Dwarkesh Patel interviews Grant Sanderson (who runs the excellent 3Blue1Brown YouTube channel) about:
- Whether advanced math requires AGI
- What careers should mathematically talented students pursue
- Why Grant plans on doing a stint as a high school teacher
- Tips for self teaching
- Does Godel’s incompleteness theorem actually matter
- Why are good explanations so hard to find?
Kris: I snipped several excerpts for future reference. Emphasis mine. I cut up the excerpts as I want to remember them which means there are missing sections so I encourage you to listen to the whole episode or read the sections of transcript I’m pulling from if you want a closer look.
On the future of education
[key ideas: reducing distance to students, educator’s role is not just explanation but more importantly “bring out knowledge” not put it in, the non-linear influence of a teacher on a student’s future, and the chaotic concept of “sensitivity to initial conditions”]
Dwarkesh Patel 0:44:44
Should the top 0.1% of educators exclusively be on the internet because it seems like a waste if you were just a college professor or a high school professor and you were teaching 50 kids a year or something. Given the greater scale available should more of them be trying to see if they can reach more people?
Grant Sanderson 0:45:01
I think it’s not a bad thing for more educators who are good at what they’re doing to put their stuff online for sure. I highly encourage that even if it’s as simple as getting someone to put a camera in the back of the classroom. I don’t think it would be a good idea to get those people out of the classroom.
If anything I think one of the best things that I could do for my career would be to put myself into more classrooms…
One of the most valuable things that you can have if you’re trying to explain stuff online is a sense of empathy for what possible viewers that are out there. The more distance that you put between yourself and them in terms of life circumstances. I’m not a college student so I don’t have the same empathy with college students. Certainly not a high school student, so I’ve lost that empathy. That distance just makes it more and more of an uphill battle to make the content good for them and I think keeping people in regular touch with just what people in the classroom actively need is necessary for them to remain as good and as sharp as they are…
The other thing I might disagree with is the idea that the reach is lower. Yes, it’s a smaller number of people but you’re with them for much, much more time and you actually have the chance of influencing their trajectory through a social connection in a way that you just don’t over Youtube.
You’re using the word education in a way that I would maybe sub out for the word explanation. You want explanations to be online but the word education derives from the same root as the word educe, to bring out, and I really like that as a bit of etymology because it reminds you that the job of an educator is not to take their knowledge and shove it into the heads of someone else the job is to bring it out. That’s very, very hard to do in a video and in fact, even if you can kind of get at it by asking intriguing questions for the most part the video is there to answer something once someone has a question.
The teacher’s job, or the educator’s job, should be to provide the environment such that you’re bringing out from your students as much as you can through inspiration through projects, through little bits of mentorship and encouragement along the way. That requires eye contact and being there in person and being the true figure in their life rather than just an abstract voice behind a screen.
Anytime I chat with mathematicians and try to get a sense for how they got into it and what got them started, so often they start by saying there was this one teacher and that teacher did something very small — like they pulled them aside and just said, “Hey. You’re really good at this. Have you considered studying more?” or they give them an interesting problem.
And the thing that takes at most 30 minutes of the teacher’s time, maybe even 30 seconds, has these completely monumental rippling effects for the life of the student they were talking to that then sets them on this whole different trajectory.
Two examples of this come to mind. One is this woman who was saying she had this moment when she got pulled aside by the teacher and he just said, “Hey, I think you’re really good at math. You should consider being a math major.” which had been completely outside of her purview at that time. That changed the way she thought about it. And then later she said she learned that he did that for a large number of people. He just pulled them and was like, “Hey, you’re really good at math.” So that’s a level of impact that you can have as a figure in their lives in a way that you can’t over screen.
Another one which was very funny. I was asking this guy why he went into the specific field that he did. It was a seemingly arbitrary thing in my mind but I guess all pure math seems to be. He said that in his first year of grad school he was sitting in this seminar and at the end of the seminar the professor, who was this old professor who he had never met him before, they didn’t have any kind of connection. He seeks this guy out and comes up and he says, “You. I have a problem for you. A good research problem that I think I think might be a good place for you to start in the next couple months” and this guy was like “Oh, okay” and he gets this research problem and he spends some months thinking about it and he comes back and then it later came to light that the professor mistook him for someone else that was someone he was supposed to be mentoring. He was just the stereotypical image of like a doddering old math professor who’s not very in tune with the people in his life that was the actual situation but nevertheless that moment of accidentally giving someone a problem completely shifted the research path for him, which if nothing else, shows you the sensitivity to initial conditions that takes place when you are a student and how the educator is is right on that nexus of sensitivity who can completely swing the fences one way or another for what you do.
For every one of those stories there’s going to be an unfortunate counterbalancing story about people who are demotivated from math. I think this was seventh grade. There was this math class that I was in and I was one of the people who was good at math and enjoyed it and would often help the people in the class understand it. I had enough ego built up to have a strong shell around things. For context, I also really liked music and there was this concert that had happened where I had a certain solo or something earlier in that week.
