compare these with Pynchon’s reading. The first three terms refer, respectively, to the moments of inertia, of air resistance, and of lateral air impact when the rocket yaws, and the term on the right side of the equal sign represents the steering moment of the rudders (Müller, 1957: 90, 91; Kirschstein, 1951: 73, 74). In other words, the left-hand terms describe the orientation of the rocket during flight, which is influenced by external forces such as wind currents and air resistance.
ellauri097.html on line 149: Mencken repeatedly identified mathematics with metaphysics and theology. According to Mencken, mathematics is necessarily infected with metaphysics because of the tendency of many mathematical people to engage in metaphysical speculation. In a review of Alfred North Whitehead's The Aims of Education, Mencken remarked that, while he agreed with Whitehead's thesis and admired his writing style, "now and then he falls into mathematical jargon and pollutes his discourse with equations," and "[t]here are moments when he seems to be following some of his mathematical colleagues into the gaudy metaphysics which now entertains them."[50] For Mencken, theology is characterized by the fact that it uses correct reasoning from false premises. Mencken also uses the term "theology" more generally, to refer to the use of logic in science or any other field of knowledge. In a review for both Arthur Eddington's The Nature of the Physical World and Joseph Needham's Man a Machine, Mencken ridiculed the use of reasoning to establish any fact in science, because theologians happen to be masters of "logic" and yet are mental defectives:
ellauri285.html on line 755: The first consequential re-evaluation of the mathematical modeling behind the critical positivity ratio was published in 2008 by a group of Finnish researchers from the Systems Analysis Laboratory at Aalto University (Jukka Luoma, Raimo Hämäläinen, and Esa Saarinen). The authors noted that "only very limited explanations are given about the modeling process and the meaning and interpretation of its parameters... [so that] the reasoning behind the model equations remains unclear to the reader"; moreover, they noted that "the model also produces strange and previously unreported behavior under certain conditions... [so that] the predictive validity of the model also becomes problematic."
ellauri285.html on line 759: Fredrickson wrote a response in which she conceded that the mathematical aspects of the critical positivity ratio were "questionable" and that she had "neither the expertise nor the insight" to defend them, but she maintained that the empirical evidence for the existence of a critical positivity ratio was solid. Brown, Sokal, and Friedman, the rebuttal authors, published their response to Fredrickson´s "Update" the next year, maintaining that there was no evidence for a critical positivity ratio. Losada declined to respond to the criticism (indicating to the Chronicle of Higher Education that he was too busy running his consulting business).[verification needed] Hämäläinen and colleagues responded later, passing over the Brown-Sokal-Friedman rebuttal claim of failed criteria for use of differential equations in modeling, instead arguing that there were no fundamental errors in the mathematics itself, only problems related to the model´s justification and interpretation.
ellauri285.html on line 763: Building on research by Barbara Fredrickson suggesting that individuals with a higher ratio of positive to negative emotions tend to have more successful life outcomes, and on studies by Marcial Losada applying differential equations from fluid dynamics to human emotions,[citation needed] Fredrickson and Losada proposed as informative a ratio of positive to negative affect derived from nonlinear dynamics modelling (based on Lorenz systems), which appeared in 2005 in a paper in American Psychologist. The derived combination of expressions and default parameters led them to conclude that a critical ratio of positive to negative affect of exactly 2.9013 separated flourishing from languishing individuals, and to argue that the ideal positivity/negativity ratio lies between 2.9013 and an upper limit ratio of 11.6346. Hence, they claimed that their model predicted cut-off points for the minimum and maximum positivity ratios within which one should observe qualitative changes in an individual´s level of flourishing, specifically, that those within this range of ratios would "flourish", and those outside would "languish".[non-primary source needed] As of January 2014, the 2005 Fredrickson and Losada´s paper had been cited more than 320 times in the psychology literature.
ellauri285.html on line 766: the data used by Losada in several analyses do not meet basic criteria for the use of differential equations (such as the use of continuous variables that evolve smoothly and deterministically over time);
ellauri285.html on line 768: differential equations used by Losada to calculate the critical positivity ratio use parameters taken directly from Lorenz´s simplified, illustrative, and arbitrary models for fluid dynamics, with Losada giving no rationale for his choice of parameters;
ellauri285.html on line 772: the butterfly-like first figure provided by Fredrickson and Losada is not a model of the data taken from their human participants, but "the results of computer simulations of the Lorenz equations, nothing more"; and based on the maths, even if precise positivity/negativity ratios could be derived, several "windows" of desirable and undesirable positivity/negativity ratios above a certain value should exist, rather than a simple range of ratios in which "flourishing" should occur.
ellauri285.html on line 775: With regard to these, and especially the last, the Brown-Sokal-Friedman rebuttal argues that it is likely that Fredrickson and Losada did not fully grasp the implications of applying nonlinear dynamics to their data. Brown, Sokal, and Friedman state that one can only marvel at the astonishing coincidence that human emotions should turn out to be governed by exactly the same set of equations that were derived in a celebrated article several decades ago as a deliberately simplified model of convection in fluids, and whose solutions happen to have visually appealing properties. An alternati
ellauri285.html on line 776: ve explanation – and, frankly, the one that appears most plausible to us – is that the entire process of "derivation" of the Lorenz equations has been contrived to demonstrate an imagined fit between some rather limited empirical data and the scientifically impressive world of nonlinear dynamics.
xxx/ellauri104.html on line 36: Johnny Nash was responsible for multiple equations and mathematical breakthroughs that influenced everything from economics to geometry. Like Nash equilibrium in game theory, one of the worst ideas an ape ever stumbled on. In addition to being a genius intellectual and genius mathematician he also suffered from schizophrenia his entire adult life. Not to put too find a point to it, he was mad as a march hare.
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