5 ms·

Often I find I spend days or weeks deciphering mathematics in compsci papers only to find the underlying concept is intuitive and plain, but you're forced to le

by cs702 13y ago

Often I find I spend days or weeks deciphering mathematics in compsci papers only to find the underlying concept is intuitive and plain, but you're forced to learn it bottom up, constructing the authors original genius from the cryptic scrawlings they left in their paper... and you realise a couple of block diagrams and a few short paragraphs could have made the process a lot less frustrating. This is SO TRUE. The same thing happens to me regularly, and not just with "computer science" but with other technical fields, hard sciences, and mathematics. The purpose of most academic papers is not to explain (let alone teach!) ideas in an intuitive manner, but rather to express them in formal, correct, unambiguous terms -- that is, to make them as accurate and critique-proof as possible for publication in some journal.

coldpie 13y ago
Just as a specific example, I had this experience with Bayes' Theorem <http://en.wikipedia.org/wiki/Bayes%27_theorem> http://en.wikipedia.org/wiki/Bayes%27_theorem>. As an informal paper for my computer security class, we used Bayes' theorem to implement aimbot detection in a simple FPS. It sounds like a big, complicated theorem with a special name that some genius had to come up with and has complicated notation involving probabilities and logic symbols. And then it's basically (paraphrasing with reckless abandon) just the probably of your event divided by the total probability space. Lots of words and jargon and theory given in countless papers and articles, and it pretty much just boils down to intuitive addition, multiplication, and division. And our aimbot detector actually worked pretty damn well! Just gather some data points to determine probabilities, plug them into the simple formula, and it was always correct in our test cases.
- nly 13y ago
  It's the same with the crypto we rely on. There are some quite complex mathematical underpinnings for the primitives, but once understand their properties all the common protocols are actually incredibly trivial. DSA and various other iconic crypto protocols are just linear algebra using these new mathematical primitives. The complexity is about the same as using hash functions to build hash tables. Making protocols secure is actually mostly an implementation challenge (as it is with hash tables), and keeping systems secure, pragmatically, is about key management and social challenges. I was incredibly proud when I noticed, just through algebraic manipulation, without reading it anywhere first, that you should be able to extract the public key used to create an an ECDSA signature. Schnorr signatures don't have this property. This is kind of sad in a way becaue it's trivial, but you have no know how the primitive functions and the difference between a field and a group.
- applesinjuice 13y ago
  Fixed link for the lazy: http://en.wikipedia.org/wiki/Bayes_theorem http://en.wikipedia.org/wiki/Bayes_theorem
  - coldpie 13y ago
    Thanks. I reported this bug nearly two years ago :) https://news.ycombinator.com/item?id=4112327 https://news.ycombinator.com/item?id=4112327
- ska 13y ago
  "and it pretty much just boils down to intuitive addition, multiplication, and division." Or does it? After all, probability is one of the very first mathematical tools to be divised, but a rigorous theoretical underpinning for probability and statistics had to wait until measure theory, millenia later. And this was not for want of trying. Part of what makes things "boil down" to the simple and intuitive is years of hard work. Reading Newtons original work on the calculus is painful and convoluted, it took many hands to polish it to the point you might have seen it in. If we've done our jobs well as mathematicians, eventually the essence of an idea will be easy to understand an apply. If you really want to understand it though, you may have to dig into some much deeper work. And often, as with many thing is in mathematics, human intuition will just tend to be wrong about it (e.g. the Monty Hall problem).
deleted 13y ago
[deleted]
pygy_ 13y ago
> The purpose of most academic papers is not to explain (let alone teach!) ideas in an intuitive manner, but rather to express them in formal, correct, unambiguous terms -- that is, to make them as accurate and critique-proof as possible for publication in some journal. Their intended audience is subject matter experts. Their purpose really is to let the authors show off how smart they are, impress their peers, and advance their careers. The other properties derive from that. ;-) edit: I don't want to disparage research in general, BTW, but specifically, the scientific paper redaction process.
- ska 13y ago
  I assume you mean the "reduction" process. The "redaction" process is an important part of the scientific process! I know you were being sarcastic, but I think you are also being a bit unfair. Publication is necessary these days at perhaps an unfortunate rate, I agree. However at least most research mathematicians publish largely to share ideas. After all, that's the best part of the job. Certainly this is true of the vast majority of them in my experience, and the ones weren't motivated by this tended to be very focused on teaching and very good at it.
  - cmsd2 13y ago
    Could be mr pygy_ isn't english.. e.g. redaction in german means editing
jseliger 13y ago
The purpose of most academic papers is not to explain (let alone teach!) ideas in an intuitive manner, but rather to express them in formal, correct, unambiguous terms -- that is, to make them as accurate and critique-proof as possible for publication in some journal. In other words, the purpose is primarily tenure and advancement. This may be a problem.
- logicallee 13y ago
  The issue is that a lot of intuitive stuff is wrong. When you formalize, you remove the simple, intuitive explanation - but you make it much harder for you to remain wrong, if you are wrong - or to become wrong, if you started off right. As a simple explanation, consider the difference between explaining the Monty Hall problem - which might seem to be philosophical, open to interpretation - and coding it up. The moment you code it up --- go ahead, code up a monte carlo simulation that compares the two alternatives of switching doors or maintaining the same choices, and spits out a running count of which is what percentage correct. I'll wait while you code. --- the moment you do that, you see two lines in your code that make the explanation 100% irrefutable and completely obvious. That is why papers are written this way. Intuition can go both ways.
  - SilasX 13y ago
    That would be more convincing if the scientific papers were written in a way that make the point as clearly as the coded-up version of Monty Hall problem. In practice, it's more like they publish the assembly code and when you ask why they didn't do it in Python or something, they lecture you about the need for formal rigor.
    - tel 13y ago
      I think there's generally selection bias about what part of an exposition makes the "a-ha" hit in two ways. First, your a-ha moment may not be the same as someone else's, but you're less likely to observe theirs. Second, your own a-ha is likely the product of a larger production than the moment itself of which you're most attuned to. A good mathematical author must be guarding against both of these selection biases.
abecedarius 13y ago
formal, correct, unambiguous terms Unambiguous? I wish! The notation in most fields is way more ambiguous than code; you're expected to resolve the ambiguity by the norms of whatever research community it's for. Code isn't necessarily clear, but at least all the information is there to be decoded. An example of trying to do better: http://groups.csail.mit.edu/mac/users/gjs/6946/sicm-html/book-Z-H-4.html#%_chap_Temp_2 http://groups.csail.mit.edu/mac/users/gjs/6946/sicm-html/boo...
tipsy 13y ago
And what's sad is that this "formal, correct, unambiguous term" pattern doesn't only apply in academic papers, but also in textbooks and learning and education (e.g. have you ever read a statistics textbook?) -- when we are trying to teach students concepts, we end up getting the opposite of what we wanted to achieve.

