Talk:Gödel's incompleteness theorems

message: I've just removed the following from the article
: (Note: Computer programs typically represent sentences in Unicode rather than ASCII, and convert them more efficiently to produce smaller numbers. But we only need to choose some method and then apply it consistently to every sentence, and joining together the decimals is simpler to describe.) 
The reason being that it is not correct. To start with unicode is not an encoding, so computer programs do not generally represent anything in unicode.  Rather they use a specific encoding, which is usually compliant with some version of the Unicode standard. This might seem like a nitpick, and it is something that I could have just fixed. UTF-8, the most common encoding on the internet, is probably what is meant. However, the real issue with this claim is that UTF-8 is backwards compatible with the US-ASCII standard. So to say that UTF-8 is used "rather than ASCII" would be misleading at the very least.  Additionally the second clause
: Computer programs typically [...] convert them more efficiently to produce smaller numbers.
does not have a very clear meaning to me.  However it seems to imply that UTF-8 is a more dense encoding than US-ASCII which is just not true; a character in US-ASCII encoded in UTF-8 is still the same byte, because UTF-8 is backwards compatible with US-ASCII.
So given that, if someone still wants to put a version of this claim into the article I would strongly recommend getting a reliable source for the claim.
AquitaneHungerForce (talk) 10:14, 1 November 2021 (UTC)
replies: text: In fact, there is an issue here: Unicode has problems with numerical encoding of strings that ASCII doesn't, since the proposed encoding was essentially base-1000, which is works for ASCII and coding up the byte array representation of any encoding but is not collision-free if you work with Unicode codepoints. But while a gesture at practical encoding is appropriate, discussion of the technicalities facing actual computer systems quickly distracts the reader from grappling with the topic of the article. I'm against explicit treatment of this point at any length, regardless of sourcing. I'm wondering if the discussion can readably be made more concise.— Charles Stewart (talk) 11:34, 1 November 2021 (UTC)
replies: text: If the issue of ASCII vs Unicode ever comes up in this article, then the text in which it comes up should be reworded to remove the need for it.  Considerations like that are far off-topic for this article.  I understand the desire to make the ideas accessible to readers whose shortest path may be through their computer knowledge, but if specific character encodings ever come up, then we've lost the thread. --Trovatore (talk) 16:31, 1 November 2021 (UTC)

text: I think that a short mention in a footnote, along the lines of "Actual computer systems use more complex or specialized methods to encode strings  UTF-8" would be fine.  But I agree that this article does not need to get in the details and I think it should not be in a parenthetical but rather a footnote because this is not the point. AquitaneHungerForce (talk) 19:02, 1 November 2021 (UTC)
thread_title:  Unicode and ASCII 

message: Regarding Jochen's addition of an image, here.
Jochen says in the edit summary "no idea how to illustrate the theorem itself", and I basically agree.  Oh, someone could probably come up with something, maybe some sort of block diagram, but I doubt it would actually be helpful.
But to be honest I don't think the proffered image is particularly helpful either.
So my vote would be just not to have an image.  I don't think there's any great value in having an image purely pro forma.  If there's no image that genuinely helps direct the reader to the point of the article, then why have one at all? --Trovatore (talk) 20:25, 20 February 2023 (UTC)
thread_title:  Image 

message: : However, since the Gödel sentence cannot itself formally specify its intended interpretation, the truth of the sentence  may only be arrived at via a meta-analysis from outside the system. In general, this meta-analysis can be carried out within the weak formal system known as primitive recursive arithmetic, which proves the implication , where  is a canonical sentence asserting the consistency of .
Could this part confuse the reader? I am not sure what it would mean for a sentence to "specify its intended interpretation" (perhaps meaning that no sentence can single out the standard/true natural numbers?) For the second sentence it may help to mention that T proving Con(PA) -> (Goedel sentence for PA) and T proving (Goedel sentence for PA) are different phenomena, and while PRA is an example of such a theory T in the former case, much stronger theories need to be considered in the latter case (theories stronger than PA). C7XWiki (talk) 22:39, 19 April 2024 (UTC)
thread_title: Confusing part about truth of Goedel sentence?

message: Please see Talk:BEW#BEW, Bew, bew and reply there, if desired. I am proposing that the redirect Bew be pointed to BEW instead of to Gödel's incompleteness theorems#Bew. - dcljr (talk) 02:17, 24 April 2024 (UTC)
thread_title:  bew redirects to here