It is usually supposed that the central limit theorem explains why various quantities we find in nature are approximately normally distributed—people's heights, examination grades, snowflake sizes, and so on. This sort of explanation is found in many textbooks across the sciences, particularly in biology, economics, and sociology. Contrary to this received wisdom, I argue that in many cases we are not justified in claiming that the central limit theorem explains why a particular quantity is normally distributed, and that in some (...) cases, we are actually wrong. 1 Introduction2 Normal Distributions and the Central Limit Theorem2.1 Normal distributions2.2 The central limit theorem2.3 Terminology3 Explaining Normality3.1 Loaves of bread3.2 Varying variances and probability densities3.3 Tensile strengths and problems with summation3.4 Products of factors and log-normal distributions3.5 Transforming factors and sub-factors3.6 Transformations of quantities3.7 Quantitative genetics3.8 Inference to the best explanation4 Maximum Entropy Explanations5 Conclusion. (shrink)

Alternate View Column AV-109 Keywords:carbon nanotube space orbital elevator high tensile strength conductor semiconductor hydrogen energy storage Published in the December-2001 issue of Analog Science Fiction & Fact Magazine ; This column was written and submitted 6/19/2001 and is copyrighted ©2001 by John G. Cramer. All rights reserved. No part may be reproduced in any form without the explicit permission of the author.

In lieu of an abstract, here is a brief excerpt of the content:Plato and Leibniz against the MaterialistsEmily GrosholzImportant parallels hold between Leibniz’s attitude towards materialism and that of Plato. Both philosophers were interested in and hostile to materialism, and their qualified rejection of materialism became crucial to the systems of their maturity. Leibniz’s attachment to Plato began very early: in a text of 1664 Leibniz quoted the Timaeus, 1 and in another of 1670 he claimed that the Timaeus, along (...) with the Parmenides and the Phaedo, were his favorite dialogues. 2 The influence of the Timaeus is quite apparent in Leibniz’s correspondence with the French Platonist Nicholas Remond (1713–16) and certain essays (particularly “On the Ultimate Origination of Things” [1697] and “Tentamen Anagogicum”), where he appeals to Plato in distinguishing his own position from the materialism of his day, which revived and transformed that of Leucippus and Democritus, Epicurus, and the poet Lucretius.The way in which Leibniz resists and circumvents materialism in these letters and essays has a family resemblance with the way Plato addresses and solves certain metaphysical problems, some of them raised by materialism, in the Timaeus. All the same, the Platonic and Leibnizian strategies also diverge in significant respects. For Plato belongs to the ancient world and Leibniz to the modern world, in which the topic of subjectivity becomes central. Although both philosophers make essential use of abstract mathematical schemata to organize and inform their philosophical positions, Plato tends to give them a constitutive role and Leibniz a regulative role. [End Page 255]What is the point of establishing this analogy, a likeness nuanced by unlikeness, in the metaphysical strategies of Plato and Leibniz? First, it is important to examine philosophical genealogies. In this case the genealogy is attested by Leibniz himself, who feels at once indebted to and impatient with his forebear. Yet it has received much less scholarly recognition than the more obvious link between Aristotle and Leibniz. Second, this kind of examination exhibits the shape and tensile strength of metaphysical systems, as tragedy or fiction exhibits the extent and limits of moral and political systems. I assume that certain metaphysical problems and certain possibilities for metaphysical systems recur through time and that those things that are perennial in philosophy point to what is eternal about it, but I also believe that there is something peculiar about modernity, which imposes a sea-change on philosophy after Descartes. Materialism is a recurrent metaphysical possibility with which contemporary philosophers must still come to terms; the peculiar nature of modern philosophy introduces new ways to address materialism. Surely the study of how Plato and Leibniz took the measure of materialism will be illuminating for philosophers interested in such questions.I. Modern scholars debate over whether Plato knew the writings of Democritus and addressed himself to them. The classical authors were unanimous in the opinion that Plato regarded Democritus as one of his most important opponents. According to an often repeated anecdote, Plato wanted all the writings of Democritus burnt and only gave up this wish when it was clear that the writings were already too widely circulated. 3Commentators have pursued this alleged opposition in various directions. Hammer-Jensen 4 and Natorp 5 have argued that Plato discovered the works of Democritus in the midst of writing the Timaeus and that one can trace their influence in the latter part of the dialogue. Thus they find Plato heavily indebted to Democritus. Taylor, by contrast, rejects the influence of Democritus on Plato altogether. [End Page 256]There is no need to bring in Democritus, and it is perhaps most likely that Plato had never read his works. We cannot prove such a proposition, but we shall at least see that there is not a single sentence in the Timaeus which shows any knowledge of Democritus. Moreover, it is very doubtful whether Plato would have learned anything from Democritus if he had read him. 6However, Taylor’s conviction that Plato would not have been interested in Democritus is based on the assumption, central to his commentary, that the Timaeus must be read as a Pythagorean text, and this in itself is debatable. After all, Plato chose Timaeus the Locrian as the protagonist of... (shrink)

The ArgumentThe argument developed herein, a countertheme to the Merton thesis, is that the ideal of science pursued by Galileo and his contemporaries in Italy would be unaffected by their Catholic faith if it could achieve apodictic proof in the subject of its investigations, in which case it would attain truth – the very goal sought by that faith. Unfortunately such proof was hard to come by in early seventeenth-century mechanics. A case study is proposed to show Galileo's difficulty demonstrating (...) the tensile strength of columns in mathematical physics on the basis of improper suppositions, contrasting these with the suppositions of a contemporary, Giovanni de Guevara. The case study casts new light on the subject of Galileo's atomism and its relation to the Eucharist, refuting Redondi's claim that this was the real motive behind Galileo's trial in 1633. A further lesson relating to the Merton thesis can also be drawn, namely, that while challenges to science from religious orthodoxy may appear as temporary obstacles, in the long run they are an aid to science in its efforts to bring mankind closer to the truth. (shrink)

