This week, David Spivak from the MIT math department will give a talk, briefing us on his ideas and asking for our input.
WHO: David Spivak (MIT Math)
WHAT: Communication Networks
WHEN: September 15, 1:30PM-3:00PM
WHERE: 32-D831
WHAT EXACTLY:
Every person has his or her own ideolect, or way of using language; in fact every subculture has its own language. I propose that every interacting group, however small, has its own language. Two people engaged in conversation have a common ground, which each can use to explain new concepts to the other. As they learn from each other, the common ground grows with shared terminology and experience, and the ability to communicate new concepts is enhanced.
Consider then the network of all human interactions. These interactions are not all “2-way”: when three people have a group conversation it brings a different dynamic than when only the pairs can privately converse. I’ll explain how the geometric notion of “simplicial complex” can be used to model a network of n-way interactions.
Thus every node and every n-way connection in a network has its own language and worldview. To make this precise we must define what these worldviews are. To that end, I’ll explain what a category is and give several examples. Then I’ll propose that we can model worldviews as categories. The network of human interactions becomes a “sheaf” of categories on a simplicial complex: local languages interacting to create a higher-order entity trying to understand its world.