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.