Rockburst phenomenon is the primary cause of many fatalities and accidents during deep underground projects constructions. As a result, its prediction at the early design stages plays a significant role in improving safety. The article describes a newly developed model to predict rockburst intensity grade using Adaptive Boosting classifier. A database including 165 rockburst case histories was collected from across the world to achieve a comprehensive representation, in which four key influencing factors such as maximum tangential stress of the excavation (...) boundary, uniaxial compressive strength of rock, tensile rock strength, and elastic energy index were selected as the input variables, and the rockburst intensity grade was selected as the output. The output of the AdaBoost model is evaluated using statistical parameters including accuracy and Cohen's kappa index. The applications for the aforementioned approach for predicting the rockburst intensity grade are compared and discussed. Finally, two real-world applications are used to verify the proposed AdaBoost model. It is found that the prediction results are consistent with the actual conditions of the subsequent construction. (shrink)

This paper proposes a new design of bridge-subgrade transition sections in high-speed railways, in attempt to avoid typical defects observed in such sections. Field observations show that two types of defects tend to occur at bridge-subgrade transition sections of high-speed railways: ① the stiffness of the transition is usually too high so that tensile stress and even tensile cracks occur at the top surface of reserved trapezoid transition section and ② the compaction quality cannot be guaranteed within the (...) first two meters from the abutment, which leads to excessive differential deformation within the transition section. For solving the above defects, a new design of the transition is proposed here: the section of the first 2 m from the abutment is filled with a graded gravel that is mixed with fly ash and cement to achieve specific stiffness and strength requirement, and the rest of the transition section is filled with roller-compacted concrete. For this new type of transition section, its dynamic performance is evaluated with on-site tests and numerical analysis. The results show that the bending angle of rail surface is almost constant along the route and the settlement of the rail surface along the route is in a linear distribution, which verifies the smoother transition from the rigid abutment to the flexible subgrade. Meanwhile, this new type of bridge-subgrade transition section has been successfully applied in the 680 km-long third bidding section of the Beijing-Shanghai high-speed railway, which provides valuable experiences for promoting and popularizing it in future construction of high-speed railways. In addition, the construction cost of the new type of bridge-subgrade transition section is verified by an economical efficiency analysis. (shrink)

The Stoic theory of recurrence is founded on Stoic biological and cosmological doctrines. This paper argues that these connections are far more elaborate and well-determined than generally assumed. Evidence from the Stoic theory of the motion of pneuma is brought to bear and a rival geometric model of time is supported against the standard linear and circular models supported by Salles and Long. The new ‘torus model’ is inspired by Alexander of Aphrodisias’ inquisitive questioning of what form the peculiar motion (...) of pneuma may possibly have and based on the evidence in which the Stoics discuss the simultaneous inward/outward motion of pneuma. A new perspective is offered as to what form this motion may take, which ultimately offers an insight into the mechanics of recurrence as also some of the long-standing paradoxes of recurrence. (shrink)

This groundbreaking handbook of character strengths and virtues is the first progress report from a prestigious group of researchers who have undertaken the systematic classification and measurement of widely valued positive traits. Character Strengths and Virtues classifies twenty-four specific strengths under six broad virtues that consistently emerge across history and culture. This book demands the attention of anyone interested in psychology and what it can teach about the good life.

Character strengths profiles in the specific setting of medical professionals are widely unchartered territory. This paper focused on an overview of character strengths profiles of medical professionals (medical students and physicians) based on literature research and available empirical data illustrating their impact on well-being and work engagement. A literature research was conducted and the majority of peer-reviewed considered articles dealt with theoretical or conceptually driven ‘virtues’ associated with medical specialties or questions of ethics in patient care (e.g., professionalism, or what (...) makes a good physician). The virtues of compassion, courage, altruism, and benevolence were described most often. Only a limited number of papers addressed character strengths of medical students or physicians according to the VIA-classification. Those articles showed that the VIA-character strengthsfairness, honesty,kindness, andteamworkwere considered most often by respondents to be particularly important for the medical profession. Available cross-sectional (time span: six years) and longitudinal (time span: three years) data regarding VIA-character strengths profiles of medical professionals were analyzed (N= 584 medical students, 274 physicians). These profiles were quite homogenous among both groups. The character strengthsfairness,honesty,judgment,kindness, andlovehad the highest means in both samples. Noteworthy differences appeared when comparing medical specialties, in particular concerning general surgeons and psychiatrists, with the former reporting clearly higher levels of e.g.,honesty(d= 1.02) orprudence(d= 1.19). Long-term results revealed significant positive effects of character strengths on well-being and work engagement (e.g.,perseveranceon physicians’ work engagement) but also significant negative effects (e.g.,appreciation of beauty and excellenceon students’ well-being). Further,hopewas significantly associated both positively with physicians’ well-being and negatively with students’ work engagement, possibly indicating specific issues concerning medical education or hospital working conditions. According to the modern-day physician’s pledge, medical professionals should pay attention to their own well-being and health. Therefore, promoting self-awareness and character building among medical professionals could be a beneficial strategy. (shrink)

Many Humeans are persuaded by an argument (separately) from Roberts, Lange and Woodward that strength ought not to be sacrificed in the competition for best system because scientific practice does not exhibit such a sacrifice. I here show that Humeans should not be so persuaded. The argument from Roberts, Lange and Woodward misses the fact that scientists can only systematise their experience, whereas the best system must systematise the entire world. However, while my demonstration shows that the argument against (...) sacrificing strength should not have been persuasive in the way it has been, it does raise new and difficult questions for the Humean. (shrink)