Applied category theorist and Topos Institute co-founder David Spivak joins Sarah and Taiyo to explore the mathematics of thinking together. They begin with a question that runs through the episode: when does a resemblance between two fields become useful enough to carry knowledge from one into the other? From epidemics and information to the institutional conditions for adopting AI, they explore how recognizing shared structures can open up questions we would not otherwise know to ask.
David explains why he helped build an independent research institute around teaching, interdisciplinary work, and practical applications; how “ontology logs,” or Ologs, make our mental models explicit; and why two eyes offer such a useful analogy for collective intelligence. In the closing conversation, Sarah and Taiyo show how they put these ideas to work: recording their discussions, using AI to examine the transcripts, and correcting its interpretations together. A lengthy disagreement about learning becomes a concrete example of how people can hear the same word, mean different things, and gradually learn to understand each other.
Also in this episode:
What disease transmission and information spread can teach us about borrowing models across disciplines
AI adoption as a phase transition: early adopters, connected groups, and institutional conditions
When an analogy becomes useful—and why mathematical isomorphism is a more precise idea
Why optimizing individual parts can create friction across a system
Functors and ologs: translating between mental models and making their structure visible
The practical difficulty of turning everyday relationships into formal models
What gardening can teach us about abstraction and cultivating learning
“Always be recording”: using a conversation archive to trace assumptions and revisit disagreements
Why AI mediation becomes useful through shared review, correction, and iteration
CHAPTERS
00:00-11:58 - Chapter 1 Introduction: Same Shape, Different Domains
11:59-16:31 - Chapter 2 Topos Institute and a Different Model for Research
16:32-25:01 - Chapter 3 What Is Applied Category Theory?
25:01-28:10 - Chapter 4 Collective Sensemaking and Translating Perspectives
28:11-35:44 - Chapter 5 Ologs: Making Mental Models Explicit
35:45-40:04 - Chapter 6 Seeing Analogies More Easily
40:04-47:31 - Chapter 7 Always Be Recording: Revisiting Conversations and Learning to Think Together
My Robot Teacher is hosted by Sarah Senk and Taiyo Inoue, produced by editaudio, and funded by the California Education Learning Lab, incentivizing innovation in teaching and learning in California’s public higher education.
📄 Full transcripts available on Substack: https://calearninglab.substack.com/s/my-robot-teacher-podcast
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Tags/Keywords:
David Spivak, category theory, applied category theory, Topos Institute, cross-disciplinary analogies, cross-domain isomorphisms, collective intelligence, AI in education, higher education, AI adoption, diffusion of innovation, phase transitions, abstraction, ontology, ologs, mental models, AI mediation, conversation transcripts, Codex, ChatGPT, Claude, My Robot Teacher, Sarah Senk, Taiyo Inoue, California Education Learning Lab
