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2 - Isaac Beeckman in the Context of the Scientific Revolution
- Edited by Klaas van Berkel, Albert Clement, Arjan van Dixhoorn
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- Knowledge and Culture in the Early Dutch Republic
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- Amsterdam University Press
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- 07 October 2022
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- 24 June 2022, pp 31-50
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Abstract
This chapter locates Beeckman in the most important, ‘critical’, phase of the Scientific Revolution, taken as a long process of several overlapping stages. His de novo invention of corpuscular-mechanical natural philosophy, a seminal event in that phase, offers a test case for analysing the contextual causes of this breakthrough. Beeckman's significance for the later stages of the process resided primarily in the little noticed Beeckmanian conceptual genes at the heart of Descartes’ mechanism – in his vortex celestial mechanics, the ‘engine room’ of his system and key to his radical Copernican realism. Finally, to illustrate that the experimentally oriented corpuscular-mechanism of indirect Beeckmanian origin was central to the next phase of the Scientific Revolution, a counterfactual scenario is offered concerning the work of a ‘Beeckman’ still alive in the 1660s.
Keywords: Isaac Beeckman, Scientific Revolution, corpuscular-mechanical philosophy, René Descartes, contextual explanation
Riding Orders: ‘What Was Beeckman Doing – in the Context of the Scientific Revolution?’
I have been concerned about Isaac Beeckman as a figure in the Scientific Revolution for just short of 50 years, having begun to read his Latin writings on mechanics in 1971, under the guidance of the late Michael S. Mahoney in the Princeton History of Science Program. Mahoney and I started terming the early mechanists such as Beeckman, Descartes, Hobbes and Gassendi, ‘corpuscular-mechanists’. Stimulated by another faculty member, Theodore K. Rabb, we began to think of the generation in which corpuscular-mechanical natural philosophy was invented as the critical stage in a multiphase process of the Scientific Revolution. Mahoney pointed out to me that in 1618 Beeckman had recalled the young Descartes to study, including the study of corpuscular-mechanical natural philosophy. Later, in my doctoral dissertation, the Beeckman/Descartes relationship covered 80 pages out of about 750.
However, I am not a fully-fledged Beeckman scholar. Believing in the importance of Beeckman in the Scientific Revolution and having a particular interest in his relations with Descartes, I have had a watching brief on Beeckman scholarship. When the organizers of the Middelburg Beeckman conference invited me to deliver a plenary lecture on the topic that is now the title of this chapter, I requested more guidance about my assignment. Klaas van Berkel asked me: ‘What do you think Beeckman was doing?’ My answer in the plenary talk and this chapter is that Beeckman was practising natural philosophy, in a novel register.
Nothing in (sponge) biology makes sense – except when based on holotypes
- Dirk Erpenbeck, Merrick Ekins, Nicole Enghuber, John N.A. Hooper, Helmut Lehnert, Angelo Poliseno, Astrid Schuster, Edwin Setiawan, Nicole J. De Voogd, Gert Wörheide, Rob W.M. Van Soest
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- Journal of the Marine Biological Association of the United Kingdom / Volume 96 / Issue 2 / March 2016
- Published online by Cambridge University Press:
- 04 May 2015, pp. 305-311
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Sponge species are infamously difficult to identify for non-experts due to their high morphological plasticity and the paucity of informative morphological characters. The use of molecular techniques certainly helps with species identification, but unfortunately it requires prior reference sequences. Holotypes constitute the best reference material for species identification, however their usage in molecular systematics and taxonomy is scarce and frequently not even attempted, mostly due to their antiquity and preservation history. Here we provide case studies in which we demonstrate the importance of using holotype material to answer phylogenetic and taxonomic questions. We also demonstrate the possibility of sequencing DNA fragments out of century-old holotypes. Furthermore we propose the deposition of DNA sequences in conjunction with new species descriptions.
