The Boogie-Woogie Illusion

Perception ◽  
10.1068/p3378 ◽  
2002 ◽  
Vol 31 (8) ◽  
pp. 1005-1011 ◽  
Author(s):  
Patrick Cavanagh ◽  
Stuart Anstis

A grid of vertical and horizontal lines, each composed of light and dark squares, is moved rigidly at 45° to the vertical on a gray surround. When the luminance of the background is set midway between the luminances of the light and dark squares, the squares appear to race along the lines even though they are actually ‘painted’ on the lines. The effect arises from the unequal apparent speeds of the lines and their textures. The light and dark squares along the lines define a first-order pattern whose apparent speed, parallel or along the line, is close to veridical. The lines themselves have no overall luminance difference from the background so that they are defined by a second-order difference. As reported elsewhere, apparent speed is reduced for second-order motion so that the motion perpendicular to the line is perceived as slower than the motion along the line even though they are physically equal. The imbalance creates the impression that the small squares are moving along the lines rather than moving rigidly with them.

2002 ◽  
Vol 39 (5) ◽  
pp. 749-764 ◽  
Author(s):  
Nicholas Culshaw ◽  
Peter Reynolds ◽  
Gavin Sinclair ◽  
Sandra Barr

We report amphibole and mica 40Ar/39Ar ages from the Makkovik Province. Amphibole ages from metamorphic rocks decrease towards the interior of the province, indicating a first-order pattern of monotonic cooling with progressive migration of the province into a more distal back-arc location. The amphibole data, in combination with muscovite ages, reveal a second-order pattern consisting of four stages corresponding to changing spatial and temporal configurations of plutonism and deformation. (1) The western Kaipokok domain cooled through muscovite closure by 1810 Ma, long after the cessation of arc magmatism. (2) The Kaipokok Bay shear zone, bounding the Kaipokok and Aillik domains, cooled through amphibole closure during 1805–1780 Ma, synchronous with emplacement of syn-tectonic granitoid plutons. (3) Between 1740 and 1700 Ma, greenschist-facies shearing occurred along the boundary between the Kaipokok domain and Nain Province synchronous with A-type plutonism and localized shearing in the western Kaipokok domain, cooling to muscovite closure temperatures in the Kaipokok Bay shear zone, and A-type plutonism and amphibole closure or resetting in the Aillik domain. (4) In the period 1650–1640 Ma, muscovite ages, an amphibole age from a shear zone, and resetting of plutonic amphibole indicate a thermal effect coinciding in part with Labradorian plutonism in the Aillik domain. Amphibole ages from dioritic sheets in the juvenile Aillik domain suggest emplacement between 1715 and 1685 Ma. Amphibole ages constrain crystallization of small mafic plutons in the Kaipokok domain (reworked Archean foreland) to be no younger than 1670–1660 Ma. These ages are the oldest yet obtained for Labradorian plutonism in the Makkovik Province.


Author(s):  
Farid P. Bakti ◽  
Moo-Hyun Kim

Abstract Kelvin & Newman introduced a linearization method to include the current (or forward speed) effect into the diffraction & radiation wave field for large-slender floating bodies. The K-N method assumes a steady far-field current while disregarding the steady potential field due to the presence of the body. The method is proven to be reliable when the Froude number is relatively small, the body shape is relatively slender (∂∂x≪∂∂y,∂∂z), and the sea condition is mild. This requirement is fulfilled for typical FPSOs and ship-shaped vessels in a typical current (or forward speed) condition. Several studies suggested that the presence of the current might change the first order hydrodynamic coefficients such as the first order diffraction force, added mass, and radiation damping. Currents also contributed to a change in the second-order slowly-varying drift force. However, the effect of current in the second-order difference-frequency force is yet to be investigated. By expanding the Kelvin-Newman approximation up to the second order, and solving the problem in the frequency domain, we can save computational time while expanding the accuracy of the scheme. The second order quadratic force is the main focus of this study, since it is the main contributor to the total second order difference frequency forces especially near the diagonal. By implementing the Kelvin-Newman wave current interaction approach up to the wave’s second order, we can assess the performance of the Kelvin-Newman wave current interaction formulation in various sea conditions.


2011 ◽  
Vol 2011 ◽  
pp. 1-14 ◽  
Author(s):  
Mehmet Emir Koksal

The second-order one-dimensional linear hyperbolic equation with time and space variable coefficients and nonlocal boundary conditions is solved by using stable operator-difference schemes. Two new second-order difference schemes recently appeared in the literature are compared numerically with each other and with the rather old first-order difference scheme all to solve abstract Cauchy problem for hyperbolic partial differential equations with time-dependent unbounded operator coefficient. These schemes are shown to be absolutely stable, and the numerical results are presented to compare the accuracy and the execution times. It is naturally seen that the second-order difference schemes are much more advantages than the first-order ones. Although one of the second-order difference scheme is less preferable than the other one according to CPU (central processing unit) time consideration, it has superiority when the accuracy weighs more importance.


