Daunting papers/books and how to read them(mathoverflow.net)
mathoverflow.net
Daunting papers/books and how to read them
https://mathoverflow.net/questions/463287/daunting-papers-books-and-how-to-finally-read-them
27 comments
Shameless plug: I created website [1] to help with this. It's like an online paper club where you can ask questions / get answers from the authors and community on research papers, directly on the PDF.
[1] https://gotit.pub
[1] https://gotit.pub
Nice idea. (Site is broken with firefox+ublock. Seems like dependency on google recaptcha is breaking stuff.)
When a text is hard I normally don't focus on understanding everything on the first (or second) pass. After reading through, taking a break and reflecting on what I did and didn't understand helps immensely on the subsequent rereads. After that talking it over with others generally helps identify gaps.
That said, I have much more time and patience then when I was in school which also helps immensely.
That said, I have much more time and patience then when I was in school which also helps immensely.
I am reminded of Mochizuki’s claimed proof of the abc conjecture: an impenetrable paper, building on other work of the same author, building on work in an already complex and abstract subject. It was said that the only people who had done enough of the background reading to understand the paper were the author’s own students - and therefore not independent enough to validate its claims. The legendary Peter Scholze got far enough to offer a debunking, but the trial continues…
It seems inevitable that the theoretically infinite world of math will be finitely bound by the limits of the human mind. There’s only so much time in one lifespan to do all the pre-reading.
It seems inevitable that the theoretically infinite world of math will be finitely bound by the limits of the human mind. There’s only so much time in one lifespan to do all the pre-reading.
“Then,” said the Alchemist, “we have discovered something surprising. The art of architecture is limited by the human lifespan. The greatest building that can ever be designed is the one that would take seventy years of studying architecture to master; God has drawn a line in the sand forever closing off buildings grander than these.”
https://slatestarcodex.com/2017/11/09/ars-longa-vita-brevis/
https://slatestarcodex.com/2017/11/09/ars-longa-vita-brevis/
La Sagrada Familia would disagree…
Just don’t read it then. You are not the intended audience for that book. It’s ok to not to read a book
As JL Borges said,
> [...] If a book bores you, leave it; don’t read it because it is famous, don’t read it because it is modern, don’t read a book because it is old. If a book is tedious to you, leave it, even if that book is 'Paradise Lost' — which is not tedious to me — or 'Don Quixote' — which also is not tedious to me. But if a book is tedious to you, don't read it; that book was not written for you. Reading should be a form of happiness, so I would advise all possible readers of my last will and testament—which I do not plan to write— I would advise them to read a lot, and not to get intimidated by writers' reputations, to continue to look for personal happiness, personal enjoyment. It is the only way to read.”
Anyway, being science/academic books/papers the point of discussion in the thread, I doubt one would always have the privilege to just leave it.
> [...] If a book bores you, leave it; don’t read it because it is famous, don’t read it because it is modern, don’t read a book because it is old. If a book is tedious to you, leave it, even if that book is 'Paradise Lost' — which is not tedious to me — or 'Don Quixote' — which also is not tedious to me. But if a book is tedious to you, don't read it; that book was not written for you. Reading should be a form of happiness, so I would advise all possible readers of my last will and testament—which I do not plan to write— I would advise them to read a lot, and not to get intimidated by writers' reputations, to continue to look for personal happiness, personal enjoyment. It is the only way to read.”
Anyway, being science/academic books/papers the point of discussion in the thread, I doubt one would always have the privilege to just leave it.
Math and adjacent literature are there to rewire your brain, they will always be a struggle to read since rewiring your brain takes effort. The exception is if you already know the topic really really well so you don't have to rewire anything, you just put it in places you have already created, but that is impossible for topics new to you.
why do they have to write papers in a way that the readers have to chewing on them.
The trite reasons:
1. Journals have length limits. And readers don't read long papers at all.
2. Many academics have not worked hard enough to attain excellent writing skills - they were too busy becoming excellent at their discipline.
The most important reason.
- Given a clear lucid explanation of new knowledge that no one but you know, is incredibly difficult. Honestly, anyone, who thinks it's easy should take a stab at undertaking a research project and then trying to summarize months or years of work into 6-10 pages.
1. Journals have length limits. And readers don't read long papers at all.
2. Many academics have not worked hard enough to attain excellent writing skills - they were too busy becoming excellent at their discipline.
The most important reason.
- Given a clear lucid explanation of new knowledge that no one but you know, is incredibly difficult. Honestly, anyone, who thinks it's easy should take a stab at undertaking a research project and then trying to summarize months or years of work into 6-10 pages.
Papers are designed to be read by a specific audience of highly technical, skilled people in a topic where if it is original research, must be very explicit, and prove and disprove multiple things simultaneously.
Of course, standards vary significantly institution to institution and even person to person, and highly technical, skilled people are not indicative of full capability of reading, let alone reviewing the topic, doubly so when it is original research.
Of course, standards vary significantly institution to institution and even person to person, and highly technical, skilled people are not indicative of full capability of reading, let alone reviewing the topic, doubly so when it is original research.
Let me translate this for the layman: papers are written using terms and notation that only makes sense if you've gone through the the process of learning their derivation from first principles in the narrow field in which they apply.
It has the odd effect of making this stuff comprehensible only to those that essentially already know what it is, and possibly a few people academically adjacent to those people.
Other people can decipher it, after long and arduous labor, but it essentially requires rediscovering the path that brought it about, knowing what the outcome will be. In that sense these papers are less useful than they seem.
