Perceptual-cognitive universals as reflections of the world

2001 ◽  
Vol 24 (4) ◽  
pp. 581-601 ◽  
Author(s):  
Roger N. Shepard

The universality, invariance, and elegance of principles governing the universe may be reflected in principles of the minds that have evolved in that universe – provided that the mental principles are formulated with respect to the abstract spaces appropriate for the representation of biologically significant objects and their properties. (1) Positions and motions of objects conserve their shapes in the geometrically fullest and simplest way when represented as points and connecting geodesic paths in the six-dimensional manifold jointly determined by the Euclidean group of three-dimensional space and the symmetry group of each object. (2) Colors of objects attain constancy when represented as points in a three-dimensional vector space in which each variation in natural illumination is canceled by application of its inverse from the three-dimensional linear group of terrestrial transformations of the invariant solar source. (3) Kinds of objects support optimal generalization and categorization when represented, in an evolutionarily-shaped space of possible objects, as connected regions with associated weights determined by Bayesian revision of maximum-entropy priors.

2021 ◽  
Author(s):  
Keiko Yamazaki ◽  
Fujiko Abe ◽  
Ichiro Hagiwara

Abstract The Japanese traditional fan, which is a form of origami originating in Japan with a folding culture, has a variety of three-dimensional expression that differs from two-dimensional expression. The image painted on the fan deforms when the fan is folded. In this study, we create a digital fan model for clarifying the deformation on the fan face according to parameters such as length of the bamboo bones. We then validate the digital model with an actual fan. Furthermore, we obtain the original plan view from images of the folded fan as a reverse problem. Because folding fans are made of paper and bamboo and held in the hand, old traditional folding fans are more or less damaged; for example, many culturally valuable folding fans have lost their bones and have damaged edges, have been stretched flat, and have been framed like paintings. Reproducing the original fan without information of the original form is difficult. In the present study, we provide a digital fan model for examining the original fan shape. Old valuable folding fans are treasured by museums and collectors around the world. In future research, we would like to capture such precious folding fans in three-dimensional space applying our digital fan model and to exhibit these fans in a digital museum, providing opportunities not only to enjoy the value of the fans but also to encourage the research of Japanese traditional culture.


Philosophy ◽  
1982 ◽  
Vol 57 (221) ◽  
pp. 339-355 ◽  
Author(s):  
Roderick Millar

It is commonly believed that there are, in the world, large numbers of objects which occupy three-dimensional space. It is also commonly believed that at least a large part of people's experience is of the surfaces of these material objects. Nevertheless, arguments have been adduced in favour of the view that we are never aware of such surfaces but only of distinct items called ‘sense-data’. It has also been suggested that if we couple the view that experience is limited to sense-data with an empiricist thesis to the effect that knowledge is limited by experience then we are forced to the conclusion that we cannot have any knowledge of material objects. There have been many attempts to reconcile the sense-data thesis with common beliefs about material objects. Among them have been representative realism and phenomenalism. However, a view which may have found favour recently is the Quinean one that ‘the myth of physical objects is epistemologically superior to most in that it has proved more efficacious than other myths as a device for working a manageable structure into the flux of experience’.1


2007 ◽  
Vol 37 (6) ◽  
pp. 1714-1732 ◽  
Author(s):  
Trevor J. McDougall ◽  
David R. Jackett

Abstract It is shown that the ocean’s hydrography occupies little volume in the three-dimensional space defined by salinity–temperature–pressure (S–Θ–p), and the implications of this observation for the mean vertical transport across density surfaces are discussed. Although ocean data have frequently been analyzed in the two-dimensional temperature–salinity (S–Θ) diagram where casts of hydrographic data are often locally tight in S–Θ space, the relatively empty nature of the World Ocean in the three-dimensional S–Θ–p space seems not to have received attention. The World Ocean’s data lie close to a single surface in this three-dimensional space, and it is shown that this explains the known smallness of the ambiguity in defining neutral surfaces. The ill-defined nature of neutral surfaces means that lateral motion along neutral trajectories leads to mean vertical advection through density surfaces, even in the absence of small-scale mixing processes. The situation in which the ocean’s hydrography occupies a large volume in S–Θ–p space is also considered, and it is suggested that the consequent vertical diapycnal advection would be sufficiently large that the ocean would not be steady.