Kepler, Johannes (1571–1630)
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- By John A. Schuster, University of Sydney
- Edited by Lawrence Nolan, California State University, Long Beach
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- The Cambridge Descartes Lexicon
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- 05 January 2016
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- 01 January 2015, pp 421-422
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Kepler was the greatest mathematical astronomer of his generation and, with Galileo, the strongest advocate of the Copernican system in the first third of the seventeenth century. His determination of the elliptical orbit of Mars and his three laws of planetary motion, taken together with his attempt to delineate the forces that cause planetary motion, effectively instituted the new discipline of celestial mechanics (Kepler 1992 [1609]). Kepler also made major advances in optics. In his Ad vitellionem paralipomena (Kepler 2000 [1604]), he established the modern theory of vision and of the functioning of the eye as an optical device. Then, in his Dioptrice (1611), he significantly advanced the theory of the telescope. Descartes’ intellectual debt to Kepler is deep and complex and has often been misunderstood or oversimplified.
In a rare display of candor, Descartes confessed to Mersenne in 1638 that Kepler had been “his first master in optics” (AT II 86). This refers, first of all, to Descartes’ successful demonstration of the anaclastic properties of planohyperbolic lenses, following his discovery of the law of refraction of light in 1626–27. Descartes was stimulated by Kepler's surmise along these lines in the Dioptrice, where he had to employ an approximate version of the law. Equally importantly, in his Dioptrics (1637), Descartes transposed into mechanistic terms Kepler's revolutionary theory of vision.
However, the intellectual links between Descartes and Kepler extend further, to their overall natural philosophical agendas and results: just as Kepler was not simply an astronomer, so Descartes was not simply a mathematician or metaphysician. Descartes, like Kepler, was a bold, pro-Copernican and anti-Aristotelian natural philosopher. Both also envisioned the mathematization of natural philosophy, pursuing that aim in the form of what Descartes explicitly called “physico-mathematics.” The goal was to revise the Aristotelian view of the mixed mathematical sciences – such as astronomy, optics, and mechanics – as merely descriptive or instrumental. These disciplines were to become more intimately related to natural philosophical issues of matter and cause, the details depending upon the brand of natural philosophy an aspiring physico-mathematician endorsed. This is the deeper lesson that Kepler's novel, more physicalized optics taught to the young Descartes, and what he pursued in optics and theory of light throughout his career, employing corpuscular-mechanical rather than Keplerian Neoplatonic conceptions of matter and cause (Schuster 2012, Dupré 2012).
Light
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- By John A. Schuster, University of Sydney
- Edited by Lawrence Nolan, California State University, Long Beach
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- The Cambridge Descartes Lexicon
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- 05 January 2016
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- 01 January 2015, pp 452-458
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Descartes’ corpuscular-mechanical natural philosophy is intended to replace the Aristotelianism of the late medieval universities and the resurgent Neoplatonic natural philosophies, in which light is conceived as the intermediary between base matter and higher spiritual and immaterial entities. In the simplest version of his theory, Descartes explains light mechanically as a tendency to motion, an impulse, propagated instantaneously through continuous optical media. This has the very important implication that in Descartes’ theory the propagation of light is instantaneous, but the magnitude of the force conveyed by the tendency to motion constituting light can vary – there can be stronger and weaker light rays, all propagated instantly (Schuster 2000, 261).
Descartes’ theory of light cannot be understood in detail without his theory of corpuscular dynamics (see force and determination). Descartes holds that bodies in motion, or tending to motion, are characterized from moment to moment by the possession of two sorts of dynamical quantity: the absolute quantity of the “force of motion”; and the directional modes of that quantity of force, which Descartes calls “determinations.” As corpuscles undergo instantaneous collisions, their quantities of force of motion and determinations alter according to the laws of nature. Descartes focuses on instantaneous tendencies to motion, rather than finite translations in space and time. His exemplar for applying these concepts is the dynamics of a stone rotated in a sling (Figure 13) (AT XI 45–46, 85; G 30, 54–55).
Descartes considers the stone at the instant that it passes point A. The instantaneously exerted force of motion of the stone is directed along the tangent AG. If the stone were released and nothing affected its trajectory, it would move along ACG at a uniform speed reflecting its conserved quantity of force of motion. However, the sling continuously constrains what can be termed the “principal” determination of the stone and, acting over time, deflects its motion along the circle AF. The other component of determination acts along AE, completely opposed by the sling, so that only a tendency to centrifugal motion occurs rather than centrifugal translation. It is this conception of centrifugal tendency that Descartes uses when he articulates his theory of light inside his cosmological theory of vortices.
