7 ms·

Fractal Learning

78 points by reisub0 6y ago

HuShifang 6y ago
This is nicely put. It reminds me a bit of David Perkins's [0] "whole ballgame" approach (i.e. the best way to learn how to play baseball is to play a few games or approximations thereof, e.g. tee-ball; you'll struggle mightily at first, but you'll ultimately benefit by having a sense of how the game as a whole works, and it provides valuable context and motivation for subsequently working on specific skills like throwing the ball, swinging the bat, etc. And the ultimate result is greater mastery than if you had started from the skills and worked your way up to playing the game piecewise.) Fast.ai's pedagogy is based in part on this principle, and (as someone inclined to go down rabbit holes) it's been a huge help to me as I go through the course and book. [1] I'd add too, recently released personal knowledge base apps (Obsidian, Roam, et al) are very well suited to fractal learning. I partition my notes into content (summaries) and concepts (with some Zettelkasten-style ephemeral notes mixed in). When I come across new concepts, I create a stub; then I fill it in when necessary with the necessary degree of detail, adding new details, revising, and forcing myself to make my account of it coherent as I encounter different facets of the concept in different books, articles, etc. [0]: http://www.pz.harvard.edu/resources/making-learning-whole-how-seven-principles-of-teaching-can-transform-education http://www.pz.harvard.edu/resources/making-learning-whole-ho... [1]: http://course.fast.ai/ http://course.fast.ai/
- calebkaiser 6y ago
  I second everything in this. I recently switched my note taking to be organized around concept "hubs" with Zettelkasten-esque linking between them, and it's maybe the biggest improvement I've made in terms of organizing my learning. I sometimes cover material a bit slower, but I rarely have a single session now where I don't have some kind of aha moment. This is a direct product of having to explain what I'm learning in order to fit it into my system, a la the Feynman technique.
nendroid 6y ago
This isn't really a learning technique. It's an analogy on learning. Every other day there's some blog post on HN about some analogy on some self improvement topic like learning, project management or complexity or whatever... I'll tell you what learning isn't. Learning isn't coming up with new analogies for concepts you already completely understand over and over again. I and pretty much everyone on this planet already knows what learning is, and unless you have a new learning technique, what is the point of comparing learning to a fractal? There's nothing new here. I'm not trying to reprimand what this person wrote this but when you see some flavor of this on HN all the time it gets old.
- jlelonm 6y ago
  > Learning isn't coming up with new analogies for concepts you already completely understand over and over again. You completely understand learning? :)
  - nendroid 6y ago
    :) A better phrase is "Learning isn't coming up with new analogies for concepts you already more or less understand over and over again." Happy? does that satisfy your overly pedantic mind?
    - jlelonm 6y ago
      You missed my point (and the author’s it appears). You’re claiming to understand learning. People do phds in learning from multiple domains (psych, neuro, ux, etc). You already know it all? The rabbit hole is deep. Coming in here and saying yeah yeah we all get it already is a sign that you don’t.
      - nendroid 6y ago
        No. You missed the point. You're not a stupid person so you being not stupid knows that I and pretty much everyone on the face of this earth knows that we all are aware that no one understands ALL of learning. So if you're not stupid, and you already know this, why did you take the time to point out some pointless flaw in my wording? I'll tell you why. Because you liked this analogy. You thought it was profound to compare learning to DFS and BFS and fractals and you were sort of offended when someone like me didn't find it profound. Not only do I not find it profound, I find it obvious and trivial. Comparing learning to fractals is like some offhand thought I can have for like 5 seconds than forget about because it's so trivial. Too each his own man. If this article blew your mind great. It didn't do anything for me. Here's another analogy for you. Learning is like traveling down a path and encountering a several forks in the road. You can BFS the paths or you can DFS the paths Replace Learning with "Life" and remove BFS. In life you can only choose one path every time you encounter a fork and the decision is permanent. No popping the stack like in BFS to try the other paths. It's just DFS all the way to the last final leaf node. You have one life so live it right. Did that analogy blow your mind? Because I made it up 3 seconds ago. That's how trivial these analogies are.
