Wikipedia talk:Articles for deletion/Radical integer

I disagree very strongly with this idea that we shouldn't trust Weisstein's book as a source.

Wikipedia has its standards for what is and what isn't an acceptable source, and Weisstein has his standards, and they apparently aren't the same. However, the fact that Weisstein doesn't adhere to OUR STANDARDS doesn't mean he isn't reliable. He apparently takes the tack that certain discussions on usenet or mailing lists are valid sources; we couldn't do that here, because only an expert could do it that way. Weisstein's book was published, and if it contains this (which I can't verify, but I'm assuming it does as Kotepho claims), it's a reasonable source: the publisher of that book obviously knew that Weisstein would have some intellectual standards in his encyclopedia, and trusted that he could decide on reasonable ones. Perhaps we'd be justified in weaseling, i.e. "According to Weisstein's book, a radical integer is ..." but this level of dismissing a published book for its academic quality is simply inappropriate in a project of non-experts. Put another way, I'd rather trust Weisstein's judgement that this term exists than trust my fellow editors' judgement that he's wrong: he's an expert. I can even agree that I don't like his research quality on this topic, but I still don't think that means we delete Radical integer for lack of verifiability. (Notability is another matter.) Mangojuice 20:35, 13 April 2006 (UTC)


 * You're right that with many kinds of books, an author usually adds the weight of authority behind the contents, even if somebody might find a source objectionable. The authority comes from the author being a subject matter expert, not from the sole fact of being an author.  Is Weisstein an expert?  Well, at what, should be the question!  He has a degree in astronomy, but since MathWorld is about math, that's mostly irrelevant.  But in no way is he a math expert.  That wouldn't be so bad if he just compiled stuff written by experts, but he often creates an entry, having no background in the topic.  I'm curious...why do you insist on calling him an expert?  --C S (Talk) 01:08, 14 April 2006 (UTC)


 * Wikipedia isn't a project of non-experts; it's a project that anyone can edit, including experts, and let me assure you, there are experts editing here. -lethe talk [ +] 20:45, 13 April 2006 (UTC)
 * I thought someone would bring that up, which is part of why I moved this to the talk page. Yes, I totally agree with you.  I know there are some experts on here (for instance, I am one in my area, which is Cryptography.)  However, if it's ONLY on the basis of someone's expertise that we accept one source over another, I think that's invalid... it's like a backdoor form of original research.  An expert isn't allowed to write new ideas that aren't verifiable, right?  For similar reasons, experts shouldn't be simply trusted with their expertise to evaluate the quality of sources.  If they've got an opinion, they should publish it, and then we can report it.  I don't mean to devalue the contributions of experts at all, but they need to back up their expertise with sources.  We are wikipedia editors first, and experts second.


 * And one other thing: everyone is free to have the opinion they want to have, and this is especially true of experts. But calls for others to disregard certain sources is a different matter: it goes too far.  Mangojuice 20:56, 13 April 2006 (UTC)
 * I don't have the book but the second link in my first post is to the page on google book search. The book is an exact or near exact reprint of the MathWorld article, with the same source.  It is easily demonstratable that MathWorld has errors.  As mentioned, even the one in question does.  We should always be atributing things to a source though unless they are patently factual.  I have no V problems with citing MathWorld as long as we do it properly.  The article doesn't really stand alone well, thus the merge suggestion.  Frankly though, I am quite apathetic over the whole thing. le edit conflict. Kotepho 20:50, 13 April 2006 (UTC)
 * I think I may change my vote to merge, but my opinion on this has everything to do with notability rather than verifiability. I agree with you that we should always cite sources properly, and it's useful to be alerted that the book is not that thoroughly researched and may have some errors (for instance, if it disagrees with a more reputable source, that would be helpful in deciding which one to trust).  On the other hand, the notability of this concept is fairly minimal.  Mangojuice 20:56, 13 April 2006 (UTC)


 * Velikovsky published books too. Should we take what they say at face value?
 * To expand on what Lethe says, there are genuine experts on number theory who edit Wikipedia. I'm not one personally (my field is set theory), but User:Magidin is certainly one. Unfortunately I think he's on break at the moment.
 * Weisstein on the other hand is not AFAIK an expert on number theory (his degree is in astronomy), and I don't think he's reliable at all. Obviously a smart fella, but flaky as a biscuit. That wouldn't matter so much if he were simply doing science; there are lots of valuable contributors who need to be cleaned up after. It's his encyclopedic pretensions that cause the problem. They—or rather, editors who blindly incorporate his claims—are a clear and present danger to the integrity of the math articles on WP. --Trovatore 21:05, 13 April 2006 (UTC)
 * Mmmm... biscuits... -lethe talk [ +] 23:43, 13 April 2006 (UTC)

