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)...
ellauri073.html on line 443: “seemed intuitively to sense that it was a matter not of reduction at all, but—perversely—of expansion, the aleatory flutter of uncontrolled, metastatic growth—each well-shot ball admitting of n possible responses, n-squared possible responses to those responses, and on into what Incandenza would articulate to anyone who shared both his backgrounds as a Cantorian continuum of infinities of possible move and response, Cantorian and beautiful because infoliating, contained, this diagnate infinity of infinities of choice and execution, mathematically uncontrolled but humanly contained, bounded by the talent and imagination of self and opponent, bent in on itself by the containing boundaries of skill and imagination that brought one player finally down, that kept both from winning, that made it, finally, a game, these boundaries of self.”
ellauri078.html on line 34: Infinity is something we are introduced to in our math classes, and later on we learn that infinity can also be used in physics, philosophy, social sciences, etc. Infinity is characterized by a number of uncountable objects or concepts which have no limits or size. This concept can be used to describe something huge and boundless. It has been studied by plenty of scientists and philosophers of the world, since the early Greek and early Indian epochs. In writing, infinity can be noted by a specific mathematical sign known as the infinity symbol (∞) created by John Wallis, an English mathematician who lived and worked in the 17th century.
ellauri078.html on line 44: The infinity symbol ( ∞ {\displaystyle \infty } \infty , ∞, or in unicode ∞) is a mathematical symbol representing the concept of infinity. In algebraic geometry, the figure is called a lemniscate.
ellauri078.html on line 56: the mathematical
ellauri088.html on line 86: Gustav Fechner (1801-1887) argued for psychophysical parallelism, according to which the mental and physical worlds run parallel to each other but do not interact. Fechner developed the Weber-Fechner law, according to which the perceived intensity of a stimulus increases arithmetically as a constant multiple of the physical intensity of the stimulus or in other words, changes of physical intensity gallop along at a brisk pace while the corresponding changes of perceived intensity creep along. The Weber and the Weber-Fechner laws were the first laws to provide a mathematical statement of the relationship between the mind and the body. Another significant contribution when S. S. Stevens (1906-1973) demonstrated that psychological intensity grows as an exponential function of physical stimulus intensity, that is, equal stimulus ratios always produce equal sensory ratios although different ratios hold for different sensory modalities. (Siis mitä? Aritmeettisesti vai logaritmisesti?)
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:
ellauri097.html on line 153: Instead of mathematical "speculation" (such as quantum theory), Mencken believed physicists should just directly look at individual facts in the laboratory like chemists:
ellauri097.html on line 159: In the same article which he later re-printed in the Mencken Chrestomathy, Mencken primarily contrasts what real scientists do, which is to simply directly look at the existence of "shapes and forces" confronting them instead of (such as in statistics) attempting to speculate and use mathematical models. Physicists and especially astronomers are consequently not real scientists, because when looking at shapes or forces, they do not simply "patiently wait for further light," but resort to mathematical theory. There is no need for statistics in scientific physics, since one should simply look at the facts while statistics attempts to construct mathematical models. On the other hand, the really competent physicists do not bother with the "theology" or reasoning of mathematical theories (such as in quantum mechanics):
ellauri100.html on line 252: Academics: Graduated from Big-Ten U in the early 1960s with a B.A. in Economics. Accepted for graduate study in economics at several top schools, including Chicago, M.I.T., and some Ivy League schools. Chose M.I.T. and soon regretted the choice: gray, rainy Cambridge and robotic mathematical approach to economics made for a depressing combination. Returned to alma mater to finish the academic year, then quit to join the (somewhat) “real world” and earn some money. Read: I flunked because I was too dense for M.I.T.
ellauri100.html on line 539: The other scale is the Subjective Numeracy Scale by Angela Fagerlin and colleagues, which measures individuals’ preference for numerical information. Numeracy (adapted from the term ‘literacy’) represents individuals’ ability to comprehend and use probabilities, ratios, and fractions. Traditional measures of numeracy ask people to perform mathematical operations, such as ‘If person A’s risk of getting a disease is 1% in 10 years, and person B’s risk is double that of A’s, what is B’s risk?’ However, some participants find these types of problems stressful and unpleasant, plus they are difficult to score in online studies. Subjective numeracy measures (like the scale you just took) are shown to be equally good measures of numeracy, without burdening participants.
