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The most irritating trope of math and CS literature has to be whenever something interesting or useful is "left as an exercise to the reader." I always felt th

by pak 15y ago

The most irritating trope of math and CS literature has to be whenever something interesting or useful is "left as an exercise to the reader." I always felt that phrase has no place in the internet age, where the concept of a "page limit" is laughable and a simple hyperlink can point me to chapters upon chapters of appendices. Calling something "trivial" is swallowable, and perhaps this article's example of "it easily follows that..." is the mathematician's secret handshake that the steps in between are boring, but pointing out an interesting conclusion and then saying the reader deserves an exercise to actually make sense of it, I mean... isn't the point of academic writing to communicate research and results already performed? Wouldn't it be better to show the work for your assertion so that others could critique it or offer even better solutions? I know somebody is about to point out to me that I'm being "lazy" and should enjoy doing more work to learn so and so, but being asked regularly in the literature to reinvent somebody else's wheel seems to run counter to everything we do in CS (and academia in general, I would think). This article aside, I do sometimes feel that academic writing in the math/CS realm occasionally reeks a little bit of snobbery, where communication is held secondary to keeping up appearances.

ColinWright 15y ago
The most irritating thing to me is when someone says they want to understand something, but then they are unwilling to put in any real effort. It is a misapprehension, misunderstanding and misrepresentation to say: ... reinventing the wheel runs counter to everything we do in CS. You can read all you like about how to juggle - if you don't put in the hours, you won't be able to do it. You can read all you like about how to unicycle - if you don't put in the hours, you won't be able to do it. You can read all you like about how to program - if you don't put in the hours, you won't be able to do it. Skills require practice. These instances of "left as an exercise for the interested reader" are to help you really learn and properly understand the material. And if you don't care, don't bother. If you are unwilling to put in the time then the chances are that you would end up thinking you understand an explanation, whereas in fact you don't. The above is only for good writing, of course. There are plenty of instances of bad writing, but that's not then a complaint about the subject, it's a complaint about the writer. Someone once said of Feynman that his lectures were beautifully clear, and that those who listened gained real insight and understanding. Until they had to use it. Then they realised that they didn't really understand it at all. If you want understanding, do the exercises. So there you are, I've done as you predicted and pointed out that you're just being lazy, and that if you really want to learn then you have to put in the work. Just because you preempted it, doesn't mean it's wrong. It's right, you already know it. Complaining won't help you. Put in the time.
- pak 15y ago
  You must have only seen this phrase in places where it was used in the bright, sparkling, professorial manner assumed by your comment. I take no offense when it appears in a textbook, where the intent is to have me practice a skill. I do object to its appearance in a journal article, however; that is a context where you are supposed to communicate findings as clearly and concisely as possible. In particular, I've come across its use more and more often where one of the following likely applies: 1. it is doubtful that the author has actually done the work to prove his own assertion, and uses the phrase to cast his own burden on the reader, 2. the author has possibly done the work, but can't be bothered to condense it to the quality required for publication, 3. showing the work would clearly be useful for the target audience, but the author is more concerned with making the material appear difficult, or 4. the author is being ironic, because the assertion is either superfluous, outright incorrect, or known to be unprovable. In fact, all these bad use-cases are common sources of humor among math nerds (http://www.jargon.net/jargonfile/e/exerciseleftasan.html http://www.jargon.net/jargonfile/e/exerciseleftasan.html), (http://abstrusegoose.com/12 http://abstrusegoose.com/12), (http://fasterdonuts.tumblr.com/post/4516834904/the-proof-is-left-as-an-exercise-for-the http://fasterdonuts.tumblr.com/post/4516834904/the-proof-is-...) ... so I think I'm being fair in calling this phrase a trope. As in, its overuse is well-known, tolerated, and occasionally ridiculed. tldr: I am indeed complaining about bad writing, not the subject--specifically that "left as an exercise" has become a common idiom behind which bad writers in math and CS hide, and its inappropriate use is now all too common.
  - ColinWright 15y ago
    Yes, it's used too often. Yes, it's used sometimes when it's inappropriate. Yes, sometimes I suspect that the author doesn't really know the answer. I'm less sure that the author uses it it all seriousness when the know the result is unproven or unprovable. But it is a phrase that has its place, there are times when it's exactly right to use it. Don't reject it outright. I've used it in publication where the editor actually asked me to remove details and put the phrase in its place. It's not always the author.
contravert 15y ago
I completely agree. This phrase appears in even some of the most hallowed tomes of computer science, such as Introduction to Algorithms. The textbook puts important theorems and proofs in the exercises section, and does not even provide solutions online (at least for the later sections). Keep in mind that this book is used as a reference manual for many implementations of algorithms and data structures.
pyninja 15y ago
> I mean... isn't the point of academic writing to communicate research and results already performed? Obviously mathematicians don't leave "exercises for the reader" in research papers, but it is common in textbooks or expository writing. > I always felt that phrase has no place in the internet age, where the concept of a "page limit" is laughable and a simple hyperlink can point me to chapters upon chapters of appendices. The constraint is not page length, of course, but time. It is a much better use of a mathematician's time to leave easily reproducible proofs to the reader, and focus on the interesting ideas. Anyway, doing these kinds of exercises is actually very useful in understanding new ideas.
- pak 15y ago
  >Obviously mathematicians don't leave "exercises for the reader" in research papers ORLY? I'll leave this right here for you: http://scholar.google.com/scholar?hl=en&q=left+as+an+exercise&btnG=Search&as_subj=eng&as_sdt=1%2C31&as_ylo=&as_vis=0 http://scholar.google.com/scholar?hl=en&q=left+as+an+exe... That's >100k hits from what Google Scholar can index alone--a few are from books, but the vast majority are journal articles.
  - pyninja 15y ago
    I looked at the first few pages and saw only a few math papers, and in those the exercises were uninteresting details (e.g. just computation, or the second of two analogous cases where only the first is proved in the paper). Do you really think anyone would benefit from such proofs in a paper? I would be interested if you could give an actual example of a paper where a reader might be inconvenienced by something being left as an exercise.

