## 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

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.

Qualitative day-to-day dimensionality reduction sounds like woo to me. Not a bit more convincing than quantum woo (Deepak Chopra et al.). Whatever you're doing, it's surely not like doing SVD on a data matrix or eigen-decomposition on the covariance matrix of your observations.

Of course, you can often identify motivations behind people's actions. A lot of psychology is basically trying to uncover these motivations. Basically an intentional interpretation and a theory of mind are examples of dimensionality reduction in some sense. Instead of explaining behavior by reasoning about receptors and neurons, you imagine a conscious agent with beliefs, desires and intentions. You could also link it to data compression (dimensionality reduction is a sort of lossy data compression). But I wouldn't say I'm using advanced data compression algorithms when playing with my dog. It just sounds pretentious and shows a desperate need to signal smartness.

So, what is the evidence that you are consciously doing something similar to PCA in social life? Do you write down variables and numbers, or how can I imagine qualitative dimensionality reduction. How is it different from somebody just getting an opinion intuitively and then justifying it with afterwards?

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

emotionallevel?