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>The benefit in single letter variable names in math is that you're able to write the information in a more compact, digestible manner. You missed my point ent

>The benefit in single letter variable names in math is that you're able to write the information in a more compact, digestible manner. You missed my point entirely. I said that you should not optimize for writing math, you should optimize for reading math. And that's where the same argument as for code holds true as well: It doesn't matter if it takes longer to write, it will be read magnitudes more often, and that is what matters most. Again, if you're just doing quick calculations on paper or hacking something into your shell/REPL, I really don't care if you use cryptic variable names. I do, too. But I don't want to ever see this in a good program, and I think that it doesn't belong into a good math text, either. >The reason this latter point is important is for the same reason short, compact programming languages are a boon to comprehension. And again you missed what I explicitly stated: it's good to write in a concise way, but only as long as it doesn't become cryptic. And I disagree with your belief about information processing. It's better to build semantic relations by having meaningful names than it is to process a lot of information in a short time. It really doesn't matter how fast you are able read something - if it doesn't make sense, you won't understand it.

hackinthebochs 14y ago
>You missed my point entirely. I said that you should not optimize for writing math, you should optimize for reading math. My point is that these goals are nearly one in the same when you get to the high level. Many mathematical relationships are very complex, usually not the step-by-step procedures that is common in code. Thus being able to hold the entire relationship in your head at once is crucial. Single letter names for variables and functions are critical here (for the previously mentioned reason working-memory-decay). I basically have a bachelors in math, and I could not imagine reading complex equations with full variable names. The hard part is understanding the whole, not remembering what x or i means. If you find an equation cryptic, that just means you don't have the requisite knowledge to really understand it.
- slowpoke 14y ago
  Sorry, if all you have left is the (very typical) argument of "if you think that way you just don't understand it", then I'll consider this discussion over. I have no interest in hearing endless appeals to tradition. I'm sure people made similar arguments for GOTO back in the day. Good thing we moved on.
  - hackinthebochs 14y ago
    I would like to think my argument is far more nuanced than you're giving it credit. This isn't an appeal to tradition; I'm making an argument that explains why traditionally math has stayed with the "cryptic" notation rather than descriptive variable names. You're completely ignoring the working memory argument I'm making. A large part of math is pattern matching: recognizing a common relationship between variables (a common pattern or "theme") and investigating that relationship further. This ability is critical to mathematical ability. Visual compactness is crucial here. Using descriptive names will completely bog down your visual system with reading words rather than identifying patterns. Pattern matching is a critical skill when one becomes an expert in any field; in math its of utmost importance. Math is optimized for reading by other experts who have those same visual patterns committed to memory. This is the optimal approach for the work's target audience. Yes, it makes advanced math largely inaccessible to outsiders, but that's a part of the trade off.
    - slowpoke 14y ago
      >You're completely ignoring the working memory argument I'm making. I'm not ignoring it. I said I don't buy it. I generally don't believe that you need visual compactness to to point of being cryptic to make use of pattern matching. I'm not saying this is necessarily easy. Neither is choosing good variable names in programming, especially at high abstraction levels. But that's no excuse for not doing it. The other thing is that mathematicians will finally have to accept that they aren't the only ones who need math. It's not, for the most part, a "field for experts" (to paraphrase you) which only those who are willing to become experts at it are allowed to understand. It's a beautiful science with lots of appliance in almost every other field. But it's inaccessible as hell in large parts due to mathematicians with your attitude. I strongly believe that math can be made more accessible and more "user-friendly" for people who aren't experts at it. It will be hard to do that without sacrificing its tremendous power and flexibility (which I am totally against in software, as well). But it must (and will) eventually be done. Take note, by the way, that the accessibility problem is less and less important the more specialized the math you are doing becomes. I don't really care if some hyper-abstract field of math that a few dozen people in the world are even able to grasp the basics of is arcane and cryptic. That's something only experts will care for and if they are fine with their niche field being overly cryptic, so be it. What I'm concerned about is math in general. I firmly agree with the position that math should not be taught as an appliance, because that is missing the point. However, it's downright fatuous to ignore the fact that math has appliances, and that therefore, a lot of people will have to learn a subset of it. To excuse bad practices which have survived by virtue of no one questioning them with nothing but "it's optimized for edge cases (experts)" is a cop-out. It ignores the problem. I also find it funny that I already met with such vehement opposition for just proposing meaningful variable and function names. That was just an example. There are a lot more problems to be solved. Stuff like "this is trivial" or "left as an exercise" as a way to avoid writing out cumbersome, but nonetheless important (for non-experts) parts, the general terseness of mathematical texts, including the parts in plain English. I could probably find more. Let me conclude with this: Math as a whole has accessibility problems, just like a lot of CS and computer stuff. Flat out ignoring them or even asserting "it must be this way" is incredibly ignorant. And we need dialogue to do this - not condescending "there is no problem" rebuttals.

