The biggest challenge for anybody claiming that "math isn't real" is providing a plausible explanation for why math has been so incredibly successful at predicting phenomena in the real world. How can something that's not real still predict real things?
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Replying to @geomblog @kareem_carr
It's incredible that one of my favorite intellectual topics—not as something I will make a claim on, just one I like to ponder as one of the great, wonderful mysteries of the universe—has become source for a meme fight on Twitter dot com in 2020 in the middle of a pandemic.
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Replying to @zeynep @kareem_carr
Too much time and too much general annoyance at the world because of being cooped up?
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Replying to @geomblog @kareem_carr
But but but I want to read about the "unreasonable effectiveness" and the "math is isomorphic to the world" and the "oh hey, it's all axioms" stuff but all we get is meme wars about 2+2... Not fair! I feel cheated.
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Sometimes I think math is so general it can represent almost anything, it's just that we mostly explore(d) math that's useful to us, and so it feels like it's unreasonably effective. On the other hand it's quite curious why it was so easy to axiomatize the physical sciences 1/2
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Actually even in the physical sciences, biology has resisted the same level of precise mathematical characterization that physics has allowed. So maybe life itself resists axiomatization, not just humans :)
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Replying to @geomblog @_joaogui1 and
William Wimsatt has a nice phrase for this: "causal thickets". He distinguishes cases where causal structure can be approximately decomposed into "horizontal" levels, "cross-cutting" perspectives, and causal thickets, which permit neither.pic.twitter.com/bIwgPmEqyB
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Causal thickets, wicked problems, complex systems... Many names. So many interesting and crucial problems lie in that domain, and somehow people keep trying to apply physics-like methodology as if a mismatch between problem and method is good just because mumble mumble physics...
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Replying to @zeynep @nkrishnaswami and
Another name that
@BlairDSullivan introduced to me is "mesoscale" analysis. Neither local nor global, and where all the complexity lies1 reply 0 retweets 4 likes -
In an SDE/SPDE context, one of my favorite (late, alas) profs wrote this, which I enjoyed very much: https://www.springer.com/gp/book/9780387743165 …
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