I don’t have direct exposure to CS academia, which, as you comment, is known to be healthier :-). I was speaking in broad brushstrokes , I’ll qualify my claims and impressions more carefully later.
JonahS
Karma: 3,494
I’ll be writing more about this later.
The most scary thing to me is that the most mathematically talented students are often turned off by what they see in math classes, even at the undergraduate and graduate levels. Math serves as a backbone for the sciences, so this may badly undercutting scientific innovation at a societal level.
I honestly think that it would be an improvement on the status quo to stop teaching math classes entirely. Thurston characterized his early math education as follows:
I hated much of what was taught as mathematics in my early schooling, and I often received poor grades. I now view many of these early lessons as anti-math: they actively tried to discourage independent thought. One was supposed to follow an established pattern with mechanical precision, put answers inside boxes, and “show your work,” that is, reject mental insights and alternative approaches.
I think that this characterizes math classes even at the graduate level, only at a higher level of abstraction. The classes essentially never offer students exposure to free-form mathematical exploration, which is what it takes to make major scientific discoveries with significant quantitative components.
Yes, this seems like a fair assessment o the situation. Thanks for disentangling the issues. I’ll be more precise in the future.
I’m speaking based on many interactions with many members of the community. I don’t think this is true of everybody, but I have seen a difference at the group level.
Do people pathologize Grothendieck as having gone crazy?
His contribution of math is too great for people to have explicitly adopted a stance that was too unfavorable to him, and many mathematicians did in fact miss him a lot. But as Perelman said:
Of course, there are many mathematicians who are more or less honest. But almost all of them are conformists. They are more or less honest, but they tolerate those who are not honest.” He has also said that “It is not people who break ethical standards who are regarded as aliens. It is people like me who are isolated.
If pressed, many mathematicians downplay the role of those who behaved unethically toward him and the failure of the community to give him a job in favor of a narrative “poor guy, it’s so sad that he developed mental health problems.”
The top 3 answers to the MathOverflow question Which mathematicians have influenced you the most? are Alexander Grothendieck, Mikhail Gromov, and Bill Thurston. Each of these have expressed serious concerns about the community.
Grothendieck was actually effectively excommunicated by the mathematical community and then was pathologized as having gone crazy. See pages 37-40 of David Ruelle’s book A Mathematician’s Brain.
Gromov expresses strong sympathy for Grigory Perelman having left the mathematical community starting on page 110 of Perfect Rigor. (You can search for “Gromov” in the pdf to see all of his remarks on the subject.)
Thurston made very apt criticisms of the mathematical community in his essay On Proof and Progress In Mathematics. See especially the beginning of Section 3: “How is mathematical understanding communicated?” Terry Tao endorses Thurston’s essay in his obituary of Thurston. But the community has essentially ignored Thurston’s remarks: one almost never hears people talk about the points that Thurston raises.
I’m not claiming otherwise: I’m merely saying that Paul and Jacob don’t dismiss LWers out of hand as obviously crazy, and have in fact found the community to be worthwhile enough to have participated substantially.
One of the things I find most charming about LW, compared to places like RationalWiki, is how much emphasis there is on self-improvement and your mistakes, not mistakes made by other people because they’re dumb.
I agree that LW is much better than RationalWiki, but I still think that the norms for discussion are much too far in the direction of focus on how other commenters are wrong as opposed to how one might oneself be wrong.
I know that there’s a selection effect (with respect to the more frustrating interactions standing out). But people not infrequently mistakenly believe that I’m wrong about things that I know much more about than they do, with very high confidence, and in such instances I find the connotations that I’m unsound to be exasperating.
I don’t think that this is just a problem for me rather than a problem for the community in general: I know a number of very high quality thinkers in real life who are uninterested in participating on LW explicitly because they don’t want to engage with commenters who are highly confident that their own positions are incorrect. There’s another selection effect here: such people aren’t salient because they’re invisible to the online community.
I’m sympathetic to everything you say.
In my experience there’s an issue of Less Wrongers being unusually emotionally damaged (e.g. relative to academics) and this gives rise to a lot of problems in the community. But I don’t think that the emotional damage primarily comes from the weird stuff that you see on Less Wrong. What one sees is them having born the brunt of the phenomenon that I described here disproportionately relative to other smart people, often because they’re unusually creative and have been marginalized by conformist norms
Quite frankly, I find the norms in academia very creepy: I’ve seen a lot of people develop serious mental health problems in connection with their experiences in academia. It’s hard to see it from the inside: I was disturbed by what I saw, but I didn’t realize that math academia is actually functioning as a cult, based on retrospective impressions, and in fact by implicit consensus of the best mathematicians of the world (I can give references if you’d like) .
Thanks so much for sharing. I’m astonished by how much more fruitful my relationships have became since I’ve started asking.
I think that a lot of what you’re seeing is a cultural clash: different communities have different blindspots and norms for communication, and a lot of times the combination of (i) blindspots of the communities that one is familiar with and (ii) respects in which a new community actually is unsound can give one the impression “these people are beyond the pale!” when the actual situation is that they’re no less rational than members of one’s own communities.
