Extended simple regions have been the focus of recent developments in philosophical logic, metaphysics, and philosophy of physics. However, only a handful of works provides a rigorous characterization of an extended simple region. In particular, a recent paper in this journal defends a definition based on an extrinsic notion of least distance. Call it the Least Distance proposal. This paper provides the first assessment of it. It argues that Least Distance faces difficulties and drawbacks. The paper then goes on to (...) suggest a different proposal, the Diameter proposal that is able to handle such drawbacks and difficulties. (shrink)

We classify countable metrically homogeneous graphs of diameter 3.

We classify countable metrically homogeneous graphs of diameter 3.

This paper addresses the issues related to designing and estimating the strength of solid-alloy elements in the deforming broaches of significant diameter (exceeding 150 mm) for the developed process of discrete broaching. The tool limit condition was assessed based on two strength criteria: the specific potential energy of shape change and the maximum tangent stresses. Numerical modeling using the finite element method has made it possible to derive the distribution of equivalent stresses in the tool elements and the contact (...) stresses at the surface of the contact between a solid-alloy insert and the body, which enabled the analysis of tool strength under loading. The simulation was performed under a single normal load, which ensured the versatility of the calculation for any contact pressure values. We have derived formulae to calculate the acceptable contact pressure depending on unit load. The effect of the insert protrusion height over the body on the strength of tool elements has been established. We have derived engineering dependences that determine the required magnitude of insert protrusion over the body depending on the ultimate load. An example of calculating the strength of a prefabricated deforming element in the machining of a sleeve made from gray modified cast iron of hardness HB230 has been considered. Our calculations have shown that the deforming element designed for the new technological process corresponds to the conditions of strength, provided the ratio h1/h=0.15 is maintained (where h1 is the insert height above the body, h is the insert height). The results obtained could be used in engineering calculations when designing the prefabricated tool for discrete deformation, as well as to assess the strength of prefabricated tools, such as cutters, core drills, reamers, when refining external loads. (shrink)

ABSTRACTMany of our emotions arise in social contexts, as we interact with and learn about others. What is not yet clear, however, is how such emotions unfold when we either react to others or attempt to regulate our emotions. To address this issue, 30 healthy volunteers reacted to or reappraised positive or negative information that was paired with neutral faces. While they were doing this task, we assessed pupillary responses. We also asked participants to provide ratings of accountability and experienced (...) emotion. Findings indicated that appraised accountability increased in response to emotional information, and changes in accountability were associated with commensurate changes in valence reports and increased pupil diameter. During reappraisal, accountability and emotion decreased, but pupil diameter increased. The findings highlight the importance of accountability appraisals during the generation and regulation of emotional reactions to others, while also documenting pupillary increases during emot... (shrink)

There is increasing interest in how the pupil dynamics of the eye reflect underlying cognitive processes and brain states. Problematic, however, is that pupil changes can be due to non-cognitive factors, for example luminance changes in the environment, accommodation and movement. In this paper we consider how by modeling the response of the pupil in real-world environments we can capture the non-cognitive related changes and remove these to extract a residual signal which is a better index of cognition and performance. (...) Specifically, we utilize sequence measures such as fixation position, duration, saccades, and blink-related information as inputs to a deep recurrent neural network (RNN) model for predicting subsequent pupil diameter. We build and evaluate the model for a task where subjects are watching educational videos and subsequently asked questions based on the content. Compared to commonly-used models for this task, the RNN had the lowest errors rates in predicting subsequent pupil dilation given sequence data. Most importantly was how the model output related to subjects' cognitive performance as assessed by a post-viewing test. Consistent with our hypothesis that the model captures non-cognitive pupil dynamics, we found (1) the model's root-mean square error was less for lower performing subjects than for those having better performance on the post-viewing test, (2) the residuals of the RNN (LSTM) model had the highest correlation with subject post-viewing test scores and (3) the residuals had the highest discriminability (assessed via area under the ROC curve, AUC) for classifying high and low test performers, compared to the true pupil size or the RNN model predictions. This suggests that deep learning sequence models may be good for separating components of pupil responses that are linked to luminance and accommodation from those that are linked to cognition and arousal. (shrink)

