Title: Accounting for our Inventiveness
Abstract:
This talk is written to be heard in two registers: one that category theorists can trust and another that biologists can find motivating. These two audiences may seem to have very little in common. However, every mathematician is a biological entity, and our ability to "do mathematics," e.g. to invent and employ abstractions, is one that biology had to produce in a stack of technologies that grounds out in bare physics. I'll try to make clear that humans are not the first biological systems to be inventive: biology is a story rife with inventiveness at every stage. The key inventions all tend to increase portability of form so that it can take hold in new substrates, and this is the heart of abstraction. I'll propose that the mechanism is accounting: a system develops sensitivities, works to bring them into coherence, and when the accounts settle, what emerges is a new portable capacity. This is sensemaking, and its product is abstraction.
I'll then pivot to discuss polynomial functors in one variable, which I think is itself a highly portable abstraction. As a category, Poly is easy to generate (the free completely distributive category on a point), yet extraordinarily rich and computationally tractable, with a wide range of monoidal closed structures, (co)free (co)monads, and applications from dependent type theory to interacting dynamical systems. In the remainder of the talk I'll discuss my attempt to model living systems and suggest that the accounts are not yet settled: we do not have a formal account of our own physical ability to create new abstractions. I believe this is a problem both audiences can work on.
Bio: David Spivak leads the Collective Intelligence research group at Topos, after a decade as a researcher at MIT. Since his PhD from UC Berkeley in 2007, he has worked to bring category-theoretic ideas into science, technology, and society, through novel mathematical research, through collaboration with scientists and engineers from disciplines including Materials Science, Chemistry, Robotics, Aeronautics, and Computer Science. His mission at Topos is to help develop the ability for people, organizations, and societies to make sense of—and hence to serve—the systems which sustain them.
The NSF-Simons National Institute for Theory and Mathematics in Biology Seminar Series aims to bring together a mix of mathematicians and biologists to foster discussion and collaboration between the two fields. The seminar series will take place on Fridays from 10am - 11am at the NITMB in the John Hancock Center in downtown Chicago. There will be both an in-person and virtual component.
Tiffany Leighton
Email