3 ms·

>Hah, no, "-> -> a b c" is not easy to parse, except for a computer. going are people not to read easily. It's a silly argument that prefix is fundamentally eas

by konkin 5y ago

>Hah, no, "-> -> a b c" is not easy to parse, except for a computer. going are people not to read easily. It's a silly argument that prefix is fundamentally easier for humans when it disrupts the flow even in your example. The only argument I'm seeing here is that you can't parse prefix notation and won't put the effort into trying it, which is the same argument people used against Arabic numerals in the middle ages. A prefix only language is fundamentally easier to read and write to anyone who hasn't spend two decades learning the mishmash of pre, in, post, and upside-down fix that mathematics currently uses. >But even then, we have things like the integral which uses physical placement to take (typically) up to 3 arguments: Using four variables. It's amazing to me people defend this type of mess as something meaningful instead of a terrible historical contingency which we should get rid of as quickly as we can. In prefix notation you can just use "integral upper lower function" to convey the same information in pure text without the need for inventing TeX and vector displays.

Jtsummers 5y ago
Try out your notation, which I will agree can be unambiguous in a technical sense, but will quickly become unreadable for actual human beings, on a few modest examples. = 1 + square sin x square cos x -- a trig identity / + - b √ - square b * * 4 a c * 2 a ^ oops, ambiguous, you need a new symbol for negation Note as well, in that second example, the great distance between the division operation and the divisor. This does not lend itself to readability by people, they have to keep the entire stack of operations in their head. Ok, so you switch the notation to be more tree-like and use indentation (how I write complex Lisp math expressions): v still ambiguous, what alternate symbol can we use? / + - b √ - square b * * 4 a c * 2 a Ok, somewhat clearer, but hardly "easy" to read for a person. At this point you may as well just put back the parentheses (and be back at Lisp s-exprs, which as you noted earlier is not well-suited to handwriting). The mathematical expression is clearer for people. It requires them to keep less in their head at any one point in the reading. _________ -b + √b^2 - 4ac --------------- 2a I'm not saying this is perfect, there is room for improvement in this form, but it is going to be better for the average math literate person (by which I mean, someone who has at least covered high school algebra). Even if you taught prefix notation from the start, the user of that notation still has to keep more in their head as they try to parse it.
- konkin 5y ago
  > Try out your notation, which I will agree can be unambiguous in a technical sense, but will quickly become unreadable for actual human beings, on a few modest examples. It's perfectly legible to me and I use it daily in my (mathematical) work. Again all you're saying is that you're not used to it and it must be a bad notation. Just like how people who were shown Arabic numerals defended Roman numerals. I'd do you one better and point out that the example should be = 1 λ x square sin x square cos x since having unbound variables is poor form after someone invented lambda calculus. And yes, you need a symbol for negation which is a step up since a-b is also ambiguous in the same sense. For the second one you easily see why words are superior to symbols when you stop trying to use hieroglyphs and start using letters instead: div add neg b sqrt sub pow b 2 sub times 4 times a c times 2 a. I can define new functions with well known meaning without having to copy special characters or invent type setting systems.
  - Jtsummers 5y ago
    So, you're a troll then, you can't even be consistent in your presentation. + and - are bad to use, but λ is ok to use? Words are the thing to use for "add" and "sub" and "div" (why not the whole word?), but not "equals" or "define function"? And the words you choose are strictly English, which makes your mathematical notation no longer mutually comprehensible across most of the globe? Those are all positives to you? That's how math notation will be dragged into the 20th century? And, what, we now teach lambda calculus to elementary school kids once they start learning about variables? At least try to come up with a plausible argument. > I use it daily in my (mathematical) work. I find this highly unlikely, but sure, if you're not a troll, you've found a notation that (apparently) works for you (what kind of math?) and you think it's better but haven't bothered to think it though. And you still haven't answered the question on the second example, you just made it more verbose. The reader still has to remember (with zero punctuation or other indicators in your example) that the dividend for the div is the next 14 tokens and the divisor the last 3. Because that's totally readable and comprehensible. If you're not a troll, your idea isn't even half-baked.
    - konkin 5y ago

by konkin 5y ago

Jtsummers 5y ago

Try out your notation, which I will agree can be unambiguous in a technical sense, but will quickly become unreadable for actual human beings, on a few modest examples. = 1 + square sin x square cos x -- a trig identity / + - b √ - square b * * 4 a c * 2 a ^ oops, ambiguous, you need a new symbol for negation Note as well, in that second example, the great distance between the division operation and the divisor. This does not lend itself to readability by people, they have to keep the entire stack of operations in their head. Ok, so you switch the notation to be more tree-like and use indentation (how I write complex Lisp math expressions): v still ambiguous, what alternate symbol can we use? / + - b √ - square b * * 4 a c * 2 a Ok, somewhat clearer, but hardly "easy" to read for a person. At this point you may as well just put back the parentheses (and be back at Lisp s-exprs, which as you noted earlier is not well-suited to handwriting). The mathematical expression is clearer for people. It requires them to keep less in their head at any one point in the reading. _________ -b + √b^2 - 4ac --------------- 2a I'm not saying this is perfect, there is room for improvement in this form, but it is going to be better for the average math literate person (by which I mean, someone who has at least covered high school algebra). Even if you taught prefix notation from the start, the user of that notation still has to keep more in their head as they try to parse it.

konkin 5y ago
> Try out your notation, which I will agree can be unambiguous in a technical sense, but will quickly become unreadable for actual human beings, on a few modest examples. It's perfectly legible to me and I use it daily in my (mathematical) work. Again all you're saying is that you're not used to it and it must be a bad notation. Just like how people who were shown Arabic numerals defended Roman numerals. I'd do you one better and point out that the example should be = 1 λ x square sin x square cos x since having unbound variables is poor form after someone invented lambda calculus. And yes, you need a symbol for negation which is a step up since a-b is also ambiguous in the same sense. For the second one you easily see why words are superior to symbols when you stop trying to use hieroglyphs and start using letters instead: div add neg b sqrt sub pow b 2 sub times 4 times a c times 2 a. I can define new functions with well known meaning without having to copy special characters or invent type setting systems.
- Jtsummers 5y ago
  So, you're a troll then, you can't even be consistent in your presentation. + and - are bad to use, but λ is ok to use? Words are the thing to use for "add" and "sub" and "div" (why not the whole word?), but not "equals" or "define function"? And the words you choose are strictly English, which makes your mathematical notation no longer mutually comprehensible across most of the globe? Those are all positives to you? That's how math notation will be dragged into the 20th century? And, what, we now teach lambda calculus to elementary school kids once they start learning about variables? At least try to come up with a plausible argument. > I use it daily in my (mathematical) work. I find this highly unlikely, but sure, if you're not a troll, you've found a notation that (apparently) works for you (what kind of math?) and you think it's better but haven't bothered to think it though. And you still haven't answered the question on the second example, you just made it more verbose. The reader still has to remember (with zero punctuation or other indicators in your example) that the dividend for the div is the next 14 tokens and the divisor the last 3. Because that's totally readable and comprehensible. If you're not a troll, your idea isn't even half-baked.
  - konkin 5y ago