galaxyLogic 6y ago
This doesn't sound very practical advice to me. It seems to be saying: Do a bit of breadth-first mixed with some depth-first. But whatever you do don't do only depth-first. But maybe that is an important point. Don't dig too much into details try to get the overall picture so you can decide what you should focus on most.
- taneq 6y ago
  That sounds pretty reasonable to me. You don't want to dive straight into depth-first because then you disappear down a rabbit hole with no context to tell you whether it's the right rabbit hole. Start out with breadth-first until you have a feel for the lay of the land, then pick a direction to journey in.
  - galaxyLogic 6y ago
    Right that sounds very reasonable. My issue is that it is so reasonable that it is not a great insight worthy of an article. It is good but quite basic advice. It also must be dependent on the topic under examination largely therefore the advice can only very generic. Let's think about an example topic, say "Mathematics". What would be the best strategy for learning mathematics?
- webmaven 6y ago
  > This doesn't sound very practical advice to me. It seems to be saying: Do a bit of breadth-first mixed with some depth-first. But whatever you do don't do only depth-first. It seems to be saying that to me too. Given the tree and maze visualizations, I'm a bit surprised that there was no corresponding visualization of the recommended strategy of switching back and forth between depth-first and breadth-first search (at regular or perhaps random intervals). Regarding the optimality of various strategies, there is a distinction to be made between the optimal strategy for an individual learner/searcher, and the optimal individual strategy for searching collectively. Also, there is a difference between strategies for acquiring existing knowledge that is new to you, vs. expanding the boundary of existing knowledge. Regarding the "expanding the boundary of knowledge collectively" problem space specifically, it is worth noting that a pure depth-first approach isn't really possible in practice. Even in fields that reward depth-first individual search strategies such as math, an individual searcher's search is bounded by the length of their career, and each new searcher starts semi-randomly somewhere along the then-current boundary of collective knowledge.
orbifold 6y ago
The starkest example to me of breadth first vs depth first learning are math geniuses. They typically ignore everything except mathematics to begin with and then hyper focus on a specific area of mathematics intensely. The most striking I know of is Peter Schulze who basically never attended an undergraduate class in mathematics and picked up Linear Algebra while he worked out the requirements to understand the Langlands Conjecture. He got awarded his bachelor by doing a 6 hour exam when he entered University.
- yeellow 6y ago
  > He got awarded his bachelor by doing a 6 hour exam when he entered University. I wanted to read more about that (I like such stories) but I couldn't find that story online. On Wikipedia it says that bachelor took him 3 semesters. Does anyone have the source?
  - orbifold 6y ago
    I might misremember it slightly, I got told this by a professor (he was one of his examiners) and people that knew him at Bonn in ~2010. He could also have been awarded the majority of the credit points towards the Bachelor at entrance.
- orbifold 6y ago
  It should be "Scholze" of course.
agumonkey 6y ago
There's a quantum aspect to learning, if your learn speckles of everything, your 'energy' level doesn't go up. If you go breadth first, you have to cross some pragmatic, practical, real newness barriers, keep that in mind.
jlelonm 6y ago
Oh my goodness, you literally wrote the ideas I was thinking about from a learning perspective. I wrote about very similar things from a teaching perspective here: https://lelon.io/blog/how-to-teach-math https://lelon.io/blog/how-to-teach-math In fact, I've thought a lot about how to generalize these techniques to a data structure (i.e. knowledge graph) so that anyone can zoom in or out to whatever level of abstraction they please: https://lelon.io/blog/boosting-scientific-productivity-again https://lelon.io/blog/boosting-scientific-productivity-again Would love to chat sometime!
brenschluss 6y ago
A large mistake this article makes is assuming that knowledge is forking, like a tree. Instead, knowledge is a graph. Or even a map.

