This so called “conceptual pathfinding” doesn’t seem like an intermediate approach. I don’t understand what the differences between “conceptual pathfinding” and “information/material bootstrapping” are.
You defined conceptual pathfinding as a process that uses textbook explanations and involves figuring out how to get from rough intuitions to detailed mathematical formalizations. Basically, starting from basic information and deriving to target information.
My interpretation of your post is that you are dividing “information bootstrapping” into multiple parts and each part focuses on one concept and then doing information bootstrapping or conceptual pathfinding on those parts. I don’t think there is any real difference between “conceptual pathfinding” and “information/material bootstrapping”.
Thank you for making me the recipient of your first LessWrong comment!
First, a response to your concrete question.
An example of what I regard as “bootstrapping” is a class that entails rederiving calculus from a small set of starting axioms. In case you didn’t know, this is a real thing that people do, including some here on LessWrong.
On the opposite extreme might be the act of memorizing a proof. I am not talking about empty memorization, where you can recite the words but don’t understand what they mean. Instead, I mean that as you rehearse the steps in the proof, you come to understand the proof, and at the end, you also have it memorized.
To me, “conceptual pathfinding” is an intermediate between these two.
Let’s say you were trying to understand what a t test is in statistics. To start with, it’s just words on the page, maybe a fuzzy mental picture of a bell curve, the idea of a comparison or of significance, the memory that you don’t know the “real” standard deviation.
You might start by saying something like, “a t test is a way of checking if there’s really a difference between two groups. There’s a t value and a p value… and if the p value is low enough, then the test is significant!”
Obviously, that’s an inadequate understanding, but it starts you going in the right direction. Based on your performance, you can then self-reflect and make additional comments or ask questions. You might think thoughts like “OK, and that’s what alpha is—a way of saying whether the p value is “low enough” for the test to be significant.” Or you might say, “how do we calculate a t value?” Or you might notice, “it’s important that all the data points are numeric for a t test.” Or you might say, “a t test assumes we’re dealing with roughly Normally distributed data.”
And then you might start over, saying something like “a t test models numeric data as coming from a Normal distribution, and asks whether two samples are significantly different. We choose an alpha value to say what our signficance threshold is, and then calculate a t value, which we use to get a p vlaue, and then compare it with the alpha value to decide if the test is significant or not.”
Again, still inadequate, but displaying a maturing understanding. And you can just keep repeating this process, looking up individual facts when you need to, until you’re satisfied. For me, this sort of process keeps me engaged. When I look up individual facts, I feel like I’m fitting them like a puzzle piece into a puzzle.
Responding to your point of view
If I’m understanding you correctly, you seem to think that what I’m calling “bootstrapping” is still what’s fundamentally going on in the above—that there’s no real difference between, say, rederiving calculus from first principles and going from one’s hazy impressions of the t test to iteratively building a more full and precise articulation of it. That may be true. There’s probably a lot of what I’m calling “conceptual pathfinding” that would go into an effort to rederive calculus—it’s just the scale of the challenge that’s different.
My underlying motivation here is that sometimes, when people are confused about topic X, advice is given that if they’d just commit to understanding topic X from first principles, rather than trying to learn it in the typical college textbook format, that they wouldn’t be so confused.
And in the struggle to learn, I have also found myself gravitating toward the very actionable, but not very helpful or meaningful activity of just trying to memorize stuff to make the ideas go in.
The point of this post is to articulate what I do find helpful. It may not be very good as a crisp formalization, but I stand by it as practical learning advice for people with brains like mine.
I don’t find much use in defining conceptual pathfinding as local information bootstrapping since you mentioned only the scale of the challenge is different. What I often experience is that studying one concept always lead to me studying another concept since it depends on other concepts. This means that I am going to end up deriving all of calculus as long as I have the time and will. And that implies that given enough time and will, a single conceptual pathfinding turns into a global information bootstrapping (a very holistic understanding).
Basically, what I found useful about this post were:
-The concept of bootstrapping
What I don’t like:
-Algorithm does not state how to manage the information that will come out of information bootstrapping.
Thanks for the feedback, Duck Duck.
What I liked about your comments:
You clearly read and thought about my post
You honestly expressed your own experience, including disagreement, in enough depth to promote a discussion
What I didn’t like:
Sharp tone (“pointless” categorization)
Complaining (“Algorithm does not state how to manage the information that will come out of information bootstrapping,” “I don’t think there is any real difference between “conceptual pathfinding” and “information/material bootstrapping”)