scholarly journals A language of thought for the mental representation of geometric shapes

2021 ◽  
Author(s):  
Mathias Sablé-Meyer ◽  
Kevin Ellis ◽  
Joshua Tenenbaum ◽  
Stanislas Dehaene
Keyword(s):  
Programming Language ◽  
Mental Representation ◽  
Minimum Description Length ◽  
Language Of Thought ◽  
Minimal Set ◽  
Geometric Shapes ◽  
Line Drawings ◽  
Compositional Language ◽  
Produce Line ◽  
Geometric Primitives

Why do geometric shapes such as lines, circles, zig-zags or spirals appear in all human cultures, but are never produced by other animals? Here, we formalize and test the hypothesis that all humans possess a compositional language of thought that can produce line drawings as recursive combinations of a minimal set of geometric primitives. We present a programming language, similar to Logo, that combines discrete numbers and continuous integration in higher-level structures based on repetition, concatenation and embedding, and show that the simplest programs in this language generate the fundamental geometric shapes observed in human cultures. On the perceptual side, we propose that shape perception in humans involves searching for the shortest program that correctly draws the image (program induction). A consequence of this framework is that the mental difficulty of remembering a shape should depend on its minimum description length (MDL) in the proposed language. In two experiments, we show that encoding and processing of geometric shapes is well predicted by MDL. Furthermore, our hypotheses predict additive laws for the psychological complexity of repeated, concatenated or embedded shapes, which are experimentally validated.

scholarly journals Where to Draw The Line?

2021 ◽  
Author(s):  
Heping Sheng ◽  
John Wilder ◽  
Dirk B. Walther
Keyword(s):  
Computational Analysis ◽  
Scene Recognition ◽  
Scene Categorization ◽  
Line Drawings ◽  
Complex Information ◽  
Artistic Experience ◽  
Original Photograph ◽  
Small Set ◽  
Occlusion Boundaries ◽  
Produce Line

Abstract We often take people’s ability to understand and produce line drawings for granted. But where should we draw lines, and why? We address fundamental principles that underlie efficient representations of complex information in line drawings. First, 58 participants with varying degree of artistic experience produced multiple drawings of a small set of scenes by tracing contours on a digital tablet. Second, 37 independent observers ranked the drawings by how representative they are of the original photograph. Overall, artists’ drawings ranked higher than non-artists’. Matching contours between drawings of the same scene revealed that the most consistently drawn contours tend to be drawn earlier. We generated half-images with the most-versus least-consistently drawn contours by sorting contours by their consistency scores. Twenty five observers performed significantly better in a fast scene categorization task for the most compared to the least consistent half-images. The most consistent contours were longer and more likely to depict occlusion boundaries. Using psychophysics experiments and computational analysis, we confirmed quantitatively what makes certain contours in line drawings special: longer contours mark occlusion boundaries and aid rapid scene recognition. They allow artist and non-artists to convey important information starting from the first few strokes in their drawing process.

Introduction

2017 ◽  
Author(s):  
Roberto G. de Almeida
Keyword(s):  
Cognitive Science ◽  
Mental Representation ◽  
Cognitive Architecture ◽  
Language Of Thought ◽  
Conceptual Representation ◽  
Jerry Fodor ◽  
Present Book ◽  
Cognitive Revolution ◽  
The Subject ◽  
Language Of Thought Hypothesis

It is patent that the so-called cognitive revolution of the 1950s and 1960s was the result of ideas emerging at the confluence of psychology, linguistics, philosophy, computer science, and neuroscience—what became known as cognitive science. In the last 60 years or so, Jerry Fodor has been one of the most important exponents of this revolution. He has advanced key ideas on the foundations of cognitive science, in particular on the nature of mental representation and on mental processes seen as computations over symbols. Many of his contributions have been the subject of deep divides and have generated classical controversies. The chapter provides a rough guide to Fodor’s contributions to psycholinguistics, to the modularity of mind, to atomism as a theory of conceptual representation, to the language of thought hypothesis, and to cognitive architecture more broadly—topics that figure prominently in the present book.

