Constructing a Concept of Number

Numbers are concepts whose content, structure, and organization are influenced by the material forms used to represent and manipulate them. Indeed, as argued here, it is the inclusion of multiple forms (distributed objects, fingers, single- and two-dimensional forms like pebbles and abaci, and written notations) that is the mechanism of numerical elaboration. Further, variety in employed forms explains at least part of the synchronic and diachronic variability that exists between and within cultural number systems. Material forms also impart characteristics like linearity that may persist in the form of knowledge and behaviors, ultimately yielding numerical concepts that are irreducible to and functionally independent of any particular form. Material devices used to represent and manipulate numbers also interact with language in ways that reinforce or contrast different aspects of numerical cognition. Not only does this interaction potentially explain some of the unique aspects of numerical language, it suggests that the two are complementary but ultimately distinct means of accessing numerical intuitions and insights. The potential inclusion of materiality in contemporary research in numerical cognition is advocated, both for its explanatory power, as well as its influence on psychological, behavioral, and linguistic aspects of numerical cognition.

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The Role of Resources in the Success or Failure of Diverse Teams: Resource Scarcity Activates Negative Performance-Detracting Resource Dynamics in Social Category Diverse Teams

Organization Science ◽

10.1287/orsc.2021.1560 ◽

2022 ◽

Author(s):

Siyu Yu ◽

Lindred L. Greer

Keyword(s):

Team Performance ◽

Work Teams ◽

Explanatory Power ◽

Resource Scarcity ◽

Social Category ◽

Power Struggles ◽

The Social ◽

The Face ◽

Resource Dynamics ◽

And Behaviors

Increasing the social category diversity of work teams is top of mind for many organizations. However, such efforts may not always be sufficiently resourced, given the numerous resource demands facing organizations. In this paper, we offer a novel take on the relationship between social category diversity and team performance, seeking to understand the role resources may play in both altering and explaining the performance dynamics of diverse teams. Specifically, our resource framework explains how the effects of social category diversity on team performance can be explained by intrateam resource cognitions and behaviors and are dependent on team resource availability. We propose that in the face of scarcity in a focal resource (i.e., budget), diverse (but not homogenous) teams generalize this scarcity perception to fear that all resources (i.e., staff, time, etc.) are scarce, prompting performance-detracting power struggles over resources within the team. We find support for our model in three multimethod team-level studies, including two laboratory studies of interacting teams and a field study of work teams in research and development firms. Our resource framework provides a new lens to study the success or failure of diverse teams by illuminating a previously overlooked danger in diverse teams (negative resource cognitions (scarcity spillover bias) and behaviors (intrateam power struggles)), which offers enhanced explanatory power over prior explanations. This resource framework for the study of team diversity also yields insight into how to remove the roadblocks that may occur in diverse teams, highlighting the necessity of resource sufficiency for the success of diverse teams.

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Sounding the depths at the confluence of numerosity and language

Linguistics Vanguard ◽

10.1515/lingvan-2014-1002 ◽

2015 ◽

Vol 1 (1) ◽

Cited By ~ 1

Author(s):

Caleb Everett

Keyword(s):

Recent Work ◽

Numerical Cognition ◽

Number Words ◽

Number Systems ◽

The Relationship

AbstractResearchers in a variety of disciplines are currently exploring how number words and other culturally variant symbols for quantities enable and enhance numerical cognition. In this article I survey the ways in which fieldwork among Amazonian languages is helping to elucidate the relationship between numerical cognition and language. I highlight several noteworthy findings in recent work on this topic, address their implications, and also consider the potential of future fieldwork on languages with typologically remarkable number systems.

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Multiple forms of tubulin in the cytoskeletal and flagellar microtubules of polytomella

The Journal of Cell Biology ◽

10.1083/jcb.91.2.352 ◽

1981 ◽

Vol 91 (2) ◽

pp. 352-360 ◽

Cited By ~ 30

Author(s):

TW McKeithan ◽

JL Rosenbaum

Keyword(s):

Protein Synthesis ◽

Gel Electrophoresis ◽

Cold Temperature ◽

Two Dimensional ◽

Multiple Forms ◽

Cytoplasmic Fraction ◽

Two Dimensional Gel Electrophoresis ◽

Brain Tubulin ◽

Β Tubulin

The alga polytomella contains several organelles composed of microtubules, including four flagella and hundreds of cytoskeletal microtubules. Brown and co-workers have shown (1976. J. Cell Biol. 69:6-125; 1978, Exp. Cell Res. 117: 313-324) that the flagella could be removed and the cytoskeletans dissociated, and that both structures could partially regenerate in the absence of protein synthesis. Because of this, and because both the flagella and the cytoskeletons can be isolated intact, this organism is particularly suitable for studying tubulin heterogeneity and the incorporation of specific tubulins into different microtubule-containing organelles in the same cell. In order to define the different species of tubulin in polytonella cytoplasm, a (35)S- labeled cytoplasmic fraction was subjected to two cycles of assembly and disassembly in the presence of unlabeled brain tubulin. Comparison of the labeled polytomella cytoplasmic tubulin obtained by this procedure with the tubulin of isolated polytomella flagella by two-dimensional gel electrophoresis showed that, whereas the β-tubulin from both cytoplasmic and flagellar tubulin samples comigrated, the two α-tubulins had distinctly different isoelectic points. As a second method of isolating tubulin from the cytoplasm, cells were gently lysed with detergent and intact cytoskeletons obtained. When these cytoskeletons were exposed to cold temperature, the proteins that were released were found to be highly enriched in tubulin; this tubulin, by itself, could be assembled into microtubules in vitro. The predominant α-tubulin of this in vitro- assembled cytoskeletal tubulin corresponded to the major cytoplasmic α-tubulin obtained by coassembly of labeled polytomella cytoplasmic extract with brain tubulin and was quite distinct from the α-tubulin of purified flagella. These results clearly show that two different microtubule-containing organelles from the same cell are composed of distinct tubulins.

