几何线索直接性和显著性对儿童菱形空间再定向的影响

以25名幼儿园中班儿童为研究对象,采用在一个边或角有颜色标记的菱形平面的四个角或边位置中藏物找物的任务,来探究几何线索的直接性和显著性如何影响5岁儿童对几何及非几何线索的利用。研究发现:几何线索优先性并不稳定;几何线索的直接性影响了几何线索的使用;在几何线索直接的条件下,几何线索的显著性影响了几何线索的使用;几何线索直接性及显著性均不影响儿童对颜色线索的使用。     

Does the brain prefer geometrical homogeneity?

Some patients with frontotemporal lobar degeneration (FTLD) have shown the development of painting or musical abilities after the onset of the disease. In this report, we present another emergent ability. A female patient with FTLD showing dense atrophy of the bilateral anterior lobes and a loss of voluntary activity in aspects of daily living, presented with the characteristic behaviours when given a paper and a pair of scissors. When a shape was already drawn on the paper, she showed reasonable skills with the scissors, cutting without any hesitation. When she cut a blank piece of paper, she showed quite unique geometrical preferences. Her severely degenerated brain combined with her geometrical abilities suggests that the human brain is naturally affected by geometrical homogeneity.     

Continuity of Theory Structure: A Conceptual Spaces Approach

By understanding laws of nature as geometrical rather than linguistic entities, this paper addresses how to describe theory structures and how to evaluate their continuity. Relying on conceptual spaces as a modelling tool, we focus on the conceptual framework an empirical theory presupposes, thus obtain a geometrical representation of a theory’s structure. We stress the relevance of measurement procedures in separating conceptual from empirical structures. This lets our understanding of scientific laws come closer to scientific practice, and avoids a widely recognised deficit in current philosophy of science accounts, namely to risk a collapse of the physical into the mathematical.     

The Importance of Cartesian Triangles: A New Look at Descartes's Ontological Argument

In this paper, I argue that commentators have missed a significant clue given by Descartes in coming to understand his 'ontological' proof for the existence of God. In both the analytic and synthetic presentations of the proof throughout his writings, Descartes notes that the proof works 'in the same way' as a particular geometrical proof. I explore the significance of such a parallel, and conclude that Descartes could not have intended readers to think that the argument consists of some kind of intuition. I argue that for Descartes the attribute of existence is a 'second-order' attribute that is demonstrated to belong to the idea of God on the basis of 'first-order' attributes. The proof, properly understood, is in fact a demonstration. Having brought to light the geometrical parallels between the ontological and geometrical proofs, we have new evidence to resolve the 'intuition versus demonstration' controversy that has characterized much of the discussion of Descartes's ontological argument.     

Pictorial surface attitude and local depth comparisons

We measured local surface attitude for monocular pictorial relief and performed pairwise depthcomparison judgments on the same picture. Both measurements were subject to internal consistency checks. We found that both measurements were consistent with a relief (continuous pictorial surface) interpretation within the session-to-session scatter. We reconstructed the pictorial relief from both measurements separately, and found results that differed in detail but were quite similar in their basic structures. Formally, one expects certain geometrical identities that relate range and attitude data. Because we have independent measurements of both, we can attempt an empirical verification of such geometrical identities. Moreover, we can check whether the statistical scatter in the data indicates that, for example, the surface attitudes are derivable from a depth map or vice versa. We estimate that pairwise depth comparisons are an order of magnitude less precise than might be expected from the attitude data. Thus, the surface attitudes cannot be derived from a depth map as operationally defined by our methods, although the reverse is a possibility.     

Masked transposition effects for simple versus complex nonalphanumeric objects

When two letters/digits/symbols are switched in a string (e.g., jugde–judge; 1492–1942; *?When two letters/digits/symbols are switched in a string (e.g., jugde-judge; 1492-1942; *?$&-*$?&), the resulting strings are perceptually similar to each other and produce a sizable masked transposition priming effect with the masked priming same-different matching task. However, a parallel effect does not occur for strings of pseudoletters (e.g., [letters in the text]); García-Orza, Perea, & Mu?oz, Quarterly Journal of Experimental Psychology, 63, 1603-1618, 2010). In the present study, we examined whether masked transposition priming is specific to alphanumeric stimuli or whether it also occurs with strings composed of other "objects"-namely, line drawings of common objects (Experiment 1) and geometrical shapes (Experiment 2). Results showed a significant masked transposition priming effect for geometrical shapes (e.g., [geometrical shapes in the text]), but not for line drawings of common objects (e.g., [symbols in the text]). These findings suggest that the mechanism involved in the coding of position in masked priming works only with perceptually simple, familiar "objects" (i.e., letters, numbers, symbols, or geometrical shapes), once their identities have been well ascertained.     