Hydrostatics
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- By John A. Schuster, University of Sydney
- Edited by Lawrence Nolan, California State University, Long Beach
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- The Cambridge Descartes Lexicon
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- 05 January 2016
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- 01 January 2015, pp 382-384
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Hydrostatics was one of the areas of “mixed mathematics” – including geometrical optics, positional astronomy, harmonics, and mechanics – developed by Alexandrian authors in the Hellenistic era. Until the late sixteenth century the canonical work on hydrostatics was “On Floating Bodies” by Archimedes (ca. 287–212 B.C.E.). It deals in a rigorous geometrical manner with the conditions under which fluids are at rest in statical equilibrium and with the equilibrium conditions of solid bodies floating in or upon fluids.
At the end of 1618, the twenty-two-year-old Descartes, working with Isaac Beeckman, addressed some problems in hydrostatics involving the “hydrostatic paradox.” In 1586 Simon Stevin, the leading exponent of the mixed mathematical sciences at the time, brilliantly extended Archimedean hydrostatics. He demonstrated that a fluid filling two vessels of equal base area and height exerts the same total pressure on the base, irrespective of the shape of the vessel and hence, paradoxically, independently of the amount of fluid it contains. Stevin's mathematically rigorous proof applied a condition of static equilibrium to various volumes and weights of portions of the water (Stevin 1955–66, 1:415–17).
In Descartes’ treatment of the hydrostatic paradox (AT X 67–74), the key problem involves vessels B and D, which have equal areas at their bases and equal height and are of equal weight when empty (see Figure 12). Descartes proposes to show that “the water in vessel B will weigh equally upon its base as the water in D upon its base” – Stevin's hydrostatic paradox (AT X 68–69).
First Descartes explicates the weight of the water on the bottom of a vessel as the total force of the water on the bottom, arising from the sum of the pressures exerted by the water on each unit area of the bottom. This “weighing down” is explained as “the force of motion by which a body is impelled in the first instant of its motion,” which, he insists, is not the same as the force of motion that “bears the body downward” during the actual course of its fall (AT X 68).
Physico-Mathematics
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- By John A. Schuster, University of Sydney
- Edited by Lawrence Nolan, California State University, Long Beach
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- The Cambridge Descartes Lexicon
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- 05 January 2016
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- 01 January 2015, pp 585-587
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In November 1618, Descartes, then twenty-two, met and worked for two months with Isaac Beeckman, a Dutch scholar seven years his senior. Beeckman was one of the first supporters of a corpuscular-mechanical approach to natural philosophy. However, it was not simply corpuscular mechanism that Beeckman advocated to Descartes. He also interested Descartes in what they called “physico-mathematics.” In late 1618, Beeckman (1939–53, I:244) wrote, “There are very few physico-mathematicians,” adding, “(Descartes) says he has never met anyone other than me who pursues enquiry the way I do, combining Physics and Mathematics in an exact way; and I have never spoken with anyone other than him who does the same.” They were partly right. While there were not many physico-mathematicians, there were of course others, such as Kepler, Galileo, and certain leading Jesuit mathematicians, who were trying to merge mathematics and natural philosophy (Dear 1995, 168–79).
Physico-mathematics, in Descartes’ view, deals with the way the traditional mixed mathematical disciplines, such as hydrostatics, statics, geometrical optics, geometrical astronomy, and harmonics, were conceived to relate to the discipline of natural philosophy. In Aristotelianism, the mixed mathematical sciences were interpreted as intermediate between natural philosophy and mathematics and subordinate to them. Natural philosophical explanations were couched in terms of matterand cause, something mathematics could not offer, according to most Aristotelians. In the mixed mathematical sciences, mathematics was used not in an explanatory way, but instrumentally for problem solving and practical aims. For example, in geometrical optics, one represented light as light rays. This might be useful but does not facilitate answering the underlying natural philosophical questions: “the physical nature of light” and “the causes of optical phenomena.” In contrast, physico-mathematics involved a commitment to revising radically the Aristotelian view of the mixed mathematical sciences, which were to become more intimately related to natural philosophical issues of matter and cause. Paradoxically, the issue was not mathematization. The mixed mathematical sciences, which were already mathematical, were to become more “physicalized,” more closely integrated into whichever brand of natural philosophy an aspiring physico-mathematician endorsed.