hackinthebochs 14y ago

>You missed my point entirely. I said that you should not optimize for writing math, you should optimize for reading math. My point is that these goals are nearly one in the same when you get to the high level. Many mathematical relationships are very complex, usually not the step-by-step procedures that is common in code. Thus being able to hold the entire relationship in your head at once is crucial. Single letter names for variables and functions are critical here (for the previously mentioned reason working-memory-decay). I basically have a bachelors in math, and I could not imagine reading complex equations with full variable names. The hard part is understanding the whole, not remembering what x or i means. If you find an equation cryptic, that just means you don't have the requisite knowledge to really understand it.

slowpoke 14y ago
Sorry, if all you have left is the (very typical) argument of "if you think that way you just don't understand it", then I'll consider this discussion over. I have no interest in hearing endless appeals to tradition. I'm sure people made similar arguments for GOTO back in the day. Good thing we moved on.
- hackinthebochs 14y ago
  I would like to think my argument is far more nuanced than you're giving it credit. This isn't an appeal to tradition; I'm making an argument that explains why traditionally math has stayed with the "cryptic" notation rather than descriptive variable names. You're completely ignoring the working memory argument I'm making. A large part of math is pattern matching: recognizing a common relationship between variables (a common pattern or "theme") and investigating that relationship further. This ability is critical to mathematical ability. Visual compactness is crucial here. Using descriptive names will completely bog down your visual system with reading words rather than identifying patterns. Pattern matching is a critical skill when one becomes an expert in any field; in math its of utmost importance. Math is optimized for reading by other experts who have those same visual patterns committed to memory. This is the optimal approach for the work's target audience. Yes, it makes advanced math largely inaccessible to outsiders, but that's a part of the trade off.
  - slowpoke 14y ago
    >You're completely ignoring the working memory argument I'm making. I'm not ignoring it. I said I don't buy it. I generally don't believe that you need visual compactness to to point of being cryptic to make use of pattern matching. I'm not saying this is necessarily easy. Neither is choosing good variable names in programming, especially at high abstraction levels. But that's no excuse for not doing it. The other thing is that mathematicians will finally have to accept that they aren't the only ones who need math. It's not, for the most part, a "field for experts" (to paraphrase you) which only those who are willing to become experts at it are allowed to understand. It's a beautiful science with lots of appliance in almost every other field. But it's inaccessible as hell in large parts due to mathematicians with your attitude. I strongly believe that math can be made more accessible and more "user-friendly" for people who aren't experts at it. It will be hard to do that without sacrificing its tremendous power and flexibility (which I am totally against in software, as well). But it must (and will) eventually be done. Take note, by the way, that the accessibility problem is less and less important the more specialized the math you are doing becomes. I don't really care if some hyper-abstract field of math that a few dozen people in the world are even able to grasp the basics of is arcane and cryptic. That's something only experts will care for and if they are fine with their niche field being overly cryptic, so be it. What I'm concerned about is math in general. I firmly agree with the position that math should not be taught as an appliance, because that is missing the point. However, it's downright fatuous to ignore the fact that math has appliances, and that therefore, a lot of people will have to learn a subset of it. To excuse bad practices which have survived by virtue of no one questioning them with nothing but "it's optimized for edge cases (experts)" is a cop-out. It ignores the problem. I also find it funny that I already met with such vehement opposition for just proposing meaningful variable and function names. That was just an example. There are a lot more problems to be solved. Stuff like "this is trivial" or "left as an exercise" as a way to avoid writing out cumbersome, but nonetheless important (for non-experts) parts, the general terseness of mathematical texts, including the parts in plain English. I could probably find more. Let me conclude with this: Math as a whole has accessibility problems, just like a lot of CS and computer stuff. Flat out ignoring them or even asserting "it must be this way" is incredibly ignorant. And we need dialogue to do this - not condescending "there is no problem" rebuttals.