78 points by reisub0 6y ago

This is nicely put. It reminds me a bit of David Perkins's [0] "whole ballgame" approach (i.e. the best way to learn how to play baseball is to play a few games or approximations thereof, e.g. tee-ball; you'll struggle mightily at first, but you'll ultimately benefit by having a sense of how the game as a whole works, and it provides valuable context and motivation for subsequently working on specific skills like throwing the ball, swinging the bat, etc. And the ultimate result is greater mastery than if you had started from the skills and worked your way up to playing the game piecewise.) Fast.ai's pedagogy is based in part on this principle, and (as someone inclined to go down rabbit holes) it's been a huge help to me as I go through the course and book. [1] I'd add too, recently released personal knowledge base apps (Obsidian, Roam, et al) are very well suited to fractal learning. I partition my notes into content (summaries) and concepts (with some Zettelkasten-style ephemeral notes mixed in). When I come across new concepts, I create a stub; then I fill it in when necessary with the necessary degree of detail, adding new details, revising, and forcing myself to make my account of it coherent as I encounter different facets of the concept in different books, articles, etc. [0]: http://www.pz.harvard.edu/resources/making-learning-whole-how-seven-principles-of-teaching-can-transform-education http://www.pz.harvard.edu/resources/making-learning-whole-ho... [1]: http://course.fast.ai/ http://course.fast.ai/

calebkaiser 6y ago
I second everything in this. I recently switched my note taking to be organized around concept "hubs" with Zettelkasten-esque linking between them, and it's maybe the biggest improvement I've made in terms of organizing my learning. I sometimes cover material a bit slower, but I rarely have a single session now where I don't have some kind of aha moment. This is a direct product of having to explain what I'm learning in order to fit it into my system, a la the Feynman technique.

nendroid 6y ago

This isn't really a learning technique. It's an analogy on learning. Every other day there's some blog post on HN about some analogy on some self improvement topic like learning, project management or complexity or whatever... I'll tell you what learning isn't. Learning isn't coming up with new analogies for concepts you already completely understand over and over again. I and pretty much everyone on this planet already knows what learning is, and unless you have a new learning technique, what is the point of comparing learning to a fractal? There's nothing new here. I'm not trying to reprimand what this person wrote this but when you see some flavor of this on HN all the time it gets old.

jlelonm 6y ago
> Learning isn't coming up with new analogies for concepts you already completely understand over and over again. You completely understand learning? :)
- nendroid 6y ago
  :) A better phrase is "Learning isn't coming up with new analogies for concepts you already more or less understand over and over again." Happy? does that satisfy your overly pedantic mind?
  - jlelonm 6y ago
    You missed my point (and the author’s it appears). You’re claiming to understand learning. People do phds in learning from multiple domains (psych, neuro, ux, etc). You already know it all? The rabbit hole is deep. Coming in here and saying yeah yeah we all get it already is a sign that you don’t.
    - nendroid 6y ago
      No. You missed the point. You're not a stupid person so you being not stupid knows that I and pretty much everyone on the face of this earth knows that we all are aware that no one understands ALL of learning. So if you're not stupid, and you already know this, why did you take the time to point out some pointless flaw in my wording? I'll tell you why. Because you liked this analogy. You thought it was profound to compare learning to DFS and BFS and fractals and you were sort of offended when someone like me didn't find it profound. Not only do I not find it profound, I find it obvious and trivial. Comparing learning to fractals is like some offhand thought I can have for like 5 seconds than forget about because it's so trivial. Too each his own man. If this article blew your mind great. It didn't do anything for me. Here's another analogy for you. Learning is like traveling down a path and encountering a several forks in the road. You can BFS the paths or you can DFS the paths Replace Learning with "Life" and remove BFS. In life you can only choose one path every time you encounter a fork and the decision is permanent. No popping the stack like in BFS to try the other paths. It's just DFS all the way to the last final leaf node. You have one life so live it right. Did that analogy blow your mind? Because I made it up 3 seconds ago. That's how trivial these analogies are.