Three of Descartes’ exercises in physico-mathematics survive. The most important is his attempt, at Beeckman's urging, to supply a corpuscular-mechanical explanation for the hydrostatic paradox, which had been rigorously derived in mixed mathematical fashion by Simon Stevin (AT X 67–74, 228; Gaukroger and Schuster 2002).
Vortex
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- By John A. Schuster, University of Sydney
- Edited by Lawrence Nolan, California State University, Long Beach
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- The Cambridge Descartes Lexicon
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- 05 January 2016
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- 01 January 2015, pp 757-761
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The theory of vortical celestial mechanics, as presented in the Principles of Philosophy and The World, is the “engine room” of Descartes’ system of natural philosophy. Descartes starts his vortex theory with an “indefinitely” large chunk of divinely created matter or extension in which there are no void spaces whatsoever. When God injects motion into this extension, it is shattered into microparticles, and myriads of “circular” displacements ensue, forming gigantic whirlpools or vortices. This process eventually produces three species of corpuscle, or elements, along with the birth of stars and planets. The third element forms all solid and liquid bodies on all planets throughout the cosmos, including the earth. Interspersed in the pores of such planetary bodies are the spherical particles of the second element. The second element also makes up the bulk of every vortex, while the spaces between these spherical particles are filled by the first element, which also constitutes the stars, including our sun.
The key to Descartes’ celestial mechanics is his concept of the “massiveness” or “solidity” of a planet, meaning its aggregate volume to surface ratio, which is indicative of its ability to retain acquired motion or to resist the impact of other bodies. The particles of the second element making up a vortex also vary in volume to surface ratio with distance from the central star, as gathered from Descartes’ stipulations concerning the variation of the size (and speed) of the second-element particles with distance from the central star (Figure 32). Note also the important inflection point in the size and speed curves at radius K (Schuster 2005, 49). A planet is locked into an orbit at a radial distance at which its centrifugal tendency, related to its aggregate solidity, is balanced by the counter force arising from the centrifugal tendency of the second-element particles composing the vortex in the vicinity of the planet – that tendency similarly depending on the volume to surface ratio of the those particular particles.
Magnetism
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- By John A. Schuster, University of Sydney
- Edited by Lawrence Nolan, California State University, Long Beach
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- The Cambridge Descartes Lexicon
- Published online:
- 05 January 2016
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- 01 January 2015, pp 466-466
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Magnetism, long considered the exemplar of an occult, spiritual power, posed a challenge to mechanical philosophers like Descartes. William Gilbert's De Magnete (1600) offered an impressive natural philosophy, grounded in experiments, which could lead to interpreting magnetism as an immaterial power that possesses in its higher manifestations the capabilities of soul or mind. In his Principles of Philosophy, Descartes accepts Gilbert's experiments, but he explains magnetism mechanistically, according to the movements of two species, right – and left – handed, of “channeled” or cylindrical screw-shaped particles of his first element. Descartes claims that magnetic bodies – naturally occurring lodestone, or magnetized iron or steel – have two sets of pores running axially between their magnetic poles: one set accepts only right – handed channeled particles; the other set of pores accepts only the left – handed particles. Descartes thus explained Gilbert's experiments, including his use of a sphere of loadstone, to demonstrate the properties of magnetized compass needles.
However, Descartes did more than appropriate and reinterpret Gilbert's “laboratory” work. Gilbert called his sphere of lodestone a terrella, a “little earth,” arguing that because compass needles behave identically on the terrella as on the earth itself, the earth is, essentially, a magnet. Hence, according to his natural philosophy, the earth possesses a magnetic “soul,” capable of causing it to spin. Magnetic “souls” similarly cause the motions of other heavenly bodies. In his Principles, Descartes, aiming to displace Gilbert's natural philosophy, focuses on the “cosmic” genesis and function of his channeled magnetic particles. Descartes argues that the spaces between the spherical corpuscles of the second element that make up his vortices are roughly triangular, so that particles of the first element, constantly being forced through the interstices of second-element spheres, become “channeled” or “grooved” with triangular cross sections. Such first-element corpuscles tend to be flung by centrifugal tendency out of the equatorial regions of vortices and into neighboring vortices along the north and south directions of their axes of rotation, thus receiving opposite axial twists (see vortex). The resulting left – and right – handed screw shaped first-element particles penetrate into the polar regions of central stars and then bubble up toward their surfaces to form, Descartes claims, sunspots. Stars are thus magnetic, as Gilbert maintained, but in a mechanistic sense.
