Wait, how do you get from function spaces to the double-slit experiment? Or is it just for illustration of two moments... With regards to your message, I think

Wait, how do you get from function spaces to the double-slit experiment? Or is it just for illustration of two moments... With regards to your message, I think it's impossible to say whether another person understands something well from reaction. Unfortunately, that is why student focused textbooks (vs. graduate textbooks) usually have a lot of exercises. Edit: By the way, on a somewhat unrelated topic, I have been told that Lawvere thought that set theory was a "historical error" (these kind of semi-biographical stories are code for trying to explain a mathematician's personality, a futile exercise). I wonder if I'll ever be able to meet him and ask him why he thinks that. (I suspect that it will lead to some Lisptopians becoming excited about objects being immaterial. At which point one should remind Lisptopians not to mix programming the activity with mathematics the activity.) It's ironic that set theory is the best way to learn category theory, at which point you to some extent abandon set theory. Maybe it's the pedagicical value of set theory? I wonder if Lawvere would take all my persistent questions kindly.