Mathematical engineering and mathematical change 1

In this paper, I introduce and examine the notion of “mathematical engineering” and its impact on mathematical change. Mathematical engineering is an important part of contemporary mathematics and it roughly consists of the “construction” and development of various machines, probes and instruments used in numerous mathematical fields. As an example of such constructions, I briefly present the basic steps and properties of homology theory. I then try to show that this aspect of contemporary mathematics has important consequences on our conception of mathematical knowledge, in particular mathematical growth.     

Developmental and content effects in reasoning with causal conditionals

Two predictions derived from Markovits and Barrouillet's (2001) developmental model of conditional reasoning were tested in a study in which 72 twelve-year-olds, 80 fifteen-year-olds, and 104 adults received a paper-and-pencil test of conditional reasoning with causal premises ("if cause P then effect Q"). First, we predicted that conditional premises would induce more correct uncertainty responses to the Affirmation of the consequent and Denial of the antecedent forms when the antecedent term is weakly associated to the consequent than when the two are strongly associated and that this effect would decrease with age. Second, uncertainty responding to the Denial of the antecedent form ("P is not true") should be easier when the formulation of the minor premise invites retrieval of alternate antecedents ("if something other than P is true"). The results were consistent with the hypotheses and indicate the importance of retrieval processes in understanding developmental patterns in conditional reasoning with familiar premises.     

Selective influence of second target exposure duration and Task1 load effects in the attentional blink phenomenon

The purpose of the experiments was to constrain the locus of interference in the attentional blink (AB) paradigm. Two visual stimuli, T₁ and T₂, were shown 300 msec apart, and each was followed by a mask. T₁ was an “H,” an “S,” an “ &, ” or a blank field; T₂ consisted of five letters. In Task₁, blank fields and & characters could be ignored, whereas Hs and Ss had to be identified and reported. Task₂ was always to report as many letters as possible from T₂. Task₂ performance was lower when T₁ had to be reported, as expected from the attentional blink phenomenon (AB). The exposure duration of T₂ was also manipulated. More letters could be reported as exposure duration was increased. However, this effect was additive with manipulations of Task₁ processing load that produced the AB effect. Log-linear analyses assuming that effects of T₂ exposure duration and Task₁ load effects occur at functionally distinct stages of processing provided satisfactory fits to the results, suggesting that none of the AB effect occurs as early as those of T₂ exposure duration. The results suggest that the locus of the AB effect is later than the stage(s) of processing affected by exposure duration.     

Changes in the neuropsychological correlates of clinical dimensions between the acute and stable phase of schizophrenia

This study was designed to investigate whether the neuropsychological correlates of the symptom dimensions of schizophrenia vary with the clinical state in patients followed from the acute to stable the phase of the illness. Fifteen patients were assessed for symptoms (SAPS-SANS) and undergone a complete neuropsychological assessment at two sessions. The first session (S1) was carried out within six days after admission, i.e., acute phase and the second (S2) at least two month after hospitalization, i.e., stable phase. The data were analyzed using stepwise regression models in which neuropsychological scores were in entered to predict each dimensional score. This analysis was applied on the S1 and S2 data as well as on the S2-S1 difference to assess the neuropsychological predictors of clinical changes. Generally, the results replicate the previous associations between neuropsychological and dimensional measures found in stable patients. In addition, this study shows if each dimension appears to rely on a key structure, symptom variations seems to involve changes in the spread of the dysfunction and/or changes in the connectivity between the key and other regions. The results also suggest that functional changes related to some symptoms dimensions occur to compensate for the dysfunction associated with other symptoms.     

Cytokine production by spleen cells after social defeat in mice: activation of T cells and reduced inhibition by glucocorticoids

Social disruption (SDR) is an effective model of social stress associated with an enhanced inflammatory reactivity of the immune system. The aim of the present study was to further describe SDR effects on cytokine production by spleen cells, testing selectively monocyte and T cell functions as a result of this stressor. For this purpose, splenocytes from control mice (C) and mice socially stressed for 7 days (SDR) were cultured in the presence of lipopolysaccharide (LPS) or concanavalin A (Con A). Splenocyte proliferation, cytokine production and sensitivity of spleen cells to corticosterone were assessed in vitro. The humoral response to keyhole limpet hemocyanin (KLH) immunization was assessed. SDR induced splenomegaly and enhanced splenocyte basal proliferation. The pro-inflammatory influence of SDR was confirmed by an increased release of interleukin-6 (IL-6) by LPS-stimulated cultures and by a reduced sensitivity of spleen cells to the anti-inflammatory effect of corticosterone. The mechanism increasing cytokine production in response to LPS was cytokine specific, since among inflammatory cytokines, IL-6 but not interferon-gamma (IFN-gamma) was enhanced by stress. In stressed mice, the increase in IL-6 and IFN-gamma and the decrease in IL-10 release in Con A-stimulated cultures indicate that SDR did not modify the Th1/Th2 cytokine balance but globally activated T cells. Plasma anti-KLH antibody levels were similar in both groups. Wounded and non-wounded mice presented similar responses to stress. This study shows that social disruption stress enhances the reactivity of cells from both the acquired and innate immune systems.     

Changing features do not guide attention in change detection: Evidence from a spatial cuing paradigm

Smilek, Eastwood, and Merikle (2000) demonstrated that the detection of change was facilitated when the target character changed in many rather than few of its features. Specifically, the function relating search response time to display set size was shallower when more features changed than when fewer features changed. The researchers interpreted these results as indicating that large feature changes provide preattentive guidance of focal attention to the location of the change. We tested this preattentive guidance hypothesis by examining change detection performance in the context of a spatial cuing paradigm. The hypothesis predicts that (1) the cost on invalidly cued trials should be less when more features change than when fewer features change, and (2) the features manipulation should have no effect on validly cued trials. In contrast to these predictions, our results show that cuing effects are equivalent across all levels of feature change and that a robust effect of the features manipulation is observable for both validly and invalidly cued trials. We argue that large feature changes do not provide preattentive guidance and in fact can be detected more readilyafter attention is already in place at the target location.     

Virtually no evidence for virtually perfect time-sharing

An examination of previous claims for virtually perfect time-sharing in dual-task situations reveals confounding effects that may have obscured dual-task interference. Two experiments are conducted in which these confounding effects are minimized, revealing statistically significant dual-task interference. These results support the hypothesis that human information processing is dominated by a structural central capacity limitation and call into question the hypothesis that dual-task interference can be eliminated by meeting the 5 conditions outlined by D. Meyer and D. Kieras (1999).