> This discussion started because the person you replied to was saying "[I was] dissappointed with myself for not taking more notes ... This quote made me feel better about simply reading, getting whatever I get out of it". You replied "This is the way to approach it, particularly in these times when knowledge is so vast and there is so much to read.

No, you seem to have conveniently ignored the particular phrase of the parent's comment to which i was commenting, to wit; "simply reading, getting whatever I get out of it, and trusting that I’ve gained some perspective," It is right there at the beginning of my comment and i am expanding only on this sentiment and nothing else. Hence i am not sure where you are getting your other assumptions from. If i had wanted to expand on note-taking i would have explicitly called out the parent's relevant phrases which i did not.

> I would counter that one does not see the existence of such connections with only superficial understandings.

Hard Disagree, you can definitely see some connections with even "superficial" understanding however fuzzy/incomplete they might be. For example, i can tell a programmer to think of the types of his program variables as a set and the variable itself ranging over the collection of values in this set. Next i can tell him to think of his logical conditions using these variables as logical predicates establishing a mathematical relation between various values amongst the above sets. With just this "superficial" knowledge of Sets, Cartesian Product, Relations and Predicates he can now see a connection between Mathematics and his Program enabling him to come up with better and more comprehensive Pre/Post conditions and write "correct" code.

> Yes there is great value in being able to go between many domains and to tie them together, but it is not immediately obvious why this would be more valuable than digging deeply in a smaller number

This should be obvious by now; you are increasing the size of your "known unknowns" and hopefully decreasing the size of "unknown unknowns".

> You don't have time to learn about all of them. And when choosing to pick what to look at next, I argue that searching for the thing related to your current problem is more valuable knowledge than a that which you get "just in case"

Of course Time/Energy are limited and universal constraints on everything a Human can do; that is not an argument. If you are working towards something specific, your study should be targeted but not necessarily limited to it. This is where "Reading broad/wide" is needed. As an example, you have loads of Web programmers today who limit themselves to only using higher level frameworks/libraries to write distributed apps but have no clue (not even "superficial") of the underlying TCP/IP stack. Having some idea of the application layer HTTP protocol and its interactions with the underlying TCP/IP stack is a must for any distributed app developer but because things have been abstracted and encapsulated so nicely many don't even bother getting a "superficial" knowledge of these fundamental technologies thus severely limiting their effectiveness troubleshooting when things go wrong.