ellauri147.html on line 862: In physical attractiveness studies, averageness describes the physical beauty that results from averaging the facial features of people of the same gender and approximately the same age. The majority of averageness studies have focused on photographic overlay studies of human faces, in which images are morphed together. The term "average" is used strictly to denote the technical definition of the mathematical mean. An averaged face is not unremarkable, but is, in fact, quite good looking. Nor is it typical in the sense of common or frequently occurring in the population, though it appears familiar, and is typical in the sense that it is a good example of a face that is representative of the category of faces.
ellauri151.html on line 576: languages and pseudo-mathematical ideal languages are not possible.
ellauri172.html on line 265: The situation of Buridan's ass was given a mathematical basis in a 1984 paper by American computer scientist Leslie Lamport (LaTex -ladontaskriptikielen kexijä, LOL), in which Lamport presents an argument that, given certain assumptions about continuity in a simple mathematical model of the Buridan's ass problem, there is always some starting condition under which the ass starves to death, no matter what strategy it takes. He points out that just because we do not see people's asses starving to death through indecision, this does not disprove the principle. The persistence of a Buridan's undecided state for the required length of time may just be sufficiently improbable that it has not been observed.
ellauri197.html on line 534: Gilles Saint-Paul (2008) argued, based on mathematical models, that human female hypergamy occurs because women have greater lost mating opportunity costs from monogamous mating (given their slower reproductive rate and limited window of fertility),[clarification needed] and thus must be compensated for this cost of marriage. Marriage reduces the overall genetic quality of her offspring by precluding the possibility of impregnation by a genetically higher quality male, with or without his parental investment. However, this reduction may be compensated by greater levels of parental investment by her genetically lower quality husband.
ellauri207.html on line 89: Like no work since the Arithmetica of Diophantus two millennia before, L. C. Parnault’s Dimensions in Mathematics presents the fullness of mathematical knowledge attained by man. From Thales to Turing, Pythagoras to Euclid, Archimedes to Newton, the Riemann Hypothesis to Fermat’s Last Theorem, Parnault escorts both serious mathematicians and the non-mathematical mind through the deepest mysteries of mathematics. Along the way he offers the greatest expositions yet of number theory, combinatorial topology, the analytics of complexity, and his own groundbreaking work on spherical astronomy. Dimensions equips even elementary readers with the tools to solve the logical puzzles of the perfect universe that can exist only in the mind of a mathematician.
ellauri207.html on line 91: “Dr. Parnault’s elegant explications of seemingly every extant mathematical concept or quandary make this text as indispensible as any in our field,” says Fields Medal-winning MIT Professor Gerald Lambeau. “His presentation of combinatorial mathematics left me breathless.”
ellauri222.html on line 611: Padilla is a classmate of Augie’s. Born in the slums of Mexico, he is a genius of mathematical physics. He steals books for money and gets Augie involved in that, too.
ellauri266.html on line 325: General semantics, a philosophy of language-meaning that was developed by Alfred Korzybski (1879–1950), a Polish-American scholar, and furthered by S.I. Hayakawa, Wendell Johnson, and others; it is the study of language as a representation of reality. Korzybski’s theory was intended to improve the habits of glib upper-class response to hostile low-class environment. Drawing upon such varied disciplines as relativity theory, quantum mechanics, and mathematical logic, Korzybski and his followers sought a scientific, non-Aristotelian basis for clear understanding of the differences between symbol (word) and reality (referent) and the ways in which they themselves can influence (or manipulate) and limit other humans´ ability to think.
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 757: Later, but of more critical importance, the Fredrickson and Losada work on modeling the positivity ratio aroused the skepticism of Nick Brown, a graduate student in applied positive psychology, who questioned whether such work could reliably make such broad claims, and perceived that the paper´s mathematical claims underlying the critical positivity ratio were suspect. Brown contacted and ultimately collaborated with physics and maths professor Alan Sokal and psychology professor Harris Friedman on a re-analysis of the paper´s data (hereafter the Brown-Sokal-Friedman rebuttal). They argued that Losada´s earlier work on positive psychology and Fredrickson and Losada´s 2005 critical positivity ratio paper contained "numerous fundamental conceptual and mathematical errors", errors of a magnitude that completely invalidated their claims.
