3 ms·

It seems clear enough to me what the GP might have meant, at least clear enough that it need not be responded to with remarks like "Like what do you think the w

by JadeNB 3y ago

It seems clear enough to me what the GP might have meant, at least clear enough that it need not be responded to with remarks like "Like what do you think the word "abstracted" actually means?" that reads to me as saying that, whatever the GP thinks, it is wrong. Type notation presumably started off as a very concrete thing—probably just about anyone can read something like BOOL = TRUE | FALSE. But then—I'm speaking here from a general perspective of computer-theoretic notation, so it's entirely possible that these are not actual notations that occur in type theory—things were added like syntactic sugar, say, for character classes, about whose abstract-ness we can argue but which definitely adds a decoding layer for people not used to it; and things like parametrized types/higher types that very definitely do add abstraction. It's very likely that, almost any time a definition benefits from an extra side remark, "For example, …", it is illustrating an additional abstraction.

mathisfun123 3y ago
>that reads to me as saying that, whatever the GP thinks, it is wrong. let me give you an example sentence and you tell me if the word "abstracted" makes sense, in context: "the accounting spreadsheet abstracts away all of the calculus because all the numbers are written down exhaustively"
- JadeNB 3y ago
  > let me give you an example sentence and you tell me if the word "abstracted" makes sense, in context: > "the accounting spreadsheet abstracts away all of the calculus because all the numbers are written down exhaustively" I'm not even sure what the meaning is supposed to be, because I would not expect to use a spreadsheet to do calculus. (Of course there are ways of forcing calculus into a spreadsheet, but I wonder if you just meant 'calculation'.) Here I would say that it is absolutely relevant to speak of a spreadsheet abstracting away the details of a computation: the logic of the spreadsheet will probably refer often to the contents of cells, without worrying about what the contents are, and that is very definitely a kind of abstraction. I would certainly not call the process of entering numbers into a spreadsheet an abstraction; but it seems to be the opposite of what type theory does. For example, type theory allows general reasoning about families of types, without reasoning case by case for each individual one. This seems to be the very essence of abstraction (in which capacity it is, conceptually, not completely distinct from the formulas in a spreadsheet). If you see no abstraction, only concreteness, in type-theory notation, I suspect that is more an indication that you have learned to see through the abstraction than that it isn't there.
  - mathisfun123 3y ago
    >This seems to be the very essence of abstraction yes and that's exactly my point... how does it make sense to utter the sentence "this has been abstracted [away]" when the `this` is itself the essence of abstraction. i'm not really sure how people aren't getting what i'm putting down here: type theory can't be abstracted away because type theory itself is the thing that does the abstracting.
    - JadeNB 3y ago
      > how does it make sense to utter the sentence "this has been abstracted [away]" when the `this` is itself the essence of abstraction. I think that you and I are reading this sentence (https://news.ycombinator.com/item?id=37140437 https://news.ycombinator.com/item?id=37140437) differently: > > It’s a testament to computer science that this has been so thoroughly abstracted over the years As your brackets indicate, you are reading a word "[away]" that is not explicitly present in the text. It seems to me to make more sense to read it without adding "away". (Wiktionary, for example, does not require that, or any, preposition in sense 6 of https://en.wiktionary.org/wiki/abstract#Verb https://en.wiktionary.org/wiki/abstract#Verb, which is the one that seems to me to fit here.) For example, I am a mathematician, and I could say that mathematics has been abstracted over the years (millennia!). I do not mean that the mathematics has been abstracted away, which I agree with you would be in some sense meaningless, but rather that the mathematics itself has literally been abstracted: from only being able to count and do arithmetic with specific real-world objects, to being able to do count and do arithmetic with numerals that did not refer to a specific thing, to being able to use letter to refer to numerals of unknown or variable value, to … well, there's not such a clear linear progression after that, but there's definitely a tower of abstraction. I hope that this sense of "mathematics has been thoroughly abstracted over the years" is an intelligible one (even if phrased differently from the way I assume you, or perhaps even I, might phrase it ourselves). It is in that sense that I take the sentence "It’s a testament to computer science that this [meaning, I think, notation in type theory] has been so thoroughly abstracted over the years".
      - mathisfun123 3y ago

by JadeNB 3y ago

mathisfun123 3y ago

>that reads to me as saying that, whatever the GP thinks, it is wrong. let me give you an example sentence and you tell me if the word "abstracted" makes sense, in context: "the accounting spreadsheet abstracts away all of the calculus because all the numbers are written down exhaustively"

JadeNB 3y ago
> let me give you an example sentence and you tell me if the word "abstracted" makes sense, in context: > "the accounting spreadsheet abstracts away all of the calculus because all the numbers are written down exhaustively" I'm not even sure what the meaning is supposed to be, because I would not expect to use a spreadsheet to do calculus. (Of course there are ways of forcing calculus into a spreadsheet, but I wonder if you just meant 'calculation'.) Here I would say that it is absolutely relevant to speak of a spreadsheet abstracting away the details of a computation: the logic of the spreadsheet will probably refer often to the contents of cells, without worrying about what the contents are, and that is very definitely a kind of abstraction. I would certainly not call the process of entering numbers into a spreadsheet an abstraction; but it seems to be the opposite of what type theory does. For example, type theory allows general reasoning about families of types, without reasoning case by case for each individual one. This seems to be the very essence of abstraction (in which capacity it is, conceptually, not completely distinct from the formulas in a spreadsheet). If you see no abstraction, only concreteness, in type-theory notation, I suspect that is more an indication that you have learned to see through the abstraction than that it isn't there.
- mathisfun123 3y ago
  >This seems to be the very essence of abstraction yes and that's exactly my point... how does it make sense to utter the sentence "this has been abstracted [away]" when the `this` is itself the essence of abstraction. i'm not really sure how people aren't getting what i'm putting down here: type theory can't be abstracted away because type theory itself is the thing that does the abstracting.
  - JadeNB 3y ago
    > how does it make sense to utter the sentence "this has been abstracted [away]" when the `this` is itself the essence of abstraction. I think that you and I are reading this sentence (https://news.ycombinator.com/item?id=37140437 https://news.ycombinator.com/item?id=37140437) differently: > > It’s a testament to computer science that this has been so thoroughly abstracted over the years As your brackets indicate, you are reading a word "[away]" that is not explicitly present in the text. It seems to me to make more sense to read it without adding "away". (Wiktionary, for example, does not require that, or any, preposition in sense 6 of https://en.wiktionary.org/wiki/abstract#Verb https://en.wiktionary.org/wiki/abstract#Verb, which is the one that seems to me to fit here.) For example, I am a mathematician, and I could say that mathematics has been abstracted over the years (millennia!). I do not mean that the mathematics has been abstracted away, which I agree with you would be in some sense meaningless, but rather that the mathematics itself has literally been abstracted: from only being able to count and do arithmetic with specific real-world objects, to being able to do count and do arithmetic with numerals that did not refer to a specific thing, to being able to use letter to refer to numerals of unknown or variable value, to … well, there's not such a clear linear progression after that, but there's definitely a tower of abstraction. I hope that this sense of "mathematics has been thoroughly abstracted over the years" is an intelligible one (even if phrased differently from the way I assume you, or perhaps even I, might phrase it ourselves). It is in that sense that I take the sentence "It’s a testament to computer science that this [meaning, I think, notation in type theory] has been so thoroughly abstracted over the years".
    - mathisfun123 3y ago