David Spivak

Information seems to work by resonance. Reading a sentence, it's as though the words are either flowing or jarring, either fulfilling a cadence or violating it, either fitting together or not. When we see information and it's getting across, the feeling is one of smoothness; there is resonance between the expected and the given. When it's not getting across (and hence is not informative) it's like we're always misinterpreting, things aren't making good sense. Syntax in a language is a basic cadence through which a speaker can resonate with a listener. But even the ideas seem to form a song, striking the right sequence of notes so as to be both interesting and yet sensical.
-- 2012 / 03 / 20

Information seems to work by resonance. Reading a sentence, it's as though the words are either flowing or jarring, either fulfilling a cadence or violating it, either fitting together or not. When we see information and it's getting across, the feeling is one of smoothness; there is resonance between the expected and the given. When it's not getting across (and hence is not informative) it's like we're always misinterpreting, things aren't making good sense. Syntax in a language is a basic cadence through which a speaker can resonate with a listener. But even the ideas seem to form a song, striking the right sequence of notes so as to be both interesting and yet sensical.

-- 2012 / 03 / 20

Senior Research Scientist and Institute Fellow at Topos Institute

Curriculum Vitae

Email: dspivak@gmail.com

Current research projects

Functorial Dynamics and Interaction. Using polynomial functors to model dynamical systems, decision processes, data migration, and more! (I'm completely enthralled with the category Poly.) A book on the subject is in preparation. Idris code can be found here.

Structure and dynamics of working language Using polynomial functors to account for how language works, in the sense of physics. This grant has been recommended for funding, but has not yet started.

Introductory books on Applied Category theory

Category Theory for the Sciences was published by MIT Press, also available on Amazon.
Here are reviews by the MAA, by the AMS, and by SIAM.
Course materials (MIT OCW) can be found here.

Seven Sketches in Compositionality. This material has been published by Cambridge University Press as An Invitation to Applied Category Theory by Brendan Fong and David I. Spivak. This version is free to view and download for personal use only. Not for re-distribution, re-sale or use in derivative works. © Brendan Fong and David Spivak 2019. Also available on Amazon.
Here is a review by the MAA and a review by Acta Crystallographica.
Course materials (MIT OCW) can be found here.

Past research subjects

Applied Category Theory. Various ACT grants, some funded and others not.

Derived manifolds. The category of derived manifolds contains arbitrary intersections of manifolds, even if they are not transverse, while retaining enough structure so that every compact derived manifold has a fundamental class in cobordism.

Mapping spaces in quasi-categories. Joint work with Dan Dugger.

Anomaly-free sets of fermions. A physics paper I coauthored with Puneet Batra and Bogdan Dobrescu.

Metric realization of fuzzy simplicial sets A draft I never published, and may contain errors, but which has gotten some attention from the creators of UMAP and others.

What is Information? These are notes I took from ten-minute "What is information?" contemplations, which I was doing daily in 2012. And a guide by NotebookLM.

Values Statement

Values Statement. This is a first attempt to convey the values that seem to motivate me.

This work by David I. Spivak is licensed under a Creative Commons Attribution-Share Alike 3.0 Unported License.