Thoughts on thinking

Anyone who has learned a second language can tell you that you aren't proficient just by memorizing vocabulary and grammar. Having a conversation and forming sentences on the fly just feels different- either as a different skill or using a different part of the brain.

I also don't think the nature of LLMs being a negative crutch is new knowledge per se; when I was in school, calculus class required a graphing calculator but the higher end models (TI-92 etc) that had symbolic equation solvers were also banned, for exactly the same reason. Having something that can give an answer for you fundamentally undermines the value of the exercise in the first place, and cripples your growth while you use it.

Same with drawing which is easy to teach, but hard to master because of the coordination between eyes and hand. You can trace a photograph, but that just bypass the whole point and you don’t exercise any of the knowledge.

Another case in point is that memorizing vocabularies and grammar, although could seem like an efficient way to learn a language, is incredibly unrewarding. I've been learning japanese from scratch, using only real speech to absorb new words, without using dictionaries and anything else much. The first feeling of reward came immediately when I learned that "arigatou" means thanks (although I terribly misheard how the word sounded, but hey, at least I heard it). Then after 6 month, when I could catch and understand some simple phrases. After 6-7 years I can understand about 80% of any given speech, which is still far, but I gotta say it was a good experience.

With LLM's giving you ready-made answers I feel like it's the same. It's not as rewarding because you haven't obtained the answer yourself. Although it did feel rewarding when I was interrogating an LLM about how CSRF works and it said I asked a great question when I asked whether it only applies to forms because it seems like fetch has a different kind of browser protection.

Well I can extract a square root by hand. We all had to learn it and got tested on it.

No one to day learns that anymore. The vast, vast majority have no idea and I don’t think people are dumber because of it.

That is to say, I think it’s not cut-and-dried. I agree you need to learn something, but something’s it’s okay use a tool.

How much hours would you estimate did you watch (I assume it was video, not just audio) in those years? What kind of material? Just curious.

I very much agree with your sentiment here.

I tried to encapsulate that to some degree when writing something (perhaps poorly?) recently actually - https://smcleod.net/2025/03/the-democratisation-paradox-what...

Comparing extracting a square root my hand is rather different in scope than reducing / simplifying equations entirely. The TI-92 could basically do all of your coursework for you up to college level, if memory serves.

The real question isn't "is it okay to use a tool" but "how does using a tool affect what you learn".

In the cases of both LLMs and symbolic solving calculators, I believe the answer is "highly detrimental".

Feels different, comes naturally, without conscious thought, just like we don't focus on beating our hearts.

And agree about learning by practicing a skill being best. But you and I both know the school system has worked on rote memorisation for hundreds of years at least and still is now.

Huh? While I essentially never have need to compute a square root by hand (unless it is a perfect square of course), shouldn’t one know how one would?

The manual methods are also the foundation for higher approaches involving approximation and iterative solutions. These are widely used in engineering and science.

Pressing a calculator key doesn’t give the same insight.

Using a tool like that is opposite to mastering the skill. There's no royal road to mastery and never will be. One does not have to master all skills, of course, and may do well not mastering any (or mastering dark ones).

> the higher end models (TI-92 etc) that had symbolic equation solvers were also banned

I'm surprised it was a problem in the first place. Don't equation solving exercises require you to leave intermediary steps, and you can't just put a "x=5" as a one liner answer ?

Yeah and I'm of the age when teachers in all grades would say "you're not going to carry around a calculator your whole adult life"

Hilarious miscalculation.

Why should one? Perhaps they should if it's relevant to their work, daily routine, or interests. But if they have no need for it?

Yes they are dumber because of it, not in the mental retardation kind of way but a more nuanced way, among others the mental work you put into trying to find another simpler way than the one the professor is teaching you, and the understanding about numbers such attempts can give you, even if they are unsuccessful.

I am waiting for the day (maybe it's already here) when I can talk to an LLM to practice my 2nd language. It can correct everything I say, it can talk forever, it can challenge me to use new grammar or vocabularly. Note: I can speak all day in my 2nd language with friends but I wouldn't give a business presentation nor could I explain, as a native, how something technical works. If I watch a TV show I might understand 30%-99% but the more lawyers/military/goverment/science parts there are the more it's beyond my current level.

