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It doesn't work like that. Some of the same symbols are used in two different places with vastly different meanings, even within this paper. To give an imperfe

It doesn't work like that. Some of the same symbols are used in two different places with vastly different meanings, even within this paper. To give an imperfect programming language analogy, imagine that every symbol is implicitly defined and has lexical scope. The grammar is as far from being context-free as possible. What may sometimes look like individual symbols to you are in fact a collection of inseparable symbols with its own semantic parse.

pantalaimon 8y ago
That's not really helpful. I struggle with the same problem, in fact the notation intimidates me to a point where I decided to forego getting deeper into theoretical computer science and haunts me every time I try to read a paper. A resource that would explain formal mathematical notation would be great, much like a dictionary. You can't google those symbols properly either.
- jordigh 8y ago
  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.
- karakot 8y ago
  This might help https://www.amazon.com/dp/1466230525 https://www.amazon.com/dp/1466230525
dclowd9901 8y ago
Hm, that’s fair but I don’t think it’s an excuse for an easy reference to not exist. All you need to do is then provide context with the example. There are many languages with hard an fast rules about usage or formation of words that are products of their context.

pantalaimon 8y ago

That's not really helpful. I struggle with the same problem, in fact the notation intimidates me to a point where I decided to forego getting deeper into theoretical computer science and haunts me every time I try to read a paper. A resource that would explain formal mathematical notation would be great, much like a dictionary. You can't google those symbols properly either.

jordigh 8y ago
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.
karakot 8y ago
This might help https://www.amazon.com/dp/1466230525 https://www.amazon.com/dp/1466230525

dclowd9901 8y ago

Hm, that’s fair but I don’t think it’s an excuse for an easy reference to not exist. All you need to do is then provide context with the example. There are many languages with hard an fast rules about usage or formation of words that are products of their context.