5 ms·

That doesn’t mean that it’s wrong, it means that you need to read more. In a lot of fields, undergraduate material doesn’t qualify you to read papers, a PhD doe

by knzhou 7y ago

That doesn’t mean that it’s wrong, it means that you need to read more. In a lot of fields, undergraduate material doesn’t qualify you to read papers, a PhD does. If all papers actually were written to undergraduate level, many would be 500 pages long. Who has time to write a book-length exposition of the basics of their field every time they publish? I mean, have you ever published a technical work? If so, did you go out of your way to make it completely accessible to high schoolers? If you didn’t, you get why professors don’t do the same for undergrads.

thanhhaimai 7y ago
The above statement is true with the assumption that the topic being discussed is truly above the level of understanding for undergraduates. For the majority of the papers, that assumption is not true though. Papers are hard to read has more to do with the idea that if it's not filled with jargons, its chance of getting published is greatly reduced. Papers are not rewarded for being easy to understand. People/organizations get rewarded for publishing "complicate" papers. That misalignment is the issue.
- knzhou 7y ago
  Depends on the field. Many CS papers can be understood by undergrads because CS is a very young and very broad field; the path to the frontier in any direction is short. Theoretical physics and math are not like that. They have been building cumulatively for centuries.
  - Silhouette 7y ago
    Theoretical physics and math are not like that. They have been building cumulatively for centuries. For state-of-the-art research in obscure specialisms, of course you're right. However, numerous papers and books cover more mundane subjects and there is no good reason they could not be readily accessible to anyone with an undergraduate-level background or at least a masters delving a bit deeper into the field of interest. Often the problem isn't dumbing down the material, it's simply poor communication skills. Put another way, while our cumulative understanding of mathematics now covers a very broad range of areas, that doesn't necessarily mean the depth to reach a good understanding of any particular specialism has increased at the same rate. On the contrary, given that even the most specialised of theories must be something that an individual can come to understand and build upon within a single career, there is an inherent limit to how deep our understanding of the subject can go. That limit fundamentally depends on how efficiently we can build the layers of more elementary understanding on which the start of the art must rest.
hyperbovine 7y ago
A B.A. in math gets you to the forefront of mathematical research as it was circa 1912. (Source: https://slate.com/human-interest/2003/05/is-math-a-young-man-s-game.html https://slate.com/human-interest/2003/05/is-math-a-young-man...) This is purely my impression as somebody who switched away from pure math early in their career, but: amazingly, in pure math, unless you are really advanced, you are not even that close to engaging independently in cutting-edge research until well after your Ph.D. Math has been continuously researched by all the smartest people for hundreds of years (thousands, depending on how you view the dark ages). The low hanging fruit got gobbled up centuries ago. The same could be said for physics and various other "classical" scientific fields.
- thethirdone 7y ago
  > The same could be said for physics and various other "classical" scientific fields. I think mathematics is in a different class than physics or other scientific endeavors because there is meaningful mathematics going back to ancient Greece whereas I am not aware of any physics that was known thousands of years ago that is still relevant.
nemonemo 7y ago
Suppose a narrow field where only two human beings can understand. How could the society judge the progress of the field or the merit of a new project? I don't think it is possible to avoid collusion or groupthink in such a field and it would be difficult to differentiate the two. So does it mean we should curb some superhuman thinking and let them explain better to other human being? I'd think so. It is all about balance or trade-off, but at some point, a field would become too esoteric for a society and it might need to slow down the short-term progress to ensure consistent long-term progress. It seems the math field as a whole (or more specifically the number theorists?) needs more of good communicators who can link the cutting edge and more general public. The math academia could give incentives to such activities in addition to pushing the boundaries.
- sandworm101 7y ago
  That assumes there is some link to the general public, to the real world. Lots of math has absolutely no practical use, yet. Why bother explaining the cutting edge when even those who understand it cannot fathom how it would ever be used?
- knzhou 7y ago
  Scientists and mathematicians already spend an extreme amount of energy trying to think of the shortest, cleanest possible route for people to learn their fields. The resulting documents take years to create, and are called textbooks. (At least, the good textbooks are like this.) Often people will work for thousands of hours on their books, essentially for free. Students go from outsiders to participants by reading them, all the time. The problem is that things genuinely are hard, and there's only so much compression you can do before you're reduced to meaningless handwaving. Textbooks are already compressed by a factor of 100 relative to the original research literature, sometimes even oversimplified. Demanding something a factor of 100 better than a textbook is going to get you something like one of those useless "learn C++ in 24 hours" paperbacks.
nilkn 7y ago
The problem is really that a PhD doesn't get you to reading level either. It might get you there in only one specialized subfield. And there might only be a few dozen other people who are also at reading level for that area. How much do you trust that small group to catch every single subtle, abstract error in papers published in the area?
- knzhou 7y ago
  I don't, I'm just saying that trying to make every paper accessible to undergrads (or high schoolers, or elementary schoolers, or whatever) is going to bloat their length by so much that errors become harder to check, not easier.
Hasz 7y ago
Not trying to imply it's wrong -- if anything, research should be written to a professional level. I also don't think the background should take you from high school calc to topology or differential geometry in one fell sweep.

