4 ms·

I will die on the hill that most of math would benefit from better naming, less short names and longer format. Yes, the crack math guys have no problems with te

by HdS84 1y ago

I will die on the hill that most of math would benefit from better naming, less short names and longer format. Yes, the crack math guys have no problems with terse symbols. But most people do. Good example is Greek letters for geometry. They are not really taught in school so an easy formula gets 'weird squiggly thing times another squiggly thing....' and that does not help understanding at all

ndriscoll 1y ago
For any given problem, you usually know what it is your studying, so writing out names doesn't have much benefit. On the other hand, a more visual language (which is what mathematical writing is) lets you easily look at specific portions of the picture and read off how it behaves, which is very useful. Basically, getting hung up on names means you're reading it wrong.
globular-toast 1y ago
This is like trying to change English or arguing that we should all speak Esperanto. Mathematical notation isn't the way it is to save ink or make it look difficult. It's that way because it works. Notation isn't set by committee, it's just a way of communication that works. If you read cutting edge research you'll find notations being invented all over the place. Most of them will never go anywhere, some will become standard in their field (like big-O) and others will become universally used (like dropping the multiplication symbol and using epsilon for a small number).
- tenacious_tuna 1y ago
  I think this is a very limited take for a hacker forum. We talk about how useful accurate names for variables are all the time, or generally how working to encode more natural/context-related semantics to code helps anyone reading it understand what the goal is better than an extremely terse symbology. Yeah, lots of existing math texts will forever exist with greek alphabet soup, but we don't have to rely on those as our be-all-end-all teaching tools. To operate at a high level in mathematics I would agree that having the skill of easily abstracting complex things into compact symbols is a necessary skill, just as I would agree to the same concept applied to software engineering or really any complex engineering system; by the same token, we don't have to START on hard mode with all of our students. Math is infamously difficult for some, largely (I think) because we make it unnecessarily opaque out of some misguided sense of traditionalism. If we want to have lots of people who are good at math we should embrace whatever pedagogy is effective.
  - globular-toast 1y ago
    Many programs are at a much higher level of abstraction than mathematics. If you are implementing domain logic then you should definitely use names from the domain. But when implementing an algorithm often the most meaningful name is a single character. I find it odd when people try to force the "no single character" rule everywhere. But I've got to say, the short names are not the problem. If you rewrote F=ma as "force is equal to mass multiplied by acceleration" this wouldn't suddenly make it more accessible to swathes of the population. People who are good at maths anyway have no problem with this.
  - nh23423fefe 1y ago
    imagining that alpha is what stops people from being good at math is a useless take. why pretend that such a low bar could prevent anyone from understanding? its some fake generosity towards "newcomers" that is completely unwarranted. math notation is by and for professional mathematicians. are you really saying that "let function(argument has type RealNumber) has type RealNumber be a function from a real number argument to a real number" is somehow superior to "let f(x) : R->R"
    - tenacious_tuna 1y ago
      > why pretend that such a low bar could prevent anyone from understanding? I don't know why this is a startling take. If you encode your ideas in an unfamilar symbology, of course that's going to make it more difficult for someone who isn't familiar with the space. I'm not arguing that we should teach real analysis this way, or any other high level math class. I'm only contesting GP's comment that there is NO value to be had in using more familiar language to explain a new concept to an unfamiliar audience. This is the entire reasoning behind "word problems" at the elementary level; they're meant to ground the abstract modeling of a math problem (193 - 3 * 12 = ?) into something more intuitive for a child to understand (If you start with 193 eggs, and you take three dozen away to bake a cake, how many are left?) > are you really saying that "let function(argument has type RealNumber) has type RealNumber be a function from a real number argument to a real number" is somehow superior to "let f(x) : R->R" No, I'm saying the there's tradeoffs on either side, and our educators ought to be aware of this. > math notation is by and for professional mathematicians. I agree, but we teach math to plenty of people who aren't professional mathematicians. I wouldn't want to do formal abstract algebra proofs in a more verbose form, I'm perfectly happy using the domain notation, but my friends from biological sciences who have to take a calculus course now have to learn both a new symbology alongside the problem domain. I've watched enough of my (clearly intelligent) biology friends slam face first into calculus and spin out. They're not dumb, they can do circles around me when it comes to chemistry, yet they Just Can't wrap their heads around calculus-style math, which leads me to wonder what the difference is between how we teach complex chemistry vs complex math. Questioning the pedagogy is a fairly logical extension of that.

