This weekly roundup thread is intended for all culture war posts. 'Culture war' is vaguely defined, but it basically means controversial issues that fall along set tribal lines. Arguments over culture war issues generate a lot of heat and little light, and few deeply entrenched people ever change their minds. This thread is for voicing opinions and analyzing the state of the discussion while trying to optimize for light over heat.
Optimistically, we think that engaging with people you disagree with is worth your time, and so is being nice! Pessimistically, there are many dynamics that can lead discussions on Culture War topics to become unproductive. There's a human tendency to divide along tribal lines, praising your ingroup and vilifying your outgroup - and if you think you find it easy to criticize your ingroup, then it may be that your outgroup is not who you think it is. Extremists with opposing positions can feed off each other, highlighting each other's worst points to justify their own angry rhetoric, which becomes in turn a new example of bad behavior for the other side to highlight.
We would like to avoid these negative dynamics. Accordingly, we ask that you do not use this thread for waging the Culture War. Examples of waging the Culture War:
-
Shaming.
-
Attempting to 'build consensus' or enforce ideological conformity.
-
Making sweeping generalizations to vilify a group you dislike.
-
Recruiting for a cause.
-
Posting links that could be summarized as 'Boo outgroup!' Basically, if your content is 'Can you believe what Those People did this week?' then you should either refrain from posting, or do some very patient work to contextualize and/or steel-man the relevant viewpoint.
In general, you should argue to understand, not to win. This thread is not territory to be claimed by one group or another; indeed, the aim is to have many different viewpoints represented here. Thus, we also ask that you follow some guidelines:
-
Speak plainly. Avoid sarcasm and mockery. When disagreeing with someone, state your objections explicitly.
-
Be as precise and charitable as you can. Don't paraphrase unflatteringly.
-
Don't imply that someone said something they did not say, even if you think it follows from what they said.
-
Write like everyone is reading and you want them to be included in the discussion.
On an ad hoc basis, the mods will try to compile a list of the best posts/comments from the previous week, posted in Quality Contribution threads and archived at /r/TheThread. You may nominate a comment for this list by clicking on 'report' at the bottom of the post and typing 'Actually a quality contribution' as the report reason.
Jump in the discussion.
No email address required.
Notes -
I agree with all of this except the jab at “slow but deep thinkers”. I think that with regard to mathematical talent specifically, there really is a pool of talented/high-IQ individuals who punch below their weight in math competitions where speed is important, like the AMC and AIME. This is a shame, because the USAMO and IMO are much more “slow but deep”-loaded, but you can’t qualify for them unless you get past the AIME. The USAMTS (a proof-based exam taken over the course of multiple weeks) helps alleviate this disadvantage somewhat, but it still only helps you skip the AMC level; I wish there were a second round of USAMTS for skipping the AIME and advancing to USAMO.
To be completely fair, I think the absolute cream of the crop in mathematical talent are both fast and deep, and hence the current system of contests will correctly identify them. We are certainly not at risk of being unable to field a competitive IMO team, or of failing to identify those who are most likely to become HYPSM math faculty in a decade or so.
But the “second string” of talent tends to be underserved until their strengths shine through in late undergrad/early grad school—assuming they stick with math that long, which sadly many don’t because they incorrectly think (on the basis of math contests) that they’re not good enough for graduate-level math research.
The specific mechanism by which being “deep” helps with research is having a holistic understanding of how different concepts in math relate to one another, and having a greater ability to perceive similarities/analogies between disparate things, which is important when bringing techniques from vastly different subfields of mathematics to bear on unsolved problems; this happens all the time in number theory, for instance, and it’s also what Grothendieck did when he revolutionized algebraic geometry. See also: the Langlands program.
“Fast but shallow” thinkers, on the other hand, are good at quickly pattern-matching problems to known solution techniques, which is also important: you won’t get anywhere in math without a well-developed, organized, and quickly-accessible stock of knowledge in your noodle. But they tend to be unable to generalize/extend/apply those techniques to very different domains.
Full disclosure: I was a “slow but deep” thinker with regard to math when I was in school and I may be just a little bit salty about my lackluster performance in time-constrained math contests.
This brings back bad memories.
Full disclosure: I've always been a "fast but relatively superficial" thinker with regards to basically everything. As you can expect I did very well at Olympiads until the questions got to about IMO level, and yes my performance was better in earlier years of undergrad vs later (though still extremely good even in the later years).
More options
Context Copy link
More options
Context Copy link