Mechanisms revisited

This paper defends an interventionist treatment of mechanisms and contrasts this with Waskan (forthcoming). Interventionism embodies a difference-making conception of causation. I contrast such conceptions with geometrical/mechanical or “actualist” conceptions, associating Waskan’s proposals with the latter. It is argued that geometrical/mechanical conceptions of causation cannot replace difference-making conceptions in characterizing the behavior of mechanisms, but that some of the intuitions behind the geometrical/mechanical approach can be captured by thinking in terms of spatio-temporally organized difference-making information.     

Axiomatizing Relativistic Dynamics without Conservation Postulates

A part of relativistic dynamics is axiomatized by simple and purely geometrical axioms formulated within first-order logic. A geometrical proof of the formula connecting relativistic and rest masses of bodies is presented, leading up to a geometric explanation of Einstein’s famous E = mc ². The connection of our geometrical axioms and the usual axioms on the conservation of mass, momentum and four-momentum is also investigated.     

Empirical Conditions for a Reidean Geometry of Visual Experience

Thomas Reid’s Geometry of Visibles, according to which the geometrical properties of an object’s perspectival appearance equal the geometrical properties of its projection on the inside of a sphere with the eye in its centre allows for two different interpretations. It may (1) be understood as a theory about phenomenal visual space—i.e. an account of how things appear to human observers from a certain point of view—or it may (2) be seen as a mathematical model of viewpoint-relative but mind-independent relational properties of objects. This paper makes a systematic and a historical claim. I shall argue, first, that given certain features of the human visual system phenomenal visual space differs in several aspects from Reidean visual space. Secondly, I suggest that, since Reid was aware of some of these empirical facts, we should interpret Reid as endorsing the second interpretation of the Geometry of Visibles.     

Learning a new geometric concept: The role of working memory and of domain-specific abilities

It has been suggested that not only domain-specific factors but also working memory (WM) may play a crucial role in mathematical learning included Geometry, but the issue has not been deeply explored. In the present study, we examined the role of domain-specific factors and of verbal versus visuospatial WM on geometric learning of a new geometrical figure (trapezoid), never presented previously by the teachers participating to the study, after a lecture also involving manipulatives. Results on 105 children in their Year 4 indicated that not only some domain-specific components (geometric declarative knowledge and calculation) but also visuospatial working memory had a significant specific impact on the ability of solving geometric problems requiring to calculate the perimeter and the area of the new figure. On the contrary, verbal WM and geometrical mental imagery did not offer a specific contribution. These findings could have important educational implications, stressing the importance of taking into account the main different aspects supporting the acquisition of geometry.     

NEWTON AND PROCLUS: GEOMETRY,IMAGINATION, AND KNOWING SPACE

I aim to clarify the argument for space that Newton presents in De Gravitatione (composed prior to 1687) by putting Newton's remarks into conversation with the account of geometrical knowledge found in Proclus's Commentary on the First Book of Euclid's Elements (ca. 450). What I highlight is that both Newton and Proclus adopt an epistemic progression (or “order of knowing”) according to which geometrical knowledge necessarily precedes our knowledge of metaphysical truths concerning the ontological state of affairs. As I argue, Newton's commitment to this order of knowing clarifies the interplay of the imagination and understanding in geometrical inquiry and illuminates how geometrical knowledge of space can lead to knowledge that space depends on and is related to God. In general, appreciating the Proclean elements of Newton's argument brings added light to the significance of geometrical inquiry for his general natural philosophical program and grants us insight into the philosophical grounding for the notion of absolute space that is presented in the Principia mathematica (1687).     

Why do animals differ in their susceptibility to geometrical illusions?

In humans, geometrical illusions are thought to reflect mechanisms that are usually helpful for seeing the world in a predictable manner. These mechanisms deceive us given the right set of circumstances, correcting visual input where a correction is not necessary. Investigations of non-human animals’ susceptibility to geometrical illusions have yielded contradictory results, suggesting that the underlying mechanisms with which animals see the world may differ across species. In this review, we first collate studies showing that different species are susceptible to specific illusions in the same or reverse direction as humans. Based on a careful assessment of these findings, we then propose several ecological and anatomical factors that may affect how a species perceives illusory stimuli. We also consider the usefulness of this information for determining whether sight in different species might be more similar to human sight, being influenced by contextual information, or to how machines process and transmit information as programmed. Future testing in animals could provide new theoretical insights by focusing on establishing dissociations between stimuli that may or may not alter perception in a particular species. This information could improve our understanding of the mechanisms behind illusions, but also provide insight into how sight is subjectively experienced by different animals, and the degree to which vision is innate versus acquired, which is difficult to examine in humans.     

