Agreed. The section basically boils down to "despite maybe looking simpler, Single-Decree Paxos is still tricky." I don't think something particular and formal like Kolmogorov complexity even fits the tone there.
This article would be really interesting with more context and explanation, but I find a bit unreadable in its current state.
That being said, I enjoyed the algorithm for generating the next Paxos algorithm. That's fun, but I'm still not sure that I really understood what the author was saying.
It's weird. It definitely reads like the Quanta author either didn't know what a mathematical category is, or didn't think it merited explanation, despite explaining simpler things in excruciating detail in the article.
first sentence in the doc:
The goal of this document is to present an introduction to probability and markets in what
we hope is a fairly intuitive and accessible way
> that maybe they're trying to bedazzle more than explain
I don't know much abstract algebra as well but I have studied elliptic curve pairings before, so from what I can tell, every sentence in the article counts (maybe not every word, though). The article may sound bedazzling to a reader not experienced in the subject, but its complexity can totally be justified by the complexity of technical details that it tries to explain clearly.
That said, it's indeed hard to distinguish between a bedazzling article and an article that actively tries to explain concepts as clearly and concisely as possible. I do have such feelings with many AI papers these days, but not this one.
This blog post seems to be a comment or response aimed at people who already understand the paper, not an exposition for someone encountering it for the first time. I think I'm moderately well versed in probability and information theory and couldn't make heads or tails of it.
I really didn't like this paper, and gave up on reading it three pages in when they started using differences between probabilities as a measure of distance instead of, say KL divergence. I thought the English was fine, but the technical details and ability to explain were pretty lacking.
This is a pretty frustrating read. Interpretability of automatic decision making processes is a genuine, important issue, but I'm not sure this issue is best explained by a writer who, as far as I can tell, has made no effort to understand basic questions like what an algorithm is. The generalized bafflement of the author is just mystification, a vague sense of spooky machines we can't understand, which doesn't help us understand the specific difficulties in understanding the decision making process that depend on processing huge quantities of data.
Awful article. It repeatedly conflates two very distinct arguments for simplicity in science: (a) an a priori elegance criterion when choosing between two theories that are observationally indistinguishable, and (b) a trade-off between simplicity and accuracy of two different approximations.
I only skimmed through it, but I can not take it seriously. They talk about general mathematical proofs, but it feels more like a few very arbitrarily chosen definitions, without addressing the most standard argument ("what is so difficult about simulating a human brain in principle, except for the (not fundamental) problem of having a big computer and precise classical measurements").
I agree, I just skimmed it but the examples they used and their arguments were weak. It reads as if they haven't actually dug deep into the material they are presenting.
When they mentioned not being able to calculate double pendulum, my mind immediately jumped to concepts of computability. For instance, we know that the Halting Problem cannot be solved by a Turing machine. We (or aliens) can introduce an oracle, but that would have it's own equivalent halting problem. These are truths that have been proven.
This follows for any and all theorems. You start with a set of axioms, and then successively arrive at your proof through logical steps. Aliens might come up with new questions, new answers, etc. But that has no bearing on the validity of our mathematics.
> What really upset me was that there was practically no surrounding discussion of the intuition behind the algorithm. Behind all the rigor of mathematics lies very simple and powerful ideas. This book did nothing to emphasize those simple ideas.
I would just respond to this by saying that the mathematics do express the ideas. It's just a different language than most people are used to.
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