Moreover, for Descartes, planets are also magnetic, as Gilbert claimed, but again the explanation is mechanical. Descartes describes how a star may become totally encrusted by sunspots. This extinguishes the star, its vortex collapses, and it is drawn into a neighboring vortex to orbit its central star as a planet. But such planets, including our earth, bear the magnetic imprint of their stellar origins, by possessing axial channels between their magnetic poles accommodated to the right- or left-handed screw particles. Descartes’ explanation ranges from the cosmic production of magnetic particles, through the nature of stars and sunspots, to the birth and history of planets. He accepts the cosmic importance of magnetism but renders the explanation mechanical, thus binding his natural philosophy into a cosmogonical and cosmological whole.
See also Cosmology, Element, Experiment, Explanation, Principles of Philosophy, Subtle Matter, Vortex
Peter Machamer and J. E. McGuire. Descartes's Changing Mind. Princeton: Princeton University Press, 2009. viii + 258 pp. index. bibl. $39.50. ISBN: 978–0–691–13889–3.
- John A. Schuster
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- Renaissance Quarterly / Volume 63 / Issue 2 / Summer 2010
- Published online by Cambridge University Press:
- 20 November 2018, pp. 579-581
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- Summer 2010
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The case for strategic international alliances to harness nutritional genomics for public and personal health†
- Jim Kaput, Jose M. Ordovas, Lynnette Ferguson, Ben van Ommen, Raymond L. Rodriguez, Lindsay Allen, Bruce N. Ames, Kevin Dawson, Bruce German, Ronald Krauss, Wasyl Malyj, Michael C. Archer, Stephen Barnes, Amelia Bartholomew, Ruth Birk, Peter van Bladeren, Kent J. Bradford, Kenneth H. Brown, Rosane Caetano, David Castle, Ruth Chadwick, Stephen Clarke, Karine Clément, Craig A. Cooney, Dolores Corella, Ivana Beatrice Manica da Cruz, Hannelore Daniel, Troy Duster, Sven O. E. Ebbesson, Ruan Elliott, Susan Fairweather-Tait, Jim Felton, Michael Fenech, John W. Finley, Nancy Fogg-Johnson, Rosalynn Gill-Garrison, Michael J. Gibney, Peter J. Gillies, Jan-Ake Gustafsson, John L. Hartman IV, Lin He, Jae-Kwan Hwang, Jean-Philippe Jais, Yangsoo Jang, Hans Joost, Claudine Junien, Mitchell Kanter, Warren A. Kibbe, Berthold Koletzko, Bruce R. Korf, Kenneth Kornman, David W. Krempin, Dominique Langin, Denis R. Lauren, Jong Ho Lee, Gilbert A. Leveille, Su-Ju Lin, John Mathers, Michael Mayne, Warren McNabb, John A. Milner, Peter Morgan, Michael Muller, Yuri Nikolsky, Frans van der Ouderaa, Taesun Park, Norma Pensel, Francisco Perez-Jimenez, Kaisa Poutanen, Matthew Roberts, Wim H.M. Saris, Gertrud Schuster, Andrew N. Shelling, Artemis P. Simopoulos, Sue Southon, E. Shyong Tai, Bradford Towne, Paul Trayhurn, Ricardo Uauy, Willard J. Visek, Craig Warden, Rick Weiss, John Wiencke, Jack Winkler, George L. Wolff, Xi Zhao-Wilson, Jean-Daniel Zucker
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- Journal:
- British Journal of Nutrition / Volume 94 / Issue 5 / November 2005
- Published online by Cambridge University Press:
- 08 March 2007, pp. 623-632
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- November 2005
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Nutrigenomics is the study of how constituents of the diet interact with genes, and their products, to alter phenotype and, conversely, how genes and their products metabolise these constituents into nutrients, antinutrients, and bioactive compounds. Results from molecular and genetic epidemiological studies indicate that dietary unbalance can alter gene–nutrient interactions in ways that increase the risk of developing chronic disease. The interplay of human genetic variation and environmental factors will make identifying causative genes and nutrients a formidable, but not intractable, challenge. We provide specific recommendations for how to best meet this challenge and discuss the need for new methodologies and the use of comprehensive analyses of nutrient–genotype interactions involving large and diverse populations. The objective of the present paper is to stimulate discourse and collaboration among nutrigenomic researchers and stakeholders, a process that will lead to an increase in global health and wellness by reducing health disparities in developed and developing countries.