Segmentation and coupling in complex movements

In two experiments we explore the structure of complex sequences of drawing movements. We find that in these movements a single parameter--the velocity gain factor--relates the geometrical and kinematic aspects of the movement trajectory via a two-thirds power law. In Experiment 1 we investigate the relation between the velocity gain factor and the linear extent of the trajectory. In Experiment 2 we demonstrate that the gain factor provides a criterion for segmenting the movement into distinct units of motor action, and we investigate the effects of the speed of execution on this segmentation. A theoretical analysis shows that the results of both Experiments 1 and 2 can be given a unitary interpretation by assuming a coupling function of variable strength between segments. The general problem of representing motor programs is discussed within this theoretical framework.     

Understanding scale-dependent yield stress of metals at micrometre scales

The mechanical softening behaviour of micrometre-scale metals (free-standing metal foils and wires) with decreasing either the geometrical or the microstructural scale (i.e. the smaller, the weaker) has recently been reported. Here, we present a mechanism-based model to understand the softening behaviour, which is based on competition between the effects of surface grain relaxation and the interior grain strengthening effect. The model describes well the yield stress of Cu foils with different ratios of the thickness to grain size.     

4-5年级学生的空间表征与几何能力的相关性研究

本研究是“学生空间能力和几何能力关系”研究的一部分,以小学4、5年级学生为被试(共117人),以空问表征能力测验和几何能力测验为测验工具,初步探讨了学生空间表征与几何能力的关系。对数据结果的分析表明:①就总成绩而言,五年级学生的空间表在成绩明显高于四年级学生的成绩,但并不是空间表征的所有方面都存在着显著的年级差异;②就空间测验的总成绩而言,无论是四、五年级分别考察还是总起来考察,空间成绩与几何成绩之间的相关显著,但就各个分项而言,并不是空间测验的各项都与几何测验成绩有显著相关;学生的几何成绩在一定程度上可通过回归方程:Y_i=0.5736X_i+0.7635加以预测。     

Does the use of natural stimuli facilitate amodal completion in pigeons?

Three experiments were carried out to investigate whether amodal completion in pigeons can be facilitated by the use of colour photographs instead of highly artificial stimuli such as geometrical shapes. Ten pigeons were trained in a go/no-go procedure to discriminate between photographs of complete and of incomplete pigeon figures. In the subsequent test, the birds classified pictures of partly occluded pigeons as though they were complete (experiment 1). However, we found evidence that classification was based on spurious stimulus features that paralleled the intended class rule of figural completeness versus incompleteness. In particular, classification was shown to be guided by white background gaps that separated the parts of the fragmented pigeon figures (experiment 2), as well as by cues related to overall Gestalt (experiment 3). In summary, the present results indicate that the use of more natural stimuli such as photographs instead of geometrical shapes is insufficient for providing amodal completion in pigeons. It is suggested that a combination of various cues, including, eg, 3-D information and common motion in addition to surface and contour properties, may be required to induce a perceptual bias favouring visual completion of occluded portions.     

Information Processing and Dynamics in Minimally Cognitive Agents

There has been considerable debate in the literature about the relative merits of information processing versus dynamical approaches to understanding cognitive processes. In this article, we explore the relationship between these two styles of explanation using a model agent evolved to solve a relational categorization task. Specifically, we separately analyze the operation of this agent using the mathematical tools of information theory and dynamical systems theory. Information‐theoretic analysis reveals how task‐relevant information flows through the system to be combined into a categorization decision. Dynamical analysis reveals the key geometrical and temporal interrelationships underlying the categorization decision. Finally, we propose a framework for directly relating these two different styles of explanation and discuss the possible implications of our analysis for some of the ongoing debates in cognitive science.     

The global non-entropic arrow of time: from global geometrical asymmetry to local energy flow

Since the nineteenth century, the problem of the arrow of time has been traditionally analyzed in terms of entropy by relating the direction past-to-future to the gradient of the entropy function of the universe. In this paper, we reject this traditional perspective and argue for a global and non-entropic approach to the problem, according to which the arrow of time can be defined in terms of the geometrical properties of spacetime. In particular, we show how the global non-entropic arrow can be transferred to the local level, where it takes the form of a non-spacelike local energy flow that provides the criterion for breaking the symmetry resulting from time-reversal invariant local laws.     

Kant on geometry and spatial intuition

I use recent work on Kant and diagrammatic reasoning to develop a reconsideration of central aspects of Kant??s philosophy of geometry and its relation to spatial intuition. In particular, I reconsider in this light the relations between geometrical concepts and their schemata, and the relationship between pure and empirical intuition. I argue that diagrammatic interpretations of Kant??s theory of geometrical intuition can, at best, capture only part of what Kant??s conception involves and that, for example, they cannot explain why Kant takes geometrical constructions in the style of Euclid to provide us with an a priori framework for physical space. I attempt, along the way, to shed new light on the relationship between Kant??s theory of space and the debate between Newton and Leibniz to which he was reacting, and also on the role of geometry and spatial intuition in the transcendental deduction of the categories.