{"id":12422,"date":"2020-09-02T10:33:53","date_gmt":"2020-09-02T14:33:53","guid":{"rendered":"https:\/\/carleton.ca\/cognitivescience\/?page_id=12422"},"modified":"2020-09-25T00:20:50","modified_gmt":"2020-09-25T04:20:50","slug":"ics-colloquium-fall-2020-sept-30","status":"publish","type":"page","link":"https:\/\/carleton.ca\/cognitivescience\/ics-colloquium-fall-2020-sept-30\/","title":{"rendered":"Cog. Sci. Colloquium \u2013 Fall 2020 \u2013 Sept 30"},"content":{"rendered":"<p><strong>Date<\/strong>: Sept 30, 2020 03:00pm -4:30pm<\/p>\n<p><strong>Location<\/strong>: Online<\/p>\n<p><strong>Title<\/strong>: The\u00a0Predicament\u00a0of\u00a0Quantity\u201d:\u00a0 Analog Magnitudes and the Emergence\u00a0of\u00a0Number<\/p>\n<p><strong>Speaker<\/strong>:\u00a0 John Opfer:<\/p>\n<p>Bio:\u00a0John Opfer (Ph.D., 2000, Michigan) is a Professor of Psychology at The Ohio State University.\u00a0 His research concerns the role of relational reasoning in conceptual development, especially concepts from science and mathematics.<\/p>\n<p><strong>Abstract<\/strong>:<\/p>\n<p>Prior to the 19th C., mathematics was considered to be the \u201cscience\u00a0of\u00a0quantity.\u201d As a way\u00a0of\u00a0ensuring that mathematics hadn\u2019t lost its grip on reality and as a way\u00a0of\u00a0approximating indirect measurements, this geometrical approach had its virtues.\u00a0 However, 19th C. mathematicians began to wonder if the geometrical approach had hit its limits. In this post-\u201cscience\u00a0of\u00a0quantity\u201d era, scholars also began to wonder about the ontogeny\u00a0of\u00a0number and speculated that the representation\u00a0of\u00a0quantity\u00a0was inadequate for even the precursors\u00a0of\u00a0direct measurement.\u00a0 But what exactly are the limits\u00a0of\u00a0the representation\u00a0of\u00a0non-symbolic\u00a0quantity?\u00a0 How far can this representation take the developing child? Are these limits transcended just if children learn a symbolic code for numbers? In this talk, I examine evidence suggesting that (1) the limits\u00a0of\u00a0the analog magnitude system are real but grossly overstated and apply to perception\u00a0of\u00a0symbols too, (2) a series\u00a0of\u00a0visuo-spatial transformations (normalization, concatenation, and alignment) can be made to convert the cardinality\u00a0of\u00a0a set so that it can be compared to another cardinality as quickly and accurately as the comparison\u00a0of\u00a0two symbolic numbers. These results suggest that perception\u00a0of\u00a0quantity\u00a0can play a much more supportive role in the ontogeny\u00a0of\u00a0number than is suggested by set-theoretic considerations.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Date: Sept 30, 2020 03:00pm -4:30pm Location: Online Title: The\u00a0Predicament\u00a0of\u00a0Quantity\u201d:\u00a0 Analog Magnitudes and the Emergence\u00a0of\u00a0Number Speaker:\u00a0 John Opfer: Bio:\u00a0John Opfer (Ph.D., 2000, Michigan) is a Professor of Psychology at The Ohio State University.\u00a0 His research concerns the role of relational reasoning in conceptual development, especially concepts from science and mathematics. Abstract: Prior to the 19th [&hellip;]<\/p>\n","protected":false},"author":31,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_relevanssi_hide_post":"","_relevanssi_hide_content":"","_relevanssi_pin_for_all":"","_relevanssi_pin_keywords":"","_relevanssi_unpin_keywords":"","_relevanssi_related_keywords":"","_relevanssi_related_include_ids":"","_relevanssi_related_exclude_ids":"","_relevanssi_related_no_append":"","_relevanssi_related_not_related":"","_relevanssi_related_posts":"","_relevanssi_noindex_reason":"","_mi_skip_tracking":false,"_exactmetrics_sitenote_active":false,"_exactmetrics_sitenote_note":"","_exactmetrics_sitenote_category":0,"footnotes":"","_links_to":"","_links_to_target":""},"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.2 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Cog. Sci. 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