by knzhou 7y ago

thanhhaimai 7y ago

The above statement is true with the assumption that the topic being discussed is truly above the level of understanding for undergraduates. For the majority of the papers, that assumption is not true though. Papers are hard to read has more to do with the idea that if it's not filled with jargons, its chance of getting published is greatly reduced. Papers are not rewarded for being easy to understand. People/organizations get rewarded for publishing "complicate" papers. That misalignment is the issue.

knzhou 7y ago
Depends on the field. Many CS papers can be understood by undergrads because CS is a very young and very broad field; the path to the frontier in any direction is short. Theoretical physics and math are not like that. They have been building cumulatively for centuries.
- Silhouette 7y ago
  Theoretical physics and math are not like that. They have been building cumulatively for centuries. For state-of-the-art research in obscure specialisms, of course you're right. However, numerous papers and books cover more mundane subjects and there is no good reason they could not be readily accessible to anyone with an undergraduate-level background or at least a masters delving a bit deeper into the field of interest. Often the problem isn't dumbing down the material, it's simply poor communication skills. Put another way, while our cumulative understanding of mathematics now covers a very broad range of areas, that doesn't necessarily mean the depth to reach a good understanding of any particular specialism has increased at the same rate. On the contrary, given that even the most specialised of theories must be something that an individual can come to understand and build upon within a single career, there is an inherent limit to how deep our understanding of the subject can go. That limit fundamentally depends on how efficiently we can build the layers of more elementary understanding on which the start of the art must rest.

hyperbovine 7y ago

A B.A. in math gets you to the forefront of mathematical research as it was circa 1912. (Source: https://slate.com/human-interest/2003/05/is-math-a-young-man-s-game.html https://slate.com/human-interest/2003/05/is-math-a-young-man...) This is purely my impression as somebody who switched away from pure math early in their career, but: amazingly, in pure math, unless you are really advanced, you are not even that close to engaging independently in cutting-edge research until well after your Ph.D. Math has been continuously researched by all the smartest people for hundreds of years (thousands, depending on how you view the dark ages). The low hanging fruit got gobbled up centuries ago. The same could be said for physics and various other "classical" scientific fields.

thethirdone 7y ago
> The same could be said for physics and various other "classical" scientific fields. I think mathematics is in a different class than physics or other scientific endeavors because there is meaningful mathematics going back to ancient Greece whereas I am not aware of any physics that was known thousands of years ago that is still relevant.

nemonemo 7y ago

Suppose a narrow field where only two human beings can understand. How could the society judge the progress of the field or the merit of a new project? I don't think it is possible to avoid collusion or groupthink in such a field and it would be difficult to differentiate the two. So does it mean we should curb some superhuman thinking and let them explain better to other human being? I'd think so. It is all about balance or trade-off, but at some point, a field would become too esoteric for a society and it might need to slow down the short-term progress to ensure consistent long-term progress. It seems the math field as a whole (or more specifically the number theorists?) needs more of good communicators who can link the cutting edge and more general public. The math academia could give incentives to such activities in addition to pushing the boundaries.

sandworm101 7y ago
That assumes there is some link to the general public, to the real world. Lots of math has absolutely no practical use, yet. Why bother explaining the cutting edge when even those who understand it cannot fathom how it would ever be used?
knzhou 7y ago
Scientists and mathematicians already spend an extreme amount of energy trying to think of the shortest, cleanest possible route for people to learn their fields. The resulting documents take years to create, and are called textbooks. (At least, the good textbooks are like this.) Often people will work for thousands of hours on their books, essentially for free. Students go from outsiders to participants by reading them, all the time. The problem is that things genuinely are hard, and there's only so much compression you can do before you're reduced to meaningless handwaving. Textbooks are already compressed by a factor of 100 relative to the original research literature, sometimes even oversimplified. Demanding something a factor of 100 better than a textbook is going to get you something like one of those useless "learn C++ in 24 hours" paperbacks.

nilkn 7y ago

The problem is really that a PhD doesn't get you to reading level either. It might get you there in only one specialized subfield. And there might only be a few dozen other people who are also at reading level for that area. How much do you trust that small group to catch every single subtle, abstract error in papers published in the area?

knzhou 7y ago
I don't, I'm just saying that trying to make every paper accessible to undergrads (or high schoolers, or elementary schoolers, or whatever) is going to bloat their length by so much that errors become harder to check, not easier.

Hasz 7y ago

Not trying to imply it's wrong -- if anything, research should be written to a professional level. I also don't think the background should take you from high school calc to topology or differential geometry in one fell sweep.