Academia is a little like religion: to outsiders the language and rituals make little sense, only those indoctrinated in its tenets can achieve enlightenment.
It has the odd effect of making this stuff comprehensible only to those that essentially already know what it is, and possibly a few people academically adjacent to those people.
Other people can decipher it, after long and arduous labor, but it essentially requires rediscovering the path that brought it about, knowing what the outcome will be. In that sense these papers are less useful than they seem.
Academia is a little like religion: to outsiders the language and rituals make little sense, only those indoctrinated in its tenets can achieve enlightenment.
This is a very poor and inaccurate "translation". Papers from math and physics are hard to understand not because of specific choice of "terms and notation" but because of actual concepts they are based on. Terms and notation actually make it easier to understand, compressing pages of words into a single symbol. Without these the best you get is quanta article, where you can get a vague feeling of what is being done, but no actual understanding.
If you talk about a modern city with a hunter gatherer, how many words would you have to explain? Do these words exist because modern life is "like a religion" and hunter gatherer is not "indoctrinated"?
If you talk about a modern city with a hunter gatherer, how many words would you have to explain? Do these words exist because modern life is "like a religion" and hunter gatherer is not "indoctrinated"?
I think this completely misses the point. A paper presents one new idea and builds on top of many existing ideas and generally assumes that the reader is familiar with all the existing ideas. And that is completely reasonable, the purpose of a paper is to concisely present the new idea, not to be a textbook that teaches you the entire field from the ground up.
That said, conveying an idea in an easily understandable way is hard and some authors will do better or worse than others. Also papers will usually not purely present the new idea but provide some context so that the reader only needs to be familiar with the topic up to the context but the amount of context given will vary a lot between papers.
That said, conveying an idea in an easily understandable way is hard and some authors will do better or worse than others. Also papers will usually not purely present the new idea but provide some context so that the reader only needs to be familiar with the topic up to the context but the amount of context given will vary a lot between papers.
I understand what papers are and I accept that they naturally end up being how they are.
Even if you study textbooks, which themselves suffer the same fate, requiring other textbooks or knowledge of terms and notation as prerequisites, and have knowledge in the field it doesn't mean you can understand most papers. Fields and subfields have their own (obscure) terminology and notation, often individual practitioners do. Even if they don't terminology and notation isn't used consistently, which becomes critical when you're trying to learn and understand.
I'm just lamenting how inscrutable this knowledge is and how sad and frustrating that is. Most of this stuff is not that complicated once you know what they're actually talking about. Instead you end up banging your head against the wall for hours trying to divine the intent of the author or go on endless yak shaving expeditions trying to nail down terms and concepts.
Even if you study textbooks, which themselves suffer the same fate, requiring other textbooks or knowledge of terms and notation as prerequisites, and have knowledge in the field it doesn't mean you can understand most papers. Fields and subfields have their own (obscure) terminology and notation, often individual practitioners do. Even if they don't terminology and notation isn't used consistently, which becomes critical when you're trying to learn and understand.
I'm just lamenting how inscrutable this knowledge is and how sad and frustrating that is. Most of this stuff is not that complicated once you know what they're actually talking about. Instead you end up banging your head against the wall for hours trying to divine the intent of the author or go on endless yak shaving expeditions trying to nail down terms and concepts.
I guess it's more about the reader's lack of knowledge.
They shouldn’t. It makes papers less accessible which means they’re less impactful. That said, a lot of academics are good at their discipline and bad at writing.
A big problem is prior knowledge. Most papers incrementally increase knowledge so by necessity they have to assume the reader knows it, lest they find themselves repeating it alot. How far back are you expected to go to help your audience understand?
The answer in most of academia is: not at all. You're expected to have learnt everything in the field up to that point. Academia is for academics and generally doesn't care about impact outside of academia, who seldom understand it anyway (because of its academic nature).
The answer in most of academia is: not at all. You're expected to have learnt everything in the field up to that point. Academia is for academics and generally doesn't care about impact outside of academia, who seldom understand it anyway (because of its academic nature).
Every field has jargon and assumed knowledge. If you're writing a computer science paper, you're not going to start by teaching the reader grade school math.
Not necessarily. I agree, being a smart scientist doesn’t make one a good writer , however, most of the times the inaccessibility of a text comes from a high presumed knowledge of the reader. But if you dial the presumption down, then the readers versed in the field would have to drag through the text full of explanations they already know. And, excuse my assumption, most relevant citations come from the people in the field.
I think the chances of a human being existing who knows enough about a specific topic that they can write a paper about it, and who is also an exceptionally clear writer, is pretty low.
So if you want the knowledge, you go in knowing this. If you don't want the knowledge that much, wait until it becomes a popular topic and people make books or blogs about it.
So if you want the knowledge, you go in knowing this. If you don't want the knowledge that much, wait until it becomes a popular topic and people make books or blogs about it.
Because you can't avoid that in many cases.
Important topics that are read by many people get rewritten into textbooks that are very easy to read compared to the original papers, but people complain a ton about those textbooks as well so there is no way to placate people like you here, no matter how hard they try people demand them to try harder.
Important topics that are read by many people get rewritten into textbooks that are very easy to read compared to the original papers, but people complain a ton about those textbooks as well so there is no way to placate people like you here, no matter how hard they try people demand them to try harder.
same reason we have to wear a suit to a funeral. culture.
To sum up: let AI simplify it for you.
Easy: Trust the experts.
Why question science, when you have fact-checkers?
There was a time this has been the case. How far we have come. Relevant: https://amp.theguardian.com/science/2013/dec/06/peter-higgs-...