Minimum Description Length Adaptive Bayesian Mining

2011 ◽  
pp. 1231-1235
Author(s):  
Diego Liberati
Keyword(s):  
Information Theory ◽  
Bayesian Networks ◽  
Everyday Life ◽  
Present Article ◽  
Minimum Description Length ◽  
Wide Spread ◽  
Minimal Set ◽  
Present Contribution ◽  
Data Set ◽  
Classification Procedures

In everyday life, it often turns out that one has to face a huge amount of data, often not completely homogeneous, often without an immediate grasp of an underlying simple structure. Many records, each instantiating many variables are usually collected with the help of several tools. Given the opportunity to have so many records on several possible variables, one of the typical goals one has in mind is to classify subjects on the basis of a hopefully reduced meaningful subset of the measured variables. The complexity of the problem makes it natural to resort to automatic classification procedures (Duda and Hart, 1973) (Hand et al., 2001). Then, a further questions could arise, like trying to infer a synthetic mathematical and/or logical model, able to capture the most important relations between the most influencing variables, while pruning (O’Connel 1974) the not relevant ones. Such interrelated aspects will be the focus of the present contribution. In the First Edition of this encyclopedia we already introduced three techniques dealing with such problems in a pair of articles (Liberati, 2005) (Liberati et al., 2005). Their rationale is briefly recalled in the following background section in order to introduce the kind of problems also faced by the different approach described in the present article, which will instead resort to the Adaptive Bayesian Networks implemented by Yarmus (2003) on a commercial wide spread data base tool like Oracle. Focus of the present article will thus be the use of Adaptive Bayesian Networks are in order to unsupervisedly learn a classifier direcly form data, whose minimal set of features is derived through the classical Minimun Description Lenght (Barron and Rissanen, 1998) popular in information theory. Reference will be again made to the same popular micro-arrays data set also used in (Liberati et al., 2005), not just to have a common benchmark useful to compare results and discuss complementary advantages of the various procedures, but also because of the increasing relevance of the bioinformatics field itself.

SOFTWARE EXECUTORS IN THE DIGITAL PEDAGOGICAL ENVIRONMENTS: PIKTOMIR, ROBOTLANDIA AND KUMIR

2019 ◽  
pp. 54-61
Author(s):  
A. G. Leonov ◽  
Yu. А. Pervin ◽  
Ya. N. Zaidelman
Keyword(s):  
Primary School ◽  
Programming Language ◽  
Gradual Transition ◽  
Specific Training ◽  
Minimal Set ◽  
Training Systems ◽  
Time Work

The article analyzes the necessity and possibility of studying the basics of programming in preschool and primary school. A well-known technology for studying programming based on software executors is considered, while it is proposed to significantly reduce the age at which teaching begins. The possibility of this decrease is justified by changes in the environment in which modern children live, their early acquaintance with a variety of software-controlled devices, accumulated experience in managing such devices. The article discusses specific training systems that implement this approach: PiktoMir, Robotlandia, KuMir. A gradual transition from non-text programming using pictograms (PiktoMir) through text management using a minimal set of constructions (Robotlandia) to a full-fledged programming language (KuMir) is shown. At the same time, work in the Kumir environment also begins with the management of performers, thereby ensuring continuity of approaches and the gradual assimilation of increasingly complex programming methods. The article summarizes the authors ’experience in the development and pedagogical testing of the application of the above systems, the conclusion is made about the possibility, methodological preparedness and educational soundness of the early study of the basics of programming using software-controlled executors.

scholarly journals Tolerance Zone-Based Grouping Method for Online Multiple Overtracing Freehand Sketches

