The potential of symbolic approximation. Disentangling the effects of approximation vs. calculation demands in nonsymbolic and symbolic representations.

Mathematical skills that we acquire during formal education mostly entail exact numerical processing. Besides this specifically human faculty, an additional system exists to represent and manipulate quantities in an approximate manner. We share this innate approximate number system (ANS) with other nonhuman animals and are able to use it to process large numerosities long before we can master the formal algorithms taught in school. Dehaene´s (1992) Triple Code Model (TCM) states that also after the onset of formal education, approximate processing is carried out in this analogue magnitude code no matter if the original problem was presented nonsymbolically or symbolically. Despite the wide acceptance of the model, most research only uses nonsymbolic tasks to assess ANS acuity. Due to this silent assumption that genuine approximation can only be tested with nonsymbolic presentations, up to now important implications in research domains of high practical relevance remain unclear, and existing potential is not fully exploited. For instance, it has been found that nonsymbolic approximation can predict math achievement one year later (Gilmore, McCarthy, & Spelke, 2010), that it is robust against the detrimental influence of learners´ socioeconomic status (SES), and that it is suited to foster performance in exact arithmetic in the short-term (Hyde, Khanum, & Spelke, 2014). We provided evidence that symbolic approximation might be equally and in some cases even better suited to generate predictions and foster more formal math skills independently of SES. In two longitudinal studies, we realized exact and approximate arithmetic tasks in both a nonsymbolic and a symbolic format. With first graders, we demonstrated that performance in symbolic approximation at the beginning of term was the only measure consistently not varying according to children´s SES, and among both approximate tasks it was the better predictor for math achievement at the end of first grade. In part, the strong connection seems to come about from mediation through ordinal skills. In two further experiments, we tested the suitability of both approximation formats to induce an arithmetic principle in elementary school children. We found that symbolic approximation was equally effective in making children exploit the additive law of commutativity in a subsequent formal task as a direct instruction. Nonsymbolic approximation on the other hand had no beneficial effect. The positive influence of the symbolic approximate induction was strongest in children just starting school and decreased with age. However, even third graders still profited from the induction. The results show that also symbolic problems can be processed as genuine approximation, but that beyond that they have their own specific value with regard to didactic-educational concerns. Our findings furthermore demonstrate that the two often con-founded factors ꞌformatꞌ and ꞌdemanded accuracyꞌ cannot be disentangled easily in first graders numerical understanding, but that children´s SES also influences existing interrelations between the different abilities tested here.

Years 2 to 6 students' ability to generalise : models, representations and theory for teaching and learning

Over the last three years, in our Early Algebra Thinking Project, we have been studying Years 3 to 5 students’ ability to generalise in a variety of situations, namely, compensation principles in computation, the balance principle in equivalence and equations, change and inverse change rules with function machines, and pattern rules with growing patterns. In these studies, we have attempted to involve a variety of models and representations and to build students’ abilities to switch between them (in line with the theories of Dreyfus, 1991, and Duval, 1999). The results have shown the negative effect of closure on generalisation in symbolic representations, the predominance of single variance generalisation over covariant generalisation in tabular representations, and the reduced ability to readily identify commonalities and relationships in enactive and iconic representations. This chapter uses the results to explore the interrelation between generalisation and verbal and visual comprehension of context. The studies evidence the importance of understanding and communicating aspects of representational forms which allowed commonalities to be seen across or between representations. Finally the chapter explores the implications of the studies for a theory that describes a growth in integration of models and representations that leads to generalisation.

Visual representations as 'artifacts of knowing'

How does the manipulation of visual representations play a role in the practices of generating, evolving and exchanging knowledge? The role of visual representation in mediating knowledge work is explored in a study of design work of an architectural practice, Edward Cullinan Architects. The intensity of interactions with visual representations in the everyday activities on design projects is immediately striking. Through a discussion of observed design episodes, two ways are articulated in which visual representations act as 'artefacts of knowing'. As communication media they are symbolic representations, rich in meaning, through which ideas are articulated, developed and exchanged. Furthermore, as tangible artefacts they constitute material entities with which to interact and thereby develop knowledge. The communicative and interactive properties of visual representations constitute them as central elements of knowledge work. The paper explores emblematic knowledge practices supported by visual representation and concludes by pinpointing avenues for further research.

