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Math notation isn't inherently bad. Even in this example, it could be justified. If it was accompanied by any sort of explanation of what it meant. No matter h

Math notation isn't inherently bad. Even in this example, it could be justified. If it was accompanied by any sort of explanation of what it meant. No matter how familiar with the notation, it's always going to be less clear and take time to unravel it. "OK, I see the author is multiplying a bunch of numbers together? Why are they doing this? [Reads over it 10 more times]... Oh... it's to tell if it's even or odd. Why on Earth couldn't they just say that.." And literally every use of notation in this paper is like that. I was incredibly fortunate they decided to stop at some point, and just say they then draw a line with those parameters. They could have kept going and defined a procedure for drawing lines. I would not be remotely surprised. I believe it's entirely about signalling. Math notation looks professional and academic. Just like describing yourself as "we". There's also something called the illusion of transparency. It's a bias where people believe they are much more understandable than they actually are. Like if you explain an idea to someone, you will expect them to have a much higher chance of understanding it then they actually do. I believe people that write papers are incredibly guilty of that. And every freaking academic paper is like this. So many papers pointlessly give exact equations for a neural network. Instead of just saying "and we created a 3 layer neural net with a softmax output trained withstochastic gradient descent." But figuring out that's what the equations describe is going to take 15 minutes and lots of confusion. Really, imagine a programmer that explained his ideas entirely in code without any comments. With one letter, undescriptive variable names. Who used as much premature optimization as possible to obscure it further. I doubt such a post would make it to the top of HN. But this crap regularly does.

yorwba 10y ago
> If it was accompanied by any sort of explanation of what it meant. Most of the paper is just text, explaining their results in plain English, interspersed with technical vocabulary. > "OK, I see the author is multiplying a bunch of numbers together? Why are they doing this? [Reads over it 10 more times]... Oh... it's to tell if it's even or odd. Why on Earth couldn't they just say that.." Using powers of -1 to test for parity is a fairly standard trick, and they explain it right at the bottom of page 2. Did you overlook that, were you unfamiliar with this use, or is the explanation not clear enough? Only one of these possibilities can be blamed on the authors. Or maybe you were talking about the formulas at the top of page 4, were they are multiplying two of those random parity functions together? That's not really to check whether they are even or odd, it's to prove their mutual orthogonality, which it says in the sentence above. In these transformations, the notation using powers of -1 is very convenient, since it allows to apply simple algebraic transformations. Those would have been very tedious had they used a boolean even/odd indicator. > They could have kept going and defined a procedure for drawing lines. They do this: Note that as the images space is discrete, we round the values corresponding to the points on the lines to the closest integer coordinate. They don't use notation for this, because it's not required for clarity. Basically, I think the ideas in this paper are laid out pretty clearly for someone who is already familiar with the notation and conventions used. Research papers are primarily about communicating ideas to people working in the same field, who don't need to have the basics explained to them. That this makes the results hard to understand for a more general audience, even if they are experts in their field, is unfortunate, but basically unavoidable. Adding links to definitions and examples in introductory textbooks to every research paper would be pretty awesome, but it shouldn't be the author's burden.
- reader5000 10y ago
  The first author on this paper does have a great intro book on precisely this area where the notation ramps up more slowly.
soVeryTired 10y ago
But he's not testing whether it's even or odd. The lines don't necessarily pass through the origin.

yorwba 10y ago

> If it was accompanied by any sort of explanation of what it meant. Most of the paper is just text, explaining their results in plain English, interspersed with technical vocabulary. > "OK, I see the author is multiplying a bunch of numbers together? Why are they doing this? [Reads over it 10 more times]... Oh... it's to tell if it's even or odd. Why on Earth couldn't they just say that.." Using powers of -1 to test for parity is a fairly standard trick, and they explain it right at the bottom of page 2. Did you overlook that, were you unfamiliar with this use, or is the explanation not clear enough? Only one of these possibilities can be blamed on the authors. Or maybe you were talking about the formulas at the top of page 4, were they are multiplying two of those random parity functions together? That's not really to check whether they are even or odd, it's to prove their mutual orthogonality, which it says in the sentence above. In these transformations, the notation using powers of -1 is very convenient, since it allows to apply simple algebraic transformations. Those would have been very tedious had they used a boolean even/odd indicator. > They could have kept going and defined a procedure for drawing lines. They do this: Note that as the images space is discrete, we round the values corresponding to the points on the lines to the closest integer coordinate. They don't use notation for this, because it's not required for clarity. Basically, I think the ideas in this paper are laid out pretty clearly for someone who is already familiar with the notation and conventions used. Research papers are primarily about communicating ideas to people working in the same field, who don't need to have the basics explained to them. That this makes the results hard to understand for a more general audience, even if they are experts in their field, is unfortunate, but basically unavoidable. Adding links to definitions and examples in introductory textbooks to every research paper would be pretty awesome, but it shouldn't be the author's burden.

reader5000 10y ago
The first author on this paper does have a great intro book on precisely this area where the notation ramps up more slowly.

soVeryTired 10y ago

But he's not testing whether it's even or odd. The lines don't necessarily pass through the origin.