Sorry to harp on it again, but to enjoy real analysis one does require a fair amount of math aptitude,
Is there a reason why you keep bringing up this subject? I’m not complaining – I just want to know whether there’s a point that you’ve been trying to make that I’ve been missing.
In my present post I was advocating learning real analysis for the sake of getting into the habit of reasoning carefully, not for enjoyment.I think that a large fraction of LWers have the mathematical aptitude required to find it tolerable, even if not exciting. I usually don’t advocate people learning things that they don’t find especially interesting, but in this particular case, the skill is so important that I think it might be worth it – I see it as analogous to literacy.
Naturally it depends on the other alternatives on the table, and how far one wants to go. But I do know several people who report that learning the subject changed how they think in general, not only in the context of math.
I would have to add another point on the anecdotal side for this. I made it through Real Analysis (barely!) when I was a math major—and it made a significant difference on the thought process I go through when I consider things. If nothing else, it was very instrumental in breaking the “good rhetoric = good argument” connection I’d been operating under up until that point. And this was long before I’d any notion that places like CFAR or LW even existed.
(I will disclaimer that it also made certain kinds of communication more difficult—because most folks don’t like it when you try to make their opinions rigorous—but that could as easily be from how I implemented those ideas as from the change in thinking itself. )
Is there a reason why you keep bringing up this subject? I’m not complaining – I just want to know whether there’s a point that you’ve been trying to make that I’ve been missing.
In my present post I was advocating learning real analysis for the sake of getting into the habit of reasoning carefully, not for enjoyment.I think that a large fraction of LWers have the mathematical aptitude required to find it tolerable, even if not exciting. I usually don’t advocate people learning things that they don’t find especially interesting, but in this particular case, the skill is so important that I think it might be worth it – I see it as analogous to literacy.
I am not sure the cost-benefit analysis is favorable, in particular for people who do not intend to become professional mathematicians.
Naturally it depends on the other alternatives on the table, and how far one wants to go. But I do know several people who report that learning the subject changed how they think in general, not only in the context of math.
I would have to add another point on the anecdotal side for this. I made it through Real Analysis (barely!) when I was a math major—and it made a significant difference on the thought process I go through when I consider things. If nothing else, it was very instrumental in breaking the “good rhetoric = good argument” connection I’d been operating under up until that point. And this was long before I’d any notion that places like CFAR or LW even existed.
(I will disclaimer that it also made certain kinds of communication more difficult—because most folks don’t like it when you try to make their opinions rigorous—but that could as easily be from how I implemented those ideas as from the change in thinking itself. )