Symbolic representation and distributed matching strategies for schematics

This paper describes object-centered symbolic representation and distributed matching strategies of 3D objects in a schematic form which occur in engineering drawings and maps. The object-centered representation has a hierarchical structure and is constructed from symbolic representations of schematics. With this representation, two independent schematics representing the same object can be matched. We also consider matching strategies using distributed algorithms. The object recognition is carried out with two matching methods: (1) matching between an object model and observed data at the lowest level of the hierarchy, and (2) constraints propagation. The first is carried out with symbolic Hopfield-type neural networks and the second is achieved via hierarchical winner-takes-all algorithms

The nonconceptual gateway to early word learning

My research investigates why nouns are learned disproportionately more frequently than other kinds of words during early language acquisition (Gentner, 1982; Gleitman, et al., 2004). This question must be considered in the context of cognitive development in general. Infants have two major streams of environmental information to make meaningful: perceptual and linguistic. Perceptual information flows in from the senses and is processed into symbolic representations by the primitive language of thought (Fodor, 1975). These symbolic representations are then linked to linguistic input to enable language comprehension and ultimately production. Yet, how exactly does perceptual information become conceptualized? Although this question is difficult, there has been progress. One way that children might have an easier job is if they have structures that simplify the data. Thus, if particular sorts of perceptual information could be separated from the mass of input, then it would be easier for children to refer to those specific things when learning words (Spelke, 1990; Pylyshyn, 2003). It would be easier still, if linguistic input was segmented in predictable ways (Gentner, 1982; Gleitman, et al., 2004) Unfortunately the frequency of patterns in lexical or grammatical input cannot explain the cross-cultural and cross-linguistic tendency to favor nouns over verbs and predicates. There are three examples of this failure: 1) a wide variety of nouns are uttered less frequently than a smaller number of verbs and yet are learnt far more easily (Gentner, 1982); 2) word order and morphological transparency offer no insight when you contrast the sentence structures and word inflections of different languages (Slobin, 1973) and 3) particular language teaching behaviors (e.g. pointing at objects and repeating names for them) have little impact on children's tendency to prefer concrete nouns in their first fifty words (Newport, et al., 1977). Although the linguistic solution appears problematic, there has been increasing evidence that the early visual system does indeed segment perceptual information in specific ways before the conscious mind begins to intervene (Pylyshyn, 2003). I argue that nouns are easier to learn because their referents directly connect with innate features of the perceptual faculty. This hypothesis stems from work done on visual indexes by Zenon Pylyshyn (2001, 2003). Pylyshyn argues that the early visual system (the architecture of the "vision module") segments perceptual data into pre-conceptual proto-objects called FINSTs. FINSTs typically correspond to physical things such as Spelke objects (Spelke, 1990). Hence, before conceptualization, visual objects are picked out by the perceptual system demonstratively, like a finger pointing indicating ‘this’ or ‘that’. I suggest that this primitive system of demonstration elaborates on Gareth Evan's (1982) theory of nonconceptual content. Nouns are learnt first because their referents attract demonstrative visual indexes. This theory also explains why infants less often name stationary objects such as plate or table, but do name things that attract the focal attention of the early visual system, i.e., small objects that move, such as ‘dog’ or ‘ball’. This view leaves open the question how blind children learn words for visible objects and why children learn category nouns (e.g. 'dog'), rather than proper nouns (e.g. 'Fido') or higher taxonomic distinctions (e.g. 'animal').

A quantum information retrieval approach to memory

As computers approach the physical limits of information storable in memory, new methods will be needed to further improve information storage and retrieval. We propose a quantum inspired vector based approach, which offers a contextually dependent mapping from the subsymbolic to the symbolic representations of information. If implemented computationally, this approach would provide exceptionally high density of information storage, without the traditionally required physical increase in storage capacity. The approach is inspired by the structure of human memory and incorporates elements of Gardenfors’ Conceptual Space approach and Humphreys et al.’s matrix model of memory.