I had a very similar experience to your own coming from academia, and wrote a post titled The Importance of Self-Doubt in which I raised the concern that Less Wrong was functioning as a cult. But since then I’ve realized that a lot of the apparently weird beliefs on LWers are in fact also believed by very credible people: for example, Bill Gates recently expressed serious concern about AI risk.
If you’re new to the community, you’re probably unfamiliar with my own credentials which should reassure you somewhat:
I did a PhD in pure math under the direction of Nathan Dunfield, who coauthored papers with Bill Thurston, who formulated the geometrization conjecture which Perelman proved and in doing so won one of the Clay Millennium Problems.
I’ve been deeply involved with math education for highly gifted children for many years. I worked with the person who won the American Math Society prize for best undergraduate research when he was 12.
I worked at GiveWell, which partners with with Good Ventures, Dustin Moskovitz’s foundation.
I’ve done fullstack web development, making an asynchronous clone of StackOverflow (link).
I’ve done machine learning, rediscovering logistic regression, collaborative filtering, hierarchical modeling, the use of principal component analysis to deal with multicollinearity, and cross validation. (I found the expositions so poor that it was faster for me to work things out on my own than to learn from them, though I eventually learned the official versions).You can read some details of things that I found here. I did a project implementing Bayesian adjustment of Yelp restaurant star ratings using their public dataset here
So I imagine that I’m credible by your standards. There are other people involved in the community who you might find even more credible. For example: (a) Paul Christiano who was an international math olympiad medalist, wrote a 50 page paper on quantum computational complexity with Scott Aaronson as an undergraduate at MIT, and is a theoretical CS grad student at Berkeley. (b) Jacob Steinhardt, a Hertz graduate fellow who does machine learning research under Percy Liang at Stanford.
So you’re not actually in some sort of twilight zone. I share some of your concerns with the community, but the groupthink here is no stronger than the groupthink present in academia. I’d be happy to share my impressions of the relative soundness of the various LW community practices and beliefs.
Yes, you seem to have a very clear understanding of where I’m coming from. Thanks.
See my edit. Part of where I’m coming from is realizing how socially undeveloped people’s in our reference class are tend to be, such that apparent malice often comes from misunderstandings.
See Rationality is about pattern recognition, not reasoning.
Your tone is condescending, far outside of politeness norms. In the past I would have uncharitably written this off to you being depraved, but I’ve realized that I should be making a stronger effort to understand other people’s perspectives. So can you help me understand where you’re coming from on an emotional level?
Why did you have this impression?
Groupthink I guess: other people who I knew didn’t think that it’s so important (despite being people who are very well educated by conventional standards, top ~1% of elite colleges).
Tell me how exactly you’re planning to use PCA day-to-day?
Disclaimer: I know that I’m not giving enough evidence to convince you: I’ve thought about this for thousands of hours (including working through many quantitative examples) and it’s taking me a long time to figure out how to organize what I’ve learned.
I already have been using dimensionality reduction (qualitatively) in my day to day life, and I’ve found that it’s greatly improved my interpersonal relationships because it’s made it much easier to guess where people are coming from (before people’s social behavior had seemed like a complicated blur because I saw so many variables without having started to correctly identify the latent ones).
i think the sooner you lose the need for everything to resonate deeply or have a concise insightful summary, the better.
You seem to be making overly strong assumptions with insufficient evidence: how would you know whether this was the case, never having met me? ;-)
It seem to me like to make major contributions to human knowledge you need to do a lot more than say: “Hey PCA is really great”. You actually have to understand reasons of why people aren’t using it and fixing those reasons.
Have you read my speed dating project posts? I haven’t yet written up the most important one on demographics (I can do that soon, just many conflicting priorities), but the one on individual variation in revealed preferences for attractiveness vs intelligence and sincerity starts to get at what I’m talking about.
My project gives a proof of concept for what I’m talking about in the context of social psychology. I’ve never seen such an application. So no, it’s not just the realization that it could be applied, it’s also giving a proof of concept: that’s why it took ~1500 hours rather than ~10 hours.
As far as I can tell, the situation is simply that deep knowledge of the technique hasn’t yet percolated into the social psychology community, and people who do have the relevant background knowledge haven’t actually tried doing social psychology research. All you need is to notice something that’s been missed. There are many such things (see Peter Thiel’s discussion of how there are still secrets in his book “From Zero To One.”)
If I recall correctly, Freeman Dyson has indicated that his demonstration of the equivalence of the two different formulations of quantum electrodynamics isn’t as amazing as people believe, but was largely a function of him being one of the first people to learn both formulations! :-)
So I’d strongly encourage you to pursue your ideas more. I’ve been looking some at the General Social Survey data, where I haven’t yet found something highly nontrivial (maybe I’m looking at the data the wrong way, or maybe it’s just not a good dataset for this). I’d be happy to share my code with you / a cleaned form of the data, if you’re interested in exploring factors for political labels.
