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Vladimir_Nesov comments on Less Wrong Book Club and Study Group - Less Wrong
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I thought so as well, for many years, and it cost me dearly. The problem with math is that the more elementary tools won't be even mentioned in advanced specialized books, and are not necessary to parse them. The only efficient way to obtain them is to study from the ground up. Until recently, I was getting along on ability to parse more advanced texts relatively fine, but remained much weaker and near-sighted than I could have been. This made much of my previous study a waste of time, only moderately helping me to recapture the territory now.
I think one should learn on different levels at the same time:
If you only do what's convenient, your progress stops.
If you don't revisit the basics from time to time, you build on sand.
It is necessary to challenge oneself and at the same time work on the fundamentals. It is both inspiring and necessary to strike the right balance between the two extremes: A constant back and forth between them proved to be both the most productive and most entertaining for me personally.
This is the reason I am also interested in this study group: For me, it is revisiting the fundamentals. Although this book is relatively basic, it is very well written and focuses more on the right philosophy than the actual pragmatic issues. On the other hand, it is very detailed at places that other books easily take for granted and points out issues that other just step over. It is really a great reading to deepen one's knowledge. I am unsure though, whether it is the best introductory reading for someone who just wants to acquire a practical skill set.
This should be engraved somewhere in big letters.