Language, procedures, and the non-perceptual origin of natural number concepts

2016 ◽  
Author(s):  
David Barner
Keyword(s):  
General Framework ◽  
Ad Hoc ◽  
Building Blocks ◽  
Number Words ◽  
Linguistic Markers ◽  
Logical Foundations ◽  
Large Numbers ◽  
Perceptual Representations ◽  
Positive Integers ◽  
Perceptual Systems

Perceptual representations – e.g., of objects or approximate magnitudes –are often invoked as building blocks that children combine with linguisticsymbols when they acquire the positive integers. Systems of numericalperception are either assumed to contain the logical foundations ofarithmetic innately, or to supply the basis for their induction. Here Ipropose an alternative to this general framework, and argue that theintegers are not learned from perceptual systems, but instead arise toexplain perception as part of language acquisition. Drawing oncross-linguistic data and developmental data, I show that small numbers(1-4) and large numbers (~5+) arise both historically and in individualchildren via entirely distinct mechanisms, constituting independentlearning problems, neither of which begins with perceptual building blocks.Specifically, I propose that children begin by learning small numbers(i.e., *one, two, three*) using the same logical resources that supportother linguistic markers of number (e.g., singular, plural). Several yearslater, children discover the logic of counting by inferring the logicalrelations between larger number words from their roles in blind countingprocedures, and only incidentally associate number words with perception ofapproximate magnitudes, in an *ad hoc* and highly malleable fashion.Counting provides a form of explanation for perception but is not causallyderived from perceptual systems.

scholarly journals Language, procedures, and the non-perceptual origin of number word meanings

2017 ◽  
Vol 44 (3) ◽  
pp. 553-590 ◽  
Author(s):  
DAVID BARNER
Keyword(s):  
Building Blocks ◽  
Independent Learning ◽  
Learning Problems ◽  
Number Word ◽  
Word Meanings ◽  
Number Words ◽  
Perceptual Representations ◽  
Children First ◽  
Positive Integers ◽  
Perceptual Systems

AbstractPerceptual representations of objects and approximate magnitudes are often invoked as building blocks that children combine to acquire the positive integers. Systems of numerical perception are either assumed to contain the logical foundations of arithmetic innately, or to supply the basis for their induction. I propose an alternative to this framework, and argue that the integers are not learned from perceptual systems, but arise to explain perception. Using cross-linguistic and developmental data, I show that small (~1–4) and large (~5+) numbers arise both historically and in individual children via distinct mechanisms, constituting independent learning problems, neither of which begins with perceptual building blocks. Children first learn small numbers using the same logic that supports other linguistic number marking (e.g. singular/plural). Years later, they infer the logic of counting from the relations between large number words and their roles in blind counting procedures, only incidentally associating number words with approximate magnitudes.

Mobility Analysis of Flexure Mechanisms via Screw Algebra

2011 ◽  
Author(s):  
Hai-Jun Su
Keyword(s):  
General Framework ◽  
Ad Hoc ◽  
Building Blocks ◽  
Current Approach ◽  
Mobility Analysis ◽  
Top Down ◽  
Arbitrary Topology ◽  
Flexure Mechanism ◽  
Systematic Methodology ◽  
Flexure Joints

This paper presents a general framework for studying the mobility of flexure mechanisms with an arbitrary topology using screw algebra. The current approach for mobility analysis of flexures is ad hoc and mostly done by intuition. In this methodology, we first build a library of commonly used flexure elements, flexure joints and simple chains. We then apply the screw algebra to find their motion and constraint spaces in the form of twist and wrench matrices. To analyze a general flexure mechanism, we first apply a top-down approach to hierarchically subdivide it into multiple modules or building blocks down to the level of flexure structures that are already provided in the library. We then use a bottom-up routine to study the mobility of each module up to the level of the overall mechanism. Extensive examples and case studies from simple flexure joints, chains to spatial compliant platforms are used to demonstrate the methodology. This systematic methodology is an important tool for guiding the early stages in flexure mechanism design.

Mobility Analysis of Flexure Mechanisms via Screw Algebra

2011 ◽  
Vol 3 (4) ◽  
Author(s):  
Hai-Jun Su
Keyword(s):  
General Framework ◽  
Ad Hoc ◽  
Building Blocks ◽  
Current Approach ◽  
Mobility Analysis ◽  
Top Down ◽  
Flexure Mechanism ◽  
Hybrid Topology ◽  
Systematic Methodology ◽  
Flexure Joints

This paper presents a general framework for studying the mobility of flexure mechanisms with a serial, parallel or hybrid topology using the screw algebra. The current approach for mobility analysis of flexures is ad hoc and mostly done by intuition. In this methodology, we first build a library of commonly used flexure elements, flexure joints, and simple chains. We then apply the screw algebra to find their motion and constraint spaces in the form of twist and wrench matrices. To analyze a general flexure mechanism, we first apply a top-down approach to hierarchically subdivide it into multiple modules or building blocks down to the level of flexure structures that are already provided in the library. We then use a bottom-up routine to study the mobility of each module up to the level of the overall mechanism. Examples and case studies from simple flexure joints, chains to spatial compliant platforms are used to demonstrate the methodology. This systematic methodology is an important tool for guiding the qualitative design of flexure mechanisms.