Frequency and duration of inattentive behavior after traumatic brain injury: Effects of distraction, task, and practice
- JOHN WHYTE, KRISTINE SCHUSTER, MARCIA POLANSKY, JEFFREY ADAMS, H. BRANCH COSLETT
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- Journal of the International Neuropsychological Society / Volume 6 / Issue 1 / January 2000
- Published online by Cambridge University Press:
- 01 January 2000, pp. 1-11
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Traumatic brain injury (TBI) is associated with impairments of attention, most typically measured through tests of information processing, or by subjective symptom endorsement by patients, families, and clinicians. We have previously shown increased rates of off-task behavior among patients with TBI versus controls as defined by videotaped records of independent work in distracting environments. In this research, we report on a more detailed method of coding such videotaped records which allows measurement of the precise number of off-task behaviors, their durations, and their relationship to distracting events. Using this method, we studied 20 patients with recent moderate-to-severe TBI and 20 demographically comparable controls as they performed independent work tasks while being subjected to controlled distracting events. This research confirms that patients are markedly less attentive than controls both in the presence of distractions and in their absence, that distractions have an influence on off-task behavior in both groups, and that the disruptive impact of distractors wanes relatively quickly for controls but not for patients. The duration of distraction produced by various classes of distracting events appeared similar for patients and controls, although the power to detect differences in behavioral duration between groups was limited. The pattern of inattentiveness among patients showed minimal relationship to measures of injury severity within this sample. (JINS, 2000, 6, 1–11.)
Biophysical characterization of a designed TMV coat protein mutant, R46G, that elicits a moderate hypersensitivity response in Nicotiana sylvestris
- JOHN M. TOEDT, EMORY H. BRASWELL, TODD M. SCHUSTER, DAVID A. YPHANTIS, ZENOBIA F. TARAPOREWALA, JAMES N. CULVER
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- Protein Science / Volume 8 / Issue 2 / February 1999
- Published online by Cambridge University Press:
- 01 February 1999, pp. 261-270
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- February 1999
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The hypersensitivity resistance response directed by the N′ gene in Nicotiana sylvestris is elicited by the tobacco mosaic virus (TMV) coat protein R46G, but not by the U1 wild-type TMV coat protein. In this study, the structural and hydrodynamic properties of R46G and wild-type coat proteins were compared for variations that may explain N′ gene elicitation. Circular dichroism spectroscopy reveals no significant secondary or tertiary structural differences between the elicitor and nonelicitor coat proteins. Analytical ultracentrifugation studies, however, do show different concentration dependencies of the weight average sedimentation coefficients at 4 °C. Viral reconstitution kinetics at 20 °C were used to determine viral assembly rates and as an initial assay of the rate of 20S formation, the obligate species for viral reconstitution. These kinetic results reveal a decreased lag time for reconstitution performed with R46G that initially lack the 20S aggregate. However, experiments performed with 20S initially present reveal no detectable differences indicating that the mechanism of viral assembly is similar for the two coat protein species. Therefore, an increased rate of 20S formation from R46G subunits may explain the differences in the viral reconstitution lag times. The inferred increase in the rate of 20S formation is verified by direct measurement of the 20S boundary as a function of time at 20 °C using velocity sedimentation analysis. These results are consistent with the interpretation that there may be an altered size distribution and/or lifetime of the small coat protein aggregates in elicitors that allows N. sylvestris to recognize the invading virus.
Kuhn and Lakatos and the History of Science: Kuhn and Lakatos Revisited
- John A. Schuster
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- The British Journal for the History of Science / Volume 12 / Issue 3 / November 1979
- Published online by Cambridge University Press:
- 05 January 2009, pp. 301-317
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- November 1979
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