Didn't look too deep into the paper but can I just say that I LOVE this style of academic writing? Accessible, full of examples, and in a conversing tone. Most of the math papers I come across jump right into the "Let $X \in F be ring of S^1$ and etc. I secretly believe that people heap abstractions after abstractions to purposefully shield the fact that the meat of what they've written is actually quite simple. Either that, or I've failed to understand that some ideas can't just be explained without invoking arcane symbols.
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Believe it or not, the "Let $X \in F$..." style is typically easier and more straightforward to write for mathematicians and theoretical computer scientists and closer to how they have the solution in their head (or on scraps of paper) anyway. The problem is, unless the result is super important, that style will get your paper rejected as it doesn't engage the reviewers who are not already familiar with the problem. So authors go instead for the conversational tone and try to find a good story, which is more often what actually shields that the work is quite simple or less important.
It’s also easier to spot errors in that style than in prose.
As a grad student, one of my more cynical professors said that to write a paper, you take a simple idea and then obfuscate it until it sounds complicated, and therefore seems impressive.
He also said the hardest part of reading papers is understanding the notation (thanks to that obfuscation).
If the whole academic career doesn't work out, patent drafting offers an even more baroque application of obfuscated writing skills.
Now the whole journey of Einstein from patent examiner to physics superstar makes sense to me.
He simply did not have the intellectual aptitude required for the patent business. Suddenly I don't feel so bad about becoming a math professor after failing accounting school.
He saw so many bad ideas on his patent job that he had some good ones of his own
Now I am imagining Einstein inventing general relativity as a shorthand to deny yet another perpetual motion machine patent.
I have often found that to be true. From what I've heard, it is sometimes against the author's wishes, that they have to toss in equations to "make it look good" to get past review. At least in CS, you can read the source code if it's been published, and often it's a basic technique with a slight new twist that _maybe_ works but is super hard to reproduce. Also much of the papers are fluff lol, just random equations thrown in that are just copied from the textbook.
The incentives are misaligned.
The general public wants something simple and useful.
The writers want recognition.
I learnt that when I wrote my own thesis. I tried to be simple and useful but I discovered something else when thinking about the subject: I wanted to make sure that my thesis gets good grades.
Two days ago, a friend of mine sent a link to a site with audio versions of scientific articles. He sarcastically added: "as if anyone actually still reads articles." In many discplines, articles are write only. It's publish-or-perish, not read-or-perish.
That’s nuts to me. I read aerodynamics for my masters and would have been lost without skimming 100’s of papers and fully reading about 100 papers.
Now I’m currently doing research on a niche statistics topic and I would be lost without papers.
How does one figure out “this is what we currently understand about x” without research papers and plundering scihub?
Not every discipline has a constructive literature. I worked in psycho-linguistics. There's almost no article that provides anything you can build on. Almost all of it is description of experiment and outcome, with some theoretical interpretation, but that is almost always specific to interpretation within a specific theory. But those theories are high-level fantasy about language processing, which makes the interpretation meaningless elsewhere, even if the article did get everything else right (and that's rare too).
So there are very few results you can expand upon. Lexical priming turned out to be reproducible and usable as a tool, the Stroop effect too. But those are exceptions. However, they don't explain the underlying mechanism. E.g., the Stroop effect is 90 years old, and there's no explanation of how it works. So if you read text books that explain you the state of the art of around 1980, you're practically up to date as far as real knowledge is concerned. The rest is infighting and publishing for its own sake.
And psycho-linguistics at least has some experimental standards, because it is a fairly limited topic and it is suited to lab settings. Other fields don't even have that. Social psychology is a joke. Articles are based on questionnaires and introspection.
That's why articles in those fields are not well read. They get read by a small audience, mostly people in the same school of thought, and mostly to add to the citation section. But not for knowledge.
They're exaggerating to express personal feelings re: bitterness about lack of engagement
> I secretly believe that people heap abstractions after abstractions to purposefully shield the fact that the meat of what they've written is actually quite simple.
It usually is pretty simple, but what they're going for is rigor and concision. Maybe a few papers are overconstrained and could drop a few unnecessary details, but I don't think that's all that common after enough review.
Sometimes people just want their work to sound more impressive than it actually is. Using in-words is a pretty standard technique, their peers don't mind because they speak the same language. To outsiders it sounds difficult. Quite common in academia.
That's because the second author is Jeffrey Ullman (Turing Award, Neumann medal)
Ullman is of the authors of several legendary computer science books Dragon Book (Compilers: Principles, Techniques, and Tools) the Cinderella Book (Introduction to Automata Theory, Languages, and Computation), Green Dragon Book (Principles of Compiler Design)
If you want to learn deep stuff with clarity, those old books are still the way to go.
I think it’s just that what’s being talked about is so precise and so deep in the weeds of nested definitions that you generally need to talk like that, or at least you have to be a truly gifted communicator to write a math paper without it.
>or at least you have to be a truly gifted communicator to write a math paper without it.
i know a lot of math (hence the name) - basically lots of stuff scattered around analysis, geometry, and complexity theory, at varying levels between senior undergrad and research level (MIP and SAT and SMT). this basically tracks my academic progression (from math undergrad to cs phd student).
the stuff that i can explain the best is the research level stuff. why? because i can explain it in the same relatable terms that i learned it through, since i learned it when i needed it - through relatable examples that clearly motivate the ideas. i've done it many times - often a junior phd student will ask me what i work on and i start telling a story that starts with some really common thing that gives a foothold ("how would you figure out which variables in a for loop are reused") and then step by step you "follow your nose" to the ideas behind the proofs and techniques and etc.
what's my point? lots of academic math is useless frippery that couldn't be motivated in this way and so it can't be articulated except formally.
If you want to explain something in a loose fashion, that works.
It doesn’t work so much for proofs in a lot of mathematics, especially because the “common ground” you speak pf starting at would be hours of explanation behind what you’re trying to say.
Read a paper with few hundreds of cites. They proposed a new algorithm to solve eigenvalue problem. I look at it, decrypt the equations, and then notice that it is just basically a bunch of if-then condition like this:
count = 0
for x in list:
if x == 1:
count +=1
return 3
return 1
if you want to see how cryptic it is: https://arxiv.org/abs/2103.07510
That doesn't look to try to solve the eigenvalue problem.
> secretly believe
Apparently not so secretly.