2003 ◽  
Vol 31 (2) ◽  
pp. 533-546
Author(s):  
Stepan Davtian ◽  
Tatyana Chernigovskaya

Diagnostics of a mental disorder completely bases on an estimation of patient’s behaviour, verbal behaviour being the most important. The behaviour, in turn, is ruled by a situation expressed as a system of signs. Perception of a situation could be seen as a function, which depends on the context resulting from the previous situations, structuring personal world. So the world is not given — it is being formed while the person is in action. We argue that distinctive features of behaviour, including its abnormal variants, can be explained not in categories of characters and diseases but in terms of situations taking place in individual worlds. The situation in which a person perceives himself is not simply a site in a three-dimensional space at a certain moment, but a part of the world and an episode of his life. Like a text composed of words, individual world is composed of situations. Each of them needs certain context to cope with ambiguity. This context is induced by the world as a whole. And the world, in turn, is presented as a chain of situations. If the context cannot help to interpret a situation adequately, uncertainty can be eliminated by actions clarifying a situation, which is changed in a predictable way. Thus, purposeful activity, skills to make predictions and corrections of one’s own actions are crucial. Weakness of any of them inevitably leads to the distortion of the presentation of the world, to wrong evaluation of situations and, as a result, to inadequate actions that finally reduce the activity as being ineffective. Thus, the lack of activity becomes the key factor in the development of disorder, being simultaneously its cause and effect. In periods of insufficient activity conditions for violated (and violating) sign processing arise. Possible variants of sign malfunction are: oligosemia (reduction of the number of perceivable signs), hyposemia (decrease of significance of signs), hypersemia (increase of significance of some signs at the expense of others), ambisemia (uncertainty of sign, when situation remains unclear), cryptosemia (recognition of signs not obvious for other observers), and parasemia (perverted interpretation of signs influenced by a false context).


Author(s):  
Dale Purves

Perceived motion is defined as the apparent speed and direction of objects that are translating and/or rotating in three-dimensional space. It has long been clear, however, that the perceived speeds and directions of moving objects disagree with physical measurements of motion. With respect to speed, the flash-lag effect has been a major focus; with respect to direction, the emphasis has been on the effects of apertures. These phenomena—and many others—raise the question of how we routinely succeed in the world despite blatant discrepancies between the motions we see and the physical speeds and directions of the objects we must deal with. Resolving this puzzle presents another body of evidence pertinent to whether empirical ranking is the way nervous systems link objective and subjective domains.


2020 ◽  
Vol 66 (4) ◽  
pp. 851-876
Author(s):  
Zhaowei Liu ◽  
Andrew McBride ◽  
Prashant Saxena ◽  
Paul Steinmann

Abstract An isogeometric approach for solving the Laplace–Beltrami equation on a two-dimensional manifold embedded in three-dimensional space using a Galerkin method based on Catmull–Clark subdivision surfaces is presented and assessed. The scalar-valued Laplace–Beltrami equation requires only $$C^0$$ C 0 continuity and is adopted to elucidate key features and properties of the isogeometric method using Catmull–Clark subdivision surfaces. Catmull–Clark subdivision bases are used to discretise both the geometry and the physical field. A fitting method generates control meshes to approximate any given geometry with Catmull–Clark subdivision surfaces. The performance of the Catmull–Clark subdivision method is compared to the conventional finite element method. Subdivision surfaces without extraordinary vertices show the optimal convergence rate. However, extraordinary vertices introduce error, which decreases the convergence rate. A comparative study shows the effect of the number and valences of the extraordinary vertices on accuracy and convergence. An adaptive quadrature scheme is shown to reduce the error.