I also want to object in the sharpest terms to Mangojuice's claim that expert editors should not rely on their expertise to decide what sources are reliable. What good are they in that case? All you need is typists. No, we are not automata; that's not what WP:NOR is about. Its main function is to keep out material that hasn't been properly verified. Such as—lest the point be lost—this claim of Schroeppel's (even though I'm guessing that it's probably true and his proof was probably valid). --Trovatore 21:10, 13 April 2006 (UTC)


 * That's fair. I think I explained myself badly.  What I object to is not experts relying on their knowledge to decide what sources are reliable.  They have knowledge, they should use it, they should inform us about what they know so we can all make good decisions.  What I don't like is the idea of the opinions of experts being accepted as more than an opinion, and I think that extends to their evaluation of sources.  I think this business about Weisstein's book not being considered credible is such an example: I'm glad for the information we've gotten from experts telling us about the shoddiness of his sourcing.  I have my opinion on it as a source, which is that I'd like a better source but without one this one is okay.  I think this is consistent with all the information people have disclosed about it.  However, experts here have also stated that this source is not reliable as if that were a fact we should all simply accept.


 * I concede I may be being too sensitive here: we all express opinions and try to influence each other with them, so it's not really surprising that experts would do this too. I mainly want to remind experts (really, editors in general) that they're entitled to their opinions, but they should remember that some of what they say and think are merely opinions, not fact.  Mangojuice 14:11, 14 April 2006 (UTC)

Reply from Schroeppel
Just got a reply from Schroeppel. --Salix alba (talk) 08:17, 12 April 2006 (UTC)
 * p.s. I've got other email addresses for Schroeppel, ask if needed.

I looked at the WP deletion criteria, and the discussion of the Radical_Integer article. I don't understand the keep-or-drop criteria for Wikipedia. MathWorld has a mistake about "cubic" - it should say "quintic".

The algebraic integer phi = (1 + sqrt5)/2 = 1.618 = golden ratio is an alg-int because it's a root of X^2-X-1 = 0, leading coefficient (of X^2) is 1, and other coeffs are (plain vanilla) integers. It's obvious from the expression that it's an algebraic number, but not obvious that it's an (algebraic) *integer* because the formula has a /2 in it. The algebraic number (1 + sqrt7)/2 is NOT an alg-int. In fact, the expression generates an alg-int iff 5 is replaced with another 4K+1 number like 13,17, or -3; 9 works also.

However, phi = cbrt(2 + sqrt5); in this form, the integer-ness is now obvious.

It turns out that (1 + cbrt10 + cbrt100)/3 is also an alg-int, and some playing around turned up a no-division expression for it.

I posed the question (on the math-fun list) whether any alg-int had some expression that made the integerness obvious. There's an obvious problem with alg-ints that don't have any radical expression whatsoever (such as most roots of quintic equations). So the revised question is whether an alg-int that has some radical expression also has a radical expression without division.

I invented "radical integer" to describe these expresions. (Technical nit for the WP article: the index of the root must be a positive integer, since the -1 root is just the reciprocal.)

Several people on the mailing list contributed ideas and discussion. I was able to find a proof that there is always a radical-integer expression for any alg-int that has some radical expression. The proof is in the math-fun mailing list archive, presumably in the message that Weisstein references.

It certainly doesn't count as an academic publication, and hasn't been reviewed by anyone not involved in the original discussion. I can't claim sole authorship, since others helped in the proof-creation process. I don't know what your standards for WP inclusion are: if you require reviewed journal articles, you get higher accuracy; but you lose a lot of informal math/CS that only appears on the net. I did have one inquiry from someone a few years ago, and I was able to dredge up the article. But I can't find it after a short search, and my memory is that the article wasn't publication suitable: it assumed too much of the prior background discussion on the mailing list, and my proof style is very informal.

I can make a search for the article if you want to try rewriting it for general consumption, but I don't have time for a rewrite now.

I am slightly miffed at being described as "not a number theorist", since I did a lot of factoring work in the 1970s. But I make no claims of error-free-ness: If you need vetting of the math, you'll have to find your own reviewer.

Rich Schroeppel


 * I'm sorry about the "not a number theorist" remark. But if you look, you'll see what I said is you didn't seem to be a number theorist, in the sense that your name had come up in discussion as a cryptographer rather than a number theorist. It certainly wasn't any judgment on the body of your work, which I'm not qualified to comment on. --Trovatore 16:52, 12 April 2006 (UTC)