Try this thought experiment: suppose you were a graduate student in mathematics, and went to your advisor and said: “I’d like to solve [Famous Problem X], and to start, I’m going to spend two years closely examining the work of Newton, Gauss, and Wiles, and their contemporaries, to try to discern at a higher level of generality what the cognitive stumbling blocks to solving previous problems were, and how they overcame them, and distill these meta-level insights into a meta-level technique of my own which I’ll then apply to [Famous Problem X].”
This is a terrible idea unless they’re spending half their time pushing their limits on object-level math problems. I just don’t think it works to try to do a meta phase before an object phase unless the process is very, very well-understood and tested already.
I’m sure that’s exactly what the advisor would say (if they bother to give a reasoned reply at all), with the result that nobody ever tries this.
(I’ll also note that it’s somewhat odd to hear this response from someone whose entire mission in life is essentially to go meta on all of humanity’s problems...)
But let me address the point, so as not to be logically rude. The person would be pushing their limits on object-level math problems in the course of “examining the work of Newton, Gauss, and Wiles”, in order to understand said work; otherwise, it can hardly be said to constitute a meaningful examination. I also think it’s important not to confuse meta-ness with (nontechnical) “outside views”; indeed I suspect that a lot of the thought processes of mathematical “geniuses” consist of abstracting over classes of technical concepts that aren’t ordinarily abstracted over, and thus if expressed explicitly (which the geniuses may lack the patience to do) would simply look like another form of mathematics. (Others of their processes, I speculate, consist in obsessive exercising of visual/dynamic mental models of various abstractions.)
Switching back to logical rudeness, I’m not sure the meta-ness is your true rejection; I suspect what you may be really worried about is making sure there are tight feedback loops to which one’s reasoning can be subjected.
(I’ll also note that it’s somewhat odd to hear this response from someone whose entire mission in life is essentially to go meta on all of humanity’s problems...)
That’s not the kind of meta I mean. The dangerous form of meta is when you spend several years preparing to do X, supposedly becoming better at doing X, but not actually doing X, and then try to do X. E.g. college. Trying to improve at doing X while doing X is much, much wiser. I would similarly advise Effective Altruists who are not literally broke to be donating $10 every three months to something while they are trying to increase their incomes and invest in human capital; furthermore, they should not donate to the same thing two seasons in a row, so that they are also practicing the skill of repeatedly assessing which charity is most important.
“Meta” for these purposes is any daily activity which is unlike the daily activity you intend to do ‘later’.
Tight feedback loops are good, but not always available. This is a separate consideration from doing meta while doing object.
The activity of understanding someone else’s proofs may be unlike the activity of producing your own new math from scratch; this would be the problem.
I would similarly advise Effective Altruists who are not literally broke to be donating $10 every three months to something while they are trying to increase their incomes and invest in human capital; furthermore, they should not donate to the same thing two seasons in a row, so that they are also practicing the skill of repeatedly assessing which charity is most important.
This is excellent advice. I have put a note in my calendar thee months hence to reevaluate my small monthly donation.
This is a terrible idea unless they’re spending half their time pushing their limits on object-level math problems. I just don’t think it works to try to do a meta phase before an object phase unless the process is very, very well-understood and tested already.
I’m sure that’s exactly what the advisor would say (if they bother to give a reasoned reply at all), with the result that nobody ever tries this.
(I’ll also note that it’s somewhat odd to hear this response from someone whose entire mission in life is essentially to go meta on all of humanity’s problems...)
But let me address the point, so as not to be logically rude. The person would be pushing their limits on object-level math problems in the course of “examining the work of Newton, Gauss, and Wiles”, in order to understand said work; otherwise, it can hardly be said to constitute a meaningful examination. I also think it’s important not to confuse meta-ness with (nontechnical) “outside views”; indeed I suspect that a lot of the thought processes of mathematical “geniuses” consist of abstracting over classes of technical concepts that aren’t ordinarily abstracted over, and thus if expressed explicitly (which the geniuses may lack the patience to do) would simply look like another form of mathematics. (Others of their processes, I speculate, consist in obsessive exercising of visual/dynamic mental models of various abstractions.)
Switching back to logical rudeness, I’m not sure the meta-ness is your true rejection; I suspect what you may be really worried about is making sure there are tight feedback loops to which one’s reasoning can be subjected.
That’s not the kind of meta I mean. The dangerous form of meta is when you spend several years preparing to do X, supposedly becoming better at doing X, but not actually doing X, and then try to do X. E.g. college. Trying to improve at doing X while doing X is much, much wiser. I would similarly advise Effective Altruists who are not literally broke to be donating $10 every three months to something while they are trying to increase their incomes and invest in human capital; furthermore, they should not donate to the same thing two seasons in a row, so that they are also practicing the skill of repeatedly assessing which charity is most important.
“Meta” for these purposes is any daily activity which is unlike the daily activity you intend to do ‘later’.
Tight feedback loops are good, but not always available. This is a separate consideration from doing meta while doing object.
The activity of understanding someone else’s proofs may be unlike the activity of producing your own new math from scratch; this would be the problem.
This is excellent advice. I have put a note in my calendar thee months hence to reevaluate my small monthly donation.