Oh, I would certainly love that. Statistical mechanics looks like it’s magic, and it strikes me as absolutely worth grokking, and yeah I haven’t found any entry point into it other than the Great Formal Slog.
I remember learning about “inner product spaces” as a graduate student, and memorizing structures and theorems about it, but it wasn’t until I had already finished something like a year of grad school that I found out that the intuition behind inner products was “What kind of thing is a dot product in a vector space? What would ‘dot product’ mean in vector spaces other than the Euclidean ones?” Without that guiding intuition, the whole thing becomes a series of steps of “Yep, I agree, that’s true and you’ve proven it. I don’t know why we’re proving that or where we’re going, but okay. One more theorem to memorize.”
I wonder if most “teachers” of formal topics either assume the guiding intuitions are obvious or implicitly think they don’t matter. And maybe for truly gifted researchers they don’t? But at least for people like me, they’re damn close to all that matters.
Oh, I would certainly love that. Statistical mechanics looks like it’s magic, and it strikes me as absolutely worth grokking, and yeah I haven’t found any entry point into it other than the Great Formal Slog.
I remember learning about “inner product spaces” as a graduate student, and memorizing structures and theorems about it, but it wasn’t until I had already finished something like a year of grad school that I found out that the intuition behind inner products was “What kind of thing is a dot product in a vector space? What would ‘dot product’ mean in vector spaces other than the Euclidean ones?” Without that guiding intuition, the whole thing becomes a series of steps of “Yep, I agree, that’s true and you’ve proven it. I don’t know why we’re proving that or where we’re going, but okay. One more theorem to memorize.”
I wonder if most “teachers” of formal topics either assume the guiding intuitions are obvious or implicitly think they don’t matter. And maybe for truly gifted researchers they don’t? But at least for people like me, they’re damn close to all that matters.