Getting exposure there is hard. Talking to friends just means more practice with what I already know but an LLM could help me practice things outside that area.

Needs are all fabricated, Ludwig Wittgenstein said "the limits of my language are the limits of my world", the same thing happens with logical thinking and all its tools including math.

For many languages, this is already something you can do.

I don't remember if it was the case for the TI-92+, but some calculators can show the intermediate steps, or at least some of them.

If you used subtitles over audio then why would you avoid dictionaries too ? Purely for the reward of treating it as a puzzle ? (Since you would have to figure out which word corresponds to a which concept in a phrase.)

> No one to day learns that anymore. The vast, vast majority have no idea and I don’t think people are dumber because of it.

Arguably, the kind of person who was helped by learning to do that by hand still learns to do it by hand, but because of curiosity rather than because a teacher told them to.

I remember being thirteen and trying to brute force methods for computing the square root. I didn’t have the tools yet to figure out how to do it in any systematic way, and the internet wasn’t at a point yet where it would have even occurred to me to just search online. Wikipedia wouldn’t exist for another two years.

I probably finally looked it up at some point in high school. I’m not sure exactly when, but I remember spending a lot of time practicing doing a few iterations in my head as a parlor trick (not that I ever had the opportunity to show it off).

If I were thirteen and curious about that now, I’d probably just ask ChatGPT. Then I’d have a whole follow up conversation about how it was derived. It would spit a lot of intimidating LaTeX at me, but unlike with Wikipedia, I’d be able to ask it to explain what those things meant.

This is the thing I don’t get when people talk about LLMs’ impact on education. Everybody focuses on cheating, like learning is inherently a chore that all students hate and must be carefully herded into doing despite themselves.

But that’s a problem with school, not learning. If your actual, self-motivated goal is to learn something, LLM’s are an incredible tool, not a hindrance.

Mostly anime. Surprisingly, not that much, I think somewhere in the ballpark of 100 titles. In the beginning I was also watching some grammar tutorials on YouTube to get started with grammar quicker (Otherwise convergence on solution would be too slow).

Contrary to what I said I actually did use dictionaries, but the point I was trying to make is rather than memorizing phrases in advance, I used it to translate something I thought I heard.

you put my thoughts into words I couldn't.

Any school's #1 job is to motivate learning. Schools clearly suck at this.

LLMs are a fascinating effective learning tool. early learning would be better off embracing it as such.

i imagine a combination of a video of a good tutor explaining a concept followed up with an llm to quiz and explain the concept seems far better than what we have today.

I think we need to find a way to teach without grades. That is, we do know how to teach without grades at younger levels, and many schools do it successfully.

The problem is that eventually you need to measure for placement, and Goodhart’s Law kicks in and destroys the enjoyment of learning. It’s very hard to be intrinsically motivated when the external pressure dominates.

The fact that “study for the test” is basically synonymous with “study” for most people is indicative that we’re doing something extremely wrong in education.

Memorization and manual methods also help develop intuition about what is a plausible answer and what is not. It helps build a brain that is able to sanity-check what it is being told.

> The problem is that eventually you need to measure for placement Why do you need to be "placed"? I know the answer - resources.

But why can't each individual have sort of their own bespoke governess tutoring them all through school? Pay Gilbert Strang a million dollars to do a 32 week course in LinAlg. Yes I know a normal course is shorter, expand it to cover everything in exquisite detail, so even I can keep up. Alan Kay, Donald Knuth, and John Carmack can teach computer science. Continue on for each subject.

Then let students go as fast as they want. I'd have finished some subjects of HS by the time I was in 9th grade, and others I might still be trying. ¯\_(ツ)_/¯

Where you'd still need to be "placed" is social development. Which I think should actually be a subject.

Well, I think one should be able to come up with a way of doing so on the fly just from knowing that the square root function is monotonically increasing, and knowing binary search? Of course, doing it another way might be more efficient.