galaxyLogic 6y ago

This doesn't sound very practical advice to me. It seems to be saying: Do a bit of breadth-first mixed with some depth-first. But whatever you do don't do only depth-first. But maybe that is an important point. Don't dig too much into details try to get the overall picture so you can decide what you should focus on most.

taneq 6y ago
That sounds pretty reasonable to me. You don't want to dive straight into depth-first because then you disappear down a rabbit hole with no context to tell you whether it's the right rabbit hole. Start out with breadth-first until you have a feel for the lay of the land, then pick a direction to journey in.
- galaxyLogic 6y ago
  Right that sounds very reasonable. My issue is that it is so reasonable that it is not a great insight worthy of an article. It is good but quite basic advice. It also must be dependent on the topic under examination largely therefore the advice can only very generic. Let's think about an example topic, say "Mathematics". What would be the best strategy for learning mathematics?
webmaven 6y ago
> This doesn't sound very practical advice to me. It seems to be saying: Do a bit of breadth-first mixed with some depth-first. But whatever you do don't do only depth-first. It seems to be saying that to me too. Given the tree and maze visualizations, I'm a bit surprised that there was no corresponding visualization of the recommended strategy of switching back and forth between depth-first and breadth-first search (at regular or perhaps random intervals). Regarding the optimality of various strategies, there is a distinction to be made between the optimal strategy for an individual learner/searcher, and the optimal individual strategy for searching collectively. Also, there is a difference between strategies for acquiring existing knowledge that is new to you, vs. expanding the boundary of existing knowledge. Regarding the "expanding the boundary of knowledge collectively" problem space specifically, it is worth noting that a pure depth-first approach isn't really possible in practice. Even in fields that reward depth-first individual search strategies such as math, an individual searcher's search is bounded by the length of their career, and each new searcher starts semi-randomly somewhere along the then-current boundary of collective knowledge.

orbifold 6y ago

The starkest example to me of breadth first vs depth first learning are math geniuses. They typically ignore everything except mathematics to begin with and then hyper focus on a specific area of mathematics intensely. The most striking I know of is Peter Schulze who basically never attended an undergraduate class in mathematics and picked up Linear Algebra while he worked out the requirements to understand the Langlands Conjecture. He got awarded his bachelor by doing a 6 hour exam when he entered University.

yeellow 6y ago
> He got awarded his bachelor by doing a 6 hour exam when he entered University. I wanted to read more about that (I like such stories) but I couldn't find that story online. On Wikipedia it says that bachelor took him 3 semesters. Does anyone have the source?
- orbifold 6y ago
  I might misremember it slightly, I got told this by a professor (he was one of his examiners) and people that knew him at Bonn in ~2010. He could also have been awarded the majority of the credit points towards the Bachelor at entrance.
orbifold 6y ago
It should be "Scholze" of course.

agumonkey 6y ago

There's a quantum aspect to learning, if your learn speckles of everything, your 'energy' level doesn't go up. If you go breadth first, you have to cross some pragmatic, practical, real newness barriers, keep that in mind.

jlelonm 6y ago

Oh my goodness, you literally wrote the ideas I was thinking about from a learning perspective. I wrote about very similar things from a teaching perspective here: https://lelon.io/blog/how-to-teach-math https://lelon.io/blog/how-to-teach-math In fact, I've thought a lot about how to generalize these techniques to a data structure (i.e. knowledge graph) so that anyone can zoom in or out to whatever level of abstraction they please: https://lelon.io/blog/boosting-scientific-productivity-again https://lelon.io/blog/boosting-scientific-productivity-again Would love to chat sometime!

brenschluss 6y ago

A large mistake this article makes is assuming that knowledge is forking, like a tree. Instead, knowledge is a graph. Or even a map.