2002 ◽  
Vol 17 (29) ◽  
pp. 4219-4228 ◽  
Author(s):  
MOSHE CARMELI

We use a Riemannian four-dimensional presentation for gravitation in which the coordinates are distances and velocity rather than the traditional space and time. We solve the field equations and show that there are three possibilities for the Universe to expand. The theory describes the Universe as having a three-phase evolution with a decelerating expansion, followed by a constant and an accelerating expansion, and it predicts that the Universe is now in the latter phase. It is shown, assuming Ωm = 0.245, that the time at which the Universe goes over from a decelerating to an accelerating expansion, occurs at 8.5 Gyr ago, at which time the cosmic radiation temperature was 146K. Recent observations show that the Universe's growth is accelerating. Our theory confirms these recent experimental results. The theory predicts also that now there is a positive pressure in the Universe. Although the theory has no cosmological constant, we extract from it its equivalence and show that Λ = 1.934 × 10-35 s-2. This value of Λ is in excellent agreement with measurements. It is also shown that the three-dimensional space of the Universe is Euclidean, as the Boomerang experiment shows.


Author(s):  
Taizo Okabe ◽  
Takahiro Nishimichi ◽  
Masamune Oguri ◽  
Sébastien Peirani ◽  
Tetsu Kitayama ◽  
...  

Abstract It is known observationally that the major axes of galaxy clusters and their brightest cluster galaxies are roughly aligned with each other. To understand the origin of the alignment, we identify 40 cluster-sized dark matter (DM) haloes with masses higher than 5 × 1013 M⊙ and their central galaxies (CGs) at z ≈ 0 in the Horizon-AGN cosmological hydrodynamical simulation. We trace the progenitors at 50 different epochs between 0 < z < 5. We then fit their shapes and orientations with a triaxial ellipsoid model. While the orientations of both DM haloes and CGs change significantly due to repeated mergers and mass accretions, their relative orientations are well aligned at each epoch even at high redshifts, z > 1. The alignment becomes tighter with cosmic time; the major axes of the CGs and their host DM haloes at present are aligned on average within ∼30○ in the three dimensional space and ∼20○ in the projected plane. The orientations of the major axes of DM haloes on average follow one of the eigen-vectors of the surrounding tidal field that corresponds to the slowest collapsing (or even stretching) mode, and the alignment with the tidal field also becomes tighter. This implies that the orientations of CGs and DM haloes at the present epoch are largely imprinted in the primordial density field of the Universe, whereas strong dynamical interactions such as mergers are important to explain their mutual alignment at each epoch.


2011 ◽  
Vol 8 (2) ◽  
pp. 79-88
Author(s):  
Mirna Radin Sabadoš

The proposal that the world is made of sequences of zeros and ones, overtly expressed in DeLillo’s early novel Ratner’s Star (1976), marks the first time in DeLillo’s fiction that he introduces the idea that the (creation of) reality is of mathematical nature. The “zero-oneness” of the world thirty odd years later, although it still may be an uncommon thought in literature, is ubiquitous in the visual arts, in film and in architecture, and binary code has become the basis of our digitally enhanced reality. Looking at DeLillo’s Millennial novels, this paper seeks to explore models of the space-time continuum of the fictional reality that DeLillo constructs; focusing on Ratner’s Star as a literary exploration of a three-dimensional space and on the novel Body Artist as an investigation of the fourth dimension, pondering time, we hope to register the “sum total of one’s data” (WN) as the only palpable texture of DeLillo’s reality.


2020 ◽  
Vol 223 ◽  
pp. 02005
Author(s):  
Pavel Kim

According to the Poincaré conjecture (1904) proved by Grigory Perelman (2002-2003) that any simply connected compact three- dimensional manifold without edges is homeomorphic to a three- dimensional hypersphere [1], to solve the problems of visualizing four- dimensional objects in three-dimensional space [2], it is proposed to choose a suitable manifold, in in this case, a ball, establishing a homeomorphism between objects located in different spaces by technological means of cartography. As a result of this work, it seems possible to build a dynamic video of the population distribution process on a map of the globe, which provides informational four-dimensional data flow, following the ideas embodied in 4D Anatomy [3]. The proposed technology opens up new ways of visualizing four-dimensional space This work was performed within the framework of the state assignment of the ICM MG SB RAS (project 0315-2019-0003).


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