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> I’m not trying to be controversial, but traditional mathematicians are decades behind the best computing scientists when it comes to crafting formalisms. Cou

> I’m not trying to be controversial, but traditional mathematicians are decades behind the best computing scientists when it comes to crafting formalisms. Could you provide examples? The Dijkstra article doesn't seem like a marked improvement. > Perhaps mathematicians enjoy the intellectual exercise of holding all those concepts in mind? Mathematics is not symbol manipulation. I wish it was as easy as that. Mathematics requires you to hold all the concepts in mind while studying and working. > Perhaps they, like many guilds, appreciate the barriers to outsiders that they feel increase their own prestige? I am incapable of finding an example where the barrier to outsiders is the notation and not the concepts themselves.

User23 5y ago
> Could you provide examples? The Dijkstra article doesn't seem like a marked improvement. As I said, there are hundreds of examples on that site. > Mathematics is not symbol manipulation. I wish it was as easy as that. Mathematics requires you to hold all the concepts in mind while studying and working. Of course concepts must be understood, but that doesn't mean they need to be held in mind for the vast majority of the derivation. In many cases for example it's sufficient to know that an operation is associative to perform some manipulation, without needing to fuss over the specifics of the concept that operation captures. Unless of course you insist on a notational convention where the syntax is semantically ambiguous, as is common practice among traditional mathematicians. > I am incapable of finding an example where the barrier to outsiders is the notation and not the concepts themselves. What does the following mean? What concepts must be held in mind to understand it? sin(s + i + n) Even the average graduate mathematician is absurdly above the general population average for raw cognitive ability. Because of this, the frankly primitive approach to syntax is less of an impediment to doing interesting work than it would otherwise be. On the other hand if one desires to make mathematics more accessible to persons of ordinary intelligence, then reducing the cognitive load by clearly defining the semantics of a formula using an unambigous syntax is certainly necessary. Evidently though that's of little importance to the mathematical guild.
- gjulianm 5y ago
  > As I said, there are hundreds of examples on that site. In that article or in the whole site? Because the article just seems like different notation, no great improvements. > In many cases for example it's sufficient to know that an operation is associative to perform some manipulation Whenever that's the case, mathematicians have already found a way to use notation to that advantage. See for example the case of groups and rings, where the operations are usually denoted by '+' and '·' (addition and multiplication) even when they might not necessarily be those operations just because it makes operations more intuitive. > What does the following mean? What concepts must be held in mind to understand it? Well, you need to know what the sinus is and what is addition. If you don't have those concepts it doesn't matter that I write sin(s + i + n) or 'The sinus of s plus i plus n' (not to mention that there's ambiguity there too, does 'of' refer to 's' or 's plus i plus n). > On the other hand if one desires to make mathematics more accessible to persons of ordinary intelligence, then reducing the cognitive load by clearly defining the semantics of a formula using an unambigous syntax is certainly necessary. Evidently though that's of little importance to the mathematical guild. Notation is not the issue when explaining mathematics. The mathematical guild has done a ton of effort in improving math education, and you'll be able to find videos and texts that barely have any notation or equations. Notation exists because once you learn the concepts, it reduces the cognitive load of transmitting those concepts.
  - User23 5y ago
    > Well, you need to know what the sinus is and what is addition. If you don't have those concepts it doesn't matter that I write sin(s + i + n) or 'The sinus of s plus i plus n' (not to mention that there's ambiguity there too, does 'of' refer to 's' or 's plus i plus n). Incorrect. In the example I gave one merely needed to understand multiplication, addition, and the distributive property. And you, who are observably skilled in the art of mathematics, failed to follow a grade school level formula. So much for ambiguous syntax not being an impediment to understanding even when all concepts involved are comprehended. > Notation is not the issue when explaining mathematics. The mathematical guild has done a ton of effort in improving math education, and you'll be able to find videos and texts that barely have any notation or equations. It's baffling to me that anyone would attempt to argue that ambiguous syntax is not an issue for explaining mathematics. Please understand that the following unflattering comparison is intended merely for clarity and not to insult. To me it feels like trying to argue with a flat earther that the world is round. The absurdity makes argumentation virtually impossible. > Notation exists because once you learn the concepts, it reduces the cognitive load of transmitting those concepts. I agree. In fact that's germane to my original point. The mathematics guild is using primitive notation compared to what computing scientists discovered in the latter half of the 20th century. I'm not saying that notation is bad or even that the traditional amgbigous syntax isn't an improvement over just writing everything out in some natural language. I'm saying the mathematics guild is stubbornly ignoring notational advances that further reduces cognitive load. > The mathematical guild has done a ton of effort in improving math education Then how do we explain the complete lack of measurable progress in the average American secondary school student's mathematical ability? It appears to me that regardless of how much effort has been expended, little has come of it.