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A new look at old numbers, and what it reveals about numeration

10.31235/osf.io/g9j2x ◽

2021 ◽

Author(s):

Karenleigh A. Overmann

Keyword(s):

Context Dependence ◽

Mental Calculation ◽

Number Words ◽

Number Systems ◽

Counting Methods ◽

And Behaviors ◽

New Look

In this study, the archaic counting systems of Mesopotamia as understood through the Neolithic tokens, numerical impressions, and proto-cuneiform notations were compared to the traditional number-words and counting methods of Polynesia as understood through contemporary and historical descriptions of vocabulary and behaviors. The comparison and associated analyses capitalized on the ability to understand well-known characteristics of Uruk-period numbers like object-specific counting, polyvalence, and context-dependence through historical observations of Polynesian counting methods and numerical language, evidence unavailable for ancient numbers. Similarities between the two number systems were then used to argue that archaic Mesopotamian numbers, like those of Polynesia, were highly elaborated and would have served as cognitively efficient tools for mental calculation. Their differences also show the importance of material technologies like tokens, impressions, and notations to developing mathematics.

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Thinking with Pictures

Advances in Multimedia and Interactive Technologies - Computational Solutions for Knowledge, Art, and Entertainment ◽

10.4018/978-1-4666-4627-8.ch002 ◽

2014 ◽

pp. 24-41

Keyword(s):

Visual Communication ◽

Visual Literacy ◽

Explanatory Power ◽

Three Dimensional ◽

The Internet ◽

Visual Thinking ◽

Two Dimensional ◽

Art And Design ◽

Visual Expression

Projects described in this chapter are aimed at enhancing our thinking with pictures. “Thinking with Pictures” encourages the reader to use visual thinking as an instrument of acquiring knowledge, and introduces two projects aimed at developing visual literacy and applying various ways of visual expression. “Collage” introduces collage technique as a tool for visual communication. Two projects provided in this chapter are aimed at enhancing visual literacy and skills. “Sketching a shoe” is intended to amplify one’s confidence about one’s ability to depict things, and build a feeling of being prepared to make quick drawings on a board or on iPad. This project will encourage the reader to make sketches that strengthen one’s own argumentation, show what one wants to be seen, and help to convey one’s own solution in a visual way. “Creating a Composition with a Crowd” encourages the reader to draw a group of people and apply visual reasoning by showing background scenery that has an explanatory power. The next part of the chapter tells about collage because one may say without exaggeration that in the digital times most artists apply the form of a collage in their work. The Internet is flooded with ready images, clipart, art, and design samples, intriguing specimens. More importantly, ideas are not copyrighted. Before the advent of computers many artists applied techniques of cutting and pasting readymade material, thus making collages (two dimensional) and assemblages (three dimensional) of different forms.

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Do non-verbal number systems shape grammar? Numerical cognition and Number morphology compared

Mind & Language ◽

10.1111/mila.12183 ◽

2018 ◽

Vol 34 (1) ◽

pp. 37-58 ◽

Cited By ~ 5

Author(s):

Francesca Franzon ◽

Chiara Zanini ◽

Rosa Rugani

Keyword(s):

Numerical Cognition ◽

Shape Grammar ◽

Number Systems

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Formal specification of CORBA-based distributed objects and behaviors

Fourth IEEE Conference on Cognitive Informatics, 2005. (ICCI 2005). ◽

10.1109/coginf.2005.1532649 ◽

2005 ◽

Cited By ~ 2

Author(s):

C.F. Ngolah ◽

Yingxu Wang

Keyword(s):

Formal Specification ◽

Distributed Objects ◽

And Behaviors

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T cell receptor gamma/delta chain diversity.

Journal of Experimental Medicine ◽

10.1084/jem.167.2.676 ◽

1988 ◽

Vol 167 (2) ◽

pp. 676-681 ◽

Cited By ~ 2

Author(s):

F Koning ◽

A M Kruisbeek ◽

W L Maloy ◽

S Marusic-Galesic ◽

D M Pardoll ◽

...

Keyword(s):

T Cell ◽

T Cell Receptor ◽

Cell Receptor ◽

Two Dimensional ◽

Multiple Forms ◽

Gamma Delta ◽

One Dimensional ◽

Sds Page

The TCR-gamma and -delta chains of six murine hybridomas were compared by one-dimensional SDS-PAGE and two-dimensional NEPHGE/SDS-PAGE analysis. This allowed the identification of three distinct gamma chains (gamma a, gamma b, and gamma c) and three distinct delta chains (delta a, delta b, and delta c). Four gamma/delta chain combinations (gamma a delta a, gamma b delta b, gamma b delta c, and gamma c delta a) were observed. These results indicate that multiple forms of the delta chain are expressed and suggest that the delta chains are encoded for by an Ig-like rearranging gene. This delta chain polymorphism significantly enhances the potential diversity of TCR-gamma/delta, which may be of importance for a better understanding of the putative ligand(s) recognized by this receptor.

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