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Mathematical Practice and Human Cognition
Get PDFFrank Quinn (of Jaffe-Quinn fame, see [1]) worked out the basics of his own account of mathematical practice, an account that is informed by an analysis of contemporary mathematics and its pedagogy (see [2]). Taking this account as our starting point, we can characterize the current mathematical practice to acquire and work with new concepts as a cognitive adaptation strategy that, first, emerged to meet the challenges posed by the growing abstractness of its objects and which, second, proceeds according to the following three-pronged approach:
(i) sever as many ties to ordinary language as possible and limit ordinary language explanations to an absolute minimum;
(ii) introduce axiomatic definitions and bundle them up with a sufficient num- ber of examples, lemmata, propositions, etc. into small cognitive packages;
(iii) practice hard with one new cognitive package at a time.
Drawing on research in cognitive science, and especially in mathematics ed- ucation, I will then show how cognitive science provides supporting evidence for the effectiveness of this mathematical practice. Time permitting, I will then complement these findings from a phenomenological perspective by exhibiting a fruitful convergence between mathematics, cognitive science, and phenomeno- logical analysis.
[1] Jaffe, Arthur, Quinn, Frank. “Theoretical Mathematics: Towards a synthesis of mathematics and theoretical physics,” Bulletin of the American Mathemati- cal Society NS 29:1 (1993), 113. [2] Quinn, Frank. Contributions to a Science of Mathematics, manuscript (Oc- tober 2011), 98pp
Biblical reading and critical reading: How do they inform each other in interpreting the text?
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MHC class II super-enhancer increases surface expression of HLA-DR and HLA-DQ and affects cytokine production in autoimmune vitiligo
No full textGenetic risk for autoimmunity in HLA genes is most often attributed to structural specificity resulting in presentation of self-antigens. Autoimmune vitiligo is strongly associated with the MHC class II region. Here, we fine-map vitiligo MHC class II genetic risk to three SNPs only 47 bp apart, located within a predicted super-enhancer in an intergenic region between HLA-DRB1 and HLA-DQA1, localized by a genomewide association study of 2,853 Caucasian vitiligo patients. The superenhancer corresponds to an expression quantitative trait locus for expression of HLA-DR and HLA-DQ RNA; we observed elevated surface expression of HLA-DR (P = 0.008) and HLA-DQ (P = 0.02) on monocytes from healthy subjects homozygous for the high-risk SNP haplotype. Unexpectedly, pathogen-stimulated peripheral blood mononuclear cells from subjects homozygous for the high-risk super-enhancer haplotype exhibited greater increase in production of IFN-γ and IL-1β than cells from subjects homozygous for the low-risk haplotype. Specifically, production of IFN-γ on stimulation of dectin-1, mannose, and Toll-like receptors with Candida albicans and Staphylococcus epidermidis was 2.5- and 2.9-fold higher in high-risk subjects than in low-risk subjects, respectively (P = 0.007 and P = 0.01). Similarly, production of IL-1β was fivefold higher in high-risk subjects than in low-risk subjects (P = 0.02). Increased production of immunostimulatory cytokines in subjects carrying the high-risk haplotype may act as an \u22adjuvant\u22 during the presentation of autoantigens, tying together genetic variation in the MHC with the development of autoimmunity. This study demonstrates that for risk of autoimmune vitiligo, expression level of HLA class II molecules is as or more important than antigen specificity
An Evening with George Gershwin: \u22Porgy and Bess: Symphonic Picture\u22, \u22Rhapsody in Blue\u22, and \u22An American in Paris\u22
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My Colonoscopy is Tomorrow...TMI?”: College Students’ Attitudes About Public Social Media Posts
No full textAttitudes and behaviors regarding five types of public posts were examined among 361 undergraduates. Men rated four types of posts (Gross, Sexual, Crude/Crass, Personal/Political Rants) as more appropriate and enjoyable than did women. Oversharing (or \u22TMI\u22) on social media may be relevant for emerging adults\u27 social and identity development