5 ms·

Did you know what the words meant? Can you read this and except for the symbols understand everything else? I don't think the symbols are the problem. They're

Did you know what the words meant? Can you read this and except for the symbols understand everything else? I don't think the symbols are the problem. They're a very superficial obstacle, at least in this paper. This isn't meant as a put-down. It's just that I really do think the actual material requires a lot more preparation that consists in a lot more than just learning the definition of the symbols. I could rewrite the whole paper using only text and no symbols. The symbols are just shorthand for English words. I don't think if I were to replace all of the symbols with the English words that they stand for, you would be much closer to understanding.

dclowd9901 8y ago
"The symbols are just shorthand for English words." OK, so then why would it be so difficult to produce a veritable cheat sheet to aide in reading a proof?
- jordigh 8y ago
  Because the symbols' translation to English words changes on context, culture, and even author. It's like trying to translate the word "rain" only by hearing it without having the context if it really meant "reign" or "rein". With some mathematical training, you don't really need the symbols to know what's being talked about, because you already have enough context to know what should be talked about and what fits into the context, regardless of how it's written down. Anyway are symbols really the main obstacle for you? When you read "every second countable regular Hausdorff space is metrizable" (theorem 59 in this paper), you have no problem understanding what this means?
  - dclowd9901 8y ago
    Fair point, but you know very well that, for true illustration, you'd have to expand out the meaning of the words "countable", "regular", "Hausdorff", "space" and "metrizable". And I bet you could. I get the sense you're being obstinate for a point.
    - jordigh 8y ago
      And don't forget the word "second". I'd have to explain that one too. And then I'd have to explain the words I used to explain these words. It all just takes a while. I might be able to do it, but we'd both need to spend some time understanding all of this together, going back and forth, considering examples, and building the foundations.

dclowd9901 8y ago

"The symbols are just shorthand for English words." OK, so then why would it be so difficult to produce a veritable cheat sheet to aide in reading a proof?

jordigh 8y ago
Because the symbols' translation to English words changes on context, culture, and even author. It's like trying to translate the word "rain" only by hearing it without having the context if it really meant "reign" or "rein". With some mathematical training, you don't really need the symbols to know what's being talked about, because you already have enough context to know what should be talked about and what fits into the context, regardless of how it's written down. Anyway are symbols really the main obstacle for you? When you read "every second countable regular Hausdorff space is metrizable" (theorem 59 in this paper), you have no problem understanding what this means?
- dclowd9901 8y ago
  Fair point, but you know very well that, for true illustration, you'd have to expand out the meaning of the words "countable", "regular", "Hausdorff", "space" and "metrizable". And I bet you could. I get the sense you're being obstinate for a point.
  - jordigh 8y ago
    And don't forget the word "second". I'd have to explain that one too. And then I'd have to explain the words I used to explain these words. It all just takes a while. I might be able to do it, but we'd both need to spend some time understanding all of this together, going back and forth, considering examples, and building the foundations.