Supermarkets and agro-industrial foods : the strategic manufacturing of consumer trust

There is increasing evidence of a weakened platform of consumer trust in mass produced food products. The resistance shown by consumers to the agro-industrial paradigm is evident in an emergent phase of reflexive consumerism, public reactions to an overly-concentrated retail sector and the rise of alternative food networks such as farmers' markets and organic box schemes. Supermarkets are responding strategically by aiming to manufacture new trust relations with consumers. This paper identifies three key strategies of trust manufacturing: (i) reputational enhancement though the institution of “behind the scenes,” business-to-business private standards; (ii) direct quality claims via private standard certification badges on food products, and ; (iii) discursive claimsmaking through symbolic representations of “authenticity” and “tradition.” Drawing upon the food governance literature and a “visual sociology” of supermarkets and supermarket produce, we highlight how trust is both commoditized and increasingly embedded into the marketing of mass-produced foods.

Projecting the new world city: The city as spectacle in an urban light festival

As a precursor to the 2014 G20 Leaders’ Summit held in Brisbane, Australia, the Queensland Government sponsored a program of G20 Cultural Celebrations, designed to showcase the Summit’s host city. The cultural program’s signature event was the Colour Me Brisbane festival, a two-week ‘citywide interactive light and projection installations’ festival that was originally slated to run from 24 October to 9 November, but which was extended due to popular demand to conclude with the G20 Summit itself on 16 November. The Colour Me Brisbane festival comprised a series projection displays that promoted visions of the city’s past, present, and future at landmark sites and iconic buildings throughout the city’s central business district and thus transformed key buildings into forms of media architecture. In some instances the media architecture installations were interactive, allowing the public to control aspects of the projections through a computer interface situated in front of the building; however, the majority of the installations were not interactive in this sense. The festival was supported by a website that included information regarding the different visual and interactive displays and links to social media to support public discussion regarding the festival (Queensland Government 2014). Festival-goers were also encouraged to follow a walking-tour map of the projection sites that would take them on a 2.5 kilometre walk from Brisbane’s cultural precinct, through the city centre, concluding at parliament house. In this paper, we investigate the Colour Me Brisbane festival and the broader G20 Cultural Celebrations as a form of strategic placemaking—designed, on the one hand, to promote Brisbane as a safe, open, and accessible city in line with the City Council’s plan to position Brisbane as a ‘New World City’ (Brisbane City Council 2014). On the other hand, it was deployed to counteract growing local concerns and tensions over the disruptive and politicised nature of the G20 Summit by engaging the public with the city prior to the heightened security and mobility restrictions of the Summit weekend. Harnessing perspectives from media architecture (Brynskov et al. 2013), urban imaginaries (Cinar & Bender 2007), and social media analysis, we take a critical approach to analysing the government-sponsored projections, which literally projected the city onto itself, and public responses to them via the official, and heavily promoted, social media hashtags (#colourmebrisbane and #g20cultural). Our critical framework extends the concepts of urban phantasmagoria and urban imaginaries into the emerging field of media architecture to scrutinise its potential for increased political and civic engagement. Walter Benjamin’s concept of phantasmagoria (Cohen 1989; Duarte, Firmino, & Crestani 2014) provides an understanding of urban space as spectacular projection, implicated in commodity and techno-culture. The concept of urban imaginaries (Cinar & Bender 2007; Kelley 2013)—that is, the ways in which citizens’ experiences of urban environments are transformed into symbolic representations through the use of imagination—similarly provides a useful framing device in thinking about the Colour Me Brisbane projections and their relation to the construction of place. Employing these critical frames enables us to examine the ways in which the installations open up the potential for multiple urban imaginaries—in the sense that they encourage civic engagement via a tangible and imaginative experience of urban space—while, at the same time, supporting a particular vision and way of experiencing the city, promoting a commodified, sanctioned form of urban imaginary. This paper aims to dissect the urban imaginaries intrinsic to the Colour Me Brisbane projections and to examine how those imaginaries were strategically deployed as place-making schemes that choreograph reflections about and engagement with the city.

