Sense-making: accounting for intelligibility

David Spivak
Topos Institute

A mathematical field can be thought of as an accounting system: we use arithmetic in finance to account for the flow of resources, we use Hilbert spaces in physics to account for the states and observations of elementary particles, and we use probability distributions in game theory to account for the likelihoods of different scenarios. An appropriate accounting system is one that articulates the sorts of conceptual variables that need to be tracked in order to make sense of relevant phenomena within a given domain, as well as the sorts of operations on these variables that track the interactions between the corresponding phenomena.

We seek an accounting system for collective intelligence: we want to articulate the sorts of conceptual variables that need to be tracked in order to make sense of the phenomenon called intelligence. How is the world made intelligible?

In this talk I'll propose a refinement of the problem: we need to understand collective sense-making. Our ability to interact successfully with the world—to play tennis or solve a novel math problem—arises from our ability to make sense of it: to compress the overwhelming amount of data into an abstraction that can be shared, communicated about, and acted upon in concert by the relevant players in the collective of cells and organs of which we are built. In particular, I'll discuss how systems mathematics—usually called category theory—provides an accounting system with the appropriate structures to help us collectively make sense of the phenomenon called intelligence, namely to formulate how it arises from the simpler sense-making activity of the underlying collective.

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