by pak 15y ago

ColinWright 15y ago

The most irritating thing to me is when someone says they want to understand something, but then they are unwilling to put in any real effort. It is a misapprehension, misunderstanding and misrepresentation to say: ... reinventing the wheel runs counter to everything we do in CS. You can read all you like about how to juggle - if you don't put in the hours, you won't be able to do it. You can read all you like about how to unicycle - if you don't put in the hours, you won't be able to do it. You can read all you like about how to program - if you don't put in the hours, you won't be able to do it. Skills require practice. These instances of "left as an exercise for the interested reader" are to help you really learn and properly understand the material. And if you don't care, don't bother. If you are unwilling to put in the time then the chances are that you would end up thinking you understand an explanation, whereas in fact you don't. The above is only for good writing, of course. There are plenty of instances of bad writing, but that's not then a complaint about the subject, it's a complaint about the writer. Someone once said of Feynman that his lectures were beautifully clear, and that those who listened gained real insight and understanding. Until they had to use it. Then they realised that they didn't really understand it at all. If you want understanding, do the exercises. So there you are, I've done as you predicted and pointed out that you're just being lazy, and that if you really want to learn then you have to put in the work. Just because you preempted it, doesn't mean it's wrong. It's right, you already know it. Complaining won't help you. Put in the time.

pak 15y ago
You must have only seen this phrase in places where it was used in the bright, sparkling, professorial manner assumed by your comment. I take no offense when it appears in a textbook, where the intent is to have me practice a skill. I do object to its appearance in a journal article, however; that is a context where you are supposed to communicate findings as clearly and concisely as possible. In particular, I've come across its use more and more often where one of the following likely applies: 1. it is doubtful that the author has actually done the work to prove his own assertion, and uses the phrase to cast his own burden on the reader, 2. the author has possibly done the work, but can't be bothered to condense it to the quality required for publication, 3. showing the work would clearly be useful for the target audience, but the author is more concerned with making the material appear difficult, or 4. the author is being ironic, because the assertion is either superfluous, outright incorrect, or known to be unprovable. In fact, all these bad use-cases are common sources of humor among math nerds (http://www.jargon.net/jargonfile/e/exerciseleftasan.html http://www.jargon.net/jargonfile/e/exerciseleftasan.html), (http://abstrusegoose.com/12 http://abstrusegoose.com/12), (http://fasterdonuts.tumblr.com/post/4516834904/the-proof-is-left-as-an-exercise-for-the http://fasterdonuts.tumblr.com/post/4516834904/the-proof-is-...) ... so I think I'm being fair in calling this phrase a trope. As in, its overuse is well-known, tolerated, and occasionally ridiculed. tldr: I am indeed complaining about bad writing, not the subject--specifically that "left as an exercise" has become a common idiom behind which bad writers in math and CS hide, and its inappropriate use is now all too common.
- ColinWright 15y ago
  Yes, it's used too often. Yes, it's used sometimes when it's inappropriate. Yes, sometimes I suspect that the author doesn't really know the answer. I'm less sure that the author uses it it all seriousness when the know the result is unproven or unprovable. But it is a phrase that has its place, there are times when it's exactly right to use it. Don't reject it outright. I've used it in publication where the editor actually asked me to remove details and put the phrase in its place. It's not always the author.

contravert 15y ago

I completely agree. This phrase appears in even some of the most hallowed tomes of computer science, such as Introduction to Algorithms. The textbook puts important theorems and proofs in the exercises section, and does not even provide solutions online (at least for the later sections). Keep in mind that this book is used as a reference manual for many implementations of algorithms and data structures.

pyninja 15y ago

> I mean... isn't the point of academic writing to communicate research and results already performed? Obviously mathematicians don't leave "exercises for the reader" in research papers, but it is common in textbooks or expository writing. > I always felt that phrase has no place in the internet age, where the concept of a "page limit" is laughable and a simple hyperlink can point me to chapters upon chapters of appendices. The constraint is not page length, of course, but time. It is a much better use of a mathematician's time to leave easily reproducible proofs to the reader, and focus on the interesting ideas. Anyway, doing these kinds of exercises is actually very useful in understanding new ideas.

pak 15y ago
>Obviously mathematicians don't leave "exercises for the reader" in research papers ORLY? I'll leave this right here for you: http://scholar.google.com/scholar?hl=en&q=left+as+an+exercise&btnG=Search&as_subj=eng&as_sdt=1%2C31&as_ylo=&as_vis=0 http://scholar.google.com/scholar?hl=en&q=left+as+an+exe... That's >100k hits from what Google Scholar can index alone--a few are from books, but the vast majority are journal articles.
- pyninja 15y ago
  I looked at the first few pages and saw only a few math papers, and in those the exercises were uninteresting details (e.g. just computation, or the second of two analogous cases where only the first is proved in the paper). Do you really think anyone would benefit from such proofs in a paper? I would be interested if you could give an actual example of a paper where a reader might be inconvenienced by something being left as an exercise.