This note is motivated by Whitehead’s researches in inclusion-based point-free geometry as exposed in An Inquiry Concerning the Principles of Natural Knowledge and in The concept of Nature. More precisely, we observe that Whitehead’s definition of point, based on the notions of abstractive class and covering, is not adequate. Indeed, if we admit such a definition it is also questionable that a point exists. On the contrary our approach, in which the diameter is a further primitive, enables us to (...) avoid such a drawback. Moreover, since such a notion enables us to define a metric in the set of points, our proposal looks to be a good starting point for a foundation of the geometry metrical in nature (as proposed, for example, by L.M. Blumenthal). (shrink)

This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1902 Excerpt:...earth. r' = radius of moon, or other body. P = moon's horizontal parallax = earth's angular semidiameter as seen from the moon. f = moon's angular semidiameter. Now = P (in circular measure), r'-r = r (in circular measure);.'. r: r':: P: P', or (radius of earth): (radios of (...) moon):: (moon's parallax): (moon's semidiameter). Examples. 1. Taking the moon's horizontal parallax as 57', and its angular diameter as 32', find its radius in miles, assuming the earth's radius to be 4000 miles. Here moon's semidiameter = 16';.-. 4000::: 57': 16';.-. r = 400 16 = 1123 miles. 2. The sun's horizontal parallax being 8"8, and his angular diameter 32V find his diameter in miles. ' Am. 872,727 miles. 3. The synodic period of Venus being 584 days, find the angle gained in each minute of time on the earth round the sun as centre. Am. l"-54 per minute. 4. Find the angular velocity with which Venus crosses the sun's disc, assuming the distances of Venus and the earth from the sun are as 7 to 10, as given by Bode's Law. Since (fig. 50) S V: VA:: 7: 3. But Srhas a relative angular velocity round the sun of l"-54 per minute (see Example 3); therefore, the relative angular velocity of A V round A is greater than this in the ratio of 7: 3, which gives an approximate result of 3"-6 per minute, the true rate being about 4" per minute. Annual ParaUax. 95. We have already seen that no displacement of the observer due to a change of position on the earth's surface could apparently affect the direction of a fixed star. However, as the earth in its annual motion describes an orbit of about 92 million miles radius round the sun, the different positions in space from which an observer views the fixed stars from time to time throughout the year must be separated... (shrink)

In his Brouillon Project on conic sections, Girard Desargues studies the notion of traversale, which generalizes that of diameter introduced by Apollonius. One often reads that it is equivalent to the notion of polar, a concept that emerged in the beginning of 19th century. In this article we shall study in great detail the developments around that notion in the middle part of the Brouillon project. We shall in particular show, using the notes added by Desargues after the first (...) draft was written, how here arises a new theory, that of the polarity associated to a conic section. We shall show that besides a natural correspondance between points and lines, Desargues has understood that a conic induces on every line in its plane an involution, and how he progressively handles the considerable conceptual difficulties he has to deal with when trying to explain clearly his novative ideas. (shrink)

1. The Bundle Theory I shall discuss is a theory about the nature of substances or concrete particulars, like apples, chairs, atoms, stars and people. The point of the Bundle Theory is to avoid undesirable entities like substrata that allegedly constitute particulars. The version of the Bundle Theory I shall discuss takes particulars to be entirely constituted by the universals they instantiate.' Thus particulars are said to be just bundles of universals. Together with the claim that it is necessary that (...) particulars have constituents, the fundamental claim of the Bundle Theory is: (BT) Necessarily, for every particular x and every entity y, y constitutes x if and only ify is a universal and x instantiates y. 2 The standard and supposedly devastating objection to the Bundle Theory is that it entails or is committed to a false version of the Principle of Identity of Indiscernibles (Armstrong 1978: 91, Loux 1998: 107), namely: (Pll) Necessarily, for all particulars x and y and every universal z, if z is instantiated by x if and only if z is instantiated byy, then x is numerically identical with y. The most famous counterexample to the Identity of Indiscernibles is that put forward by Max Black, consisting of a world where there are only two iron spheres two miles apart from each other, having the same diameter, temperature, colour, shape, size, etc (Black 1952: 156). Let us from now on think of the properties of the spheres in this world as universals. The possibility of this world, which I shall hereafter refer to as 'Black's world', makes (Pll) false.' And according to common philosophical opinion this means that the Bundle Theory is false.. (shrink)

