Towards a New Epistemology of Mathematics

In this introduction we discuss the motivation behind the workshop “Towards a New Epistemology of Mathematics” of which this special issue constitutes the proceedings. We elaborate on historical and empirical aspects of the desired new epistemology, connect it to the public image of mathematics, and give a summary and an introduction to the contributions to this issue.

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<Emphasis Type="Italic">Viktor Žirmunskij and German</Emphasis> Mundartforschung

German dialect geography developed, inter alia, as a means to compensate the shortcomings of the Young Grammarians’ approach to language. In contrast to the latter, it was conceived of to be a sociolinguistic project, constituting thereby one link between the development of Soviet and German linguistics. The article tries to answer such questions as who initially participated in transferring ideas of German dialectology to the Soviet Union and what kind of motivations underlay those transfers. Combining biographical facts with systematic aspects, the article surveys the filiations of some productive ideas with the help of archival sources, i.e. letters of the Soviet scholars Dinges (1891–1932) and Viktor Žirmunskij (1891–1971). Finally, I try to single out the elements in Žirmunskij dialect geography, which are specifically sociolinguistic.

Do captive mandrills invent new gestures?

Studies of intraspecific behavioral variability have documented cases where behaviors are present in some populations or groups but are absent in others. In some cases these differences cannot be explained by recourse to environmental or genetic variation, and may instead represent “traditions”. Despite many examples of animal traditions in acoustic communication, relatively few examples exist of gestural traditions. Here I report on a study of communication across eight captive groups of mandrills (Mandrillus sphinx) in which a prominent gesture (Hand extension) was unique to two groups. Habitat variability, genetic differences, and sampling bias were not sufficient to account for the gesture’s limited distribution across the study groups. Within the two groups where the gesture did occur only the juveniles in the group performed it, consistently directing it toward adults. Quantitative analysis of the contexts and responses associated with the gesture suggested that juveniles utilized it to provoke adults. Moreover, the gesture appeared to minimize the risk juveniles incurred while inciting adults, suggesting that repeated social interactions shaped the gesture’s form. Interestingly, both the groups where the gesture emerged contained few juveniles. With limited play partners, these juveniles may have resorted to harassing adults as an alternative social play outlet. The creation of this novel gesture may thus be due to the combined influence of a shortage of play partners and of the increased free time for playful social exploration afforded by captivity. Although juveniles frequently “eavesdropped” on dyadic interactions involving the gesture and would subsequently initiate an interaction with the recipient of the gesture, there was no definitive evidence for social transmission; the gesture could instead have been independently invented by each juvenile. Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Using a virtual reality system to study balance and walking in a virtual outdoor environment: a pilot study.

Falls and fall-related injuries are a major problem for elderly persons. Most falls occur during walking and turning, and the risk of falling increases when attention is diverted to something besides walking. It is often difficult to standardize methods for testing balance and fall tendency in a clinically relevant setting. We describe the development of a system using a virtual environment (VE) to assess how attention demanding and unexpected events influence a person's capacity to control balance and movement. The hardware in the system consists of a head-mounted display (HMD), a magnetic tracker system, and two SGI computers. The software consists of the image generation of the VE and the management and visualization of motion tracking data. In a preliminary pilot study eight subjects (age 23-80) participated. Each subject walked on a normal floor and was visually presented a familiar outdoor environment in the HMD. They were exposed to different unexpected events, such as a virtual snowfall and tilting of the VE. Disturbances of balance and walking patterns such as changes in speed, stride length and balance reactions like slipping were observed. Two subjects experienced symptoms of cyber sickness with a SSQ score above 25 points. Walking with sensors only did not affect walking time, but in VE the subjects generally walked more slowly. Virtual tilting of the environment had an impact on balance performance during walking. This effect was not observed while the test subjects were walking in a virtual snowfall. The model needs further development but may hold a potential for clinical use.     

Testing for the presence of 1/f noise in continuation tapping data.

A number of recent papers have suggested that the series of time intervals produced in continuation tapping may have fractal properties. This proposition, nevertheless, was only based on the visual appraisal of graphical results, and was not statistically supported. In the present study, we applied the ARMA/ARFIMA modeling procedures proposed by Wagenmakers, Farrell, and Ratcliff (2005) to test for the presence of long-range dependencies in continuation tapping data. Our results demonstrate the presence of long-range dependencies in most series and offer strong support for the hypothesis that fluctuations in tapping series are fractal in nature.     

Radical Innovation and End-User Involvement: The Ambilight Case

To make technology research more effective and to deal with fierce cost competition, technology research should be more focused on radical innovation and needs to adopt a more end-user-focused approach. Product improvement is already quite often building on knowledge collected around consumers’ experiences with these products to come with a next, improved generation of products. However, in case of creating novel products from “scratch,” this will be more difficult. The user-centered research approach including insights, scenarios, and experience prototypes provides a good method to incorporate the consumer perspective in the earliest stages of the product creation process. The development of the Ambilight TV will be used as a case to illustrate this approach.     

Defining task-set reconfiguration: The case of reference point switching

Some researchers argue that task switching involves task-set reconfiguration-that is, changing the existing task set to perform a different task. Although this idea is intriguing, it is often unclear what is reconfigured and which processes are involved in reconfiguration. We addressed these issues by defining task sets, identifying differences between them, and obtaining evidence that was diagnostic of reconfiguration. In two experiments, subjects performed relative judgment tasks that involved comparing a target with a reference point that repeated or switched across trials. The task was the same on every trial, but the task set was not, because a task-set parameter-the reference point-had to be changed. Target-reference point distance effects that changed with the reference point provided diagnostic evidence that reconfiguration occurred, and this reconfiguration led to switch costs. We discuss how our approach can be generalized to define reconfiguration more clearly in other task-switching situations. nt|mis|This research was supported by Grants BCS 0133202 and BCS 0446806 from the National Science Foundation to G.D.L.     

Seven principles of goal activation: a systematic approach to distinguishing goal priming from priming of non-goal constructs.

Countless studies have recently purported to demonstrate effects of goal priming; however, it is difficult to muster unambiguous support for the claims of these studies because of the lack of clear criteria for determining whether goals, as opposed to alternative varieties of mental representations, have indeed been activated. Therefore, the authors offer theoretical guidelines that may help distinguish between semantic, procedural, and goal priming. Seven principles that are hallmarks of self-regulatory processes are proposed: Goal-priming effects (a) involve value, (b) involve postattainment decrements in motivation, (c) involve gradients as a function of distance to the goal, (d) are proportional to the product of expectancy and value, (e) involve inhibition of conflicting goals, (f) involve self-control, and (g) are moderated by equifinality and multifinality. How these principles might help distinguish between automatic activation of goals and priming effects that do not involve goals is discussed.