It's rather sad that these kinds of math "memes" enjoy the popularity that they do, despite being wrong on many levels. I'll be very harsh here, with large dollops of sarcasm.

Take this one (which was all the rage on r/MachineLearning). What is this post saying ? That Gaussian distributions are like Soap Bubbles ? The highest density of water is at the center of the bubble ? I wonder why it floats then ?

May be it's all the Bayesian Entropic Quantum Bosonic fuzzy particles keeping bubbles up and rain down. Who knows ? May be with enough buzzwords, I can cargo-cult my way through some money bags too.

The post claims that the mass of high-dimensional Gaussian is not concentrated at the mode but on an annulus, which is correct, but why should that matter ? Unless the thing one is bothered about is essentially dependent on the norm of the vector (or to generalize, on projections to lower dimensions), the hand-waving in this post is completely and utterly meaningless. All it does is to make people stupider, by saying "math is weird, don't bother with it" !

The particular issue that this post is talking about is generally not of concern outside of things like hashing / metric embeddings / JLT / information theory / sufficient statistics and things of that sort.

A simpler setting for understanding it is in the tossing of a fair coin, multiple times. Sure, H^n is as probable as anything else, but under the statistic of "number of heads" the measures overwhelmingly disfavor unbalanced counts. It doesn't mean anything, however, if you're not concerned about this statistic.

This is also the case with the visual images example he talks about. It's obvious that humans are not particularly perceptive to the high-dimensions (which why JPEG works), and that our bio-tubes are doing some fancy low-dimensional projections to encode the information (the "manifold hypothesis" for images).

If the principles in the post were to be generously applied elsewhere, one could even question the point of Linear regression. I can almost hear the pointy-haired boss saying "I don't want one of those elitist modes, I'm a man of the people, we support diversity here!".

The illustration with Gaussian data augmentation makes me cringe even more. It'd be one thing if the author considered high-dimensional points; perturbed them with samples from the Normal distribution; projected them down to reveal rings around points, but it's clear he doesn't really understand the issue at all.

For once, I'd wish to see some modicum of rigour in such posts. You don't hear Mathematicians (or theoretical CS folk) claiming higher dimensions are strange and opaque. Sure, it's hard to visualize and so on, but the added topological freedom makes many problems much simpler. Historically, the hardest problems in Differential Topology have been those in dimensions less than 5 !

ML blog-land, however, is perturbed by the fact that Lebesgue measure increases exponentially with dimension. That functions of random variables change the distribution. Good god, what a crazy world.

I'm biased of course. I work at a startup run by a pretentious new grad who can speak all sorts of BS and can thereby derive the authority to boss around people to do his work while looking pretty. Karma's a bitch, what can you do.

To see people gain following, on the other hand, and thereby achieve monetary gain through such posts, makes my day even more miserable.

Why? It drives home the point that the world is as Darwinian, as it has ever been, and that "meritocracy" is a mere meta-justification for the law of the jungle to persist.

Sometimes I wonder why I ever bothered becoming a career CS person (or indeed a STEM person). Perhaps to satisfy my god-given role of being a clone in the modern feudal hierarchy.

Sorry. Say "Hi" to Zoubin.