In the middle part of his Brouillon Project on conics, Girard Desargues develops the theory of the traversale, a notion that generalizes the Apollonian diameter and allows to give a unified treatment of the three kinds of conics. We showed elsewhere that it leads Desargues to a complete theory of projective polarity for conics. The present article, which shall close our study of the Brouillon Project, is devoted to the last part of the text, in which Desargues puts his (...) theory of the traversal into practice by giving a very elegant tratment of the classical theory of parameters and foci. This will lead us to show that Desargues’ proofs can only be understood if one accepts that he reasons in a resolutely projective framework, completely assimilating elements at infinity to those at finite distance in his proofs. (shrink)

Recent brain imaging studies using functional magnetic resonance imaging (fMRI) have implicated insula and anterior cingulate cortices in the empathic response to another’s pain. However, virtually nothing is known about the impact of the voluntary generation of compassion on this network. To investigate these questions we assessed brain activity using fMRI while novice and expert meditation practitioners generated a loving-kindness-compassion meditation state. To probe affective reactivity, we presented emotional and neutral sounds during the meditation and comparison periods. Our main hypothesis (...) was that the concern for others cultivated during this form of meditation enhances affective processing, in particular in response to sounds of distress, and that this response to emotional sounds is modulated by the degree of meditation training. The presentation of the emotional sounds was associated with increased pupil diameter and activation of limbic regions (insula and cingulate cortices) during meditation (versus rest). During meditation, activation in insula was greater during presentation of negative sounds than positive or neutral sounds in expert than it was in novice meditators. The strength of activation in insula was also associated with self-reported intensity of the meditation for both groups. These results support the role of the limbic circuitry in emotion sharing. The comparison between meditation vs. rest states between experts and novices also showed increased activation in amygdala, right temporo-parietal junction (TPJ), and right posterior superior temporal sulcus (pSTS) in response to all sounds, suggesting, greater detection of the emotional sounds, and enhanced mentation in response to emotional human vocalizations for experts than novices during meditation. Together these data indicate that the mental expertise to cultivate positive emotion alters the activation of circuitries previously linked to empathy and theory of mind in response to emotional stimuli.. (shrink)

Platonic myth meets American noir in this haunting series of philosophical images, from gigantic ferris wheels to offshore drilling rigs. It has been said that Plato, Nietzsche, and Giordano Bruno gave us the three great mythical presentations of serious philosophy in the West. They have spawned few imitators, as philosophers have generally drifted toward a dry, scholarly tone that has become the yardstick of professional respectability. In this book, Graham Harman tries to restore myth to its central place in the (...) discipline. In Chapter One, the narrator considers the motion of a Ferris wheel of many miles in diameter, which generates disasters and other events in its endless revolutions. In Chapter Two, he moves from the Chesapeake Bay to the depths of Hell, where he observes the show trial of pre-Socratic thinkers. In Chapter Three, the narrator encounters a battered steam calliope in India that may summon tsunamis, solar flares, and other catastrophic forces. In Chapter Four, he tries to explain reports of a ghostly boat in Japanese waters. In Chapter Five, he discusses causation on an offshore drilling platform. And in Chapter Six, amidst a deadly Paris hailstorm, he proposes a theory of objects without relations. (shrink)

Pipe flow has been a challenge that gave rise to investigations on turbulence—long before turbulence was discerned as a research problem in its own right. The discharge of water from elevated reservoirs through long conduits such as for the fountains at Versailles suggested investigations about the resistance in relation to the different diameters and lengths of the pipes as well as the speed of flow. Despite numerous measurements of hydraulic engineers, the data could not be reproduced by a commonly accepted (...) formula, not to mention a theoretical derivation. The resistance of air flow in long pipes for the supply of blast furnaces or mine air appeared even more inaccessible to rational elaboration. In the nineteenth century, it became gradually clear that there were two modes of pipe flow, laminar and turbulent. While the former could be accommodated under the roof of hydrodynamic theory, the latter proved elusive. When the wealth of turbulent pipe flow data in smooth tubes was displayed as a function of the Reynolds number, the empirically observed friction factor served as a guide for the search of a fundamental law about turbulent skin friction. By 1930, a logarithmic “wall law” seemed to resolve this quest. Yet pipe flow has not been exhausted as a research subject. It still ranks high on the agenda of turbulence research—both the transition from laminar to turbulent flow and fully developed turbulence at very large Reynolds numbers. (shrink)