Beyond Statistics 101
Ok, I guess what I mean is that it’s suspicious that it maps onto a preexisting notion held by the general population, in the same way that it would be suspicious for psychology research to apparently show the existence of demon possession (which humans have in fact believed in). I wouldn’t find it suspicious if it mapped onto a notion of someone with demonstrated exceptional ability to read and connect with people (e.g. Bill Clinton).
The way scientific progress occurs is by developing progressively more refined understandings of what’s going on: for example, passing from the Ptolemaic model of the stars and planets to the Copernican model to the Newtonian model to Einstein’s theory of general relativity. One can’t hope to understand reality if one isn’t flexible enough to recognize that things might be very different from how they initially appear.
I know that many researchers know something about PCA. I do think that it’s not applied nearly enough (c.f. Sarah’s remarks about Asperger’s Syndrome, which was removed from the DSM a few years after she made her post). The main issue to my mind is that when people apply it in psychology they seem to come into it with preconceived notions concerning what they might find, rather than collecting large and diverse datasets, letting it speak for itself, and then trying to interpret what the principal components mean in human terms.
Consider the construct of conscientiousness. It’s very suspicious that it maps onto a prexisting notion, and it’s just not that predictive. I got lots of C’s and D’s in school, but worked 90 hours a week for 12 weeks on my speed dating project. Am I conscientious? ;-) As far as I can tell, they came up with questions based on preconceived notions, then did factor analysis, and came up with a construct that some meaning, while being very far from carving reality at its joints.
Yes. The basic situation is that I figured out how the methods that Charles Spearman used to discover IQ can be used to shed a lot of light on many different psychology and sociology questions. This is what I was implicitly getting at in my sequence of posts on my Speed Dating Project, though I did a poor job contextualizing the results. IQ is by far the most robust construct to come out of psychology research, so this could in principle revolutionize social science (with a huge amount of work by many talented people).
Some people would say that psychology researchers used the methodology to discover the Big 5 Personality traits among other things, but the constructs that they developed are relatively weak because they haven’t utilized the full power of Spearman’s framework. See also Sarah Constantin’s post A Yardstick for Smell: Thinking in PCA (she preempted me in recognizing the potential of the methods 4.5 years before I did, but I didn’t fully understand what she was getting at at the time).
It’s difficult to make such claims without coming across as grandiose and/or arrogant, so I should emphasize that I think that many LWers would be capable of doing such research with the right background and style of research, if they took Paul Graham and Steve Jobs’ advice. The great mathematician Alexander Grothendieck said:
In our acquisition of knowledge of the Universe ( whether mathematical or otherwise) that which renovates the quest is nothing more nor less than complete innocence. It is in this state of complete innocence that we receive everything from the moment of our birth. Although so often the object of our contempt and of our private fears, it is always in us. It alone can unite humility with boldness so as to allow us to penetrate to the heart of things, or allow things to enter us and taken possession of us.
This unique power is in no way a privilege given to “exceptional talents”—persons of incredible brain power (for example), who are better able to manipulate, with dexterity and ease, an enormous mass of data, ideas and specialized skills. Such gifts are undeniably valuable, and certainly worthy of envy from those who (like myself) were not so endowed at birth,” far beyond the ordinary”.
Yet it is not these gifts, nor the most determined ambition combined with irresistible will-power, that enables one to surmount the “invisible yet formidable boundaries ” that encircle our universe. Only innocence can surmount them, which mere knowledge doesn’t even take into account, in those moments when we find ourselves able to listen to things, totally and intensely absorbed in child play.
[...]
In fact, most of these comrades who I gauged to be more brilliant than I have gone on to become distinguished mathematicians. Still, from the perspective of 30 or 35 years, I can state that their imprint upon the mathematics of our time has not been very profound. They’ve all done things, often beautiful things, in a context that was already set out before them, which they had no inclination to disturb. Without being aware of it, they’ve remained prisoners of those invisible and despotic circles which delimit the universe of a certain milieu in a given era. To have broken these bounds they would have had to rediscover in themselves that capability which was their birth-right, as it was mine: the capacity to be alone.
The issue of multiple hypothesis testing is precisely why it took 1500 hours :-). I was dealing with the general question “how can you find the most interesting generalizable patterns in a human interpretable data set?” It’ll take me a long time to externalize what I learned.
For now I’ll just remark that dimensionality reduction reduces concerns around multiple hypothesis testing. If you have a cluster of variables A and a cluster of features B and you suspect that there’s some relationship between the variables A and the variables B, you can do PCA on the two clusters separately, then look at correlations between the first few principal components rather than looking at all pairwise correlations between variables in A and variables in B.
There is the 2014 LW survey data, which is interesting, even if less substantive than what you have in mind. I have an unfinished project that I’m doing with it (got bogged down in cleaning it to make it nicely readable).