Numerical symbols as explanations of human perceptual experience

2018 ◽  
Author(s):  
David Barner
Keyword(s):  
Perceptual Experience ◽  
Number Words ◽  
The World ◽  
Symbolic Systems ◽  
Perceptual Systems

Why did humans develop precise systems for measuring experience, like numbers, clocks, andcalendars? I argue that precise representational systems were constructed by earlier generationsof humans because they recognized that their noisy perceptual systems were not capturingdistinctions that existed in the world. Abstract symbolic systems did not arise from perceptualrepresentations, but instead were constructed to describe and explain perceptual experience. Byanalogy, I argue that when children learn number words, they do not rely on noisy perceptualsystems, but instead acquire these words as units in a broader system of procedures, whosemeanings are ultimately defined by logical relations to one another, not perception.

scholarly journals Limit theorems for multi-type general branching processes with population dependence

2020 ◽  
Vol 52 (4) ◽  
pp. 1127-1163
Author(s):  
Jie Yen Fan ◽  
Kais Hamza ◽  
Peter Jagers ◽  
Fima C. Klebaner
Keyword(s):  
Carrying Capacity ◽  
Population Model ◽  
General Framework ◽  
Limit Theorems ◽  
Mating Systems ◽  
Law Of Large Numbers ◽  
Branching Processes ◽  
Special Section ◽  
Large Numbers ◽  
Type Population

AbstractA general multi-type population model is considered, where individuals live and reproduce according to their age and type, but also under the influence of the size and composition of the entire population. We describe the dynamics of the population as a measure-valued process and obtain its asymptotics as the population grows with the environmental carrying capacity. Thus, a deterministic approximation is given, in the form of a law of large numbers, as well as a central limit theorem. This general framework is then adapted to model sexual reproduction, with a special section on serial monogamic mating systems.

scholarly journals Modeling intentional agency: a neo-Gricean framework

Synthese ◽  
2021 ◽  
Author(s):  
Matti Sarkia
Keyword(s):  
Philosophy Of Mind ◽  
General Framework ◽  
Building Blocks ◽  
Theoretical Modeling ◽  
Model Construction ◽  
Coarse Grained ◽  
Scientific Model ◽  
Types Of Knowledge ◽  
Different Types ◽  
Intentional Agency

AbstractThis paper analyzes three contrasting strategies for modeling intentional agency in contemporary analytic philosophy of mind and action, and draws parallels between them and similar strategies of scientific model-construction. Gricean modeling involves identifying primitive building blocks of intentional agency, and building up from such building blocks to prototypically agential behaviors. Analogical modeling is based on picking out an exemplary type of intentional agency, which is used as a model for other agential types. Theoretical modeling involves reasoning about intentional agency in terms of some domain-general framework of lawlike regularities, which involves no detailed reference to particular building blocks or exemplars of intentional agency (although it may involve coarse-grained or heuristic reference to some of them). Given the contrasting procedural approaches that they employ and the different types of knowledge that they embody, the three strategies are argued to provide mutually complementary perspectives on intentional agency.

The Influence of Structural Aspects of the English Counting Word System on the Teaching and Learning of Place Value

1998 ◽  
Vol 59 (1) ◽  
pp. 1-8 ◽  
Author(s):  
Ian Thompson
Keyword(s):  
Young Children ◽  
Teaching And Learning ◽  
Place Value ◽  
Single Digit ◽  
Value System ◽  
Number Words ◽  
Large Numbers ◽  
Structural Aspects

The influence of structural aspects of the English counting word system on the teaching and learning of place value In their discussion of the teaching of place value to young children Fuson and Briars (1990) describe the extent to which the English spoken system of number words constitutes a ‘named value’ system for large numbers. They argue that, because two-digit numbers are not ‘named value’, teachers should move from teaching single-digit calculations to teaching calculations with large numbers, only returning to two-digit numbers when children are familiar with the standard written algorithms. This article uses transcriptions of children calculating mentally to suggest that they appear to take advantage of the ‘partitionable’ aspect of the language associated with two-digit numbers - an aspect that Fuson and Briars (1990) appear to have ignored. These examples appear to raise questions about their recommendation that teachers should progress from single-digit to large number calculations.

scholarly journals Identifying home locations in human mobility data: an open-source R package for comparison and reproducibility

