> That the way we teach what we teach is often more important than the what.
Partially agreed.
Whatever we teach today will be solved or obsolete tomorrow anyway. In fact, in school we learn methods that are never used in real life anyway. So the "what" is not fully the point.
It's how we teach it and what the point of it. The point of it is to teach how to learn things, how to practice, how to become experts, how to struggle with them and persevere eventually. It is not a sort of an exercise for our minds, but it is exactly an exercise for our minds. That's the point.
The "what" matters in that it is a foundation of knowledge upon which future knowledge and understanding is built.
So, I agree with the spirit of the argument but it is a bit more nuanced.
Based on my experiences with the teachers my kids had a decade or so ago, all you would have to do is find a way to test for it and then put it on the state-mandated test that is used to evaluate schools.
Often the only thing that is taught is what is on those tests.
The one-two punch of Goodhart's law and the McNamara fallacy bites hard here, though. We only measure things we can easily quantify, and then we optimize around those measurements, destroying their efficacy as second-order indicators of the things we couldn't figure out how to measure.
For example is the purpose of educating children about history A) to give them a systemic, if somewhat cursory, understanding of the evolution of society, in order allow them to contextualize the present? or B) ensure they know a list of a hundred or so people and events that happened?
I can chime in about this. I’m a software engineer and about 7 years ago I decided to get a masters in pure mathematics. Because I was working full time, I could not attend any class so I self studied from textbooks and it worked well.
When I would get stuck, I would struggle with the problem, ask around, ask on Math Stackexchange and along the process I would end up learning a lot more.
With AI now, it’s like having your own tutor: you can ask personalized questions and it would answer it very well.
But that would also mean the amount of time I would spend struggling would go down considerably.
So you really have to be self disciplined and struggle with the problem a little bit before asking for help. You can also ask it to give hints only.
Do not mistake understanding the answer with learning something rigorously.
So if you are curious and doing an exposition, use it as you would normally and it will work wonderfully.
But if you want to learn it rigorously, our usual present habits with AI spitting out answers and us reading them will not work at all.
I've tried to do this but with learning poker, and it's sort of a mixed bag. You kind of have to know what you don't know before you can get anything useful out of it. It can sort of help going from "I understand this concept, but not instinctively" to "I've drilled this enough that I could do things like this in my sleep", but it takes a lot of iteration and asking questions before it can settle on a series of instructive examples that each build on top of each other. You're still much better off with a well-written textbook.
Not that it matters or anyone cares, but it's so obvious Balwani was manipulating her emotionally. There are so many instances where he says "Love you", or "love" or "I am in love with your beauty", while she is more direct like "I love you", "I am in love with you" etc.
hmm..perhaps I was biased because I watched a couple of documentaries, a tv film and read the book by John Carreyrou "Bad Blood", so my eyes were primed to look for this pattern.
But he was definitely manipulative in this regard.
Their field is extremely rigorous. As rigorous as it can possibly get in that they have to prove each and every line of their work beyond any doubt. The discipline they have cultivated in their culture shows in their response to AI as well.
As opposed to some other fields in which rigor was either not part of the culture or was not always possible. For e.g., software engineering in terms of code quality being produced. There were some indirect signals here and there but they are all subjective.
In some sense software engineering is more rigorous than mathematics, because proofs are generally informal, apart from those written in Lean, while all computer programs are strictly formal, as otherwise they wouldn't be machine-readable.
I see what you are sayings. That's an interesting point of view.
Perhaps we should define what rigor means.
Your point is that code is executable and speaks for itself whereas a Math proof (non-lean) is just someone's writing on a piece of paper.
Now let's compare the "practice" of doing Math and software engineering. In Math, every step is very intentional, and getting to a point where a proof is complete and correct is a very long, laborious, difficult and intentional process. Not to mention, the work is also peer reviewed (for published stuff). This is what I mean by rigor.
In software engineering, the practice is quite different. We defined the problem (somewhat), come up with a design that we "think" would work, write programs that we think is correct and then execute it. Most of the time it doesn't work exactly as we would have predicted. So we take the signal and adjust. So it's a more iterative part and this gets us closer to reality (what we actually want it to be), step by step.
So comparing the two, the major difference I see is in one each and every step is very intentional and we can't guess it. While in the other one we have lots of liberties, but we are still making progress.
So to me the difference is just between the practices followed in the field when it comes to rigor.
Maybe a similar comparison would be this: for proofs, the standards of correctness are purely internal and can in principle be formally defined, as in Lean. The formal conjecture has to follow from the premises. Either it is proven or not. In contrast, in 99% of ordinary software, no fully formal standard of correctness exists. The requirements are informal. So what counts as a bug and what doesn't is a judgement call that can only be checked by asking the person who wanted the software whether it works as intended.
Partially agreed.
Whatever we teach today will be solved or obsolete tomorrow anyway. In fact, in school we learn methods that are never used in real life anyway. So the "what" is not fully the point.
It's how we teach it and what the point of it. The point of it is to teach how to learn things, how to practice, how to become experts, how to struggle with them and persevere eventually. It is not a sort of an exercise for our minds, but it is exactly an exercise for our minds. That's the point.
The "what" matters in that it is a foundation of knowledge upon which future knowledge and understanding is built.
So, I agree with the spirit of the argument but it is a bit more nuanced.