Experimental Mathematics

The rise of the field of “experimental mathematics” poses an apparent challenge to traditional philosophical accounts of mathematics as an a priori, non-empirical endeavor. This paper surveys different attempts to characterize experimental mathematics. One suggestion is that experimental mathematics makes essential use of electronic computers. A second suggestion is that experimental mathematics involves support being gathered for an hypothesis which is inductive rather than deductive. Each of these options turns out to be inadequate, and instead a third suggestion is considered according to which experimental mathematics involves calculating instances of some general hypothesis. The paper concludes with the examination of some philosophical implications of this characterization.

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Inhibition of mGluR1 and IP3Rs impairs long-term memory formation in young chicks

Calcium (Ca²⁺) is involved in a myriad of cellular functions in the brain including synaptic plasticity. However, the role of intracellular Ca²⁺ stores in memory processing remains poorly defined. The current study explored a role for glutamate-dependent intracellular Ca²⁺ release in memory processing via blockade of metabotropic glutamate receptor subtype 1 (mGluR1) and inositol (1,4,5)-trisphosphate receptors (IP₃Rs). Using a single-trial discrimination avoidance task developed for the young chick, administration of the specific and potent mGluR1 antagonist JNJ16259685 (500 nM, immediately post-training, ic), or the IP₃R antagonist Xestospongin C (5 μM, immediately post-training, ic), impaired retention from 90 min post-training. These findings are consistent with mGluR1 activating IP₃Rs to release intracellular Ca²⁺ required for long-term memory formation and have been interpreted within an LTP2 model. The consequences of different patterns of retention loss following ryanodine receptor (RyR) and IP₃R inhibition are discussed.     

Optimizing inhibitory learning during exposure therapy

Prevailing models of exposure therapy for phobias and anxiety disorders construe level of fear throughout exposure trials as an index of corrective learning. However, the evidence, reviewed herein, indicates that neither the degree by which fear reduces nor the ending fear level predict therapeutic outcome. Developments in the theory and science of fear extinction, and learning and memory, indicate that 'performance during training' is not commensurate with learning at the process level. Inhibitory learning is recognized as being central to extinction and access to secondary inhibitory associations is subject to influences such as context and time, rather than fear during extinction training. Strategies for enhancing inhibitory learning, and its retrieval over time and context, are reviewed along with their clinical implications for exposure therapy and directions for future research.     

How position dependent is visual object recognition?

Visual object recognition is often assumed to be insensitive to changes in retinal position, leading to theories and formal models incorporating position-independent object representations. However, recent behavioral and physiological evidence has questioned the extent to which object recognition is position independent. Here, we take a computational and physiological perspective to review the current behavioral literature. Although numerous studies report reduced object recognition performance with translation, even for distances as small as 0.5 degrees of visual angle, confounds in many of these studies make the results difficult to interpret. We conclude that there is little evidence to support position-independent object recognition and the precise role of position in object recognition remains unknown.     

Toddlers' use of cues in a search task

Search for a ball that has undergone hidden motion rapidly improves during the second year of life (Dev. Psychol., 2000; 36 :394–401). In three experiments we investigated whether the poor performance of younger toddlers was due to attentional failure by highlighting the major cue for the hidden object. We observed only slight improvement in search behaviour. We performed two other experiments that tested the depth of understanding of 3‐year‐olds in this task and found that their performance was robust to changes in the apparatus and experimental procedures. Overall, the results point to a rapidly developing ability in the second year of life to either reason about space or select the correct motor response in search tasks. Copyright © 2008 John Wiley & Sons, Ltd.     

Using mediational models to explore the nature of tobacco motivation and tobacco treatment effects

Various theories have proposed mechanisms for drug motivation and relapse. For instance, negative reinforcement theories focus on the alleviation of withdrawal. However, other theories and some data cast doubt on the importance of withdrawal as a motivator of addictive drug use. Using data from a randomized double-blind placebo-controlled smoking cessation treatment study (N=608), this research examined the impact of withdrawal on drug motivation and the ability to maintain abstinence. Withdrawal was experimentally manipulated by randomly assigning participants to receive active bupropion versus placebo. Mediation analyses revealed that active bupropion reduced the amount of withdrawal and craving that individuals reported in the 1st week post quit; modest support was also found for smaller declines in positive affect. These effects, in turn, were all positively associated with posttreatment abstinence. These results implicate withdrawal as an important factor in motivating persistent tobacco use.     

Plato's Child and the Limit-Points of Educational Theories

This paper analyzes how the figure of the childhas been used to authorize a series ofboundaries that have constituted thelimit-points of educational theories orphilosophies. Limit-points are the conceptualboundaries that educational theories produce,move within, respond to, and make use ofbecause the perception is that they cannot beargued away or around at the time. A method ofcomparative historico-philosophy is used tocontrast limit-points in Platonic figurationsof the child and education with childcenteredand eugenic theories of the late nineteenth andtwentieth century West. The figuration of thechild in both periods is imbricated in formingboundaries around a power-motion-reason nexusand in delineating what necessity and justicemean. The meaning-space that the child canoccupy in relation to such concepts has shiftedwith them and has been important to depictingUtopian and cosmological imaginings atdifferent historical moments and forauthorizing in turn what counts as anappropriate and/or realistic educationalphilosophy.     

Intrinsic,extrinsic, and amotivational orientations: Their role in university adjustment,stress, well-being,and subsequent academic performance

The aim of this study was two-fold; first, to examine the relationship between motivational orientations and adjustment to university, stress, and well-being in a sample of students during their second year of university and second, to assess the predictive value of motivational orientations in determining subsequent academic performance. Controlling for gender and age, amotivated behaviors led to worse psychosocial adjustment to university, higher levels of perceived stress, and greater psychological distress while studying. In contrast, intrinsically motivated behaviors (to know) were associated with lower levels of stress. In relation to academic performance, neither extrinsic or intrinsic motivation, nor amotivation were related to subsequent academic achievement. Both gender and entry qualifications were significant predictors of performance; women and those individuals with greater academic aptitude prior to entering university had higher marks. These results are discussed with reference to Deci and Ryan’s (1985, 1991) self-determination theory.     

Intrinsic, extrinsic, and amotivational orientations: Their role in university adjustment, stress, well-being, and subsequent academic performance

The aim of this study was two-fold; first, to examine the relationship between motivational orientations and adjustment to university, stress, and well-being in a sample of students during their second year of university and second, to assess the predictive value of motivational orientations in determining subsequent academic performance. Controlling for gender and age, amotivated behaviors led to worse psychosocial adjustment to university, higher levels of perceived stress, and greater psychological distress while studying. In contrast, intrinsically motivated behaviors (to know) were associated with lower levels of stress. In relation to academic performance, neither extrinsic or intrinsic motivation, nor amotivation were related to subsequent academic achievement. Both gender and entry qualifications were significant predictors of performance; women and those individuals with greater academic aptitude prior to entering university had higher marks. These results are discussed with reference to Deci and Ryan’s (1985, 1991) self-determination theory.