There was a substitute teacher one day who didn’t have any of the context and she gave some lesson and had us spend the second half of the class going over the homework for it. All of the other students in the class were very confused and I think I remember like they would come to me and I would try to offer to help them and the substitute was going around the class in these circles and basically marking off a little star for how far down the homework people were just to get a sense are they progressing. That was kind of her way of measuring how far they were. When she got to me I had done none of them because I was spending my whole time trying to help all of the others and after having written a little star next to the same problem like three different times she said to me like, “Sometimes music people just aren’t math people.” and then keeps walking on.
I was in the best possible circumstance to not let that hit hard because one, I had the moral high ground of “Hey, I’ve just been helping all these people. I understand it and I’ve been doing your job for you.” This was my little egotistical seventh grade brain. I knew that I knew the stuff. Even with all of the armor that was put up, I remember it was just this shock to my system, she says this thing and it just made me strangely teary-eyed or something.
I can only imagine if you’re in a position where you’re not confident in math and the thing that you know deep in your heart is actually you are kind of struggling with it, just a little throwaway comment like that could completely derail the whole system in terms of your relationship with the subject.
So it’s another example to illustrate the sensitivity to initial conditions. I was in a robust position and wasn’t as sensitive. I was gonna love math no matter what but you envision someone who’s a little bit more on that teetering edge and the comment, one way or another, either saying you’re good at this you should consider majoring in it or saying, “Sometimes music people aren’t math people” which isn’t even true. That was the other thing about it that niggled at my brain when she said it.
All of that is just so important for people’s development that when people talk about online education as being valuable or revolutionary or anything like that, there’s a part of me that sort of rolls my eyes because it just doesn’t get at the truth that online explanations have nothing to do with all of that important stuff that’s actually happening and at best it should be like in the service of helping that side of things where the rubber meets the road.
[key ideas: not everyone responds to the same explanations so explanations that scale well are difficult to conjure. There’s room for multiple approaches and ways to communicate]
Dwarkesh Patel 1:02:22
Why are good explanations so hard to find, despite how useful they are? Obviously, other than you, there’s many other cases of good explanations. But generally, it just seems like there aren’t as many as there should be. Is it just a story of economics where it’s nobody’s incentive to spend a lot of time making good explanations? Is it just a really hard skill that isn’t correlated with being able to come up with a discovery itself? Why are good explanations scarce?
Grant Sanderson 1:02:47
I think there’s maybe two explanations.
The first less important one is going to be that there’s a difference between knowing something and then remembering what it’s like not to know it. And the characteristic of a good explanation is that you’re walking someone on a path from the feeling of not understanding up to the feeling of understanding.
Earlier, you were asking about societies that lack numeracy. That’s such a hard brain state to put yourself in, like what’s it like to not even know numbers? How would you start to explain what numbers are? Maybe you should go from a bunch of concrete examples. But like the way that you think about numbers and adding things, it’s just you have to really unpack a lot before you even start there.
And I think at higher levels of abstraction, that becomes even harder because it shapes the way that you think so much that remembering what it’s like not to understand it. You’re teaching some kid algebra and the premise of like a variable. They’re like, “What is X?” It’s not necessarily anything but it’s what we’re solving for. Like, yeah, but what is it? Trying to answer “What is X?” is a weirdly hard thing because it is the premise that you’re even starting from.
The more important explanation probably is that the best explanation depends heavily on the individual who’s learning. And the perfect explanation for you often might be very different from the perfect explanation for someone else. So there’s a lot of very good domain specific explanations. Pull up in any textbook and like chapter 12 of it is probably explaining the content in there quite well, assuming that you’ve read chapters one through 11, but if you’re coming in from a cold start, it’s a little bit hard.
So the real golden egg is like, how do you construct explanations which are as generally useful as possible and generally appealing as possible? And that because you can’t assume shared context, it becomes this challenge. And I think there’s like tips and tricks along the way, but because the people that are often making explanations have a specific enough audience, it is this classroom of 30 people. Or it’s this discipline of majors who are in their third year. All the explanations from the people who are professional explainers in some sense are so targeted that maybe it’s the economic thing you’re talking about. There’s not, or at least until recently in history, there hasn’t been the need to or the incentive to come up with something that would be motivating and approachable and clear to an extremely wide variety of different backgrounds.
Putting in work with calculations
Dwarkesh Patel 1:20:44
If you’re self teaching yourself a field that involves mathematics, let’s say it’s Physics or some other thing like that, there’s problems where you have to understand how do I put this in terms of a derivative or an integral and from there, can I solve this integral? What would you recommend to somebody who is teaching themselves quantum mechanics and they figured out how to put how to get the right mathematical equation here. Is it important for their understanding to be able to go from there to getting it to the end result or can they just say well, I can just abstract that out. I understand the broader way to set up the problem in terms of the physics itself.
Grant Sanderson 1:22:00
I think where a lot of self-learners shoot themselves in the foot is by skipping calculations by thinking that that’s incidental to the core understanding. But actually, I do think you build a lot of intuition just by putting in the reps of certain calculations. Some of them maybe turn out not to be all that important and in that case, so be it, but sometimes that’s what maybe shapes your sense of where the substance of a result really came from.