User23 5y ago

> Could you provide examples? The Dijkstra article doesn't seem like a marked improvement. As I said, there are hundreds of examples on that site. > Mathematics is not symbol manipulation. I wish it was as easy as that. Mathematics requires you to hold all the concepts in mind while studying and working. Of course concepts must be understood, but that doesn't mean they need to be held in mind for the vast majority of the derivation. In many cases for example it's sufficient to know that an operation is associative to perform some manipulation, without needing to fuss over the specifics of the concept that operation captures. Unless of course you insist on a notational convention where the syntax is semantically ambiguous, as is common practice among traditional mathematicians. > I am incapable of finding an example where the barrier to outsiders is the notation and not the concepts themselves. What does the following mean? What concepts must be held in mind to understand it? sin(s + i + n) Even the average graduate mathematician is absurdly above the general population average for raw cognitive ability. Because of this, the frankly primitive approach to syntax is less of an impediment to doing interesting work than it would otherwise be. On the other hand if one desires to make mathematics more accessible to persons of ordinary intelligence, then reducing the cognitive load by clearly defining the semantics of a formula using an unambigous syntax is certainly necessary. Evidently though that's of little importance to the mathematical guild.

gjulianm 5y ago
> As I said, there are hundreds of examples on that site. In that article or in the whole site? Because the article just seems like different notation, no great improvements. > In many cases for example it's sufficient to know that an operation is associative to perform some manipulation Whenever that's the case, mathematicians have already found a way to use notation to that advantage. See for example the case of groups and rings, where the operations are usually denoted by '+' and '·' (addition and multiplication) even when they might not necessarily be those operations just because it makes operations more intuitive. > What does the following mean? What concepts must be held in mind to understand it? Well, you need to know what the sinus is and what is addition. If you don't have those concepts it doesn't matter that I write sin(s + i + n) or 'The sinus of s plus i plus n' (not to mention that there's ambiguity there too, does 'of' refer to 's' or 's plus i plus n). > On the other hand if one desires to make mathematics more accessible to persons of ordinary intelligence, then reducing the cognitive load by clearly defining the semantics of a formula using an unambigous syntax is certainly necessary. Evidently though that's of little importance to the mathematical guild. Notation is not the issue when explaining mathematics. The mathematical guild has done a ton of effort in improving math education, and you'll be able to find videos and texts that barely have any notation or equations. Notation exists because once you learn the concepts, it reduces the cognitive load of transmitting those concepts.
- User23 5y ago
  > Well, you need to know what the sinus is and what is addition. If you don't have those concepts it doesn't matter that I write sin(s + i + n) or 'The sinus of s plus i plus n' (not to mention that there's ambiguity there too, does 'of' refer to 's' or 's plus i plus n). Incorrect. In the example I gave one merely needed to understand multiplication, addition, and the distributive property. And you, who are observably skilled in the art of mathematics, failed to follow a grade school level formula. So much for ambiguous syntax not being an impediment to understanding even when all concepts involved are comprehended. > Notation is not the issue when explaining mathematics. The mathematical guild has done a ton of effort in improving math education, and you'll be able to find videos and texts that barely have any notation or equations. It's baffling to me that anyone would attempt to argue that ambiguous syntax is not an issue for explaining mathematics. Please understand that the following unflattering comparison is intended merely for clarity and not to insult. To me it feels like trying to argue with a flat earther that the world is round. The absurdity makes argumentation virtually impossible. > Notation exists because once you learn the concepts, it reduces the cognitive load of transmitting those concepts. I agree. In fact that's germane to my original point. The mathematics guild is using primitive notation compared to what computing scientists discovered in the latter half of the 20th century. I'm not saying that notation is bad or even that the traditional amgbigous syntax isn't an improvement over just writing everything out in some natural language. I'm saying the mathematics guild is stubbornly ignoring notational advances that further reduces cognitive load. > The mathematical guild has done a ton of effort in improving math education Then how do we explain the complete lack of measurable progress in the average American secondary school student's mathematical ability? It appears to me that regardless of how much effort has been expended, little has come of it.