- #1
Jarvis323
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If a person wants to learn about a topic that has prerequisite knowledge, there are two ways they could proceed. (1) They could identify the subjects of the prerequisite knowledge and study those subjects broadly, working their way up through a traditional educational path (e.g. work through a series of courses or textbooks). (2) They could try to narrowly learn only the prerequisite knowledge while skipping the content of those subjects which are not relevant.
I have been thinking about the second way, which I am calling selective learning through backwards traversal.
The reason I think this is important is that the body of human knowledge is increasing further and further beyond people's ability to digest, pursuits of new knowledge are becoming more and more specialized/niche and reliant on new/or diverse methods and previous results, and in general, the potential prerequisite knowledge for understanding a given piece of knowledge is increasing. More and more, people will find themselves in the position where they have to backtrack in order to understand something.
Even if one is working in their own field (and they've taken the general education requirements), they might still find themselves in such a situation. For example, a mathematician or a physicist may hear about a breakthrough in theoretical computer science, such as the discovery that MIP* = RE.
https://phys.org/news/2020-08-major-quantum-breakthrough-physics-maths.html
But MIP* = RE is not something that even if a bachelors (or maybe graduate degree) in computer science would provide. In fact, you could take a full series of theory courses in computational complexity (undergraduate and graduate level), and still come up short. And those theory courses will include lots of subtopics that aren't directly relevant. So, I think, someone flocking to the complexity zoo will either have to invest several years learning the broad foundational subjects, or they'll have to attempt backwards propagation. Theoretical computer scientists will also probably need to learn the physics before they can understand it. Actually, it's niche enough and advanced enough research level work, so I think most computer scientists will even need to backtrack to understand even the complexity theory parts.
In my experience, often when I find I need to backtrack, I find myself in a very arduous situation, trying to navigate a complex graph of knowledge, fairly blindly, as if I were trying to solve a complex puzzle with lots of small clues. Alternatively, I could work my way up from the bottom, but that could take years.
The solution I think, is that people should eventually have sophisticated systems which guide you, e.g. by deducing a feasible path to understanding a given piece of knowledge. I imagine this must be an active area of research. But it would also require some infrastructure. For example, people would need to probably manually go through our body of knowledge, and narrowly identify all of the dependencies. Is this something people are already working on? Is it even possible? It seems like something that could be open sourced, like Wikipedia. It's also possible that research journals in the future could require the authors to carefully map out the prerequisites to understanding their paper using this kind of sophisticated guidance system.
I have been thinking about the second way, which I am calling selective learning through backwards traversal.
The reason I think this is important is that the body of human knowledge is increasing further and further beyond people's ability to digest, pursuits of new knowledge are becoming more and more specialized/niche and reliant on new/or diverse methods and previous results, and in general, the potential prerequisite knowledge for understanding a given piece of knowledge is increasing. More and more, people will find themselves in the position where they have to backtrack in order to understand something.
Even if one is working in their own field (and they've taken the general education requirements), they might still find themselves in such a situation. For example, a mathematician or a physicist may hear about a breakthrough in theoretical computer science, such as the discovery that MIP* = RE.
https://phys.org/news/2020-08-major-quantum-breakthrough-physics-maths.html
But MIP* = RE is not something that even if a bachelors (or maybe graduate degree) in computer science would provide. In fact, you could take a full series of theory courses in computational complexity (undergraduate and graduate level), and still come up short. And those theory courses will include lots of subtopics that aren't directly relevant. So, I think, someone flocking to the complexity zoo will either have to invest several years learning the broad foundational subjects, or they'll have to attempt backwards propagation. Theoretical computer scientists will also probably need to learn the physics before they can understand it. Actually, it's niche enough and advanced enough research level work, so I think most computer scientists will even need to backtrack to understand even the complexity theory parts.
In my experience, often when I find I need to backtrack, I find myself in a very arduous situation, trying to navigate a complex graph of knowledge, fairly blindly, as if I were trying to solve a complex puzzle with lots of small clues. Alternatively, I could work my way up from the bottom, but that could take years.
The solution I think, is that people should eventually have sophisticated systems which guide you, e.g. by deducing a feasible path to understanding a given piece of knowledge. I imagine this must be an active area of research. But it would also require some infrastructure. For example, people would need to probably manually go through our body of knowledge, and narrowly identify all of the dependencies. Is this something people are already working on? Is it even possible? It seems like something that could be open sourced, like Wikipedia. It's also possible that research journals in the future could require the authors to carefully map out the prerequisites to understanding their paper using this kind of sophisticated guidance system.
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