During high summer 1721, while rioters and bankrupts gathered outside Parliament, Robert Walpole's new ministry forced through a bill to clear up the wreckage left by the stock-market crash, the South Sea Bubble, and the visionary projects swept away when it burst. In early August the President of the Royal Society Isaac Newton, a major investor in South Sea stock, and the Society's projectors, learned of a new commercial scheme promising apparently automatic profits, a project for a perpetual motion. Their (...) informants were a young Viennese courtier Joseph Emmanuel Fischer von Erlach, a contact of Desaguliers recently engaged in industrial espionage in northern England, and the Leiden physics professor Willem 'sGravesande, who had visited London five years earlier. They reported that they had been summoned to a remarkable series of demonstrations in the castle of Weissenstein, the seat of the Landgrave of Hesse-Kassel. In a carefully guarded room of the castle there was set up a hollow wooden wheel covered in oilcloth, about 12 feet in diameter and 18 inches thick on an axle 6 feet in length. Its designer, a Saxon engineer and clockmaker Johann Bessler, who travelled Germany under the name Orffyreus, had been in Kassel for four years, published schemes for perpetual motion and been appointed commercial councillor. The Landgrave, well-known as a patron of advanced engineering schemes, commissioned him to build a new machine and put it on show before expert witnesses (Figure 1). (shrink)

Recent work on Kant’s conception of space has largely put to rest the view that Kant is hostile to actual infinity. Far from limiting our cognition to quantities that are finite or merely potentially infinite, Kant characterizes the ground of all spatial representation as an actually infinite magnitude. I advance this reevaluation a step further by arguing that Kant judges some actual infinities to be greater than others: he claims, for instance, that an infinity of miles is strictly smaller than (...) an infinity of earth-diameters. This inequality follows from Kant’s mereological conception of magnitudes (quanta): the part is (analytically) less than the whole, and an infinity of miles is equal to only a part of an infinity of earth-diameters. This inequality does not, however, imply that Kant’s infinities have transfinite and unequal sizes (quantitates). Because Kant’s conception of size (quantitas) is based on the Eudoxian theory of proportions, infinite magnitudes (quanta) cannot be assigned exact sizes. Infinite magnitudes are immeasurable, but some are greater than others. (shrink)

Topologists Nabutovsky and Weinberger discovered how to embed computably enumerable (c.e.) sets into the geometry of Riemannian metrics modulo diffeomorphisms. They used the complexity of the settling times of the c.e. sets to exhibit a much greater complexity of the depth and density of local minima for the diameter function than previously imagined. Their results depended on the existence of certain sequences of c.e. sets, constructed at their request by Csima and Soare, whose settling times had the necessary dominating (...) properties. Although these computability results had been announced earlier, their proofs have been deferred until this paper. Computably enumerable sets have long been used to prove undecidability of mathematical problems such as the word problem for groups and Hilbert's Tenth Problem. However, this example by Nabutovsky and Weinberger is perhaps the first example of the use of c.e. sets to demonstrate specific mathematical or geometric complexity of a mathematical structure such as the depth and distribution of local minima. (shrink)