by cs702 13y ago

coldpie 13y ago

Just as a specific example, I had this experience with Bayes' Theorem <http://en.wikipedia.org/wiki/Bayes%27_theorem> http://en.wikipedia.org/wiki/Bayes%27_theorem>. As an informal paper for my computer security class, we used Bayes' theorem to implement aimbot detection in a simple FPS. It sounds like a big, complicated theorem with a special name that some genius had to come up with and has complicated notation involving probabilities and logic symbols. And then it's basically (paraphrasing with reckless abandon) just the probably of your event divided by the total probability space. Lots of words and jargon and theory given in countless papers and articles, and it pretty much just boils down to intuitive addition, multiplication, and division. And our aimbot detector actually worked pretty damn well! Just gather some data points to determine probabilities, plug them into the simple formula, and it was always correct in our test cases.

nly 13y ago
It's the same with the crypto we rely on. There are some quite complex mathematical underpinnings for the primitives, but once understand their properties all the common protocols are actually incredibly trivial. DSA and various other iconic crypto protocols are just linear algebra using these new mathematical primitives. The complexity is about the same as using hash functions to build hash tables. Making protocols secure is actually mostly an implementation challenge (as it is with hash tables), and keeping systems secure, pragmatically, is about key management and social challenges. I was incredibly proud when I noticed, just through algebraic manipulation, without reading it anywhere first, that you should be able to extract the public key used to create an an ECDSA signature. Schnorr signatures don't have this property. This is kind of sad in a way becaue it's trivial, but you have no know how the primitive functions and the difference between a field and a group.
applesinjuice 13y ago
Fixed link for the lazy: http://en.wikipedia.org/wiki/Bayes_theorem http://en.wikipedia.org/wiki/Bayes_theorem
- coldpie 13y ago
  Thanks. I reported this bug nearly two years ago :) https://news.ycombinator.com/item?id=4112327 https://news.ycombinator.com/item?id=4112327
ska 13y ago
"and it pretty much just boils down to intuitive addition, multiplication, and division." Or does it? After all, probability is one of the very first mathematical tools to be divised, but a rigorous theoretical underpinning for probability and statistics had to wait until measure theory, millenia later. And this was not for want of trying. Part of what makes things "boil down" to the simple and intuitive is years of hard work. Reading Newtons original work on the calculus is painful and convoluted, it took many hands to polish it to the point you might have seen it in. If we've done our jobs well as mathematicians, eventually the essence of an idea will be easy to understand an apply. If you really want to understand it though, you may have to dig into some much deeper work. And often, as with many thing is in mathematics, human intuition will just tend to be wrong about it (e.g. the Monty Hall problem).