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 761: A formal retraction for the mathematical modeling elements of the Losada and Fredrickson (2005) paper was issued by the journal, American Psychologist, concluding that both the specific critical positivity ratio of 2.9013 and its upper limit were invalid. The fact that the problems with the paper went unnoticed for years despite the widespread adulatory publicity surrounding the critical positivity ratio concept contributed to a perception of social psychology as a field lacking scientific soundness and rigorous critical thinking. Sokal later stated, "The main claim made by Fredrickson and Losada is so implausible on its face that some red flags ought to have been raised", as would only happen broadly in graduate student Brown´s initiating the collaboration that resulted in the Brown-Sokal-Friedman rebuttal.
ellauri285.html on line 777: Fredrickson responded to the critique by agreeing that Losada´s mathematical modelling was "questionable" and did not show that there are precise values of the ratio, but also arguing that the evidence for the benefits of a high positivity/negativity ratio is solid. Fredrickson noted that Losada declined to respond to the criticism.[11] The American Psychologist proceeded to formally retract as invalid the mathematical modeling elements of Fredrickson and Losada´s paper, including the specific critical positivity ratios of 2.9013 and its upper limit.
ellauri285.html on line 791: Losada´s coauthor, Fredrickson, continues to insist on the measurability of such a ratio, and the existence tipping-points, but has distanced herself from the mathematical portions of the 2005 paper, which were subsequently retracted by the journal; Fredrickson reports that Losada declined to respond to the criticism. Lsada kicked the bucket in 2020.[where?][citation needed].
ellauri375.html on line 313: I'm happy to engage in a deeper discussion about the meaning of 42! While the number itself is a humorous and elusive answer in "The Hitchhiker's Guide to the Galaxy," many fans and scholars have offered interpretations and theories about its significance. Some see it as a commentary on the absurdity of seeking ultimate meaning in a seemingly random universe, while others suggest mathematical, religious, or philosophical connections. What's your take on it?
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.
xxx/ellauri113.html on line 482: Berlinski´s books have received mixed reviews, and been criticized for containing historical and mathematical inaccuracies. One critic said, "I haven't learned anything from [Berlinski's] book except that the novel of mathematics is best written in another style." He is the author of several detective novels starring private investigator Aaron Asherfeld, and a number of shorter works of fiction and non-fiction.
xxx/ellauri127.html on line 241: Lewis Carroll (January 27, 1832 – January 14, 1898), whose real name was Charles Lutwidge Dodgson – etymologically, « Lewis » is related to « Lutwidge » and « Carroll » to « Charles » – was a young mathematical lecturer at Christ Church college in Oxford.
xxx/ellauri200.html on line 580: compelled to courses mathematical Kulkee pakonomaisesti ennustettava määrärataa
xxx/ellauri225.html on line 143: In 1754, a naturalist named Charles Bonnet observed that plants sprout branches and leaves in a pattern, called phyllotaxis. Bonnet saw that tree branches and leaves had a mathematical spiral pattern that could be shown as a fraction. The amazing thing is that the mathematical fractions were the same numbers as the Fibonacci sequence! On the oak tree, the Fibonacci fraction is 2/5, which means that the spiral takes five branches to spiral two times around the trunk to complete one pattern. Other trees with the Fibonacci leaf arrangement are the elm tree (1/2); the beech (1/3); the willow (3/8) and the almond tree (5/13) (Livio, Adler).
xxx/ellauri250.html on line 700: Bankman-Fried attended Canada/USA Mathcamp, a summer program for mathematically talented high-school students.He attended high school at Crystal Springs Uplands School in Hillsborough, California. From 2010 to 2014, Bankman-Fried attended the Massachusetts Institute of Technology. There, he lived in a coeducational group house called Epsilon Theta.In 2014, he graduated with a bachelor's degree in physics and a minor in mathematics.
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