Identiteettien maisemat Saskatchewanin Uudessa Suomessa : Uudisasutuksesta uusidentifikaatioon

The present study examines how the landscape of the rural immigrant colony of New Finland (Saskatchewan, Canada) has reflected the Finnish origins of the about 350 settlers and their descendants, their changing ideologies, values, sense of collectiveness and the meanings of the Finnish roots. The study also reveals the reasons and power structures behind the ethnic expressions. Researched time period runs from the beginning of the settlement in 1888 to the turn of the millennium. The research concentrates on buildings, cemeteries, personal names and place names which contain strong visual and symbolic messages and are all important constituents of mundane landscapes. For example, the studied personal names are important identity-political indexes telling about the value of the Finnish nationalism, community spirit, dual Finnish-Canadian identities and also the process of assimilation which, for example, had differences between genders. The study is based on empirical field research, and iconographical and textual interpretations supported by classifications and comparative analyses. Several interviews and literature were essential means of understanding the changing political contexts which influenced the Finnish settlement and its multiple landscape representations. Five historical landscape periods were identified in New Finland. During these periods the meanings and representations of Finnish identity changed along with national and international politics and local power structures. For example, during the Second World War Canada discouraged representations of Finnish culture because Finland and Canada were enemies. But Canada s multicultural policy in the 1980s led to several material and symbolic representations indicating the Finnish settlement after a period of assimilation and deinstitutionalization. The study shows how these representations were indications of the politics of a (selective) memory. Especially Finnish language, cultural traditions and the Evangelical-Lutheran values of the pioneers, which have been passed down to new generations, are highly valued part of the Finnish heritage. Also the work of the pioneers and their participation in the building of Saskatchewan is an important collective narrative. The selectiveness of a memory created the landscape of forgetting which includes deliberately forgotten parts of the history. For example, the occasional disputes between the congregations are something that has been ignored. The results show how the different landscape elements can open up a useful perspective to diaspora colonies or other communities also by providing information which otherwise would be indistinguishable. In this case, for example, two cemeteries close together were a sign of religious distributions among the early settlers.

La fiesta, socialización y prevención del conflicto : Castilla, siglos XIV y XV

Integran este número de la revista ponencias presentadas en Studia Hispanica Medievalia VIII: Actas de las IX Jornadas Internacionales de Literatura Española Medieval, 2008, y de Homenaje al Quinto Centenario de Amadis de Gaula.

Representações simbólicas em percurso efêmero: o Corpus Christi em cor e areia

Através da pesquisa de campo realizada nas festas de Corpus Christi da cidade de Matão/SP nos anos 2011 e 2012, são abordados os temas festa, imagem, cultura e sagrado. Especificamente focada na confecção dos tapetes, são observados e analisados seus processos e representações em aspectos individuais e coletivos. São inúmeros seus significados e interpretações se o percebemos em sua forma viva de seu lastro histórico até os dias atuais. Saliento a importância do registro desta manifestação cultural, pois através dele do estudo de suas imagens e significações buscamos um maior entendimento de como este evento acontece e de como é percebida e interiorizada pelo seu público

