A Cognitive Model of Discovering Commutativity
نویسندگان
چکیده
Mathematics is often seen as the uncovering of eternal truths that exist independently of the human mind. However, even if this epistemological view is correct, the mathematics that humans can know can only be the result of cognitive processes. We investigate this ability of the human mind to make mathematical discoveries. More precisely, we present a cognitive model of how the ability to use metaphors and analogies plays a key role in such discoveries. As a proof of concept we present an ACT-R model that uses path-mapping and that is capable of discovering the commutativity property of addition.
منابع مشابه
Finite groups with three relative commutativity degrees
For a finite group $G$ and a subgroup $H$ of $G$, the relative commutativity degree of $H$ in $G$, denoted by $d(H,G)$, is the probability that an element of $H$ commutes with an element of $G$. Let $mathcal{D}(G)={d(H,G):Hleq G}$ be the set of all relative commutativity degrees of subgroups of $G$. It is shown that a finite group $G$ admits three relative commutativity degrees if a...
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