i just woke up but im reading this immediately

Thank you so much for the interesting observations and resources! I've always wanted to learn Russian and German for scientific purposes. I really ought to pick them back up again. I would imagine that many language learners who persist to fluency do so for reasons similar to that quote attributed to Nelson Mandela. To paraphrase: "If you talk to a person in their language, it goes to their heart."

The joys of human connection! Unfortunately, as you've eloquently pointed out, there are two significant obstacles: The most effective way for one to approach their own study of a language often only becomes apparent in hindsight, and a significant core of every langauge is idiomatic and conditioned through use rather than the result of some type of inherent logic.

I also agree with much of what suboptimalism mentioned. It often comes down to cultivating a mindset, having a clear intention and a strong motivation. Learning materials that try to shoehorn one language into the structure of another are more of a hinderance than a help, while translation is often an attempt at fitting a square peg into a round hole.

Therefore, it becomes a matter of learning a few fundamental pieces thoroughly, and then using them to "bootstrap" the rest of that core by repeatedly relating the language to itself through a steady stream of input and personal experiences. Developing these associations is vital if one wants to avoid my mistake of learning a lot *about* languages versus actually *using them*.

I hope you find it useful, Hui! Your recent remark on Russian is what reminded me I had this file on hand, after all :)

Thanks as always for the thoughtful comments, LLT. That Mandela quote is a classic and it endures because it's true. I like your description of "bootstrapping" the language. I've made the same mistake of learning /about/ the language; in fact this mistake is by no means unique to language learning. It reminds me of the comment you left some months ago about the act of /doing/ mathematics and how procedural knowledge

is often overlooked in favour of declarative knowledge. The gap between them hurts.

I feel your pain 😩 Haha! Well, at least sharing experiences can shorten the gap between them. Thanks again!

That Morris Kline quote reminds me of a book that I had enjoyed some years ago, "Arithmetic for Parents" by Ron Aharoni. The author goes from teaching college-level mathematics to introducing arithmetic to elementary school children. [1of4]

Throughout most of the book, he notes the physical meanings behind basic operations (e.g.: "subtraction" as either a separation of one amount from another, or a comparison, a "difference" betweeen two things without removal). [2of4]

It is very basic, but it renewed my love for applied mathematics and is a nice example of how tightly our abstractions can correspond to more familiar life experiences. Becoming aware of those relationships seems like a good way to develop a strong "mathematical intuition". [3of4]

Another really good example of this is the work of Saunders MacLane: https://en.wikipedia.org/wiki/Mathematics,_Form_and_Function#Mathematics_and_human_activities I would love to read the book that this table is derived from someday. [4of4]

Thanks for bringing up Aharoni's book - I'll have to give it a read. And that table from Mac Lane looks fascinating, I think it ties in surprisingly well to Morris Kline's overarching claim, that the origins and even the present motivation of mathematics were/are anything but abstract.

Can't wait to watch the movie so I can read your thoughts on it. Also been thinking about Flannery O'Connor lately. A musician I like, Sufjan Stevens, made a song called A Good Man is Hard to Find à la her short story. Read it in one of my English classes a year or so ago & still think about it. I didn't like it at the time, but the longer I carry it in my mind the fonder of it I become.

If you haven't listened to his music before, maybe you should listen to a song or two. He has a lot of allusions to Christianity in his work that quite frankly go above my head most of the time, & not like a halo, (more like a very fast bird, myself shaded under its wings for a moment).

@vashti, I love Sufjan and that album (Seven Swans, if I remember correctly?) and I'm glad you brought it up. RE: A Good Man is Hard to Find, I think O'Connor's writing has that effect - on the surface it seems ugly, brutal and arbitrary but whoever said medicine had to taste good? :)

Yes, that's the one! (Though Carrie & Lowell is my favroite album of his.) Happy to meet another fan ^^ Out of curiosity, what's your favorite song of his?

Carrie & Lowell is beautiful. I love "All of Me Wants All of You" and I used to obsessively listen to "My Little Red Fox" from his newest album. What's your favorite song of Sufjan's?

Oh man, The Only Thing hands down, though I would say it's more sentimental & important to me rather than my favorite to listen to. I kinda go through phases & lately it's been For the Fatherless in Ypsilanti, Feel the Illinoise, & Drawn to the Blood ^^