Is statistics beyond introductory statistics important for general reasoning?
Ideas such as regression to the mean, that correlation does not imply causation and base rate fallacy are very important for reasoning about the world in general. One gets these from a deep understanding of statistics 101, and the basics of the Bayesian statistical paradigm. Up until one year ago, I was under the impression that more advanced statistics is technical elaboration that doesn't offer major additional insights into thinking about the world in general.
Nothing could be further from the truth: ideas from advanced statistics are essential for reasoning about the world, even on a day-to-day level. In hindsight my prior belief seems very naive – as far as I can tell, my only reason for holding it is that I hadn't heard anyone say otherwise. But I hadn't actually looked advanced statistics to see whether or not my impression was justified :D.
Since then, I've learned some advanced statistics and machine learning, and the ideas that I've learned have radically altered my worldview. The "official" prerequisites for this material are calculus, differential multivariable calculus, and linear algebra. But one doesn't actually need to have detailed knowledge of these to understand ideas from advanced statistics well enough to benefit from them. The problem is pedagogical: I need to figure out how how to communicate them in an accessible way.
Advanced statistics enables one to reach nonobvious conclusions
To give a bird's eye view of the perspective that I've arrived at, in practice, the ideas from "basic" statistics are generally useful primarily for disproving hypotheses. This pushes in the direction of a state of radical agnosticism: the idea that one can't really know anything for sure about lots of important questions. More advanced statistics enables one to become justifiably confident in nonobvious conclusions, often even in the absence of formal evidence coming from the standard scientific practice.
IQ research and PCA as a case study
In the early 20th century, the psychologist and statistician Charles Spearman discovered the
the g-factor, which is what IQ tests are designed to measure. The g-factor is one of the most powerful constructs that's come out of psychology research. There are many factors that played a role in enabling Bill Gates ability to save
perhaps millions of lives, but one of the most salient factors is his IQ being in the top ~1% of his class at Harvard. IQ research helped the Gates Foundation to
recognize iodine supplementation as a nutritional intervention that would improve socioeconomic prospects for children in the developing world.
The work of Spearman and his successors on IQ constitute one of the pinnacles of achievement in the social sciences. But while Spearman's discovery of IQ was a great discovery, it wasn't his greatest discovery. His greatest discovery was a discovery about how to do social science research. He pioneered the use of factor analysis, a close relative of principal component analysis (PCA).
The philosophy of dimensionality reduction
PCA is a dimensionality reduction method. Real world data often has the surprising property of "dimensionality reduction": a small number of latent variables explain a large fraction of the variance in data.
This is related to the effectiveness of Occam's razor: it turns out to be possible to describe a surprisingly large amount of what we see around us in terms of a small number of variables. Only, the variables that explain a lot usually aren't the variables that are immediately visible – instead they're hidden from us, and in order to model reality, we need to discover them, which is the function that PCA serves. The small number of variables that drive a large fraction of variance in data can be thought of as a sort of "backbone" of the data. That enables one to understand the data at a "macro / big picture / structural" level.
This is a very long story that will take a long time to flesh out, and doing so is one of my main goals.
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Thanks for the detailed response! I'll respond to a handful of points:
I certainly agree that there are people here who match that description, but it's also worth pointing out that there are actual experts too.
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'm not sure this is avoidable, and in full irony I'll link to the wiki page that explains why.
In general, there are lots of concepts that seem useful, but the only way we have to refer to concepts is either to refer to a label or to explain the concept. A number of people read through the sequences and say "but the conclusions are just common sense!", to which the response is, "yes, but how easy is it to communicate common sense?" It's one thing to be able to recognize that there's some vague problem, and another thing to be able to say "the problem here is inferential distance; knowledge takes many steps to explain, and attempts to explain it in fewer steps simply won't work, and the justification for this potentially surprising claim is in Appendix A." It is one thing to be able to recognize a concept as worthwhile; it is another thing to be able to recreate that concept when a need arises.
Now, I agree with you that having different labels to refer to the same concept, or conceptual boundaries or definitions that are drawn slightly differently, is a giant pain. When possible, I try to bring the wider community's terminology to LW, but this requires being in both communities, which limits how much any individual person can do.
Part of that is just seeding effects--if you start a rationality site with a bunch of people interested in transhumanism, the site will remain disproportionately linked to transhumanism because people who aren't transhumanists will be more likely to leave and people who are transhumanists will be more likely to find and join the site.
Part of it is that those are the cluster of ideas that seem weird but 'hold up' under investigation--most of the reasons to believe that the economy of fifty years from now will look like the economy of today are just confused, and if a community has good tools for dissolving confusions you should expect them to converge on the un-confused answer.
A final part seems to be availability; people who are convinced by the case for cryonics tend to be louder than the people who are unconvinced. The annual surveys show the perception of LW one gets from just reading posts (or posts and comments) is skewed from the perception of LW one gets from the survey results.
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.