Ada Lovelace Day 2020

Abstract: In her commentary on the "Analytical Engine" created by her friend and colleague Charles Babbage, Ada Lovelace, sometimes called the world's first computer programmer, distinguished between the mechanical and rational labors of mathematics. Also, Lovelace was the first to recognize the power of computing devices to transcend mathematical calculations, to support reasoning about any domain of human experience. Lovelace's discourse poses the question of how clearly we can distinguish between mechanical and rational processes. Also, it raises the question of how each originates in the human mind, and what causal relations might exist between purely mechanical computations and moments of rational insight that lead humans to derive axioms, notice analogies between different representational formats (e.g., geometry and algebra), or to create new representational formats altogether. In this talk, I argue that the mechanical labors of the mind - particularly in the case of mathematics - allow humans to discover rational insights that otherwise would not be available to them, and that our most profound mathematical discoveries hinge upon learning from, and about, the mechanical rules of thought. To make this case, I present evidence from children's acquisition of counting procedures, and how this learning fuels their discovery that numbers, space, and time are infinite. I also argue that the logic that underpins these computations is fundamentally linguistic, and depends on the computational engine provided by human natural language.