if you surround yourself with elites, you become elite. thanks for the quote :)

I remember sitting in on office hours for one of my math classes when I saw you had uploaded that page. Fantastic timing...

I quickly read They did not expect him part before class, I’m looking forward to reading the rest afterwards, thank you very much …

I like the analogy of math and learning an instrument. To me "symbol-manipulation" is like "bad technique"...the conditioning of a habit without real understanding of the why and how. But we shouldn't forget that instruments should be fun to play, not a chore to perform.

Thank you so much for reading, blamensir ^_^

Part of my research has also gone into "raging against a machine" in a sense: https://discourse.32bit.cafe/t/creation-of-computers-on-the-local-level/1017 But a couple of those links I hadn't seen before. Thank you!

LLT, you probably know much more on this topic than I do; your post is a treasure trove of resources. Thank *you* for sharing!

Categorization & classification is antithetical to authentic writing; try to hold your own against it!

Joost A.M. Meerloo theorized the dark forest of the web: "he is reduced to the mechanical precision of an insect-like state. He cannot develop any warm friendships, loyalties, or allegiances because they may be too dangerous for him. Today’s friend may be, after all, tomorrows enemy." what draws me here is connecting with interesting people, not NPCs (or bots) on corporate platforms.

So long as you enjoy writing, I will enjoy reading it, whatever the topic may be. As the saying goes, "we are our own worst critics." Likewise, there is no pressure to conform to the expectations of an audience if we see sharing as a dialogue.

I wish the reality was gentler.

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.