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Shuxia Wang ◽  
Shouxia Wang ◽  
Weiping He ◽  
Shengfeng Qin
Keyword(s):  
3D Reconstruction ◽  
Prototype System ◽  
Polygonal Approximation ◽  
Tolerance Zone ◽  
Line Segments ◽  
Line Drawings ◽  
Stroke Group ◽  
Grouping Method ◽  
Screen Space ◽  
Geometric Primitives

Multiple overtracing strokes are common drawing behaviors in freehand sketching; that is, additional strokes are often drawn repeatedly over the existing ones to add more details. This paper proposes a method based on stroke-tolerance zones to group multiple overtraced strokes which are drawn to express a 2D primitive, aiming to convert online freehand sketches into 2D line drawings, which is a base for further 3D reconstruction. Firstly, after the user inputs a new stroke, a tolerance zone around the stroke is constructed by reference to its polygonal approximation points obtained from the stroke preprocessing. Then, the input strokes are divided into stroke groups, each representing a primitive through the stroke grouping process based on the overtraced ratio of two strokes. At last, each stroke group is fitted into one or more 2D geometric primitives including line segments, polylines, ellipses, and arcs. The proposed method groups two strokes together based on their screen-space proximity directly instead of classifying and fitting them firstly, so that it can group strokes of arbitrary shapes. A sketch-recognition prototype system has been implemented to test the effectiveness of the proposed method. The results showed that the proposed method could support online multiple overtracing freehand sketching with no limitation on drawing sequence, but it only deals with strokes with relatively high overtraced ratio.

scholarly journals Shape Synthesis in Mechanical Design

10.14311/1010 ◽  
2007 ◽  
Vol 47 (6) ◽  
Author(s):  
C. P. Teng ◽  
S. Bai ◽  
J. Angeles
Keyword(s):  
Mechanical Design ◽  
Higher Order ◽  
Cubic Splines ◽  
Structural Elements ◽  
Surfaces Of Revolution ◽  
Stress Concentrations ◽  
Smooth Curves ◽  
Geometric Shapes ◽  
Geometric Primitives ◽  
Non Parametric

The shaping of structural elements in the area of mechanical design is a recurrent problem. The mechanical designer, as a rule, chooses what is believed to be the “simplest” shapes, such as the geometric primitives: lines, circles and, occasionally, conics. The use of higher-order curves is usually not even considered, not to speak of other curves than polynomials. However, the simplest geometric shapes are not necessarily the most suitable when the designed element must withstand loads that can lead to failure-prone stress concentrations. Indeed, as mechanical designers have known for a while, stress concentrations occur, first and foremost, by virtue of either dramatic changes in curvature or extremely high values thereof. As an alternative, we propose here the use of smooth curves that can be simply generated using standard concepts such as non-parametric cubic splines. These curves can be readily used to produce either extruded surfaces or surfaces of revolution. 

scholarly journals Where to draw the line?

PLoS ONE ◽  
2021 ◽  
Vol 16 (11) ◽  
pp. e0258376
Author(s):  
Heping Sheng ◽  
John Wilder ◽  
Dirk B. Walther
Keyword(s):  
Line Drawings ◽  
Complex Information ◽  
Artistic Experience ◽  
Original Photograph ◽  
Small Set ◽  
Occlusion Boundaries ◽  
Produce Line ◽  
Digital Tablet

We often take people’s ability to understand and produce line drawings for granted. But where should we draw lines, and why? We address psychological principles that underlie efficient representations of complex information in line drawings. First, 58 participants with varying degree of artistic experience produced multiple drawings of a small set of scenes by tracing contours on a digital tablet. Second, 37 independent observers ranked the drawings by how representative they are of the original photograph. Matching contours between drawings of the same scene revealed that the most consistently drawn contours tend to be drawn earlier. We generated half-images with the most- versus least-consistently drawn contours and asked 25 observers categorize the quickly presented scenes. Observers performed significantly better for the most compared to the least consistent half-images. The most consistently drawn contours were more likely to depict occlusion boundaries, whereas the least consistently drawn contours frequently depicted surface normals.

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