2021 ◽  
Author(s):  
Qingqing Chen ◽  
Ate Poorthuis
Keyword(s):  
Software Package ◽  
Ad Hoc ◽  
Human Mobility ◽  
Building Blocks ◽  
R Package ◽  
Location Based Services ◽  
R Software ◽  
Mobility Data ◽  
Residential Population ◽  
Research Goal

Identifying meaningful locations, such as home or work, from human mobility data has become an increasingly common prerequisite for geographic research. Although location-based services (LBS) and other mobile technology have rapidly grown in recent years, it can be challenging to infer meaningful places from such data, which - compared to conventional datasets – can be devoid of context. Existing approaches are often developed ad-hoc and can lack transparency and reproducibility. To address this, we introduce an R software package for inferring home locations from LBS data. The package implements pre-existing algorithms and provides building blocks to make writing algorithmic ‘recipes’ more convenient. We evaluate this approach by analyzing a de-identified LBS dataset from Singapore that aims to balance ethics and privacy with the research goal of identifying meaningful locations. We show that ensemble approaches, combining multiple algorithms, can be especially valuable in this regard as the resulting patterns of inferred home locations closely correlate with the distribution of residential population. We hope this package, and others like it, will contribute to an increase in use and sharing of comparable algorithms, research code and data. This will increase transparency and reproducibility in mobility analyses and further the ongoing discourse around ethical big data research.

scholarly journals Changing what you see by changing what you know: the role of attention

2017 ◽  
Author(s):  
Gary Lupyan
Keyword(s):  
Perceptual Content ◽  
Current Evidence ◽  
Cognitive State ◽  
Perceptual Process ◽  
Cognitive Influences ◽  
Cognitive States ◽  
Visual Hierarchy ◽  
Visual Inputs ◽  
Perceptual Representations ◽  
Perceptual Systems

Attending is a cognitive process that incorporates a person’s knowledge, goals, and expectations. What we perceive when we attend to one thing is different from what we perceive when we attend to something else. Yet, it is often argued that attentional effects do not count as evidence that perception is influenced by cognition. I investigate two arguments often given to justify excluding attention. The first is arguing that attention is a post-perceptual process reflecting selection between fully constructed perceptual representations. The second is arguing that attention as a pre-perceptual process that simply changes the input to encapsulated perceptual systems. Both of these arguments are highly problematic. Although some attentional effects can indeed be construed as post-perceptual, others operate by changing perceptual content across the entire visual hierarchy. Although there is a natural analogy between spatial attention and a change of input, the analogy falls apart when we consider other forms of attention. After dispelling these arguments, I make a case for thinking of attention not as a confound, but as one of the mechanisms by which cognitive states affect perception by going through cases in which the same or similar visual inputs are perceived differently depending on the observer’s cognitive state, and instances where cuing an observer using language affects what one sees. Lastly, I provide two compelling counter-examples to the critique that although cognitive influences on perception can be demonstrated in the laboratory, it is impossible to really experience them for oneself in a phenomenologically compelling way. Taken together, the current evidence strongly supports the thesis that what we know routinely influences what we see, that the same sensory input can be perceived differently depending on the current cognitive state of the viewer, and that phenomenologically salient demonstrations are possible if certain conditions are met.

Separating Style and Content with Bilinear Models

2000 ◽  
Vol 12 (6) ◽  
pp. 1247-1283 ◽  
Author(s):  
Joshua B. Tenenbaum ◽  
William T. Freeman
Keyword(s):  
Expectation Maximization ◽  
General Framework ◽  
Singular Value ◽  
Familiar Face ◽  
Bilinear Models ◽  
Complex Interactions ◽  
Efficient Learning ◽  
Value Decomposition ◽  
Factor Interactions ◽  
Perceptual Systems

Perceptual systems routinely separate “content” from “style,” classifying familiar words spoken in an unfamiliar accent, identifying a font or handwriting style across letters, or recognizing a familiar face or object seen under unfamiliar viewing conditions. Yet a general and tractable computational model of this ability to untangle the underlying factors of perceptual observations remains elusive (Hofstadter, 1985). Existing factor models (Mardia, Kent, & Bibby, 1979; Hinton & Zemel, 1994; Ghahramani, 1995; Bell & Sejnowski, 1995; Hinton, Dayan, Frey, & Neal, 1995; Dayan, Hinton, Neal, & Zemel, 1995; Hinton & Ghahramani, 1997) are either insufficiently rich to capture the complex interactions of perceptually meaningful factors such as phoneme and speaker accent or letter and font, or do not allow efficient learning algorithms. We present a general framework for learning to solve two-factor tasks using bilinear models, which provide sufficiently expressive representations of factor interactions but can nonetheless be fit to data using efficient algorithms based on the singular value decomposition and expectation-maximization. We report promising results on three different tasks in three different perceptual domains: spoken vowel classification with a benchmark multi-speaker database, extrapolation of fonts to unseen letters, and translation of faces to novel illuminants.

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