Blog 5

This week, the Lupyan reading explored the problem of abstraction using the concept of a triangle as a simple example. Though the simple definition of a triangle is a three-sided polygon, Lupyan tested how people mentally conceptualize triangles through several experiments that tested three claims: 1) a person’s mental representation is more specific than their abstract definition of a triangle, 2) representation can be altered by eliciting context (“triangle” vs. “three-sided polygon”), and 3) category label “triangle” elicits more consistent and prototypical representations than does “three-sided polygon.” Lupyan found that “triangle” and “three-sided polygon” evoked systematically different representations, a finding that shows people’s representations are not strictly definitional but rather prototypical.

The Rickford reading covered the topic of linguistic study of African American Vernacular English (AAVE), and the unequal partnership between the researchers and those researched. Quantitative sociolinguistics has gained much data from the African American speech community but has not done much to give back to the community. Rickford notes the insufficient representation of African American induction onto linguistics. He also feels that African Americans should have greater representation in writing, courts, workplaces, and schools, and teaching of reading and language arts. A problem with the lack of African American voices in the sociolinguistic, ethnographic, and folklorist writing is that the presentation of the speech community is very negative.

I found that inaccurate generalizations was a topic held in common between the two papers. African Americans are often stereotyped by people outside that group, and triangles are similarly stereotyped by people outside the study of mathematics. While people know that African American is a label for people with American citizenship and some amount of African ancestry, the representations brought to mind are often much more specific and involve characteristics that do not apply to all African Americans. In the case of triangles, though people know that triangles are simply three-sided polygons, the representations brought to mind are also more specific and less general. In both cases, the mental representations cover only a small subset of the possible instantiations of “triangle” or African American. More mathematical education may correct the conceptualization of triangles and more insights from African Americans and increasing their voice in society and academia may help to correct the conceptualization of African Americans. These papers relate to the real world and the sad truth that 15% adults cannot recognize skewed triangles as triangles and the unfortunate prevalence of racism.