Talk:Self-referential function

Problems with this article

I have several problems with this article:

1. The definition "A self-referential function is a function that applies to itself" is hopeless. What does it mean ? How does any function "apply to itself" ??
2. The reference that, I assume, is intended to demonstrate the usage and notability of the term gives a "Not found" error when I try to access it.
3. The example from Cantor's diagonal argument that is meant to illustrate a self-referential function is clearly not self-referential ! The function g is not defined in terms of itself; it is defined in terms of the functions f_k. And the whole point of the argument is to show that g is not in the set {f_k}.
4. We already have a much better article at self-reference.

Unless someone can fix the definition and the example and provide some useful sources, I will seriously consider taking this article to AfD. Gandalf61 (talk) 15:51, 24 June 2009 (UTC)

I added a very consistent reference where the answers to the four concerns ( above) are available Rirunmot (talk) 16:25, 24 June 2009 (UTC)

Rirunmot - I find it difficult to tell whether you are being serious here. Your first reference The Unique Non Self-Referential q-Canonical Distribution and the Physical Temperature Derived from the Maximum Entropy Principle in Tsallis Statistics is not at the link you gave, but I found an abstract here - beyond containing the term "self-referential", it has no connection at all with the contents of this article. Your second reference Evolving Algebras and Partial Evaluation contains a short paragraph about self-referential functions, but the definition it gives is entirely different from the definition in the article, and it does not mention Cantor's diagonal argument at all. These references do not support the contents of the article and do nothing to address my concerns. Gandalf61 (talk) 18:50, 24 June 2009 (UTC)

I agree with Gandalf61. In addition, I see "translated from french wikipedia" in the edit summary of 12:08, 18 March 2009. May I see the corresponding French article? Boris Tsirelson (talk) 10:41, 25 June 2009 (UTC)

That would be fr:Fonction auto-référentielle (written by the same user). Someone has pointed out the same problems there. Algebraist 12:22, 25 June 2009 (UTC)

I removed the text about Cantor's function. There is no self-reference in that. — Carl (CBM · talk) 12:20, 25 June 2009 (UTC)

If we take seriously the definition "a self-referential function is a function that applies to itself", that is, a function that is an element of its own domain (treating a function as in Function (mathematics)#Set-theoretical definitions, then it follows easily from the axiom of regularity that such monsters do not exist. But we'd better treat all that as a joke. Boris Tsirelson (talk) 14:33, 25 June 2009 (UTC)

The article is virtually content-free, and what little content it has is completely meaningless. There was an "example" which was not, in fact, an example of what was defined in the article. There were online "references" and "see also" links which either did not exist or referred to other concepts, albeit in some cases with a similar name. (E.g. anything which uses the expression "self reference" to mean something completely different from the meaning defined in the article is irrelevant.) These have now been deleted, and all that is left is:

1. Two different definitions, "function that refers to itself" and "function that applies to itself", which are not the same, and neither of which seems to have any useful meaning, and
2. A mention of an article by Marchal Bruno. Has anyone seen a copy of this? If so is it any more relevant than the useless online "references"? Judging from the abstract I managed to find it is not relevant. It refers to Cantor's diagonalization process, but there is nothing about the concept defined in this article. It really looks to me as though all the "references" and links for this article were just formed on the basis of indiscriminately grabbing anything which used the expression "self-reference" or any variation of it, irrespective of whether it referred to the concept which this article purports to be about. Incidentally, it took me a little while to find the abstract to the article, as both the title of the article and the title of the journal were garbled, which does not suggest a great deal of care in preparing references.

I invite anyone who has seen the whole article to explain here how it relates to "a function that applies to itself", and if no such explanation is forthcoming the reference must go. JamesBWatson (talk) 16:23, 25 June 2009 (UTC)

The re-established reference gives the classification of self-referential functions; it doesn't give neither the same definition of the article nor an opposite one. It is inserted as a support to NOTABILITY. So removing this reliable and verifiable reference because it gives is entirely different from the definition in the article is nonsense. At least, one may not remove it until a consensus is reached Rirunmot (talk) 20:06, 25 June 2009 (UTC)

Rirunmot - I am still finding it difficult to tell whether you are being serious. Obviously, we need to have a reference that establishes that the term "self-referential function" is used in a reliable source with the meaning attributed to it in the article. The definition given in the reference is, as you agree, different from the definition in the article, so the reference does not meet this purpose. It is like including a reference to a paper about insects in an article on computer bugs.

Moreover, we can see that the definition in the article "A self-referential function is a function that applies to itself" is nonsense by considering the function $f:x\rightarrow 0$ whose domain is all functions. Clearly f applies to itself, as it is itself a function (indeed, we know that f(f) = 0), but it is absurd to describe f as a "self-referential" function. Gandalf61 (talk) 09:06, 26 June 2009 (UTC)

A bit off-topic, but still: the domain cannot be "all functions", since this is not a set (but only a class). Boris Tsirelson (talk) 14:34, 26 June 2009 (UTC)

Okay, perhaps the domain of f can just be the set {f}, with f(f) = 0 as before ? I still think it is clear that the definition proposed in the article is nonsense. Gandalf61 (talk) 14:59, 26 June 2009 (UTC)

Of course, nonsense. I just give another reason why.

"a = 5" is a definition of a, but "a = a+5" is an equation for a. Likewise, "f = {5}" is a definition of f, but "f = {f}" is an equation on f. In fact, this equation has no solutions (as well as the former one), which is an implication of the axiom of regularity. And similarly, "f ∈ domain(f)" is a kind of equation, also having no solutions, also by that axiom. This is what I had in mind above, at 14:33, 25 June 2009. Boris Tsirelson (talk) 17:54, 27 June 2009 (UTC)

Gandalf61 - You do not have to worry about being serious or not, just try to understand WP standards: If a notion is present in reliable, verifiable and independent sources , then it is NOTABLE regardless you like it or not. If you admit that, you won't have ; as you mentioned above: several problems with this article

Now, about the given reference, you can see that I mentioned :it doesn't give neither the same definition of the article nor an opposite one. you are saying : The definition given in the reference is, as you agree, different from the definition in the article..any one can read my sentence and understand that I do not agree that The definition is different from the definition in the article. Rirunmot (talk) 15:11, 27 June 2009 (UTC)

I think most people reading your sentences would be baffled as to what you're talking about. Can you explain yourself more clearly? Algebraist 18:00, 27 June 2009 (UTC)

In order not to be baffled, see the comment of Gandalf61 above, you will instantaneously and immediately see that I am responding to his comment! Rirunmot (talk) 18:08, 27 June 2009 (UTC)

Rirunmot - two things are either the same or they are different. If you do not agree that the definition in the reference is different from the definition in the article then you must think that the two definitions are the same - in which case you are simply wrong. Anyway, I am tired of your games. There is no useful content in this article, so I have been WP:BOLD and replaced it with a redirect to self-reference. Gandalf61 (talk) 09:19, 28 June 2009 (UTC)