Produção literária: tecer o imaginário, espaço preenchido da margem

O objetivo deste estudo é analisar como a prática da produção literária interfere, positivamente, na trajetória de indivíduos que se encontram em situação de vulnerabilidade social. A investigação deu-se no Centro Cultural Cartola, situado na comunidade da Mangueira na cidade do Rio de Janeiro, espaço que favorece a experiência individual e social de crianças e jovens por meio de ferramentas pedagógico-culturais: dança, orquestra de violinos, música, capoeira, judô, balé, oficinas literárias de leituras e de composições de texto, que possibilitam a criação de valores culturais da comunidade e dos indivíduos pelo processo de identificação. A oficina Produção Literária: Tecer o Imaginário teve início em maio de 2011, com propostas de estímulo à criação e à leitura de textos ficcionais, possibilitando que a narrativa como um vetor de (re)construção do sujeito e do coletivo, sob o ponto de vista ético e estético. A fase investigativa constou de oficinas de literatura apresentadas de duas formas: Leitura e escrita em grupos pequenos - ou individuais. O trabalho de campo da nossa pesquisa qualitativo-participativa requereu que fizéssemos um recorte espacial de nossa experiência, para que à partir dai pudéssemos inserir o recorte teórico que fosse factível ao nosso objeto de investigação. Importava a dinâmica da ação dos atores sociais. A pesquisa, estruturada sobre a ação, revelou-se detentora de inúmeras possibilidades onde o imaginário se apresenta. A interação por meio de falas que estimulam a imaginação e a reflexão exerce influência no grupo e no indivíduo na construção de si e de seu mundo. Como o objetivo da pesquisa não se adequava somente à prática oral, de contar e ouvir estórias, mas de estimular os atores à inventar e escrevê-las percebemos que este modo prevaleceu. Por exigência de que a criança dominasse de alguma forma essa modalidade, sobretudo porque o ato de escrever validava as histórias inventadas por elas e as dispostas por outras pessoas nos livros. Visto que oralidade pode dispersar a entrada da criança em seu mundo imaginário, tendo importância maior para crianças muito pequenas que não entraram ainda no mundo da linguagem. A maneira que conduzíamos a pesquisa era sempre no sentido de estimular o imaginário, capturando-o, e a partir disso inseri-lo no mundo da linguagem, da simbolização. Para Minayo (1992), O método é o próprio processo do desenvolvimento das coisas.... Nesse sentido, surgia, daquela prática, um texto/sujeito, cujas palavras eram um tronco donde se espalhavam uma infinidade de ideias criativas. O resultado da investigação constatou que a criação ficcional, estimula e desenvolve o imaginário e as representações simbólicas empobrecidas. Evidenciando o quanto é gratificante e prazeroso para crianças e jovens suas participações em atividade que fazem do campo educativo e terapêutico um campo de aventura. Observar o efeito reparador da literatura no individuo, e de consolo nos momentos de lutos e de crises de toda ordem foi evidente em situação fronteiriça, pelo uso do mundo interno dessa potente ferramenta psicopedagogica como fortalecimento psicoemocional

Some Aspects of Pattern Recognition by Computer

A computer may gather a lot of information from its environment in an optical or graphical manner. A scene, as seen for instance from a TV camera or a picture, can be transformed into a symbolic description of points and lines or surfaces. This thesis describes several programs, written in the language CONVERT, for the analysis of such descriptions in order to recognize, differentiate and identify desired objects or classes of objects in the scene. Examples are given in each case. Although the recognition might be in terms of projections of 2-dim and 3-dim objects, we do not deal with stereoscopic information. One of our programs (Polybrick) identifies parallelepipeds in a scene which may contain partially hidden bodies and non-parallelepipedic objects. The program TD works mainly with 2-dimensional figures, although under certain conditions successfully identifies 3-dim objects. Overlapping objects are identified when they are transparent. A third program, DT, works with 3-dim and 2-dim objects, and does not identify objects which are not completely seen. Important restrictions and suppositions are: (a) the input is assumed perfect (noiseless), and in a symbolic format; (b) no perspective deformation is considered. A portion of this thesis is devoted to the study of models (symbolic representations) of the objects we want to identify; different schemes, some of them already in use, are discussed. Focusing our attention on the more general problem of identification of general objects when they substantially overlap, we propose some schemes for their recognition, and also analyze some problems that are met.

Bring ART into the ACT

ACT is compared with a particular type of connectionist model that cannot handle symbols and use non-biological operations that cannot learn in real time. This focus continues an unfortunate trend of straw man "debates" in cognitive science. Adaptive Resonance Theory, or ART, neural models of cognition can handle both symbols and sub-symbolic representations, and meets the Newell criteria at least as well as these models.