I don’t know it might be something you realize like “Oh, it’s because of the square root that you get this decay.” And if you didn’t really go through the exercise, you would just come away thinking like instead of coming away thinking like such and such decays but with other circumstances, it doesn’t decay and not really understanding what was the core part of this high level result that is the thing you actually want to come out remembering.
Putting in the work with the calculations is where you solidify all of those underlying intuitions. And without the forcing function of homework, People just don’t do it. So I think that’s one thing that I learned as a big difference post college versus during college.
Post college, it’s very easy to just accidentally skip that while learning stuff and then it doesn’t sink in as well. So I think when you’re reading something, having a notebook and pencil next to you should be considered part of the actual reading process.
And if you are relying too much on reading and looking up and thinking in your head, maybe that’s going to get you something but it’s not going to be as highly leveraged as it could be.
The “failure to disrupt”
[key ideas: learning is not bottlenecked by good explanations but by social incentives. Deeply resonant. Reading between the lines — we are aspirational and good at copying others or trying to impress them, so if we know that we should provide good models for learners to emulate]
Dwarkesh Patel 1:23:39
What would be the impact of more self teaching in terms of what kinds of personalities benefit most? There’s obviously a difference in the kind of person who benefits most. In a situation where it’s a college course and everybody has to do the homework, but maybe some people are better tuned for the kind of work that’s placed there versus all this stuff is available for you on youtube and then textbooks for exercises and so on but you have to have the conscientiousness to actually go ahead and pursue it.
How do you see the distribution of who will benefit from the more modern way in which you can get whatever you want but you have to push yourself to get it.
Grant Sanderson 1:24:17
There’s a really good book that’s actually kind of relevant to some of your early questions called Failure to Disrupt that goes over the history of educational technology. It tries to answer the question of why you have these repeated cycles of people saying such and such technology that almost always is getting more explanations to more people, promises that it’ll disrupt the existing university system or disrupt the existing school system and just kind of never does.
One of the things that it highlights is how stratifying these technologies will be in that they actually are very very good for those who are already motivated or kind of already on the top in some way and they end up struggling the most just for those who are performing more poorly.
And maybe it’s because of confounding causation where the same thing that causes someone to not do poorly in the traditional system also means that they’re not going to engage as well with the plethora of tools available.
I don’t know if this answers your question, but I would reemphasize that what’s probably most important to getting people to actually learn something is not the explanation…but instead, it’s going to be the social factors. Are the five best friends you have also interested in this stuff and do they tend to push you up or they tend to pull you down when it comes to learning more things? Or do you have a reason to? There’s a job that you want to get or a domain that you want to enter where you just have to understand something or is there a personal project that you’re doing?
The existence of compelling personal projects and encouraging friend groups probably does way way more than the average quality of explanation online ever could because once you get someone motivated, they’re just they’re going to learn it and it maybe makes it a more fluid process if there’s good explanations versus bad ones and it keeps you from having some people drop out of that process,which is important.
But if you’re not motivating them into it in the first place, it doesn’t matter if you have the most world-class explanations on every possible topic out there. It’s screaming into a void effectively.
And I don’t know the best way to get more people into things. I have had a thought and this is the kind of thing that could never be done in practice but instead it’s something you would like write some kind of novel about, where if you want the perfect school, something where you can insert some students and then you want them to get the best education that you can, what you need to do is — Let’s say it’s a high school. You insert a lot of really attractive high schooler plants as actors that you get the students to develop crushes on. And then anything that you want to learn, the plant has to express a certain interest in it. They’re like, “Oh, they’re really interested in Charles Dickens.” And they express this interest and then they suggest that they would become more interested in whoever your target student is if they also read the dickens with them.
If you socially engineer the setting in that way, the effectiveness that would have to get students to actually learn stuff is probably so many miles above anything else that we could do. Nothing like that in practice could ever actually literally work but at least viewing that as this end point of “Okay, this mode of interaction would be hyper effective at education. Is there anything that kind of gets at that?”
And the kind of things that get at that would be — being cognizant of your child’s peer group or something which is something that parents very naturally do or okay, it doesn’t have to be a romantic crush, but it could be that there’s respect for the teacher. It’s someone that they genuinely respect and look up to such that when they say there’s an edification to come from reading Dickens, that actually lands in a way.
The natural extension of this:
Encourage people to mentor or teach on the side!
I think there are two things I would want to get out of teaching in a school setting. One of them, as I was emphasizing, I think you just lose touch with what it’s like not to know stuff or what it’s like to be a student and so maintaining that kind of connection so that I don’t become duller and duller over time feels important.
The other, I would like to live in a world where more people who are savvy with STEM spend some of their time teaching. I just think that’s one of the highest leverage ways that you can think of to actually get more people to engage with math
And so I would like to encourage people to do that and call for action. Some notion of spending, maybe not your whole career, a little bit of time. In teaching, there’s not as fluid a system for doing that as going through a tour of service in certain countries where everyone spends two years in the military
Shy of having a system like that for education, there’s all these kind of ad hoc things where charter schools might have an emergency credential system to get a science teacher in. Teach for America is something out there.
There’s enough ways that someone could spend a little bit of time that’s probably not fully saturated at this point that the world would be better if more people did that