Wavefunction collapse models modify Schrödinger's equation so that it describes the rapid evolution of a superposition of macroscopically distinguishable states to one of them. This provides a phenomenological basis for a physical resolution to the so-called “measurement problem.” Such models have experimentally testable differences from standard quantum theory. The most well developed such model at present is the Continuous Spontaneous Localization (CSL) model in which a universal fluctuating classical field interacts with particles to cause collapse. One “side effect” of this (...) interaction is that the field imparts energy to the particles: experimental evidence on this has led to restrictions on the parameters of the model, suggesting that the coupling of the classical field to the particles must be mass-proportional. Another “side effect” is that the field imparts momentum to particles, causing a small blob of matter to undergo random walk. Here we explore this in order to supply predictions which could be experimentally tested. We examine the translational diffusion of a sphere and a disc, and the rotational diffusion of a disc, according to CSL. For example, we find that the rms distance an isolated 10−5 cm radius sphere diffuses is ≈(its diameter, 5 cm) in (20 sec, a day), and that a disc of radius 2 ⋅ 10−5 cm and thickness 0.5 ⋅ 10−5 cm diffuses through 2πrad in about 70 sec (this assumes the “standard” CSL parameter values). The comparable rms diffusions of standard quantum theory are smaller than these by a factor 10−3±1. It is shown that the CSL diffusion in air at STP is much reduced and, indeed, is swamped by the ordinary Brownian motion. It is also shown that the sphere's diffusion in a thermal radiation bath at room temperature is comparable to the CSL diffusion, but is utterly negligible at liquid He temperature. Thus, in order to observe CSL diffusion, the pressure and temperature must be low. At the low reported pressure of 5 ⋅ 10−17 Torr, achieved at 4.2°K, the mean time between air molecule collisions with the (sphere, disc) is ≈(80, 45)min. This is ample time for observation of the putative CSL diffusion with the standard parameters and, it is pointed out, with any parameters in the range over which the theory may be considered viable. This encourages consideration of how such an experiment may actually be performed, and the paper closes with some thoughts on this subject. (shrink)

A fundamental aspect of biological systems is their spatial organization. In development, regeneration and repair, directional signals are necessary for the proper placement of the components of the organism. Likewise, pathogens that invade other organisms rely on directional signals to target vulnerable areas. It is widely understood that chemical gradients are important directional signals in living systems. Less well recognized are electrical fields, which can also provide directional information. Small, steady electrical fields can directly guide cell movement and growth and (...) can generate chemical gradients of charged macromolecules against the leveling action of diffusion. At the site of a lesion in an ion‐transporting epithelium, for example, a substantial electrical field is instantly generated and may extend over many cell diameters. There are numerous other situations in which relatively long‐range electrical fields have been shown to exist naturally. Recently, there has been substantial progress in identifying specific processes that are controlled, to some extent, by these endogenous electrical fields. This review highlights these recent data and discusses possible mechanisms by which the fields might affect biological processes. BioEssays 25:759–766, 2003. © 2003 Wiley Periodicals, Inc. (shrink)

Eye behavior is increasingly used as an indicator of internal versus external focus of attention both in research and application. However, available findings are partly inconsistent, which might be attributed to the different nature of the employed types of internal and external cognition tasks. The present study, therefore, investigated how consistently different eye parameters respond to internal versus external attentional focus across three task modalities: numerical, verbal, and visuo‐spatial. Three eye parameters robustly differentiated between internal and external attentional focus across (...) all tasks. Blinks, pupil diameter variance, and fixation disparity variance were consistently increased during internally directed attention. We also observed substantial attentional focus effects on other parameters (pupil diameter, fixation disparity, saccades, and microsaccades), but they were moderated by task type. Single‐trial analysis of our data using machine learning techniques further confirmed our results: Classifying the focus of attention by means of eye tracking works well across participants, but generalizing across tasks proves to be challenging. Based on the effects of task type on eye parameters, we discuss what eye parameters are best suited as indicators of internal versus external attentional focus in different settings. (shrink)

This article describes a method of automatically detecting, counting and classifying logs on a timber truck using a photograph. An image-processing algorithm is developed to process the photograph to calculate an estimate of the number of logs present and their respective diameters. The algorithm uses color information in multiple color spaces as well as geometrical operators to segment the image and extract the relevant information. This information enables the sawmill to better plan internal logistics and production in advance of the (...) truck’s arrival time. The algorithm is robust with respect to external factors such as varying lighting conditions and camera angle, but some inaccuracies remain, mainly caused by logs being occluded or covered in mud or snow. (shrink)