by HdS84 1y ago

ndriscoll 1y ago

For any given problem, you usually know what it is your studying, so writing out names doesn't have much benefit. On the other hand, a more visual language (which is what mathematical writing is) lets you easily look at specific portions of the picture and read off how it behaves, which is very useful. Basically, getting hung up on names means you're reading it wrong.

globular-toast 1y ago

This is like trying to change English or arguing that we should all speak Esperanto. Mathematical notation isn't the way it is to save ink or make it look difficult. It's that way because it works. Notation isn't set by committee, it's just a way of communication that works. If you read cutting edge research you'll find notations being invented all over the place. Most of them will never go anywhere, some will become standard in their field (like big-O) and others will become universally used (like dropping the multiplication symbol and using epsilon for a small number).

tenacious_tuna 1y ago
I think this is a very limited take for a hacker forum. We talk about how useful accurate names for variables are all the time, or generally how working to encode more natural/context-related semantics to code helps anyone reading it understand what the goal is better than an extremely terse symbology. Yeah, lots of existing math texts will forever exist with greek alphabet soup, but we don't have to rely on those as our be-all-end-all teaching tools. To operate at a high level in mathematics I would agree that having the skill of easily abstracting complex things into compact symbols is a necessary skill, just as I would agree to the same concept applied to software engineering or really any complex engineering system; by the same token, we don't have to START on hard mode with all of our students. Math is infamously difficult for some, largely (I think) because we make it unnecessarily opaque out of some misguided sense of traditionalism. If we want to have lots of people who are good at math we should embrace whatever pedagogy is effective.
- globular-toast 1y ago
  Many programs are at a much higher level of abstraction than mathematics. If you are implementing domain logic then you should definitely use names from the domain. But when implementing an algorithm often the most meaningful name is a single character. I find it odd when people try to force the "no single character" rule everywhere. But I've got to say, the short names are not the problem. If you rewrote F=ma as "force is equal to mass multiplied by acceleration" this wouldn't suddenly make it more accessible to swathes of the population. People who are good at maths anyway have no problem with this.
- nh23423fefe 1y ago
  imagining that alpha is what stops people from being good at math is a useless take. why pretend that such a low bar could prevent anyone from understanding? its some fake generosity towards "newcomers" that is completely unwarranted. math notation is by and for professional mathematicians. are you really saying that "let function(argument has type RealNumber) has type RealNumber be a function from a real number argument to a real number" is somehow superior to "let f(x) : R->R"
  - tenacious_tuna 1y ago
    > why pretend that such a low bar could prevent anyone from understanding? I don't know why this is a startling take. If you encode your ideas in an unfamilar symbology, of course that's going to make it more difficult for someone who isn't familiar with the space. I'm not arguing that we should teach real analysis this way, or any other high level math class. I'm only contesting GP's comment that there is NO value to be had in using more familiar language to explain a new concept to an unfamiliar audience. This is the entire reasoning behind "word problems" at the elementary level; they're meant to ground the abstract modeling of a math problem (193 - 3 * 12 = ?) into something more intuitive for a child to understand (If you start with 193 eggs, and you take three dozen away to bake a cake, how many are left?) > are you really saying that "let function(argument has type RealNumber) has type RealNumber be a function from a real number argument to a real number" is somehow superior to "let f(x) : R->R" No, I'm saying the there's tradeoffs on either side, and our educators ought to be aware of this. > math notation is by and for professional mathematicians. I agree, but we teach math to plenty of people who aren't professional mathematicians. I wouldn't want to do formal abstract algebra proofs in a more verbose form, I'm perfectly happy using the domain notation, but my friends from biological sciences who have to take a calculus course now have to learn both a new symbology alongside the problem domain. I've watched enough of my (clearly intelligent) biology friends slam face first into calculus and spin out. They're not dumb, they can do circles around me when it comes to chemistry, yet they Just Can't wrap their heads around calculus-style math, which leads me to wonder what the difference is between how we teach complex chemistry vs complex math. Questioning the pedagogy is a fairly logical extension of that.