2019 ◽  
pp. 76-80
Author(s):  
M.I. Ayzatsky

The transformation of the N-th-order linear difference equation into a system of the first order difference equations is presented. The proposed transformation opens possibility to obtain new forms of the N-dimensional system of the first order equations that can be useful for the analysis of solutions of the N-th-order difference equations. In particular for the third-order linear difference equation the nonlinear second-order difference equation that plays the same role as the Riccati equation for second-order linear difference equation is obtained. The new form of the Ndimensional system of first order equations can also be used to find the WKB solutions of the linear difference equation with coefficients that vary slowly with index.


2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Said R. Grace ◽  
Jehad Alzabut

AbstractIn this paper, we establish new oscillation criteria for nonlinear second order difference equations with mixed neutral terms. The key idea of our approach is to compare with first order equations whose oscillatory behaviors are already known. The obtained results not only improve and extend existing results reported in the literature but also provide a new platform for the investigation of a wide class of nonlinear second order difference equations. The results are supported by examples to demonstrate the validity of the theoretical findings.


1997 ◽  
Vol 36 (04/05) ◽  
pp. 315-318 ◽  
Author(s):  
K. Momose ◽  
K. Komiya ◽  
A. Uchiyama

Abstract:The relationship between chromatically modulated stimuli and visual evoked potentials (VEPs) was considered. VEPs of normal subjects elicited by chromatically modulated stimuli were measured under several color adaptations, and their binary kernels were estimated. Up to the second-order, binary kernels obtained from VEPs were so characteristic that the VEP-chromatic modulation system showed second-order nonlinearity. First-order binary kernels depended on the color of the stimulus and adaptation, whereas second-order kernels showed almost no difference. This result indicates that the waveforms of first-order binary kernels reflect perceived color (hue). This supports the suggestion that kernels of VEPs include color responses, and could be used as a probe with which to examine the color visual system.


2017 ◽  
Vol 9 (3) ◽  
pp. 17-30
Author(s):  
Kelly James Clark

In Branden Thornhill-Miller and Peter Millican’s challenging and provocative essay, we hear a considerably longer, more scholarly and less melodic rendition of John Lennon’s catchy tune—without religion, or at least without first-order supernaturalisms (the kinds of religion we find in the world), there’d be significantly less intra-group violence. First-order supernaturalist beliefs, as defined by Thornhill-Miller and Peter Millican (hereafter M&M), are “beliefs that claim unique authority for some particular religious tradition in preference to all others” (3). According to M&M, first-order supernaturalist beliefs are exclusivist, dogmatic, empirically unsupported, and irrational. Moreover, again according to M&M, we have perfectly natural explanations of the causes that underlie such beliefs (they seem to conceive of such natural explanations as debunking explanations). They then make a case for second-order supernaturalism, “which maintains that the universe in general, and the religious sensitivities of humanity in particular, have been formed by supernatural powers working through natural processes” (3). Second-order supernaturalism is a kind of theism, more closely akin to deism than, say, Christianity or Buddhism. It is, as such, universal (according to contemporary psychology of religion), empirically supported (according to philosophy in the form of the Fine-Tuning Argument), and beneficial (and so justified pragmatically). With respect to its pragmatic value, second-order supernaturalism, according to M&M, gets the good(s) of religion (cooperation, trust, etc) without its bad(s) (conflict and violence). Second-order supernaturalism is thus rational (and possibly true) and inconducive to violence. In this paper, I will examine just one small but important part of M&M’s argument: the claim that (first-order) religion is a primary motivator of violence and that its elimination would eliminate or curtail a great deal of violence in the world. Imagine, they say, no religion, too.Janusz Salamon offers a friendly extension or clarification of M&M’s second-order theism, one that I think, with emendations, has promise. He argues that the core of first-order religions, the belief that Ultimate Reality is the Ultimate Good (agatheism), is rational (agreeing that their particular claims are not) and, if widely conceded and endorsed by adherents of first-order religions, would reduce conflict in the world.While I favor the virtue of intellectual humility endorsed in both papers, I will argue contra M&M that (a) belief in first-order religion is not a primary motivator of conflict and violence (and so eliminating first-order religion won’t reduce violence). Second, partly contra Salamon, who I think is half right (but not half wrong), I will argue that (b) the religious resources for compassion can and should come from within both the particular (often exclusivist) and the universal (agatheistic) aspects of religious beliefs. Finally, I will argue that (c) both are guilty, as I am, of the philosopher’s obsession with belief. 


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