Communication is inherent to social relationships. Previous papers addressed the correlation between social and communicative complexity, and the origin of sociality in rodents. In subterranean social species, as the number of animals in the same burrow increases, so do interindividual contact rates. This is because of limitations in actually used tunnel length and diameter, leading to an increasing number of agonistic situations probably resulting in time loss, threatening, and fighting with danger of injuries. To avoid this, social species are (...) expected to have an increase in the number of particular vocalizations. Comparison of the adult vocal repertoire of 12 species through regression and phylogenetically independent contrasts suggests three main conclusions: social species increase their repertoire both in number and categories of vocal signals in relation to solitary species, although the coefficient was smaller in the PIC model; the number of agonistic vocalizations was also different between solitary and social species, with the latter displaying higher numbers of these calls; the percentage of agonistic vocalizations in relation to total repertoire was similar between social and solitary species, with no significant relationship between this parameter and the social structure. These results imply that agonistic vocalizations have also increased in number in social species, indicating the importance of these calls in the establishment of new relationships. As repertoire changes are essential to cope with new and frequent kinds of interactions sociality originates, these results suggest that at least for these organisms, communicative changes, especially at the level of agonistic signals, could be a necessary condition to fulfill in the path to the possibility of group living. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Journal of the History of Philosophy 43.1 (2005) 21-36 [Access article in PDF] Desgabets on the Creation of Eternal Truths Monte Cook For many philosophers Robert Desgabets's1 doctrine of the creation of eternal truths will be of interest for the light it throws on Descartes's doctrine of the creation of eternal truths, a doctrine receiving considerable scrutiny the past several years.2 Desgabets was one of the few followers of (...) Descartes to defend this doctrine; and he not only defended it, he made it central to his philosophy.3 He spoke of the [End Page 21] doctrine as "being of the greatest importance and having great and incomparable consequences;" and he referred to it as being "so lofty, so fine, so saintly and so worthy of God" that Descartes ought never to have departed from it (RD 208, 209).4 But, Desgabets thinks, Descartes sometimes forgets his own doctrine and says things incompatible with it. More important, he thinks, Descartes fails to realize how important the doctrine is and fails to extend it to its full consequences. In Desgabets we get from a Cartesian and a near contemporary of Descartes: an interpretation of Descartes's doctrine of the creation of eternal truths, a criticism of Descartes's version of the doctrine purportedly based on Descartes's own principles, and the development of the supposedly correct version of the doctrine that Descartes would have advocated had he been truer to his own principles.5Recent discussions have brought to the fore several controversies about how to interpret Descartes's comments on the creation of the eternal truths. I piece together both where Desgabets's own doctrine stands on these controversies and how Desgabets interprets Descartes's position on them, and I note some consequences that Desgabets draws from the doctrine that are clearly opposed to Descartes's explicit views. 1. Desgabets's Interpretation of Descartes In Critique de la Critique, Desgabets first states Descartes's doctrine of the creation of eternal truths as follows: That the Whole is greater than its part, that the circle has its diameters equal, that man is a rational animal, that two & two are four, etc., are not such of themselves but... God has made & established them with a sovereign indifference being able not to establish them so that what is now true & necessary should not be so if he had not established it. (CdC 73) This states the core of Descartes's doctrine of the creation of eternal truths, and I doubt that anyone would deny that it is in Descartes.In the next paragraph, however, Desgabets both expands and limits the scope of what he takes to be Descartes's doctrine: Descartes claims that there is neither nature, nor essence, nor reality, nor conceivability, nor truth among created things that God has not made or established with a sovereign indifference, so that before we conceive that he has freely resolved to make & establish things & truths there is nothing conceivable except his unique Essence. And we must not listen to those who say that before his free decrees & before his [End Page 22] indifferent action he already necessarily saw natures & determined essences that had by themselves a real possibility that they did not owe to him & that distinguished them from chimeras & beings of reason. (CdC 74) Whether or not Descartes subscribes to the views expressed in this paragraph, they clearly go beyond the core doctrine of the creation of eternal truths expressed in the previous paragraph.First, Desgabets expands Descartes's doctrine to include opposition not just to the view that the eternal truths exist independently of God, but also to the view that God creates by giving actual existence to pre-existent essences that determine what is possible. Desgabets believes that for Descartes God does not create by contemplating pre-existent essences, to some of which he gives actual existence. Rather, God creates the essences themselves (cf. RD 32-33, 232). Moreover, Desgabets believes that for Descartes God gives existence not just to essences but also to possibilities. God does not confront... (shrink)

