Thanks Brad, you always post great succinct insights. Do you feel that modern topology and category theory offer us useful tools for understanding the causal structure of living things? Robert Rosen seemed to think so but I haven’t seen a lot of work on it recently.
The causal structure of living things is circular. If you zoom in to the circle, it looks more and more like a line (input -> output). But life is a global section, so we can't forget about that global topology. Even though the input->output POV is incredibly tempting.
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Thanks Noah! I really enjoy your tweets too. I absolutely think they do, but you're right I don't have a lot of concrete work to point to... yet. But I do think studying these topics is well worth the effort.
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Interesting, but don't you think low-dimensional topologies (
) could be misleading frameworks for many (most?) biological systems (
).. ? -
What I think matters here is homology since the torus is 2-d and all graphs are 1-d as topological spaces but graphs can have richer homology. What I remind myself is at large scales there *is* non-trivial homology, and whatever that actually is must be taken into account.
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