deleted 13y ago

[deleted]

pygy_ 13y ago

> The purpose of most academic papers is not to explain (let alone teach!) ideas in an intuitive manner, but rather to express them in formal, correct, unambiguous terms -- that is, to make them as accurate and critique-proof as possible for publication in some journal. Their intended audience is subject matter experts. Their purpose really is to let the authors show off how smart they are, impress their peers, and advance their careers. The other properties derive from that. ;-) edit: I don't want to disparage research in general, BTW, but specifically, the scientific paper redaction process.

ska 13y ago
I assume you mean the "reduction" process. The "redaction" process is an important part of the scientific process! I know you were being sarcastic, but I think you are also being a bit unfair. Publication is necessary these days at perhaps an unfortunate rate, I agree. However at least most research mathematicians publish largely to share ideas. After all, that's the best part of the job. Certainly this is true of the vast majority of them in my experience, and the ones weren't motivated by this tended to be very focused on teaching and very good at it.
- cmsd2 13y ago
  Could be mr pygy_ isn't english.. e.g. redaction in german means editing

jseliger 13y ago

The purpose of most academic papers is not to explain (let alone teach!) ideas in an intuitive manner, but rather to express them in formal, correct, unambiguous terms -- that is, to make them as accurate and critique-proof as possible for publication in some journal. In other words, the purpose is primarily tenure and advancement. This may be a problem.

logicallee 13y ago
The issue is that a lot of intuitive stuff is wrong. When you formalize, you remove the simple, intuitive explanation - but you make it much harder for you to remain wrong, if you are wrong - or to become wrong, if you started off right. As a simple explanation, consider the difference between explaining the Monty Hall problem - which might seem to be philosophical, open to interpretation - and coding it up. The moment you code it up --- go ahead, code up a monte carlo simulation that compares the two alternatives of switching doors or maintaining the same choices, and spits out a running count of which is what percentage correct. I'll wait while you code. --- the moment you do that, you see two lines in your code that make the explanation 100% irrefutable and completely obvious. That is why papers are written this way. Intuition can go both ways.
- SilasX 13y ago
  That would be more convincing if the scientific papers were written in a way that make the point as clearly as the coded-up version of Monty Hall problem. In practice, it's more like they publish the assembly code and when you ask why they didn't do it in Python or something, they lecture you about the need for formal rigor.
  - tel 13y ago
    I think there's generally selection bias about what part of an exposition makes the "a-ha" hit in two ways. First, your a-ha moment may not be the same as someone else's, but you're less likely to observe theirs. Second, your own a-ha is likely the product of a larger production than the moment itself of which you're most attuned to. A good mathematical author must be guarding against both of these selection biases.

abecedarius 13y ago

formal, correct, unambiguous terms Unambiguous? I wish! The notation in most fields is way more ambiguous than code; you're expected to resolve the ambiguity by the norms of whatever research community it's for. Code isn't necessarily clear, but at least all the information is there to be decoded. An example of trying to do better: http://groups.csail.mit.edu/mac/users/gjs/6946/sicm-html/book-Z-H-4.html#%_chap_Temp_2 http://groups.csail.mit.edu/mac/users/gjs/6946/sicm-html/boo...

tipsy 13y ago

And what's sad is that this "formal, correct, unambiguous term" pattern doesn't only apply in academic papers, but also in textbooks and learning and education (e.g. have you ever read a statistics textbook?) -- when we are trying to teach students concepts, we end up getting the opposite of what we wanted to achieve.