At the global as well as local scales, some of the geometry of types of neuron arbors—both dendrites and axons—appears to be self-organizing: Their morphogenesis behaves like flowing water, that is, fluid dynamically; waterflow in branching networks in turn acts like a tree composed of cords under tension, that is, vector mechanically. Branch diameters and angles and junction sites conform significantly to this model. The result is that such neuron tree samples globally minimize their total volume—rather than, for example, surface (...) area or branch length. In addition, the arbors perform well at generating the cheapest topology interconnecting their terminals: their large-scale layouts are among the best of all such possible connecting patterns, approaching 5% of optimum. This model also applies comparably to arterial and river networks. S1063-651X 99 16205-6.. (shrink)

In his Metrica, Hero provides four procedures for finding the area of a circular segment (with b the base of the segment and h its height): an Ancient method for when the segment is smaller than a semicircle, $$(b + h)/2 \, \cdot \, h$$ ( b + h ) / 2 · h ; a Revision, $$(b + h)/2 \, \cdot \, h + (b/2)^{2} /14$$ ( b + h ) / 2 · h + ( b / 2 (...) ) 2 / 14 ; a quasi-Archimedean method (said to be inspired by the quadrature of the parabola) for cases where b is more than triple h, $${\raise0.5ex\hbox{$\scriptstyle 4$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle 3$}}(h \, \cdot \, b/2)$$ 4 / 3 ( h · b / 2 ) ; and a method of Subtraction using the Revised method, for when it is larger than a semicircle. He gives superficial arguments that the Ancient method presumes $$\pi = 3$$ π = 3 and the Revision, $$\pi = {\raise0.5ex\hbox{$\scriptstyle {22}$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle 7$}}$$ π = 22 / 7. We are left with many questions. How ancient is the Ancient? Why did anyone think it worked? Why would anyone revise it in just this way? In addition, why did Hero think the Revised method did not work when $$b > 3\;h$$ b > 3 h? I show that a fifth century BCE Uruk tablet employs the Ancient method, but possibly with very strange consequences, and that a Ptolemaic Egyptian papyrus that checks this method by comparing the area of a circle calculated from the sum of a regular inscribed polygon and the areas of the segments on its sides as determined by the Ancient method with the area of the circle as calculated from its diameter correctly sees that the calculations do not quite gel in the case of a triangle but do in the case of a square. Both traditions probably could also calculate the area of a segment on an inscribed regular polygon by subtracting the area of the polygon from the area of the circle and dividing by the number of sides of the polygon. I then derive two theorems about pairs of segments, that the reviser of the Ancient method should have known, that explain each method, why they work when they do and do not when they do not, and which lead to a curious generalization of the Revised method. Hero’s comment is right, but not for the reasons he gives. I conclude with an exploration of Hero’s restrictions of the Revised method and Hero’s two alternative methods. (shrink)

Monistic grounding says that there is one fundamental ground, while pluralistic grounding says that there are many such grounds. Grounding necessitarianism says that grounding entails, but is not reducible to, necessitation, while grounding contingentism says that there are at least some cases where grounding does not entail necessitation. Pluralistic grounding necessitarianism is a very popular position, but accidental generalizations, such as ‘all solid gold spheres are less than one mile in diameter’, pose well-known problems for this view: the many (...) fundamental grounds of such generalizations do not necessitate them. Though there is a straightforward response to this objection, I argue that it fails. Thus the objection from accidental generalizations stands, and proponents of pluralistic grounding necessitarianism face the following dilemma: either give up pluralistic grounding, or give up necessitarianism. (shrink)

Origin of the Yellowstone hotspot & Columbia River Basalts has remained uncertain until now. Here, we present evidence of meteorite impact origin. The hotspot is shallow, only 200 km deep, invalidating a theory of mantle plume origin. The hotspot track runs from the Yellowstone National Park in NW Wyoming to the volcanic Modoc Plateau in NE California. We present evidence of apparent remnants of an impact crater existing in the Modoc, a large multi-ring structure at least 160 km diameter. (...) Much of the complex crater has become obliterated by later Cascadia and Sierra orogenies. The crater has a tall 4,100 foot central uplift cone, locally known as Chalk Mountain, consisting of diatomaceous earth, presumably the rebound cone of a meteorite impact. This falsifies a theoretical prohibition of cosmic impact volcanism. Based on recent insights into explosive volcanism a plausible mechanism is proposed for how meteorite impacts can lead to resurgent calderas of the Yellowstone type, & of apparent LIP origin from thin crust ET impacts, invalidating theoretical constructs of mantle plumes. We mention chaotic terrains, including plutons, arising antipodal to impacts. (shrink)

Summary Tycho Brahe's lunar theory, mostly the work of his assistant Christian Longomontanus, published in the Progymnasmata (1602), was the most advanced and accurate lunar theory yet developed. Its principal innovations are: the introduction of equant motion for the first inequality in order to separate the determination of direction and distance; a more accurate limit for the second inequality although requiring a more complex calculation; additional inequalities of the variation and, in place of the annual inequality in Tycho's earlier theory, (...) a reduction in the equation of time; in the latitude theory a variation of the inclination of the orbital plane and an inequality of the motion of the nodes; a reduction in the range of variation of distance, parallax, and apparent diameter. Some of these were already present in Tycho's earlier lunar theory (1599), but all were changed in notable ways. Twenty years later Longomontanus published a modified version of the lunar theory in Astronomia Danica (1622), for the purpose of facilitating the calculation through new correction tables, and also explained his reasons for parts of the theory in the Progymnasmata. This paper is a technical study of both lunar theories. (shrink)

A classical point electron radiates when it accelerates. However, there are classical electron models with extended charge distributions which can accelerate and/or deform without radiating. Can a model be contrived that will undergo radiationless motion while accelerating (on the average) over a distance large compared to its size? The answer is no: we prove that the “center” of the electron is always closer than the electron “diameter” to a fictitious point undergoing constant-velocity motion, if the electron's motion is radiationless.

This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1752 edition. Excerpt:... to which the original Exclusion had been owing, the Points of two short and slender Hairs appear'd protruding themselves from its oval Surface. The thicker butoblong Bodies, from whose Extremities these grew, next forc'd themselves out, and it was evident to a-'n accustom'd Eye, that they were (...) the Antennze of a two wing'd Fly; next presented themselves the anterior Surfaces of two chequeffd Orbs, which were plainly the complex Eyes of anlnsect' of the same Species, separated by a plain Portion of a Forehead; and soon after the whole Head. This was no sooner all in View, than it swell'd to a Diameter equal to twice the Measure of that of the Breast. lt might have appear'd from the first, that the Head was growing under the Eye of the Observer, from the Extremity of the Thorax, but tho' a more rational Enquiry could not but produce for its Answer, that it was only now thrust forth out of the Cavity of the Breast in which it had before been lodg'd; it yet appear'd singular after this sudden Change in Size to conceive how a Thing should have been till that Moment lodg'd in a Cavityz not equal to half its own Diameter. P a The The Head was now entire and in its Place, and the Legs were firm, and supported the Body well, but the Wings did not yet appear. On examining the Place where they were to be expacted, I discover'd two irregular Protuberances of a wrinkled Surface, and considerably large, and under them the two oblong Pedicies which we see supporting the Balls under the Wings of all the two wing'd Flies. It was evident from this, that the Protuberances at the two Sides of the Base of the Thorax were the very Wings in their folded State, and this was soon prov'd by their expanding. The Wings in all this Race of Creatures are the last Part... (shrink)

We want to build tiny gnat-sized robots, a millimeter or two in diameter. They will be cheap, disposable, totally sefcontained autonomous agents able to do useful things in the world. This paper consists of two parts. The first describes why we want to build them. The second is a technical outline of how to go about it. Gnat robots are going to change the world.